Prealgebra interactive notebook foldables ebook

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Interactive Notebook Foldables, Organizers and Templates

Interactive Notebook Foldables, Organizers and Templates

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  • 1. Contributing AuthorDinah ZikeConsultantDouglas Fisher,Ph.D.Director of Professional DevelopmentSan Diego,CA
  • 2. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in theUnited States of America. Except as permitted under the United States Copyright Act,no part of this book may be reproduced in any form, electronic or mechanical, includingphotocopy, recording, or any information storage or retrieval system, without priorwritten permission of the publisher.Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027ISBN: 978-0-07-877210-8 Pre-Algebra (Student Edition)MHID: 0-07-877210-9 Noteables™: Interactive Study Notebook with Foldables™1 2 3 4 5 6 7 8 9 10 047 12 11 10 09 08 07
  • 3. Glencoe Pre-Algebra iiiCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ContentsFoldables. . . . . . . . . . . . . . . . . . . . . . . . . . . 1Vocabulary Builder. . . . . . . . . . . . . . . . . . . 21-1 Using a Problem-Solving Plan . . . . . 41-2 Numbers and Expressions . . . . . . . . 71-3 Variables and Expressions . . . . . . . 101-4 Properties . . . . . . . . . . . . . . . . . . . . 141-5 Variables and Equations . . . . . . . . 161-6 Ordered Pairs and Relations . . . . . 191-7 Scatter Plots . . . . . . . . . . . . . . . . . . 23Study Guide . . . . . . . . . . . . . . . . . . . . . . . 27Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . 31Vocabulary Builder. . . . . . . . . . . . . . . . . . 322-1 Integers and Absolute Value . . . . . 342-2 Adding Integers . . . . . . . . . . . . . . . 372-3 Subtracting Integers. . . . . . . . . . . . 412-4 Multiplying Integers. . . . . . . . . . . . 432-5 Dividing Integers . . . . . . . . . . . . . . 452-6 The Coordinate System . . . . . . . . . 47Study Guide . . . . . . . . . . . . . . . . . . . . . . . 50Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . 53Vocabulary Builder. . . . . . . . . . . . . . . . . . 543-1 The Distributive Property. . . . . . . . 563-2 Simplifying Algebraic Expressions. 593-3 Solving Equations by Addingor Subtracting. . . . . . . . . . . . . . . . . 623-4 Solving Equations by Multiplyingor Dividing . . . . . . . . . . . . . . . . . . . 653-5 Solving Two-Step Equations . . . . . 673-6 Writing Two-Step Equations . . . . . 703-7 Sequences and Equations . . . . . . . 723-8 Using Formulas . . . . . . . . . . . . . . . . 74Study Guide . . . . . . . . . . . . . . . . . . . . . . . 77Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . 81Vocabulary Builder. . . . . . . . . . . . . . . . . . 824-1 Powers and Exponents. . . . . . . . . . 844-2 Prime Factorization . . . . . . . . . . . . 874-3 Greatest Common Factor. . . . . . . . 894-4 Simplifying Algebraic Fractions. . . 914-5 Multiplying and DividingMonomials . . . . . . . . . . . . . . . . . . . 934-6 Negative Exponents . . . . . . . . . . . . 954-7 Scientific Notation . . . . . . . . . . . . . 97Study Guide . . . . . . . . . . . . . . . . . . . . . . . 99Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 103Vocabulary Builder. . . . . . . . . . . . . . . . . 1045-1 Writing Fractions as Decimals . . . 1065-2 Rational Numbers. . . . . . . . . . . . . 1095-3 Multiplying Rational Numbers . . 1115-4 Dividing Rational Numbers . . . . . 1145-5 Adding and Subtracting LikeFractions . . . . . . . . . . . . . . . . . . . . 1175-6 Least Common Multiple. . . . . . . . 1195-7 Adding and Subtracting UnlikeFractions . . . . . . . . . . . . . . . . . . . . 1225-8 Solving Equations with RationalNumbers . . . . . . . . . . . . . . . . . . . . 1245-9 Measures of Central Tendency . . 126Study Guide . . . . . . . . . . . . . . . . . . . . . . 129Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 133Vocabulary Builder. . . . . . . . . . . . . . . . . 1346-1 Ratios and Rates . . . . . . . . . . . . . . 1366-2 Proportional and NonproportionalRelationships. . . . . . . . . . . . . . . . . 1386-3 Using Proportions. . . . . . . . . . . . . 1406-4 Scale Drawings and Models. . . . . 1426-5 Fractions, Decimals, and Percents 1456-6 Using the Percent Proportion . . . 1486-7 Finding Percents Mentally . . . . . . 1516-8 Using Percent Equations . . . . . . . 1536-9 Percent of Change . . . . . . . . . . . . 1566-10 Using Sampling to Predict . . . . . . 158Study Guide . . . . . . . . . . . . . . . . . . . . . . 161Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 165Vocabulary Builder. . . . . . . . . . . . . . . . . 1667-1 Functions. . . . . . . . . . . . . . . . . . . . 1687-2 Representing Linear Functions . . 170
  • 4. Contentsiv Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.7-3 Rate of Change. . . . . . . . . . . . . . . 1737-4 Constant Rate of Change andDirect Variation . . . . . . . . . . . . . . 1767-5 Slope . . . . . . . . . . . . . . . . . . . . . . . 1797-6 Slope-Intercept Form . . . . . . . . . . 1827-7 Writing Linear Equations. . . . . . . 1847-8 Prediction Equations . . . . . . . . . . 188Study Guide . . . . . . . . . . . . . . . . . . . . . . 191Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 195Vocabulary Builder. . . . . . . . . . . . . . . . . 1968-1 Solving Equations with Variableson Each Side . . . . . . . . . . . . . . . . . 1978-2 Solving Equations with GroupingSymbols . . . . . . . . . . . . . . . . . . . . . 1998-3 Inequalities . . . . . . . . . . . . . . . . . . 2018-4 Solving Inequalities by Addingor Subtracting. . . . . . . . . . . . . . . . 2048-5 Solving Inequalities byMultiplying or Dividing . . . . . . . . 2068-6 Solving Multi-Step Inequalities . . 208Study Guide . . . . . . . . . . . . . . . . . . . . . . 210Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 213Vocabulary Builder. . . . . . . . . . . . . . . . . 2149-1 Squares and Square Roots . . . . . . 2169-2 The Real Number System . . . . . . . 2199-3 Triangles . . . . . . . . . . . . . . . . . . . . 2219-4 The Pythagorean Theorem . . . . . 2239-5 The Distance Formula. . . . . . . . . . 2269-6 Similar Figures and IndirectMeasurement . . . . . . . . . . . . . . . . 228Study Guide . . . . . . . . . . . . . . . . . . . . . . 231Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 235Vocabulary Builder. . . . . . . . . . . . . . . . . 23610-1 Line and Angle Relationships . . . 23810-2 Congruent Triangles. . . . . . . . . . . 24110-3 Transformations in theCoordinate Plane . . . . . . . . . . . . . 24410-4 Quadrilaterals. . . . . . . . . . . . . . . . 24710-5 Polygons . . . . . . . . . . . . . . . . . . . . 24910-6 Area: Parallelograms, Triangles,and Trapezoids . . . . . . . . . . . . . . . 25110-7 Circles: Circumference and Area . 25410-8 Area: Composite Figures . . . . . . . 257Study Guide . . . . . . . . . . . . . . . . . . . . . . 259Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 263Vocabulary Builder. . . . . . . . . . . . . . . . . 26411-1 Three-Dimensional Figures . . . . . 26611-2 Volume: Prisms and Cylinders . . . 26911-3 Volume: Pyramids, Cones, andSpheres . . . . . . . . . . . . . . . . . . . . . 27211-4 Surface Area: Prisms andCylinders . . . . . . . . . . . . . . . . . . . . 27511-5 Surface Area: Pyramids andCones. . . . . . . . . . . . . . . . . . . . . . . 27811-6 Similar Solids. . . . . . . . . . . . . . . . . 280Study Guide . . . . . . . . . . . . . . . . . . . . . . 283Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 287Vocabulary Builder. . . . . . . . . . . . . . . . . 28812-1 Stem-and-Leaf Plots . . . . . . . . . . . 29012-2 Measures of Variation . . . . . . . . . 29412-3 Box-and-Whisker Plots . . . . . . . . . 29812-4 Histograms . . . . . . . . . . . . . . . . . . 30112-5 Selecting an Appropriate Display 30512-6 Misleading Graphs . . . . . . . . . . . . 30712-7 Simple Probability . . . . . . . . . . . . 30912-8 Counting Outcomes . . . . . . . . . . . 31112-9 Permutations and Combinations. 31412-10 Probability of Composite Events 317Study Guide . . . . . . . . . . . . . . . . . . . . . . 320Foldables. . . . . . . . . . . . . . . . . . . . . . . . . 325Vocabulary Builder. . . . . . . . . . . . . . . . . 32613-1 Polynomials. . . . . . . . . . . . . . . . . . 32813-2 Adding Polynomials . . . . . . . . . . . 33013-3 Subtracting Polynomials . . . . . . . 33213-4 Multiplying a Polynomial bya Monomial. . . . . . . . . . . . . . . . . . 33413-5 Linear and Nonlinear Functions . 33613-6 Graphing Quadratic and CubicFunctions. . . . . . . . . . . . . . . . . . . . 339Study Guide . . . . . . . . . . . . . . . . . . . . . . 342
  • 5. Glencoe Pre-Algebra vCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Organizing Your FoldablesMake this Foldable to help you organize andstore your chapter Foldables. Begin with onesheet of 11" × 17" paper.FoldFold the paper in half lengthwise. Then unfold.Fold and GlueFold the paper in half widthwise and glue all of the edges.Glue and LabelGlue the left, right, and bottom edges of the Foldableto the inside back cover of your Noteables notebook.Foldables OrganizerReading and Taking Notes As you read and study each chapter, recordnotes in your chapter Foldable. Then store your chapter Foldables insidethis Foldable organizer.
  • 6. Chapter3Glencoe Pre-Algebra 53Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3 EquationsUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of 81_2" × 11" paper.Stack 5 sheets ofpaper 3_4inch apart.Roll up the bottomedges. All tabs shouldbe the same size.Crease and staplealong fold.Label the tabs withtopics from the chapter.NOTE-TAKING TIP: When you take notes, includedefinitions of new terms, explanations of newconcepts, and examples of problems.0053-0080_CH03_875692 .indd 1 5/26/06 11:09:12 AM54 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BUILD YOUR VOCABULARYC H A P T E R3This is an alphabetical list of new vocabulary terms you will learn in Chapter 3.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleareacoefficient[koh-uh-FIHSH-ehnt]constantequivalent equationsequivalent expressionsformula0053-0080_CH03_875692 .indd 2 5/26/06 11:09:14 AMvi Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A Note-Taking Tipprovides a helpfulhint you can usewhen taking notes.The Build Your Vocabularytable allows you to writedefinitions and examplesof important vocabularyterms together in oneconvenient place.Within each chapter,Build Your Vocabularyboxes will remind youto fill in this table.The Chapter Openercontains instructions andillustrations on how to makea Foldable that will help youto organize your notes.This note-taking guide is designed to help you succeed inPre-Algebra. Each chapter includes:
  • 7. Glencoe Pre-Algebra viiCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Glencoe Pre-Algebra 67Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–5 Solving Two-Step EquationsA two-step equation contains operations.BUILD YOUR VOCABULARY (page 55)EXAMPLE Solve Two-Step Equationsa. Solve 3x - 4 = 17.3x - 4 + = 17 + Add to each side.= Simplify.3x_ = 21_ Undo .Divide each side by .= Simplify.b. 3 = n_3+ 83 - = n_3+ 8 - Subtract from each side.-5 = n_3Simplify.(-5) = (n_3 ) Multiply each side by .= n Simplify.Check Your Progress Solve each equation.a. 4x + 3 = 19 b. w_6- 8 = -4MAIN IDEA• Solve two-stepequations.ORGANIZE ITUnder Two-StepEquations tab, write atwo-step equation. Thenwrite the order of thesteps you would use tosolve that equation.0053-0080_CH03_875692 .indd 15 5/26/06 11:09:43 AMGlencoe Pre-Algebra 77Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R3VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 3 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 3, go to:glencoe.comYou can use your completedVocabulary Builder(pages 54–55) to help yousolve the puzzle.3-1The Distributive PropertyMatch each expression with an equivalent expression.1. 5(4 + 7) a. 5 · 7 + 4 · 7b. (-4) · 5 + (-4) · (-7)c. 5 · 4 + 5 · 7d. (-4) · 5 + (-4) · 7e. -5 · 7 + (-5) · 4f. 5 · 4 + (-7) · 42. (5 + 4)73. -4(5 + 7)4. (5 - 7)45. -4(5 - 7)6. In rewriting 3(x + 2), which term is “distributed” to the otherterms in the expression?3-2Simplifying Algebraic ExpressionsUnderline the term that best completes each statement.7. A term without a variable is a (coefficient, constant).8. The expression 5z + 2z + 9 + 6z has three (like terms, terms).Simplify each expression.9. 6q + 2q 10. 12y - y11. 5 + 7x - 3 12. 4(b + 1) + bSTUDY GUIDE0053-0080_CH03_875692 .indd 25 5/26/06 11:10:07 AMLessons cover the content ofthe lessons in your textbook.As your teacher discusses eachexample, follow along andcomplete the fill-in boxes.Take notes as appropriate.Bringing It All TogetherStudy Guide reviewsthe main ideas and keyconcepts from each lesson.3–6Glencoe Pre-Algebra 71Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Write and Solve a Two-Step EquationEARNINGS Ms. Parsons earns $48,400 per year. This is$4150 more than three times as much as her daughterearns. How much does her daughter earn?WordsVariableEquationMs. Parsons earns $4150 more than threetimes as much as her daughter.Let d = daughter’s earningsthree times asmore much asMs. Parsons earns $4150 than her daughter= $4150 += 4150 + Write the equation.Subtract from each side.- = 4150 + -= Simplify.= Divide each side by .= Simplify.Ms. Parsons’ daughter earns .Check Your Progress SHOPPING Tami spent $175 at thegrocery store. That is $25 less than four times as much as Tedspent. How much did Ted spend?HOMEWORKASSIGNMENTPage(s):Exercises:0053-0080_CH03_875692 .indd 19 5/26/06 11:09:52 AMFoldables featurereminds you to takenotes in your Foldable.Examples parallel theexamples in your textbook.Check Your Progress Exercisesallow you to solve similarexercises on your own.
  • 8. viii Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Your notes are a reminder of what you learned in class. Taking good notescan help you succeed in mathematics. The following tips will help you takebetter classroom notes.• Before class, ask what your teacher will be discussing in class. Reviewmentally what you already know about the concept.• Be an active listener. Focus on what your teacher is saying. Listen forimportant concepts. Pay attention to words, examples, and/or diagramsyour teacher emphasizes.• Write your notes as clear and concise as possible. The following symbolsand abbreviations may be helpful in your note-taking.Word or PhraseSymbol orAbbreviationWord or PhraseSymbol orAbbreviationfor example e.g. not equal ≠such as i.e. approximately ≈with w/ therefore ∴without w/o versus vsand + angle ∠• Use a symbol such as a star (★) or an asterisk (*) to emphasize importantconcepts. Place a question mark (?) next to anything that you do notunderstand.• Ask questions and participate in class discussion.• Draw and label pictures or diagrams to help clarify a concept.• When working out an example, write what you are doing to solve theproblem next to each step. Be sure to use your own words.• Review your notes as soon as possible after class. During this time, organizeand summarize new concepts and clarify misunderstandings.Note-Taking Don’ts• Don’t write every word. Concentrate on the main ideas and concepts.• Don’t use someone else’s notes as they may not make sense.• Don’t doodle. It distracts you from listening actively.• Don’t lose focus or you will become lost in your note-taking.NOTE-TAKING TIPS
  • 9. Chapter1Glencoe Pre-Algebra 1Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R1Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of unlined paper.Fold the short sides so theymeet in the middle.Fold the top tothe bottom.Unfold. Cut along thesecond fold to makefour tabs.Label each of the tabsas shown.NOTE-TAKING TIP: When you take notes, be sureto describe steps in detail. Include examples ofquestions you might ask yourself during problemsolving.The Tools of Algebra
  • 10. 2 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R1This is an alphabetical list of new vocabulary terms you will learn in Chapter 1.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplealgebraalgebraic expression[al-juh-BRAY-ihk]conjecture[cuhn-JEHK-shoor]coordinate plane orcoordinate systemcounterexampledeductive reasoningdomainequationevaluateinductive reasoning[in DUHK-tihv]BUILD YOUR VOCABULARY
  • 11. Glencoe Pre-Algebra 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplenumerical expressionopen sentenceorder of operationsordered pairpropertiesrangerelationscatter plotsimplifysolutionvariable
  • 12. 4 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–1 Using a Problem-Solving PlanEXAMPLE Use the Four-Step Problem-Solving PlanMAIN IDEAS• Use a four-step planto solve problems.• Choose an appropriatemethod of computation.PIZZA The price of a large cheese pizza at Paul’s Pizzais $9.25. You receive a $0.50 discount for each additionalpizza ordered, up to 10. So, one pizza costs $9.25, twopizzas cost $8.75 each, three pizzas cost $8.25, and soon. If you need 8 pizzas for a party, what is the costper pizza?EXPLORE The problem gives the cost for the first pizza andthe discount for each additional pizza ordered. Findthe cost per pizza for 8 pizzas.PLAN Look for a pattern in the costs. Extend the patternto find the cost per pizza for 8 pizzas.SOLVE First, find the pattern.1 pizza:2 pizzas: - or3 pizzas: - orNow, extend the pattern.4 pizzas: - or5 pizzas: - or6 pizzas: - or7 pizzas: - or8 pizzas: - orThe cost per pizza for 8 pizzas is .CHECK It costs $9.25 for one pizza with a discount of $0.50for each additional pizza ordered. For an order of8 pizzas, the cost per pizza would be$9.25 - (7 × ) or$9.25 - = .REMEMBER ITAlways check tobe sure your answeris reasonable. Ifthe answer seemsunreasonable, solvethe problem again.
  • 13. 1–1Glencoe Pre-Algebra 5Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress The cost of renting movies at Mike’sMarvelous Movie House is advertised as $5 for the first movieand $3.50 for each additional movie. Find the cost of renting6 movies.,A conjecture is an guess.When you make a conjecture based on a pattern ofexamples or past events, you are using inductivereasoning.BUILD YOUR VOCABULARY (page 2)EXAMPLE Use Inductive Reasoninga. Find the next term in 1, 4, 16, 64, 256, . . .1, 4, 16, 64, 256× × × × ×b. Draw the next figure in the pattern.The shaded point on the triangle moves in the pattern: right,top, bottom, left, right, etc. If the pattern continues, the shadedpoint will be at the of the next figure.Check Your Progressa. Find the next term in 48, 43, 38, 33, 28, . . .b. Draw the next figure in the pattern.ORGANIZE ITWrite this Your TurnExercise under the Checktab of the Foldable. Thenunder the remainingtabs, record how you willexplore, plan, and solveto reach a solution.
  • 14. 1–16 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Choose the Method of ComputationPLANETS The chart shows the distance of selectedplanets from the Sun. About how much farther is it fromEarth to the Sun than from Mercury to the Sun?PlanetDistance from Sun(millions of miles)Mercury 36.00Venus 67.24Earth 92.90Mars 141.71EXPLORE You know the distance from Earth to theand the distance from to the Sun.You need to find about how much farther it is fromto the .PLAN The question uses the word about, so an exactanswer is not needed. We can solve the problemusing . Estimate each distanceand then .SOLVE Distance from Earth to the Sun: 92.9Distance from Mercury to the Sun: 36.0So, Earth is about - ormillion miles further from the Sun than Mercury.CHECK Since + = 93, the answer makes sense.Check Your Progress SCHOOL ENROLLMENT EastElementary School has 792 students enrolled. West ElementarySchool has 518 students enrolled. About how many morestudents does East Elementary have than West Elementary?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 15. Glencoe Pre-Algebra 7Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 1–2 Numbers and ExpressionsNumerical expressions contain a combination of numbersand operations such as addition, subtraction, multiplication,and division.When you evaluate an expression, you find its numericalvalue.To avoid confusion when evaluating expressions,mathematicians have agreed upon an order of operations.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Evaluate ExpressionsFind the value of each expression.a. 24 ÷ 8 × 324 ÷ 8 × 3 = × 3 Divide 24 by 8.= 9 Multiply 3 and .Explain how to simplifyexpressions insidegrouping symbols.(Prerequisite Skill)REVIEW ITb. 5(4 + 6) - 7 · 75(4 + 6) - 7 · 7 = 5( )- 7 · 7 Evaluate (4 + 6).= - 7 · 7 Multiply 5 and .= - Multiply 7 and 7.= Subtract.c. 3[(18 - 6) + 2(4)]3[(18 - 6) + 2(4)] = 3[ + 2(4)] Evaluate (18 - 6).= 3( + ) Multiply 2 and 4.= 3( ) Add.= Multiply.MAIN IDEAS• Use the order ofoperations to evaluateexpressions.• Translate verbalphrases intonumerical expressions.
  • 16. 1–28 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.d.49 + 31__19 - 14REMEMBER ITGrouping symbolsinclude parentheses,brackets, and fractionbars.49 + 31__19 - 14= (49 + 31) (19 - 14) Rewrite as a divisionexpression.= ÷ Evaluate each expression.= Divide by .Check Your Progress Find the value of each expression.a. 63 ÷ 7 + 2b. 3(12 - 10) + 14 ÷ 2c. 4[(3 + 8) - 2(4)]d.(21 - 3)__4(2) + 1EXAMPLE Translate Phrases into ExpressionsWrite a numerical expression for each verbal phrase.a. the quotient of eighteen and sixPhrase the quotient of eighteen and sixKey WordExpressionb. the sum of nine and fivePhrase the sum of nine and fiveKey WordExpression
  • 17. 1–2Glencoe Pre-Algebra 9Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Write a numerical expression foreach verbal phrase.a. the product of three and fiveb. the difference of seventeen and sixEXAMPLE Use an Expression to Solve a ProblemEARNINGS Madison earns an allowance of $5 per week.She also earns $4 per hour baby-sitting, and usuallybaby-sits 6 hours each week. Write and evaluate anexpression for the total amount of money she earns inone week.First, write an expression.$5 allowanceplus$4 per hourper week spent baby-sitting+Then evaluate the expression.5 + 4 × 6 = Multiply.= Add.Madison earns in one week.Check Your Progress SHOPPING The Good PriceGrocery Store advertises a special on 2-liter bottles of softdrinks. The first bottle purchased is $1.50 and each bottle afterthat is $1.20. Write and evaluate an expression for the totalcost when 8 bottles are purchased.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 18. 10 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A variable is a for any .An algebraic expression contains sums and/or products ofand .BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Evaluate ExpressionsEvaluate x - y + 6 if x = 27 and y = 12.x - y + 6 = Replace x with andy with .= Subtract from .= Add and .Check Your Progress Evaluate 12 + a - b if a = 7 andb = 11.EXAMPLE Evaluate ExpressionsEvaluate each expression if x = 3, y = 4, and z = 7.a. 6y - 4x6y - 4x = 6( )- 4( ) y = , x = .= Multiply.= Subtract.1–3 Variables and ExpressionsMAIN IDEAS• Evaluate expressionscontaining variables.• Translate verbalphrases into algebraicexpressions.
  • 19. 1–3Glencoe Pre-Algebra 11Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.b.(z - x)__y(z - x)__y = ( )÷ Rewrite as a divisionexpression.= ( - )÷ Replace z with 7,x with 3, and y with 4.= ÷ 4 Subtract.= Divide.c. 5z + (x + 4y) - 155z + (x + 4y) - 15= 5 + ( + 4 · )- 15 Replace z with 7, x with3, and y with 4.= 5 + ( + )- 15 Multiply and .= 5 + - 15 Add and .= + - 15 Multiply and .= - 15 Add and .= Subtract.Check Your Progress Evaluate each expression ifm = 9, n = 4, and p = 6.a. 5p - 3mb. mn_pc. p + (8n - 3m)
  • 20. 1–312 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Translate Verbal Phrases into ExpressionsList eight words orphrases that suggestaddition or subtraction.(Prerequisite Skill)REVIEW ITTranslate each phrase into an algebraic expression.a. 35 more than the number of tickets soldWordsVariableEquation35 more than the number of tickets soldLet t represent the number of tickets sold35 more than the number of tickets soldThe expression is .b. the difference of six times a number and tenWordsVariableEquationthe difference of six times a number and tenLet n represent the number.the difference of six times a number and tenThe expression is .Check Your Progress Translate each phrase into analgebraic expression.a. eight less than the number of cookies bakedb. the sum of twelve and five times a number
  • 21. 1–3Glencoe Pre-Algebra 13Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Use an Expression to Solve a ProblemTHEATER East Middle School sold tickets for a schoolplay. The price of an adult ticket was $3, and the priceof a student ticket was $1.a. Write an expression that represents the total amountof money collected.WordsVariablesEquation$3 for an adult ticket and $1 for astudent ticketLet a = number of adult tickets ands = number of student tickets.$3 for an adult ticket and $1 for a student ticket.The expression is .b. Suppose 70 adult tickets and 85 student tickets weresold. How much money was collected?3a + 1s = 3( )+ 1( ) a = 70, s = 85.= Multiply.= Add.The amount of money collected was .Check Your Progress RETAIL The Read It Bookstoreis advertising a sale. The price of hardback books is $9.50and the price of paperback books is $4.50.a. Write an expression that can be used to find the totalamount of money spent at the bookstore.b. Suppose Emily buys 5 hardback books and 4 paperbackbooks. Find the total amount she spent at the book sale.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 22. 14 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.In algebra, properties are statements that are true for anynumbers.BUILD YOUR VOCABULARY (page 3)EXAMPLE Identify PropertiesName the property shown by each statement.a. 3 · 10 · 2 = 3 · 2 · 10The order of the numbers changed. This is the.b. (2 + 5) + m = 2 + (5 + m)The way in which numbers are grouped changed.Check Your Progress Name the property shown byeach statement.a. (4 · 6) · 2 = 4 · (6 · 2)b. 12 + 9 = 9 + 12EXAMPLE Mental MathFind (18 · 20) · 5 mentally.(18 · 20) · 5 = 18 · ( ) Associative Property ofMultiplication= 18 · Multiply andmentally.= Multiply 18 andmentally.MAIN IDEAS• Identify and useproperties of additionand multiplication.• Use propertiesof addition andmultiplication tosimplify algebraicexpressions.1–4 PropertiesKEY CONCEPTSCommutative Propertiesof Addition andMultiplication The orderin which numbers areadded or multiplieddoes not change thesum or product.Associative Propertiesof Addition andMultiplication The wayin which numbers aregrouped when addedor multiplied does notchange the sum orproduct.Additive Identity When0 is added to any number,the sum is the number.Multiplicative IdentityWhen any number ismultiplied by 1, theproduct is the number.Multiplicative Property ofZero When any numberis multiplied by 0, theproduct is 0.
  • 23. 1–4Glencoe Pre-Algebra 15Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find 4 · 8 · 25 mentally.To simplify algebraic expressions means to write them in a.The process of using facts, properties, or rules toor reach validis called deductive reasoning.BUILD YOUR VOCABULARY (page 3)EXAMPLE Simplify Algebraic ExpressionsSimplify each expression.a. 5 · (3 · r)5 · (3 · r) =Associative Property ofMultiplication= Substitution Property of Equalityb. 12 + (x + 18)12 + (x + 18)= 12 + Commutative Property of Addition= + x Associative Property of Addition= Substitution Property of EqualityCheck Your Progress Simplify each expression.a. 7 + (12 + m)b. (6 · a) · 4HOMEWORKASSIGNMENTPage(s):Exercises:
  • 24. 16 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Variables and EquationsA mathematical that contains anis called an equation.An that contains a is anopen sentence.A for the variable that makes antrue is called a solution.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Solve an EquationFind the solution of 44 + p = 53. Is it 11, 9, or 7?Replace p with each value.Value for p 44 + p = 53 True or False?11 44 + 539 44 + 537 44 + 53Check Your Progress Find the solution of 24 - a = 9. Is it11, 13, or 15?MAIN IDEAS• Identify and solve opensentences.• Translate verbalsentences intoequations.1–5
  • 25. 1–5Glencoe Pre-Algebra 17Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLETEST EXAMPLE Which value of x makes the equation4x - 1 = 11 true?A 5 B 4 C 3 D 2Test each value.4x - 1 = 11 4x - 1 = 114( )- 1 = 11 4( )- 1 = 1119 11 15 114x - 1 = 11 4x - 1 = 114( )- 1 = 11 4( )- 1 = 1111 11 7 11The answer is letter .Check Your Progress Which value of x makes the equation10 + 8x = -6?F -2 G 0 H 2 J 4EXAMPLEMAPLE SYRUP It takes about 45 gallons of tree sap tomake about 1 gallon of maple syrup. The table showsthe relationship between the number of gallons of treesap and the number of gallons of maple syrup.Gallons of TreeSap, tGallons ofMaple Syrup, m45 190 2135 3180 4a. Given t, the number of gallons of tree sap used,write an equation to find m, the number of gallonsof maple syrup.(continued on the next page)
  • 26. 1–518 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.WordsVariablesEquationNumber of gallons of tree sap is 45 timesthe number of gallons of maple syrup.Let m = .Let t = .=The equation isb. How many gallons of tree sap are needed to make5 gallons?t = 45mt = 45( )t =Check Your Progress AUTO SERVICE It takes about4 quarts of motor oil to fill the oil reservoir in anautomobile. The table shows the relationship between thenumber of automobiles and the number of quarts of oil.Number ofAutomobiles, aQuarts ofOil, q1 42 83 124 6a. Given a, the number of automobiles, write an equation tofind q, the number of quarts of oil needed.b. How many quarts of oil are needed if the service shop needsto change the oil in 18 automobiles during the day?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 27. Glencoe Pre-Algebra 19Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 1–6 Ordered Pairs and RelationsThe coordinate system is formed by the intersection of twonumber lines that meet at right angles at their zero points.The is also called the coordinateplane.An ordered pair of numbers is used to locate anyon a coordinate plane.The number of an is calledthe x-coordinate.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Graph Ordered PairsGraph each ordered pair on a coordinate system.a. (3, 4)Step 1 Start at the . (3, 4)xyO 123412 3 4Step 2 Since the x-coordinate is 3,move units to the .Step 3 Since the y-coordinate is 4,move units . Draw a dot.b. (0, 2)Step 1 Start at the origin.xyO 123412 3 4(0, 2)Step 2 Since theis , you will not need tomove to the right.Step 3 Since theis 2, move units up. Draw a dot.MAIN IDEAS• Use ordered pairs tolocate points.• Use tables and graphsto represent relations.
  • 28. 1–620 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Graph each ordered pair on acoordinate system.a. (2, 5)yxO 112345672 3 4 5 6 7b. (4, 0)EXAMPLE Identify Ordered PairsWrite the ordered pair that names each point.a. Point GStart at the origin. Move right on thexyO 123412 3 4Gx-axis to find the x-coordinate ofpoint G, which is . Move up they-axis to find the y-coordinate, whichis .The ordered pair for point G is .b. Point HStart at the origin. Move right on thexyO 123412 3 4Hx-axis to find the x-coordinate ofpoint H, which is . Since they-coordinate is , you will not needto move up.The ordered pair for point H is .Check Your Progress Write theordered pair that names each point.yxO 112345672 3 4 5 6 7ABa. Ab. BWRITE ITWhere is the graph of(5, 0) located?
  • 29. 1–6Glencoe Pre-Algebra 21Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A set of such as {(1, 2), (2, 4), (3, 0),(4, 5)} is a relation.The domain of a relation is the set of coordinates.The range of a relation is the set of coordinates.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Relations as Tables and GraphsExpress the relation {(1, 4), (2, 2), (3, 0), (0, 2)} as a tableand as a graph. Then determine the domain and range.xyO 123412 3 4(3, 0)(0, 2)(2, 2)(1, 4)x y4232The domain is. The range is.Check Your Progress Express the relation {(4, 1), (3, 2),(0, 1), (2, 3)} as a table and as a graph. Then determine thedomain and range.yxO 112345672 3 4 5 6 7REMEMBER ITWhen stating thedomain and range of arelation, each value islisted only once, even ifit occurs more.
  • 30. 1–622 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEEARNINGS Austin earns $5 an hour doing yard work.Suppose x represents the number of hours Austin works.a. Make a table of ordered pairs in whichx y1103425the x-coordinate represents the hoursworked and the y-coordinate representsthe amount of money Austin earns for1, 2, 3, 4, and 5 hours of work.b. Graph the ordered pairs.Earnings501015202530Hours1 2 3 4 5c. Describe the graph.Check Your Progress BAKING Sue is following arecipe for cookies which requires 2 cups of sugar foreach batch of cookies made. Suppose x represents thenumber of batches made.a. Make a table of ordered pairs in whichthe x-coordinate represents the numberof batches made and y represents thenumber of cups of sugar needed for1, 2, 3, 4, and 5 batches made.b. Graph the10234CupsofSugar56Batches of Cookies1 2 3 4 578910ordered pairs.c. Describe the graph.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 31. Glencoe Pre-Algebra 23Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Scatter PlotsA scatter plot is a that shows thebetween two sets of data. The twosets of data are graphed as on acoordinate system.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Construct a Scatter PlotBREAD The table shows the average cost of a loaf ofbread from 1920–2000. Make a scatter plot of the data.Year 1920 1930 1940 1950 1960 1970 1980 1990 2000Cents 12 9 8 14 20 24 52 72 99Let the horizontal axis, orYearCost(cents)xyO 202030405060708090103040506070809000x-axis, represent the .Let the vertical axis, ory-axis, represent the .Then graph orderedpairs .Check Your Progress BIRTH STATISTICS The tableshows the number of babies born at Central Hospital duringthe past eight months. Make a scatter plot of the data.Month Jan. Feb. Mar. Apr. May June July Aug.Babies 12 21 17 9 15 26 18 11yxJan Mar May July51015202530NumberofBabiesMonth1–7MAIN IDEAS• Construct scatter plots.• Analyze trends inscatter plots.
  • 32. 1–724 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Interpret Scatter PlotsDetermine whether a scatter plot of the data forthe following might show a positive, negative, or norelationship. Explain your answer.height of basketball player and number of rebounds66468268 70 72 74ReboundsHeight (in.)10As the height , thenumber of rebounds .relationshipCheck Your Progress Determine whether a scatter plot ofthe data for the following might show a positive, negative, or norelationship. Explain your answer.outside temperature and heating bill$20$0$40HeatingBill$60$80Temperature (°F)0 20 40 60 80$100EXAMPLE Use Scatter Plots to Make Predictionsa. TEMPERATURE The table shows temperaturesin degrees Celsius and the correspondingtemperatures in degrees Fahrenheit. Makea scatter plot of the data.°F 32 41 50 59 68 77 86°C 0 5 10 15 20 25 30REMEMBER ITData show apositive relationshipif they appear to gouphill from left to right,and show a negativerelationship if theyappear to go downhillfrom left to right.
  • 33. 1–7Glencoe Pre-Algebra 25Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Let the horizontal axis˚C˚FxyO 53040506070809010 15 20 25 30 35 40represent degrees .Let the vertical axis representdegrees .Graph the data.b. Does the scatter plot show a relationshipbetween °C and °F? Explain.Yes, a relationship. As increase,so do .c. Predict the Fahrenheit temperature for 35°C.By looking at the pattern on˚C˚FxyO 53040506070809010 15 20 25 30 35 40the graph, we can predict thatthe Fahrenheit temperaturecorresponding to 35°C would beabout .Check Your Progress The table shows hours spentstudying for a test and the corresponding test score.Hours 3 2 5 1 4 2 6Score 72 75 90 68 85 70 92a. Make a scatter plot of the data.HoursScorexyO 1607080901002 3 4 5 6
  • 34. 1–726 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.b. Does the scatter plot show a relationship between hoursstudied and a student’s test score? Explain.c. Predict the test score for a student who spends 7 hoursstudying.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 35. Glencoe Pre-Algebra 27Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R1VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 1 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 1, go to:glencoe.comYou can use your completedVocabulary Builder(pages 2–3) to help yousolve the puzzle.1-1Using a Problem-Solving PlanUnderline the correct term or phrase to fill the blank in eachsentence.1. A is an educated guess. (reason, strategy,conjecture)2. When you make a conjecture based on a pattern of examples orpast events, you are using . (inductivereasoning, reasonableness, problem-solving)3. What is the next term: 3, 6, 12, 24 …? Explain.4. Complete this sentence. In the step of the four-stepproblem-solving plan, you check the reasonableness of youranswer.1-2Numbers and ExpressionsState whether each sentence is true or false. If false, replacethe underlined word to make a true sentence.5. Numerical expressions contain a combination of numbers andoperations.6. When you evaluate an expression, you find its numerical value.STUDY GUIDE
  • 36. 28 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BRINGING IT ALL TOGETHER1-3Variables and ExpressionsState whether each sentence is true or false. If false, replacethe underlined word to make a true sentence.7. A variable is a placeholder for any operator.8. Any letter can be used as a variable.9. Name three things that make an algebraic expression.1-4PropertiesMatch each statement with the property it shows.10. 8 · 2 = 2 · 8 a. Additive Identity Propertyb. Associative Property ofAdditionc. Commutative Property ofAdditiond. Associative Property ofMultiplicatione. Commutative Property ofMultiplication11. (3 + 2) + 7 = 3 + (2 + 7)12. 3x + 0 = 3x13. 6(st) = 6s(t)14. 10 + 2 = 2 + 101-5Variables and EquationsUnderline the correct term or phrase to fill the blank in eachsentence.15. A mathematical sentence that contains an equals sign (=) is calledan . (equation, expression, operation)16. A value for the variable that makes an equationis called a solution. (reasonable, true, false)17. Consider x - 4 = 6. Find a value for x that makes the sentencetrue and another value that makes it false.
  • 37. Glencoe Pre-Algebra 29Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BRINGING IT ALL TOGETHER1-6Ordered Pairs and RelationsFor Exercises 18–20, use the relation {(2, 1), (4, 7), (3, 2), (5, 4)}.18. Express the relation as 19. Express the relation asa table. a graph.86543211 2 3 4 5 6 7 87Oyx20. Determine the domain and range of the relation.1-7Scatter PlotsUnderline the correct term or phrase to complete eachsentence about the relationship shown by a scatter plot.21. For a positive relationship, as x increases, y(increases, decreases, stays constant).22. For a negative relationship, as x increases, y(increases, decreases, stays constant).The scatter plot compares the weights and heightsof the players on a high school football team.23. What type of relationship exists, if any?24. Based on the scatter plot, predict the weight ofa 55" player who decided to join the team.Weight (in pounds)Height61"511"510"59"58"57"56"0 160 180 20060"Heights of Football Players
  • 38. Checklist30 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R1Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 1.Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 1 Practice Test onpage 73 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 1 Study Guide and Reviewon pages 69–72 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 1 Practice Test onpage 73.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 1 Foldables.• Then complete the Chapter 1 Study Guide and Review onpages 69–72 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 1 Practice Test onpage 73.ARE YOU READY FORTHE CHAPTER TEST?
  • 39. Chapter2Glencoe Pre-Algebra 31Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R2 IntegersUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with a piece of grid paper.Fold in half.Fold the top to thebottom twice.Open and Cut alongsecond fold to makefour tabs.Fold lengthwise. Draw1-1-2-3-4-5-6 2 3 4 5 6a number line on theoutside. Label each tabas shown.NOTE-TAKING TIP: When searching for themain idea of a lesson, ask yourself, “What isthis paragraph or lesson telling me?”
  • 40. 32 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R2This is an alphabetical list of new vocabulary terms you will learn in Chapter 2.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleabsolute valueadditive inverseaveragecoordinateinequalityBUILD YOUR VOCABULARY
  • 41. Glencoe Pre-Algebra 33Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleintegermeannegative numberoppositesquadrants
  • 42. 34 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.2–1A negative number is a number less than zero.Negative numbers like -8, positive numbers like +6, andare members of the set of integers.The that corresponds to a is calledthe coordinate of that point.Any mathematical sentence containing or iscalled an inequality.BUILD YOUR VOCABULARY (pages 32–33)EXAMPLE Write Integers for Real-World SituationsWrite an integer for each situation.a. 32 feet undergroundThe integer is .b. 8 weeks after birthThe integer is .c. a loss of 6 poundsThe integer is .Check Your Progress Write an integer for eachsituation.a. a loss of 12 yardsb. 15 feet above sea levelc. the temperature decreased 4 degreesIntegers and Absolute ValueMAIN IDEAS• Compare and orderintegers.• Find the absolute valueof an expression.WRITE ITList 5 words or phrasesthat indicate positive ornegative numbers.
  • 43. 2–1Glencoe Pre-Algebra 35Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Compare Two IntegersUse the integers graphed on the number line below.Ϫ4 Ϫ2 0 2 4 6 8a. Write two inequalities involving 7 and -4.Since 7 is to the of -4, 7 -4.Since -4 is to the of 7, -4 7.b. Replace the with <, >, or = in -2 3 to make a truesentence.3 is since it lies to the of -2.So, -2 3.Check Your Progress Use the integers graphed on thenumber line below.a. Write two inequalities involving -4 and 1.b. Replace the with <, >, or = in 6 -7 to make a truesentence.EXAMPLE Order IntegersWEATHER The high temperatures for the first seven daysof January were -8°, 10°, 2°, -3°, -11°, 0°, and 1°. Orderthe temperatures from least to greatest.Graph each integer on a number line.Ϫ2Ϫ4Ϫ6Ϫ8Ϫ10Ϫ12 0 2 4 6 8 10The order from least to greatest is.
  • 44. 2–136 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress FOOTBALL The yards gainedduring the first six plays of the football game were 5, -3, 12,-9, 6 and -1. Order the yards from least to greatest.Two numbers have the same absolute value if they are onsides of zero, and are the samefrom zero.BUILD YOUR VOCABULARY (page 32)EXAMPLE Expressions with Absolute ValueEvaluate each expression.a. 5The graph of 5 is 5 units from 0.5 =b. -8 + -1-8 + -1 = -8 = , -1 == Simplify.Check Your Progress Evaluate each expression.a. -9 b. -3 + 2EXAMPLE Algebraic Expressions with Absolute ValueALGEBRA Evaluate the expression x - 8 if x = -2.x - 8 = - 8 Replace x with .= - 8 The absolute value of is .= Simplify.Check Your Progress ALGEBRA Evaluate the expression5 - x if x = 9.HOMEWORKASSIGNMENTPage(s):Exercises:KEY CONCEPTAbsolute Value Theabsolute value of anumber is the distancethe number is from zeroon the number line.The absolute value of anumber is always greaterthan or equal to zero.
  • 45. Glencoe Pre-Algebra 37Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Adding IntegersEXAMPLE Add Integers on a Number LineMAIN IDEAS• Add two integers.• Add more than twointegers.Find 3 + 4.0 1 2ϩ 33 4 5 6 7 8ϩ 4Start at .Move units to the .From there, move more units to the .3 + 4 =Check Your Progress Find -2 + -5.KEY CONCEPTAdding Integers withthe Same Sign To addintegers with the samesign, add their absolutevalues. Give the result thesame sign as the integers.EXAMPLE Add Integers with the Same SignFind -5 + (-4).-5 + (-4) = Add and .Both numbers areso the sum is .Check Your Progress Find -3 + -8.2–2ORGANIZE ITUnder the ”+“ tab,write a sum of integerswith different signs, andexplain how to add themon a number line.1-1-2-3-4-5-6 2 3 4 5 6
  • 46. 2–238 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Add Integers on a Number LineFind 7 + (-11).0Ϫ1Ϫ2Ϫ3Ϫ4Ϫ5Ϫ6 1 2 3 4 5 6 7ϩ7Ϫ11Start at .Move units to the .From there, move units to the .7 + (-11) =Check Your Progress Find each sum.a. -5 + 8 b. 3 + (-6)EXAMPLE Add Integers with Different Signsa. Find -9 + 10.KEY CONCEPTAdding Integers withDifferent Signs To addintegers with differentsigns, subtract theirabsolute values. Givethe result the same signas the integer with thegreater absolute value.-9 + 10 = To find -9 + 10, subtractfrom . The sum is positivebecause 10 > -9.b. Find 8 + (-15).8 + (-15) = -7 To find 8 + (-15), subtractfrom .The sum is negative because-15 > 8.Check Your Progress Find each sum.a. -6 + 11 b. 4 + (-7)
  • 47. 2–2Glencoe Pre-Algebra 39Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Two numbers with same absolute value but differentare called opposites.An integer and its are calledadditive inverses.BUILD YOUR VOCABULARY (pages 32–33)EXAMPLEWEATHER On February 1, the temperature at dawn was-22°F. By noon, it has risen 19 degrees. What was thetemperature at noon?WordsVariableEquationtemperatureplusincreaseequalstemperatureat dawn by noon at noonLet = .+ =-22 + 19 = To find the sum, subtract from. The sum is negative because< .The temperature at noon was .Check Your Progress HIKING Dave started his hike at32 feet below sea level. During the hike he gained an altitude of29 feet. At what altitude did Dave complete his hike?
  • 48. 2–240 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Add Three or More Integersa. Find -8 + (-4) + 8.-8 + (-4) + 8 = -8 + CommutativeProperty= + -4 Additive InverseProperty= Identity Propertyof Additionb. Find 6 + (-3) + (-9) + 2.6 + (-3) + (-9) + 2= 6 + Commutative Property= [6 + 2] + Associative Property= 8 + or Simplify.Check Your Progress Find each sum.a. 3 + (-9) + (-3) b. -2 + 11 + (-4) + 5HOMEWORKASSIGNMENTPage(s):Exercises:KEY CONCEPTAdditive Inverse PropertyThe sum of any numberand its additive inverse iszero.
  • 49. Glencoe Pre-Algebra 41Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Subtract a Positive IntegerFind each difference.a. 9 - 149 - 14 = 9 + To subtract 14, add .= Simplify.KEY CONCEPTSubtracting Integers Tosubtract an integer, addits additive inverse.b. -10 - 8-10 - 8 = -10 + To subtract 8, add .= Simplify.Check Your Progress Find each difference.a. 6 - 8 b. -9 - 13EXAMPLE Subtract a Negative IntegerORGANIZE ITWrite two examples ofsubtracting a negativenumber from a positivenumber under the”-“ tab.1-1-2-3-4-5-6 2 3 4 5 6Find each difference.a. 15 - (-4)15 - (-4) = 15 + To subtract -4, add .= Simplify.b. -11 - (-7)-11 - (-7) = -11 + To subtract -7, add .= Simplify.Check Your Progress Find each difference.a. 8 - (-2) b. -12 - (-5)Subtracting Integers2–3MAIN IDEAS• Subtract integers.• Evaluate expressionscontaining variables.
  • 50. 2–342 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Evaluate Algebraic Expressionsa. Evaluate m - (-2) if m = 4.m - (-2) = - (-2) Replace m with .= To subtract -2, add .= Add and .b. Evaluate x - y if x = -14 and y = -2.x - y = - ( ) Replace x with andy with .= To subtract -2, add .= Add and .Check Your Progressa. Evaluate p - (-6) if p = -4.b. Evaluate m - n if m = -9 and n = -3.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 51. Glencoe Pre-Algebra 43Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Multiplying IntegersEXAMPLE Multiply Integers with Different SignsFind 8(-9).8(-9) = The factors have different signs.The product is .EXAMPLE Multiply Integers with the Same SignFind -4(-16).-4(-16) = The two factors have the same sign.The product is .Check Your Progress Find each product.a. -4(12) b. -3(-8)EXAMPLETEST EXAMPLE A student missed only four problems ona test, each worth 20 points. What integer represents thetotal number of points earned for those questions?A -5 B -20 C 24 D -804(-20) = The product is .The answer is .Check Your Progress TEST EXAMPLE A football teamloses 3 yards on each of 3 consecutive plays. What integerrepresents the total loss?A -9 C 6B -6 D 92–4MAIN IDEAS• Multiply integers.• Simplify algebraicexpressions.KEY CONCEPTMultiplying IntegersThe product of twointegers with differentsigns is negative.The product of twointegers with the samesign is positive.ORGANIZE ITIn your own words,describe how to multiplyintegers under the ”דtab. Give examples ofall cases.1-1-2-3-4-5-6 2 3 4 5 6
  • 52. 2–444 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Simplify and Evaluate Algebraic Expressionsa. Simplify 8a(-5b).8a(-5b) = (8)(a)(-5)(b)= (8 · -5)(ab) Commutative Property ofMultiplication= 8 · -5 = ,a · b =b. Evaluate -3xy if x = -4 and y = 9.-3xy = -3 x = -4 and y = 9.= (9) Associative Property ofMultiplication= (9) The product ofand is positive.= The product ofand is positive.Check Your Progressa. Simplify 5m(-7n).b. Evaluate -9ab if a = -3 and b = -6.WRITE ITWhat is the name of theproperty that allows youto regroup the numbersand the variables beingmultiplied?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 53. Glencoe Pre-Algebra 45Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Dividing IntegersEXAMPLE Divide Integers with the Same Signa. Find -28 ÷ (-4).-28 ÷ (-4) = The dividend and the divisor havethe same sign. The quotient is.b. Find 96_8.96_8= 96 ÷ 8 The dividend and the divisor havethe same sign.= The quotient is .Check Your Progress Find each quotient.a. 35 ÷ 7 b. -64_-4EXAMPLE Divide Integers with Different Signsa. Find 54 ÷ (-3).54 ÷ (-3) = The signs are different. Thequotient is .b. Find -42_6.-42_6= -42 ÷ 6 The signs are different. Thequotient is .= Simplify.Check Your Progress Find each quotient.a. 72 ÷ (-8) b. -36_42–5MAIN IDEAS• Divide integers.• Find the average of aset of data.KEY CONCEPTSDividing Integers withthe Same Sign Thequotient of two integerswith the same sign ispositive.Dividing Integers withDifferent Signs Thequotient of two integerswith different signs isnegative.
  • 54. 2–546 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Evaluate Algebraic ExpressionsEvaluate 6x ÷ y if x = -4 and y = -8.6x ÷ y = 6 ÷ x = -4 and y = -8= ÷ (-8) 6(-4) == The quotient is .Check Your Progress Evaluate -4m ÷ n if m = -9and n = -3.To find the average, or mean, of a set of numbers, find theof the numbers and then by thenumber in the set.BUILD YOUR VOCABULARY (pages 32–33)EXAMPLE Find the Meana. Ian had exam scores of 89, 98, 96, 97, and 95. Find theaverage (mean) of his scores.89 + 98 + 96 + 97 + 95_____ Find the sum of the scores.Then divide by the numberof scores.= or Simplify.Check Your Progress Kyle had test scores of 89, 82, 85, 93,and 96. Find the average (mean) of his test scores.ORGANIZE ITDescribe how to findthe average of a set ofnumbers in your ownwords under the ”÷“tab.1-1-2-3-4-5-6 2 3 4 5 6HOMEWORKASSIGNMENTPage(s):Exercises:
  • 55. Glencoe Pre-Algebra 47Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 2–6 The Coordinate SystemEXAMPLE Write Ordered PairsWrite the ordered pair that names each point.a. P yxO112342 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ2Ϫ1Ϫ3Ϫ4RPQThe x-coordinate is .The y-coordinate is .The ordered pair is .b. QThe x-coordinate is .The y-coordinate is .The ordered pair is .Check Your Progress Write the ordered pair thatnames each point.a. MyxO112342 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ2Ϫ1Ϫ3Ϫ4P NMb. Nc. PThe x-axis and the y-axis separate the coordinateplane into regions, called quadrants.BUILD YOUR VOCABULARY (pages 32–33)MAIN IDEAS• Graph points on acoordinate plane.• Graph algebraicrelationships.REMEMBER ITThe coordinates in anordered pair (x, y) arelisted in alphabeticalorder.
  • 56. 2–648 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Graph Points and Name QuadrantGraph and label each point on a coordinate plane. Thenname the quadrant in which each point lies.a. S(-1, -5) yxO11232 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ2Ϫ1Ϫ3Ϫ4Ϫ5SStart at the origin.Move unit .Then move unitsand draw a dot. Quadrant .b. U(-2, 3) yxO11232 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ2Ϫ1Ϫ3Ϫ4Ϫ5UStart at the origin.Move units .Then move unitsand draw a dot. Quadrant .c. T(0, -3) yxO11232 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ2Ϫ1Ϫ3Ϫ4Ϫ5TStart at the origin.Since the x-coordinate is 0,the point lies on the .Move 3 units down, anddraw a dot. Point T is not in any quadrant.Check Your Progress Graph and label each point ona coordinate plane. Name the quadrant in which eachpoint lies.a. A(3, -4) b. B(-2, 1) c. C(-4, 0)yxO112342 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ1Ϫ2Ϫ3Ϫ4Give a definition for theorigin of a coordinatesystem. (Lesson 1-5)REVIEW IT
  • 57. 2–6Glencoe Pre-Algebra 49Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Graph an Algebraic RelationshipThe difference between two integers is 4. If x representsthe first integer and y is subtracted from it, make a tableof possible values for x or y. Then graph the orderedpairs and describe the graph.First, make a table. x - y = 4x y (x, y)210-1-2Choose values for xand y that have adifference of 4.Then graph the ordered pairs on a yxO1122 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ2Ϫ1Ϫ6Ϫ5Ϫ3Ϫ4coordinate plane.The points on the graph are ina line that slants upward tothe right. The line crosses they-axis at -4.Check Your Progress The sum of two integers is 3. If x isthe first integer and y represents the second number, make atable of possible values for x and y. Graph the ordered pairsand describe the graph.yxO112342 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ1Ϫ2Ϫ3Ϫ4HOMEWORKASSIGNMENTPage(s):Exercises:
  • 58. 50 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R2VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 2 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 2, go to:glencoe.comYou can use your completedVocabulary Builder(pages 32–33) to help yousolve the puzzle.2-1Integers and Absolute Value1. Order the integers {21, -1, 9, 7, 0 -4, -11} from least to greatest.Evaluate each expression if r = 3, s = -2, and t = -7.2. t - 6 3. 12 - s - 54. s + t - r 5. rt - 1 ÷ s2-2Adding IntegersFind each sum.6. -52 + 9 7. 7 + (-31) + 48. (-8) + 22 + (-15) + 5 9. 6 + (-10) + (-12) + 42-3Subtracting IntegersFind each difference.10. -17 -26 11. 35 - (-14)12. 42 - 19 13. 11 - (-18)STUDY GUIDE
  • 59. Glencoe Pre-Algebra 51Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 BRINGING IT ALL TOGETHEREvaluate each expression if p = -6, q = 9, and r = -2.14. q - 16 15. r - 416. p - q - r 17. q - r - p2-4Multiplying IntegersFind each product.18. -4(-16) 19. 3(-4)(-11)(2)Simplify each expression.20. 5b · (-7c) 21. 2p(-7q)(-3)2-5Dividing IntegersFind each quotient.22. 72 ÷ -9 23. -28 ÷ 424. -49_-725. -144_1826. Find the average (mean) of 9, -6, 11, 7, 2, and -5.2-6The Coordinate SystemName the ordered pair for each point graphed on thecoordinate plane.27. AyxO112342 3 4Ϫ4 Ϫ3 Ϫ2 Ϫ1Ϫ2Ϫ1Ϫ3Ϫ4BAC28. B29. C
  • 60. Checklist52 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R2Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 2 Practice Test onpage 119 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 2 Study Guide and Reviewon pages 116–118 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 2 Practice Test onpage 119.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 2 Foldable.• Then complete the Chapter 2 Study Guide and Review onpages 116–118 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 2 Practice Test onpage 119.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 2.ARE YOU READY FORTHE CHAPTER TEST?
  • 61. Chapter3Glencoe Pre-Algebra 53Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3 EquationsUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of 81_2" × 11" paper.Stack 5 sheets ofpaper 3_4inch apart.Roll up the bottomedges. All tabs shouldbe the same size.Crease and staplealong fold.Label the tabs withtopics from the chapter.NOTE-TAKING TIP: When you take notes, includedefinitions of new terms, explanations of newconcepts, and examples of problems.
  • 62. 54 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BUILD YOUR VOCABULARYC H A P T E R3This is an alphabetical list of new vocabulary terms you will learn in Chapter 3.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleareacoefficient[koh-uh-FIHSH-ehnt]constantequivalent equationsequivalent expressionsformula
  • 63. Glencoe Pre-Algebra 55Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Vocabulary TermFoundon PageDefinitionDescription orExampleinverse operationslike termsperimetersequencesimplest formtermtwo-step equationChapter 3 BUILD YOUR VOCABULARY
  • 64. 56 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–1 The Distributive PropertyMAIN IDEAS• Use the DistributiveProperty to writeequivalent numericalexpressions.• Use the DistributiveProperty to writeequivalent algebraicexpressions.The 3(4 + 2) and 3 · 4 + 3 · 2 areequivalent expressions because they have the same, 18.BUILD YOUR VOCABULARY (pages 54–55)EXAMPLE Use the Distributive PropertyKEY CONCEPTDistributive PropertyTo multiply a numberby a sum, multiplyeach number insidethe parentheses by thenumber outside theparentheses.Include theDistributive Property inyour Foldable.Use the Distributive Property to write each expressionas an equivalent expression. Then evaluate theexpression.a. 4(5 + 8)4(5 + 8) = += + Multiply.= Add.b. (6 + 9)2(6 + 9)2 = += + Multiply.= Add.Check Your Progress Use the Distributive Property towrite each expression as an equivalent expression. Thenevaluate the expression.a. 3(9 + 2)b. (7 + 3)5
  • 65. 3–1Glencoe Pre-Algebra 57Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLERECREATION A Canoe Camping class costs $80 perperson, including the cost for canoe rental. The costof food is an additional $39 per person.a. Write two equivalent expressions to find the total costof one trip for a family of four.METHOD 1 Find the cost for person, then multiply by.( + ) times the cost for personMETHOD 2 Find the cost of classes and food forpeople.( ) + ( )cost of classes cost of food for peopleb. Find the total cost.4($80 + $39) = += +=Check Your Progress MOVIES The cost of a movieticket is $7 and the cost of a box of popcorn is $2.a. Write two equivalent expressions to find the total cost fora family of five to go to the movies if each member of thefamily gets a box of popcorn.b. Find the total cost.Write a definition ofalgebraic expressionin your own words.(Lesson 1–3).REVIEW IT
  • 66. 3–158 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Simplify Algebraic ExpressionsUse the Distributive Property to write 2(x + 4) as anequivalent algebraic expression.2x + 4 = + Property= Simplify.Check Your Progress Use the Distributive Property towrite 4(m + 7) as an equivalent algebraic expression.EXAMPLE Simplify Expressions with SubtractionUse the Distributive Property to write each expressionas an equivalent algebraic expression.a. 4(x - 2)4(x - 2)= 4Rewrite x - 2 as .= + Property= + Simplify.= Definition of subtractionb. -2(n - 3)-2(n - 3)= -2Rewrite n - 3 as .= + Property= Simplify.Check Your Progress Use the Distributive Propertyto write each expression as an equivalent algebraicexpression.a. 2(a - 9) b. -7(b - 3)HOMEWORKASSIGNMENTPage(s):Exercises:
  • 67. Glencoe Pre-Algebra 59Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.When plus or minus signs separate an algebraic expressioninto parts, each part is a term.The part of a term that contains a variable iscalled the coefficient of the .Like terms are terms that contain the same ,such as 2n and 5n or 6xy and 4xy.A term without a variable is called a constant.BUILD YOUR VOCABULARY (pages 54–55)REMEMBER ITIf an expression doesnot have any plus orminus signs, then theentire expression is asingle term.EXAMPLE Identify Parts of ExpressionsIdentify the terms, like terms, coefficients, and constantsin the expression 4x - x + 2y - 3.Rewrite 4x - x + 2y - 3 as 4x + (-x) + 2y + (-3).The terms are , , , and .The like terms are and .The coefficients are , , and .The constant is .Check Your Progress Identify the terms, like terms,coefficients, and constants in the expression 5x + 3y - 2y + 6.MAIN IDEAS• Use the DistributiveProperty to simplifyalgebraic expressions.3–2 Simplifying Algebraic Expressions
  • 68. 3–260 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.An algebraic expression is in simplest form if it has noand no parentheses.When you use the Distributive Property to liketerms, you are simplifying the expression.BUILD YOUR VOCABULARY (pages 54–55)EXAMPLE Simplify Algebraic ExpressionsORGANIZE ITUnder the SimplifyingExpressions tab, explainhow you know whenan expression can besimplified. Write anexpression that can besimplified and one thatcannot.Simplify each expression.a. 8n + 4 + 4n8n + 4 + 4n= 8n + Commutative Property= Distributive Property= Simplify.b. 6x + 4 - 5x - 76x + 4 - 5x - 7= 6x + 4 + + Definition of subtraction= 6x + + 4 + Commutative Property= + 4 + (-7) Distributive Property= Simplify.Check Your Progress Simplify each expression.a. 5x + 3 + 7xb. 3m + 9 - m - 6c. 7b + 3(c - 2b)WRITE ITWhat does it mean fortwo expressions to beequivalent?
  • 69. 3–2Glencoe Pre-Algebra 61Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Translate Verbal Phrases into ExpressionsWORK Suppose you and a friend worked in the schoolstore last week. You worked 4 hours more than yourfriend. Write an expression in simplest form thatrepresents the total number of hours you both worked.WordsVariableExpressionYour friend worked some hours. You worked4 hours more than your friend.Let h = number of hours your friend worked.Let h + 4 = number of hours you worked.To find the total, add the expressions.+ = ( )+ 4 Associative Property= ( )+ 4 Identity Property= + 4 Distributive Property= Simplify.The expression represents the total numberof hours you both worked.Check Your Progress You and a friend went to the library.Your friend borrowed three more books than you did. Write anexpression in simplest form that represents the total numberof books you both borrowed.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 70. 62 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Inverse operations “undo” each other.The equations x + 4 = 7 and x = 3 are equivalent equationsbecause they have the same , 3.BUILD YOUR VOCABULARY (pages 54–55)EXAMPLE Solve Equations by SubtractionSolve x + 4 = -3.x + 4 = -3x + 4 - = -3 - Subtract from each side.= 4 - 4 = and -3 - 4 == Identity PropertyTo check your solution, replace x with .CHECK + 4 = -3+ 4 = -3= -3The solution is . To graph it, draw a dot at on anumber line.Check Your Progress Solve y + 7 = 3. Check your solutionand graph it on a number line.3–3 Solving Equations by Adding or SubtractingMAIN IDEAS• Solve equations byusing the SubtractionProperty of Equality.• Solve equations byusing the AdditionProperty of Equality.KEY CONCEPTSubtraction Property ofEquality If you subtractthe same number fromeach side of an equation,the two sides remainequal.
  • 71. 3–3Glencoe Pre-Algebra 63Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. KEY CONCEPTAddition Property ofEquality If you add thesame number to eachside of an equation, thetwo sides remain equal.Under theEquations: +, - tab,write one equationthat can be solved bysubtracting and one thatcan be solved by adding.EXAMPLE Solve Equations by AddingSolve y - 3 = -14y - 3 = -14y + = -14 Rewrite y - 3 as .y + (-3) + = -14 + Add to each side.y + = -14 + Additive Inverse Propertyy = Identity PropertyCheck Your Progress Solve x - 2 = -9.EXAMPLE Use an Equation to Solve a ProblemENTERTAINMENT Movie A earned $225 million at thebox office. That is $38 million less than Movie B earned.Write and solve an equation to find the amount Movie Bearned.WordsVariableExpressionMovie A earned $38 million less thanMovie B earned.Let B = amount Movie B earned.Movie A earned $38 million less than Movie B.(continued on the next page)
  • 72. 3–364 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Solve the equation.Write the equation.225 = B - 38 Add to each side.= Simplify.Movie B earned at the box office.Check Your Progress CONSTRUCTION Board Ameasures 22 feet. That is 9 feet more than the measure ofboard B. Write and solve an equation to find the measure ofboard B.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 73. Glencoe Pre-Algebra 65Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 3–4 Solve Equations by Multiplying or DividingEXAMPLE Solve Equations by DividingSolve 7x = -56. Check your solution and graph it on anumber line.7x = -56 Write the equation.7x_= -56_ Divide each side by .= 7 ÷ = , -56 ÷ == Identity Property; 1x =Ϫ10 Ϫ8 Ϫ6 Ϫ4 Ϫ2Check Your Progress Solve 4x = -12. Graph the solutionon a number line.EXAMPLE Use an Equation to Solve a ProblemHOBBIES Esteban spent $112 on boxes of baseball cardsIf he paid $14 per box, how many boxes of cards didEsteban buy?WordsVariableEquation$14 times the number of boxes equalsthe total.Let x represent the number of boxes.cost numberper box times of boxes equals total· =MAIN IDEAS• Solve equations byusing the DivisionProperty of Equality.• Solve equations byusing the MultiplicationProperty of Equality.KEY CONCEPTSDivision Property ofEquality When youdivide each side of anequation by the samenonzero number, the twosides remain equal.Multiplication Propertyof Equality When youmultiply each side of anequation by the samenumber, the two sidesremain equal.
  • 74. 3–466 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Solve the equation.= Write the equation.= Divide each side by .Check Your Progress TOY CARS Drew spent $18 on toycars. If the cars cost $2 each, how many cars did Drew buy?EXAMPLE Solve Equations by MultiplyingORGANIZE ITUnder the Equations:×, ÷ tab, write oneequation that can besolved by multiplying andone that can be solved bydividing.Solvey_-5= -12. Check your solution and graph it ona number line.y_-5= -12 Write the equation.y_-5= -12 Multiply each side byto undo the division.= Simplify.Check Your Progress Solve m_4= -9. Check your solutionand graph it on a number line.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 75. Glencoe Pre-Algebra 67Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 3–5 Solving Two-Step EquationsA two-step equation contains operations.BUILD YOUR VOCABULARY (page 55)EXAMPLE Solve Two-Step Equationsa. Solve 3x - 4 = 17.3x - 4 + = 17 + Add to each side.= Simplify.3x_ = 21_ Undo .Divide each side by .= Simplify.b. 3 = n_3+ 83 - = n_3+ 8 - Subtract from each side.-5 = n_3Simplify.(-5) = (n_3 ) Multiply each side by .= n Simplify.Check Your Progress Solve each equation.a. 4x + 3 = 19 b. w_6- 8 = -4MAIN IDEA• Solve two-stepequations.ORGANIZE ITUnder Two-StepEquations tab, write atwo-step equation. Thenwrite the order of thesteps you would use tosolve that equation.
  • 76. 3–568 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEMEASUREMENT The formula F = 1.8C + 32 is used toconvert Fahrenheit degrees to Celsius degrees. Solvethe equation to find the equivalent Celsius temperaturefor 59°F.= 1.8C + 32 Substitute 59° for F.59 - = 1.8C + 32 - Subtract from each side.27 = 1.8C Simplify.27__ = 1.8C__ Divide each side by 1.8.= Simplify.59°F is equal to .Check Your Progress CELL PHONES Sue signed up fora cell phone plan that charges $19 per month plus $0.10 perminute used. Her first bill was $23.30. Solve 19 + 0.10x = 23.30to find out how many minutes Sue used this month.EXAMPLE Equations with Negative CoefficientsSolve 5 - x = 7.5 - = 7 Identity Property5 + (-1x) = 7 Definition of subtraction5 + (-1x) + (-5) = 7 + (-5) Add -5 to each side.(-1x) = Simplify.= Divide each side by .= Simplify.
  • 77. 3–5Glencoe Pre-Algebra 69Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Combine Like Terms Before SolvingSolve b - 3b + 8 = 18.- 3b + 8 = 18 Identity Property+ 8 = 18 Combine like terms.+ 8 = 18 Subtract fromeach side.= Simplify.= Divide each side by .= Simplify.Check Your Progress Solve each equation.a. 9 = -4 - m. b. 9 = 13 - x + 5xHOMEWORKASSIGNMENTPage(s):Exercises:
  • 78. 70 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–6 Writing Two-Step EquationsEXAMPLE Translate Sentences into EquationsTranslate twice a number increased by 5 equals -25 intoan equation.Check Your Progress Translate five times a numberdecreased by 9 equals –6 into an equation.EXAMPLE Translate and Solve an EquationNine more than four times a number is 41. Find thenumber.WordsVariableEquationNine more than four times a number is 41.Let n = the number.9 + 4n = 419 + 4n = 41 Write the equation.9 + 4n - = 41 - Subtract fromeach side.= Simplify.= Divide each side by .Check Your Progress Six less than three times a numberis 15. Find the number.MAIN IDEAS• Write verbal sentencesas two-step equations.• Solve verbal problemsby writing and solvingtwo-step equations.ORGANIZE ITUnder the WritingEquations tab, list twowords or phrases thatcan be translated intoeach of the four basicoperations.
  • 79. 3–6Glencoe Pre-Algebra 71Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Write and Solve a Two-Step EquationEARNINGS Ms. Parsons earns $48,400 per year. This is$4150 more than three times as much as her daughterearns. How much does her daughter earn?WordsVariableEquationMs. Parsons earns $4150 more than threetimes as much as her daughter.Let d = daughter’s earningsthree times asmore much asMs. Parsons earns $4150 than her daughter= $4150 += 4150 + Write the equation.Subtract from each side.- = 4150 + -= Simplify.= Divide each side by .= Simplify.Ms. Parsons’ daughter earns .Check Your Progress SHOPPING Tami spent $175 at thegrocery store. That is $25 less than four times as much as Tedspent. How much did Ted spend?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 80. 72 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–7 Sequences and EquationsEXAMPLE Describe an Arithmetic SequenceDescribe the sequence 3, 6, 9, 12, … using words andsymbols.Term Number (n) 1 2 3 4Term (t) 3 6 9 12The difference of the term numbers is . The terms havea common difference of . Also, a term is times the. The equation describes thesequence.Check Your Progress Describe the sequence 7, 14, 21,28, … using words and symbols.EXAMPLE Find a Term in an Arithmetic SequenceFind the 11th term of 6, 9, 12, 15, … .Term Number (n) 1 2 3 4Term (t) 6 9 12 15MAIN IDEAS• Describe sequencesusing words andsymbols.• Find the terms ofarithmetic sequences.
  • 81. 3–7Glencoe Pre-Algebra 73Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The difference of the term numbers is .The terms have a common difference of .The common difference is times the of theterm numbers. This suggests that . However, you needto add to get the exact value of t. Thus, t = .Check Your Progress Find the 14th term of 4, 9, 14,19, … .EXAMPLETELEPHONE CHARGES For a telephone call to India, atelephone company charges $8 for the first minute and$4 for each additional minute. How much does it cost fora 10-minute call?Make a table to organize the sequence and find a rule.Number of Minutes (m) 1 2 3Cost (c) 8 12 16The difference of the term numbers is .The terms have a common difference of .The pattern in the table shows the equation .If c = and m = , then c =or c = .Check Your Progress READING During one month,Mitch read 3 books. Each month after, he read only 2 books.After 12 months, how many books did Mitch read?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 82. 74 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A formula is an that shows a relationshipamong certain quantities.The around a geometric figure is called theperimeter.BUILD YOUR VOCABULARY (pages 54–55)EXAMPLE Use the Distance FormulaTRAVEL If you travel 135 miles in 3 hours, what is youraverage speed in miles per hour?d = rt Write the formula.= d = , t == Divide each side by .= Simplify.Check Your Progress VACATION If you drive 520 milesin 8 hours, what is your average speed in miles per hour?EXAMPLE Find the Perimeters and Lengths of Rectanglesa. Find the perimeter of20 cm15 cmthe rectangle.Using Formula3–8MAIN IDEAS• Solve problems usingformulas.• Solve problemsinvolving theperimeters and areasof rectangles.
  • 83. 3–8Glencoe Pre-Algebra 75Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.P = Write the formula.P = = , w =P = Add and .P = Simplify.ORGANIZE ITLocate a rectangularobject in your classroomand measure its lengthand width. Under theFormulas tab, describehow to determine itsperimeter using theperimeter formula.b. The perimeter of a rectangle is 60 feet. Its widthis 9 feet. Find its length.P = 2( + w) Write the formula.P = Distributive Property= P = , w == Simplify.= Subtract fromeach side.= Simplify.= Divide each side by .The length is feet.Check Your Progressa. Find the perimeter of the rectangle.b. The perimeter of a rectangle is 36 meters. Its width is6 meters. Find its length.
  • 84. 3–876 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The measure of the surface enclosed by a figure is its area.BUILD YOUR VOCABULARY (page 54)EXAMPLE Find the Areas and Widths of Rectanglesa. Find the area of a rectangle with length 14 feet andwidth 6 feet.A = Write the formula.A = · = , w =A = Simplify.The area is square feet.b. The area of a rectangle is 40 square meters. Its lengthis 8 meters. Find its width.A = Write the formula.= A = , == Divide each side by .The width is meters.Check Your Progressa. Find the area of a rectangle with length 11 yards and width6 yards.b. The area of a rectangle is 42 square inches. Its length is14 inches. Find its width.KEY CONCEPTArea of a Rectangle Thearea of a rectangle is theproduct of the lengthand width.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 85. Glencoe Pre-Algebra 77Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R3VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 3 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 3, go to:glencoe.comYou can use your completedVocabulary Builder(pages 54–55) to help yousolve the puzzle.3-1The Distributive PropertyMatch each expression with an equivalent expression.1. 5(4 + 7) a. 5 · 7 + 4 · 7b. (-4) · 5 + (-4) · (-7)c. 5 · 4 + 5 · 7d. (-4) · 5 + (-4) · 7e. -5 · 7 + (-5) · 4f. 5 · 4 + (-7) · 42. (5 + 4)73. -4(5 + 7)4. (5 - 7)45. -4(5 - 7)6. In rewriting 3(x + 2), which term is “distributed” to the otherterms in the expression?3-2Simplifying Algebraic ExpressionsUnderline the term that best completes each statement.7. A term without a variable is a (coefficient, constant).8. The expression 5z + 2z + 9 + 6z has three (like terms, terms).Simplify each expression.9. 6q + 2q 10. 12y - y11. 5 + 7x - 3 12. 4(b + 1) + bSTUDY GUIDE
  • 86. 78 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 BRINGING IT ALL TOGETHER3-3Solving Equations by Adding or SubtractingUnderline the term that best completes each statement.13. To undo the addition of 8 in the expression y + 8, you would add-8. This is an example of (inverse operations, simplest form.)14. The equations x + 3 = 12 and x = 9 are equivalent equationsbecause they have the same (solution, variable).Solve each equation.15. 7 + z = 19 16. 19 = x - 817. Write and solve an equation for the sentence. The sum of –13 anda number is –16.3-4Solving Equations by Multiplying or DividingSolve each equation.18. 3m = 39 19. c_8= -620. What value of h makes h_-2= 16 a true statement?A -8 B -32 C 8 D 323-5Solving Two-Step EquationsSolve each equation.21. 4y + 3 = 15 22. -17 = 6q - 723. 9 = b_3- 12 24. 31 = 2x + 6 - 7x
  • 87. Glencoe Pre-Algebra 79Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3-6Writing Two-Step EquationsTranslate each sentence into an equation. Then find the number.25. Six decreased by four times a number is 18.26. Thirteen more than the quotient of a number and 3 is -5.3-7Sequences and EquationsWrite an equation that describes each sequence. Then find theindicated term.27. 9, 10, 11, 12, …; 29th term28. 13, 26, 39, 52, …; 13th term3-8Using Formulas29. What is the speed in miles perhour of a raft that travels18 miles in 3 hours?Find the perimeter and area of each rectangle.30.12 cm5 cm31.17 in.17 in.Chapter 3 BRINGING IT ALL TOGETHER
  • 88. Checklist80 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureCheck the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 3 Practice Test onpage 173 of your textbook as a final check.I used my Foldable or Study Notebook to complete the reviewof all or most lessons.• You should complete the Chapter 3 Study Guide and Reviewon pages 169–172 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 3 Practice Test onpage 173.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 3 Foldable.• Then complete the Chapter 3 Study Guide and Review onpages 169–172 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 3 Practice Test onpage 173.C H A P T E R3Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 3.
  • 89. Chapter4Glencoe Pre-Algebra 81Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R4Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with four sheets of notebook paper.Fold four sheets ofnotebook paper in halffrom top to bottom.Cut along fold. Stapleeight half-sheetstogether to form abooklet.Cut tabs into margin.Make the top tab 2 lineswide, the next tab 4 lineswide, and so on.Label each of the tabs4-34-2I dont knowthe next label4-1Factors andFractionswith the lesson numberand title.NOTE-TAKING TIP: At the end of each lesson,write a summary of the lesson, or write in yourown words what the lesson was about.Factors and Fractions
  • 90. 82 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R4This is an alphabetical list of new vocabulary terms you will learn in Chapter 4.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplealgebraic fractionbasecomposite numberexponentfactorfactor treeBUILD YOUR VOCABULARY
  • 91. Glencoe Pre-Algebra 83Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 4 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplegreatest commonfactor (GFC)monomialpowerprime factorizationprime numberscientific notationsimplest formstandard formVenn Diagram
  • 92. 84 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.4–1 Powers and ExponentsIn an expression like 24, the base is the number that is.The exponent tells how many times the base is used as a.The number that can be expressed using an iscalled a power.BUILD YOUR VOCABULARY (pages 82–83)EXAMPLE Write Expressions Using ExponentsWrite each expression using exponents.a. 6 · 6 · 6 · 6The base is . It is a factor times, so theexponent is .6 · 6 · 6 · 6 =b. pThe base is . It is a factor time, so theexponent is .p =c. (-1)(-1)(-1)The base is . It is a factor times, so theexponent is .(-1)(-1)(-1) =MAIN IDEAS• Write expressions usingexponents.• Evaluate expressionscontaining exponents.
  • 93. 4–1Glencoe Pre-Algebra 85Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. d. (5x + 1)(5x + 1)The base is . It is a factor times, so theexponent is .(5x + 1)(5x + 1) =e. 1_2· x · x · x · x · y · y · yFirst group the factors with like bases. Then write usingexponents.= 1_2· (x · x · x · x) · (y · y · y)=Check Your Progress Write each expression usingexponents.a. 3 · 3 · 3 · 3 · 3 · 3 b. m · m · mc. (-6)(-6)(-6)(-6) d. (4 - 2x)(4 - 2x)e. 9 · a · a · a · b · b · b · b · bEXAMPLE Evaluate ExpressionsEvaluate each expression.a. 42= · is a factor two times.= Multiply.b. 2 · 32= 2 · · is a factor two times.= Multiply.ORGANIZE ITUnder the tab for Lesson4-1, write a summaryabout the relationshipbetween base, exponent,and factor.4-34-2I dont knowthe next label4-1Factors andFractionsWRITE ITWhat is the differencebetween (-5)2 and-52? Explain.
  • 94. 4–186 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Evaluate each expression.a. 34b. 43· 2EXAMPLEEvaluate each expression.a. r3- 3 if r = -2r3- 3 = ( )3- 3 Replace r with= ( )( )( )- 3 Rewrite 3.= - 3 Multiply.= Subtract.b. x(y2+ 2)2if x = 2 and y = -2x(y2+ 2)2= ( )( )2+ 22Replace x with 2 andy with -2.= (2)+ 22Rewrite (-2)2.= (2)( )2Simplify.= (2)( ) Multiply.=Check Your Progress Evaluate each expression.a. 100 - x4if x = 2b. m(5 - n)3if m = -3 and n = 3HOMEWORKASSIGNMENTPage(s):Exercises:
  • 95. Glencoe Pre-Algebra 87Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Prime FactorizationA prime number is a whole number that has exactly twofactors, 1 and itself.A composite number is a whole number that has morethan two factors.BUILD YOUR VOCABULARY (pages 82–83)EXAMPLE Identify Numbers as Prime or CompositeREMEMBER ITZero and 1 areneither primenor composite.Determine whether each number is prime or composite.a. 31Find factors of 31 by listing the whole number pairs whoseproduct is 31.31 =The number 31 has only two factors. So, it isa number.b. 36Find factors of 36 by listing thewhose product is 36.36 = 36 =36 = 36 =36 =The factors of 36 are .Since the number has more than two factors, it is anumber.Check Your Progress Determine whether each numberis prime or composite.a. 49 b. 294–2MAIN IDEAS• Write the primefactorization ofcomposite numbers.• Factor monomials.
  • 96. 4–288 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.When a composite number is expressed as the productof prime factors, it is called the prime factorization ofthe number.One way to find the prime factorization of a numberis to use a factor tree.To factor a number means to write it as a product of itsfactors.BUILD YOUR VOCABULARY (page 83)EXAMPLE Write Prime FactorizationWrite the prime factorization of 56.56· 7· · 7· · · 7The prime factorization of56 is .EXAMPLE Factor MonomialsORGANIZE ITUnder the Lesson 4-2tab, describe how to usea factor tree to find theprime factorization of anumber.4-34-2I dont knowthe next label4-1Factors andFractionsa. Factor 16p2q4.16p2q4= 2 · 2 · 2 · 2 · p2· q4= · · · · · · ·· ·b. Factor -21x2y.-21x2y = -1 · · · x2· y= -1 · · · · ·Check Your Progressa. Write the prime factorization of 72.b. Factor 12a3b. c. Factor -18mn2.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 97. Glencoe Pre-Algebra 89Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Greatest Common Factor (GCF)A Venn diagram shows the relationship among setsof or objects by using overlappingin a rectangle.The number that is a of two ormore numbers is called the greatest common factor (GCF).BUILD YOUR VOCABULARY (page 83)EXAMPLE Find the GCFFind the GCF of 16 and 24.Method 1 List the factors.factors of 16:factors of 24:The greatest common factor of 16 and 24 is .Method 2 Use prime factorization.16 = 2 · 2 · 2 · 224 = 2 · 2 · 2 · 3The GFC is the product of the common .2 · 2 · 2 =Check Your Progress Find the GCF of 18 and 30.4–3MAIN IDEAS• Find the greatestcommon factor of twoor more numbers ormonomials.• Use the DistributiveProperty to factoralgebraic expressions.ORGANIZE ITUnder the Lesson 4-3tab, describe the twomethods for findingthe GCF of two or morenumbers.4-34-2I dont knowthe next label4-1Factors andFractions
  • 98. 4–390 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find the GCF of MonomialsFind the GCF of 18x3y2and 42xy2.Completely factor each expression.18x3y2= 2 · 3 · 3 · x · x · x · y · y42xy2= 2 · 3 · 7 · x · y · yCircle the common factors.The GCF of 18x3y2and 42xy2is or .Check Your Progress Find the GCF of 32mn4and 80m3n2.EXAMPLE Factor ExpressionsFactor 3x + 12.First, find the GCF of 3x and 12.3x = 3 · x12 = 2 · 2 · 3The GCF is .Now, write each term as a product of the and itsremaining factors.3x + 12 = 3( )+ 3( )= 3( ) PropertyCheck Your Progress Factor 4x + 20.HOMEWORKASSIGNMENTPage(s):Exercises:Name the operationsthat are combined bythe Distributive Property.(Lesson 3-1)REVIEW IT
  • 99. Glencoe Pre-Algebra 91Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Simplifying Algebraic FractionsA fraction is in simplest form when the GCF of theand the is 1.A fraction with in theor is called an algebraic fraction.BUILD YOUR VOCABULARY (pages 82–83)EXAMPLES Simplify FractionsWrite each fraction in simplest form.16_2416 = 2 · 2 · 2 · 2 Factor the .24 = 2 · 2 · 2 · 3 Factor the .The of 16 and 24 is · · or .16_24=16 ÷__24 ÷=Divide the numerator anddenominator by the .72_12072_120= 21· 21· 21· 31· 3___21· 21· 21· 31· 5=Divide the numerator andthe denominator by the GCF.Check Your Progress Write each fraction insimplest form.a. 12_40b. 48_804–4MAIN IDEAS• Simplify fractions usingthe GCF.• Simplify algebraicfractions.WRITE ITDescribe the result if acommon factor otherthan the GCF is used tosimplify a fraction.
  • 100. 4–492 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETEST EXAMPLE 250 pounds is what part of 1 ton?A 1_10B 1_8C 1_4D 1_2There are pounds in ton. Write the fractionin simplest form.250_2000= 21· 51· 51· 51____21· 2 · 2 · 2 · 51· 51· 51=So, 250 pounds is of 1 ton. The answer is .Check Your Progress TEST EXAMPLE 80 feet is whatpart of 40 yards?A 2_3B 1_2C 3_40D 1_3EXAMPLE Simplify Algebraic FractionsSimplify 20m3n2__65mn.20m3n2__65mn=2 · 2 · 51· m1· m · m · n1· n_____51· 13 · m1· n1Divide the numerator andthe denominator by the GCF.= Simplify.Check Your Progress Simplify14x4y2__49x2y2.ORGANIZE ITUnder the Lesson 4-4 tab,explain how to simplifyboth numeric andalgebraic fractions.4-34-2I dont knowthe next label4-1Factors andFractionsHOMEWORKASSIGNMENTPage(s):Exercises:
  • 101. Glencoe Pre-Algebra 93Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Multiplying and Dividing MonomialsEXAMPLE Multiply PowersFind 34· 36.34· 36= 3+The common base is .= 3 the exponents.Check Your Progress Find 43· 45.EXAMPLE Multiply MonomialsFind each product.a. y4· yy4· y = y+The common base is .= y the exponents.KEY CONCEPTProduct of Powers Youcan multiply powers withthe same base by addingtheir exponents.b. (3p4)(-2p3)(3p4)(-2p3) = (3 · )(p4· ) Use the Commutativeand AssociativeProperties.= ( )(p+) The common baseis p.= theexponents.Check Your Progress Find each product.a. w2· w5b. (-4m3)(6m2)4–5MAIN IDEAS• Multiply monomials.• Divide monomials.
  • 102. 4–594 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Divide Powersa. Find 811_85.811_85= = The common base is .the exponents.b. Find x12_x .x12_x = = The common base is .the exponents.Check Your Progress Find each quotient.a. 75_73b. r4_r1EXAMPLEFOLDING PAPER If you fold a sheet of paper in half, youhave a thickness of 2 sheets. Folding again, you havea thickness of 4 sheets. Continue folding in half andrecording the thickness. How many times thicker is asheet that has been folded 4 times than a sheet that hasnot been folded?Write a expression to compare the thicknesses.24_20= = 2 orThe sheet that has been folded 4 times is times thickerthan a sheet that has not been folded.Check Your Progress RACING Car A can run at a speedof 28miles per hour and car B runs at a speed of 27miles perhour. How many times faster is car A than car B?ORGANIZE ITUnder the tab forLesson 4-5, write asummary of the wayyou can use exponentsto multiply and dividepolynomials.4-34-2I dont knowthe next label4-1Factors andFractionsKEY CONCEPTQuotient of PowersYou can divide powerswith the same baseby subtracting theirexponents.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 103. Glencoe Pre-Algebra 95Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Negative ExponentsEXAMPLE Use Positive ExponentsWrite each expression using a positive exponent.a. 3-43-4= Definition of exponentb. m-2m-2= Definition of exponentCheck Your Progress Write each expression using apositive exponent.a. 5-3b. y-6EXAMPLE Use Negative ExponentsWrite 1_125as an expression using a negative exponent.1_125= 1___ Find the of 125.= 1_ Definition of exponents= Definition of negative exponentCheck Your Progress Write 1_32as an expression using anegative exponent.4–6MAIN IDEAS• Write expressions usingnegative exponents.• Evaluate numericalexpressions containingnegative exponents.REMEMBER ITA negative exponentin an expression doesnot change the sign ofthe expression.
  • 104. 4–696 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Use Exponents to Solve a ProblemATOM An atom is an incredibly small unit of matter. Thesmallest atom has a diameter of approximately 1_10of ananometer, or 0.0000000001 meter. Write the decimal as afraction and as a power of 10.0.0000000001 = Write the decimal as afraction.= 10,000,000,000 == Definition of negativeexponentCheck Your Progress AIR POLLUTION Small particlesin the air produced by a combustion process are called smoke.These particles are usually less than one micrometer, or0.000001 m, in size. Write the decimal as a fraction and as apower of 10.EXAMPLE Algebraic Expressions with Negative ExponentsEvaluate r-2if r = -4.r-2= ( )-2Replace r with .= Definition of exponent= Find (-4)2.Check Your Progress Evaluate d-3if d = 5.ORGANIZE ITUnder the tab forLesson 4-6, explainnegative exponents.Give an example of anumber written with anegative exponent andan equivalent expressionusing a positiveexponent.4-34-2I dont knowthe next label4-1Factors andFractionsHOMEWORKASSIGNMENTPage(s):Exercises:
  • 105. Glencoe Pre-Algebra 97Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Scientific NotationEXAMPLE Express Numbers in Standard FormExpress each number in standard form.a. 4.395 × 1044.395 × 104= 4.395 × 104== 43,950 Move the decimal pointplaces to the right.=b. 6.79 × 10-66.79 × 10-6= 6.79 × 10-6== 0.00000679 Move the decimal pointplaces to the .=Check Your Progress Express each number instandard form.a. 2.614 × 106b. 8.03 × 10-4EXAMPLE Express Numbers in Scientific NotationExpress each number in scientific notation.a. 800,000= 8.0 × The decimal pointmoves places.= 8.0 × The exponent is.4–7MAIN IDEAS• Express numbers instandard form and inscientific notation.• Compare and ordernumbers written inscientific notation.KEY CONCEPTScientific Notation Anumber is expressedin scientific notationwhen it is written asthe product of a factorand a power of 10. Thefactor must be greaterthan or equal to 1 andless than 10.
  • 106. 4–798 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.b. 0.01190.0119 = × The decimal point movesplaces.= × The exponent is.Check Your Progress Express each number inscientific notation.a. 65,000b. 0.00042EXAMPLE Compare Numbers in Scientific NotationSPACE The diameters of Mercury, Saturn, and Pluto are4.9 × 103kilometers, 1.2 × 105kilometers, and 2.3 × 103kilometers, respectively. List the planets in order ofincreasing diameter.First, order the numbers according to their exponents.Then, order the numbers with the same exponent bycomparing the factors.Step 14.9 × 1032.3 × 103Mercuryand Pluto1.2 × 105SaturnStep 2 2.3 × 103Pluto4.9 × 103MercuryCompare the factors:.So, the order is .Check Your Progress Order the numbers 6.21 × 105, 2.35× 104, 5.95 × 109, and 4.79 × 104in decreasing order.ORGANIZE ITUnder the tab forLesson 4-7, explain thesignificance of a positiveor negative exponent inscientific notation. Givean example of a numberwith each, written inboth standard form andin scientific notation.4-34-2I dont knowthe next label4-1Factors andFractionsHOMEWORKASSIGNMENTPage(s):Exercises:
  • 107. Glencoe Pre-Algebra 99Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R4VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 4 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 4, go to:glencoe.comYou can use your completedVocabulary Builder(pages 82–83) to help yousolve the puzzle.4-1Powers and ExponentsWrite each expression using exponents.1. 4 · 4 · 4 · 4 2. (-2)(-2)(-2) 3. 5 · r · r · m · m · mEvaluate each expression if x = 3, y = 1, and h = -2.4. 3h 5. hx36. 4(2x - 4y)34-2Prime FactorizationWrite the prime factorization of each number. Use exponentsfor repeated factors.7. 64 8. 126 9. 735Factor each monomial completely.10. 32ac 11. 49s3t12. 144x313. 25pq4STUDY GUIDE
  • 108. 100 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 4 BRINGING IT ALL TOGETHER4-3Greatest Common Factor (GCF)Find the GCF of each set of numbers or monomials.14. 25, 45 15. 36, 54, 66 16. 28a2, 42ab3Factor each expression.17. 7x + 14y 18. 50s - 10st4-4Simplifying Algebraic Fractions19. Six ounces is what part of a pound?20. Use a Venn diagram to explain how to simplify 18_45.4-5Multiplying and Dividing MonomialsFind each quotient.21. 46_4422.(-3)3_(-3)23.p2· p3__p4Find a match for each product.24. 24· 23 a. 47b. 412c. 27d. 21225. 43· 4426. 25· 27
  • 109. Glencoe Pre-Algebra 101Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 4 BRINGING IT ALL TOGETHER4-6Negative ExponentsWrite each expression using a positive exponent.27. 8-328. 5-1029. x-2Evaluate each expression if s = 4 and t = 3.30. t-331. (st)-132. s-t4-7Scientific NotationTell direction and the number of places you need to move thedecimal point to write each number in standard notation.33. 2.3 × 10434. 1.5 × 10-735. 7.1 × 101136. The table at the right shows theRadiationWave length(meters)X-rays 5.0 × 10-9Yellow light 5.8 × 10-7Blue light 4.7 × 10-7average wave lengths of 3 typesof radiation. Write the radiationtypes in order from longest toshortest wave length.
  • 110. Checklist102 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R4Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 4 Practice Test onpage 223 of your textbook as a final check.I used my Foldable or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 4 Study Guide and Reviewon pages 219–222 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 4 Practice Test onpage 223.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 4 Foldables.• Then complete the Chapter 4 Study Guide and Review onpages 219–222 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 4 Practice Test onpage 223.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 4.
  • 111. Chapter5Glencoe Pre-Algebra 103Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R5 Rational NumbersUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with two sheets of 81_2" × 11" paper.Fold the first twosheets in half fromtop to bottom.Cut along fold fromedges to margin.Fold the third sheetin half from top tobottom. Cut alongfold from marginto edge.Insert the first twosheets through thethird sheet and alignthe folds.Label each page with alesson number and title.NOTE-TAKING TIP: As you read each lesson, listexamples of ways the new knowledge has been orwill be used in your daily life.
  • 112. 104 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R5BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 5.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebar notationcommon multipledimensional analysis[duh-MEHN-chuhn-uhl]least commondenominator (LCD)least commonmultiple (LCM)mean
  • 113. Glencoe Pre-Algebra 105Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 5 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplemeasure of centraltendencymedianmixed numbermodemultiplemultiplicative inverse[muhl-tuh-PLIH-kuh-tihv IHN-vuhrs]rational number[RASH-nuhl]reciprocal[rih-SIHP-ruh-kuhl]repeating decimalterminating decimal
  • 114. 106 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.5–1 Writing Fractions as DecimalsEXAMPLE Write a Fraction as a Terminating DecimalWrite 1_16as a decimal.METHOD 1 Use paper and pencil. Divide 1 by 16.METHOD 2 Use a calculator.Ϭ ENTER 0.0625So, 1_16=EXAMPLE Write a Mixed Number as a DecimalWrite 11_4as a decimal.11_4= + Write as the sum of an integerand a .= + == Add.Check Your Progress Write each fraction or mixednumber as a decimal.a. 5_8b. 23_5MAIN IDEAS• Write fractionsas terminating orrepeating decimals.• Compare fractions anddecimals.ORGANIZE ITUnder the tab for Lesson5-1, write an example ofwhen you might wantto change two fractionsto decimals in orderto determine which islarger.
  • 115. 5–1Glencoe Pre-Algebra 107Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A decimal with one or more that repeatforever is called a repeating decimal.You can use bar notation to indicate that a digitrepeats forever.BUILD YOUR VOCABULARY (pages 104–105)EXAMPLE Write Fractions as Repeating DecimalsWrite each fraction as a decimal. Use a bar to show arepeating decimal.a. - 4_330.1212…33 -4.0000… The digits repeat.- 4_33=b. 2_110.1818…11 2.0000… The digits repeat.2_11=Check Your Progress Write each fraction as a decimal.Use a bar to show a repeating decimal.a. -2_3b. 4_15EXAMPLE Compare Fractions and DecimalsReplace with <, >, or = to make 0.7 13_20a truesentence.0.7 13_20Write the sentence.0.7 Write 13_20as a decimal.0.7 In the tenths place, .0.5 0.55 0.6 0.65 0.7 0.750.65 0.7On a number line, 0.7 is to the right of 0.65, so 0.7 13_20.
  • 116. 5–1108 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Replace with < , >, or = to make3_80.4 a true sentence.EXAMPLE Compare Fractions to Solve a ProblemGRADES Jeremy got a score of 16_20on his first quiz and 20_25on his second quiz. Which grade was the higher score?Write the fractions as and then comparethe .Quiz #1: 16_20= Quiz #2: 20_25=The scores were the same, .Check Your Progress BAKING One recipe for cookiesrequires 5_8of a cup of butter and a second recipe for cookiesrequires 3_5of a cup of butter. Which recipe uses less butter?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 117. Glencoe Pre-Algebra 109Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Rational NumbersA number that can be written as a is called arational number.BUILD YOUR VOCABULARY (page 105)EXAMPLE Write Mixed Numbers and Integers as FractionsWrite each rational number as a fraction.a. -43_8= Write -43_8as an fraction.b. 10 =EXAMPLE Write Terminating Decimals as FractionsWrite 0.26 as a thousandshundredstensonestenthshundredthsthousandthsten-thousandths0 2 6fraction or mixednumber insimplest form.0.26 = 0.26 is 26 .= Simplify. The GCF ofand is .Check Your Progress Write each number as a fractionor mixed number in simplest form.a. 23_5b. -6 c. 0.845–2MAIN IDEAS• Write rational numbersas fractions.• Identify and classifyrational numbers.ORGANIZE ITIn your notes, describethe fractions you useduring a normal day atschool and at home.
  • 118. 5–2110 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Write Repeating Decimals as FractionsWRITE ITWhat would you multiplyeach side by if threedigits repeat? Explain.Write 0.−−39 as a fraction in simplest form.N = 0.3939… Let N represent the number.N = (0.3939…) Multiply each side by .=Subtract N from to eliminate the repeating part,0.3939… .= 39.3939…_________- (N = 0.3939...)== Divide each side by .N = or Simplify.Check Your Progress Write 0.−4 as a fraction insimplest form.EXAMPLE Classify NumbersIdentify all sets to which the number 15 belongs.15 is a number, an , a naturalnumber, and a rational number.Check Your Progress Identify all sets to which the number-7 belongs.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 119. Glencoe Pre-Algebra 111Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Multiplying Rational NumbersEXAMPLE Multiply FractionsFind 2_5· 5_8. Write the product in simplest form.2_5· 5_8= __Multiply the .Multiply the .= _ or _ Simplify. The GCF ofand is .EXAMPLE Multiply Negative FractionsFind -1_4· 2_7. Write the product in simplest form.-1_4· 2_7= - 1_42· 22_7Divide 2 and 4 by their GCF, .= –1 · 1_2 · 7Multiply the numerators and multiplythe denominators.= Simplify.EXAMPLE Multiply Mixed NumbersFind 11_2· 32_3. Write the product in simplest form.11_2· 32_3= 3_2· 11_3Rename the mixed numbers.= 31_2· 11_31Divide by the GCF, .= Multiply.= or Simplify.5–3MAIN IDEAS• Multiply positive andnegative fractions.• Use dimensionalanalysis to solveproblems.KEY CONCEPTMultiplying FractionsTo multiply fractions,multiply the numeratorsand multiply thedenominators.
  • 120. 5–3112 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find each product. Write insimplest form.a. 3_8· 2_9b. 6_14· -21_40c. 22_7· 31_4EXAMPLEDONATIONS Rasheed collects cash donations forunderprivileged children every October. This Octoberhe collected $784. Last year he collected 5_8as much.How much did Rasheed collect last October?To find how much Rasheed collected last October, multiplyby .784 · 5_8= · Rename 784 as .= 78498_1· 5_81Divide by the GCF, .= or Simplify.Rasheed collected last October.Check Your Progress SHOPPING Melissa is buying asweater originally priced for $81. The sweater is discounted by2_3. Find the amount of the discount.EXAMPLE Multiply Algebraic FractionsFind3p2_q ·q2_r . Write the product in simplest form.3p2_q ·q2_r =3p · p_q1·q1· q_r The GCF of q2and q is .= Simplify.Check Your Progress Find 5mn3_p2·mp_n2.ORGANIZE ITUnder the tab forLesson 5-3, write anexpression in which youwould multiply rationalnumbers and explainwhat it means.
  • 121. 5–3Glencoe Pre-Algebra 113Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Dimensional analysis is the process of includingwhen you compute. Youcan use dimensional analysis to check whether your answersare reasonable.BUILD YOUR VOCABULARY (page 104)EXAMPLE Use Dimensional AnalysisTRACK The track at Cole’s school is 1_4mile around. IfCole runs one lap in two minutes, how far (in miles)does he run in 30 minutes?WordsVariablesFormulaDistance equals the rate multiplied by thetime.Let d = distance, r = rate, and t = time.d = rtd = mile per 2 minutes · minutes=mile__21min· 3015minDivide by the common factorsand units.= · miles Multiply.= or miles Simplify.Cole runs miles in minutes.Check Your Progress WALKING Bob walks 2_3mile in12 minutes. How far does he walk in 30 minutes?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 122. 114 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Dividing Rational Numbers5–4Two numbers whose is are calledmultiplicative inverses or reciprocals.BUILD YOUR VOCABULARY (page 105)EXAMPLE Find Multiplicatives InversesFind the multiplicative inverse of 6_7.6_7· = 1 The product is 1.The multiplicative inverse or reciprocal of 6_7is .EXAMPLE Divide by a Fraction or Whole NumberFind each quotient. Write in simplest form.a. 4_5÷ 3_104_5÷ 3_10= 4_5·Multiply by the multiplicativeof 3_10.= 4_51·102_3Divide and by theirGCF, .= or Simplify.b. 5_6÷ 35_6÷ 3 = 5_6÷ Write 3 as .= 5_6· Multiply by the multiplicative inverse of 3_1.= Simplify.MAIN IDEAS• Divide positive andnegative fractionsusing multiplicativeinverses.• Use dimensionalanalysis to solveproblems.KEY CONCEPTSInverse Property ofMultiplication Theproduct of a numberand its multiplicativeinverse is 1.Dividing Fractions Todivide by a fraction,multiply by itsmultiplicative inverse.
  • 123. 5–4Glencoe Pre-Algebra 115Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Divide by a Mixed NumberFind 42_3÷ -31_9. Write the quotient in simplest form.42_3÷ -31_9= ÷Rename the mixed numbersas .= ·Multiply by the multiplicativeinverse of .=141_31· - 93_282Divide out common factors.= or Simplify.EXAMPLE Divide by an Algebraic FractionFind 5x_8y÷ 10_16y. Write the quotient in simplest form.5x_8y÷ 10_16y= 5x_8y·Multiply by the multiplicativeinverse of .= 51x_81y1·162y1_102Divide out common factors.= or Simplify.Check Your Progressa. Find the multiplication inverse of 4_9.Find each quotient. Write in simplest form.b. 3_8÷ 5_6c. 5_12÷ 10d. 33_4÷ 25_8e. 6m_10p÷ 9m_4ORGANIZE ITUnder the tab forLesson 5-4, write a wordproblem in which youwould divide rationalnumbers to solve theproblem.
  • 124. 5–4116 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETRAVEL How many gallons of gas are needed to travel783_4miles if a car gets 251_2miles per gallon?To find how many gallons, divide by .÷ = ÷ Write as improper fractions.= · Multiply by the reciprocal.= 315105_42· 21_5117Divide out common factors.= or Simplify.So, gallons of gas are needed.Check Your Progress SEWING Emily has 322_3yards offabric. She wants to make pillows which each require 35_6yardsof fabric to complete. How many pillows can Emily make?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 125. Glencoe Pre-Algebra 117Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Adding and Subtracting Like FractionsEXAMPLE Add FractionsFind 3_4+ 3_4. Write the sum in simplest form.3_4+ 3_4= __The denominators are the same.the numerators.= or or Simplify and rename as amixed number.EXAMPLE Add Mixed NumbersFind 34_9+ 82_9. Write the sum in simplest form.34_9+ 82_9= ( )+( ) Add the whole numbersand fractions separately.= + __ Add the numerators.= or Simplify.EXAMPLE Subtract FractionsFind 11_12- 5_12. Write the difference in simplest form.11_12- 5_12= __ The denominators are the same.Subtract the numerators.= or Simplify.5–5MAIN IDEAS• Add like fractions.• Subtract like fractions.KEY CONCEPTSAdding Like FractionsTo add fractions withlike denominators, addthe numerators andwrite the sum overthe denominator.Subtracting LikeFractions To subtractfractions with likedenominators, subtractthe numerators and writethe difference over thedenominator.
  • 126. 5–5118 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Add or subtract. Write insimplest form.a. 2_9+ 8_9b. 5 3_14+ 2 5_14c. 17_20- 11_20EXAMPLE Subtract Mixed NumbersEvaluate r - q if r = 73_5and q = 91_5.r - q = - r = , q == -Write the mixed numbersas improper fractions.= Subtract the numerators.= Simplify.EXAMPLE Add Algebraic FractionsFind 5_2b+ 3_2b. Write the sum in simplest form.5_2b+ 3_2b= __ The denominators are thesame. Add the numerators.= Add the numerators.= Simplify.Check Your Progressa. Evaluate m - n if m = 47_9and n = 82_9.b. Find 3x_16+ 5x_16. Write the sum in simplest form.ORGANIZE ITUnder the tab for Lesson5-5, describe real-lifesituations in which youwould add or subtractrational numbers.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 127. Glencoe Pre-Algebra 119Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Least Common MultipleA multiple of a number is a of that numberand a whole number.Sometimes numbers have some of themultiples. These are called common multiples.The least of the nonzero common multiples of two or morenumbers is called the least common multiple (LCM).BUILD YOUR VOCABULARY (pages 104–105)EXAMPLE Find the LCMFind the LCM of 168 and 180.Number Prime Factorization Exponential Form168180The prime factors of both numbers are .Multiply the greatest powers ofappearing in either factorization.LCM = =EXAMPLE The LCM of MonomialsFind the LCM of 12x2y2and 6y3.12x2y2=6y3=LCM =Multiply the greatest powerof each prime factor.=MAIN IDEAS• Find the least commonmultiple of two ormore numbers.• Find the least commondenominator of two ormore fractions.5–6ORGANIZE ITUnder the tab forLesson 5-6, describewhat a least commonmultiple is. Give twonumbers and their leastcommon multiple.
  • 128. 5–6120 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find the least commondenominator (LCM) of each pair of numbers ormonomials.a. 144, 96 b. 18ab3, 24a2bThe least common denominator (LCD) of two or morefractions is the of the .BUILD YOUR VOCABULARY (page 104)EXAMPLE Find the LCDFind the LCD of 7_8and 13_20.8 =Write the prime factorization of8 and 20. Highlight the greatestpower of each prime factor.20 =LCM = or Multiply.The LCD of 7_8and 13_20is .Check Your Progress Find the least common denominator(LCD) of 5_9and 11_12.EXAMPLE Compare FractionsReplace with <, >, or = to make 7_153_7a truestatement.The LCD of the fractions is or .Rewrite the fractions using the LCD and then compare the.7_15=7 ·__3 · 5 ·= Multiply the fraction by tomake the denominator 105.3_7= 3 ·_7 ·= Multiply the fraction by tomake the denominator 105.
  • 129. 5–6Glencoe Pre-Algebra 121Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Since > , then 7_153_7.44105501054910548105471054610545105715373_7is to the of 7_15on thenumber line.Check Your Progress Replace with <, >, or = to make5_219_14a true statement.EXAMPLE Order Rational NumbersFOOTBALL Dane’s football Mon Tues Wed Thurs-3_813_4-5_612_3team usually practices for21_2hours. The table belowshows how many hoursfrom normal they practiced each day this week. Orderthe practices from shortest to longest.Step 1 Order the negative fractions first. The LCD of 6 and 8is . -5_6= -3_8=Compare the negative fractions. Since -20_24- 9_24,then -5_6-3_8.Step 2 Order the positive fractions. The LCD of 3 and 4is . 12_3= 13_4=Compare the positive fractions. Since 1 8_121 9_12,then 12_313_4.Since < < < , the order of the practicesfrom shortest to longest is .Check Your Progress Order the fractions from leastto greatest.a. -11_3, -15_6, -13_4, -11_2b. 17_32, 5_8, 9_16, 25_64HOMEWORKASSIGNMENTPage(s):Exercises:
  • 130. 122 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Adding and Subtracting Unlike FractionsEXAMPLE Add Unlike FractionsFind 3_4+ 1_7. Write the sum in simplest form.3_4+ 1_7= 3_4· + 1_7· Use 4 · 7 or as thecommon denominator.= +Rename each fraction with thecommon denominator. Addthe numerators.=EXAMPLE Add Fractions and Mixed NumbersKEY CONCEPTAdding Unlike FractionsTo add fractions withunlike denomintors,rename the fractionswith a commondenominator. Then addand simplify.Find each sum. Write in simplest form.a. 5_6+ (-3_10)5_6+ (- 3_10)= 5_6· + (- 3_10)· The LCD is .= +(-)Rename eachfraction with theLCD.= orAdd thenumerators.Simplify.b. 21_8+ (-32_3)21_8+ (-32_3)= _8+ (-_3) Write the mixed numbersas improper fractions.= +Rename fractions Usingthe LCD, .= Add the numerators.= Simplify.5–7MAIN IDEAS• Add unlike fractions.• Subtract unlikefractions.
  • 131. 5–7Glencoe Pre-Algebra 123Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find each sum. Write insimplest form.a. 2_3+ 1_8b. 5_12+ 5_9c. 42_5+ (-62_3)EXAMPLE Subtract Fractions and Mixed NumbersFind each difference. Write in simplest form.a. 9_16- 5_89_16- 5_8= 9_16- 5_8· The LCD is .= 9_16- Rename 5_8using the LCD.= Subtract the numerators.b. 42_3- 36_742_3- 36_7= _3- _7Write the mixed numbersas improper fractions.= -Rename the fractionsusing the LCD. Subtractthe numerators.= Simplify.Check Your Progress Find each difference. Write insimplest form.a. 11_12- 2_9b. 35_6- 21_8KEY CONCEPTSubtracting UnlikeFractions To subtractfractions with unlikedenominators, renamethe fractions with acommon denominator.Then subtract andsimplify.Under the tabfor Lesson 5-7, describea situation in which youwould add or subtractunlike fractions.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 132. 124 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Solving Equations with Rational NumbersEXAMPLE Solve by Using Addition and SubtractionSolve each equation.a. m + 8.6 = 11.2m + 8.6 = 11.2 Write the equation.m + 8.6 - = 11.2 - Subtract from each side.m = Simplify.b. y - 3_8= 3_4y - 3_8= 3_4Write the equation.y - 3_8+ = 3_4+ Add to each side.y = 3_4+ Simplify.y = +Rename the fractions usingthe and add.y = or Simplify.Check Your Progress Solve.a. 15.4 = b + 9.3 b. 2_3= x - 1_2EXAMPLE Solve by Using DivisionSolve 9a = 3.6.9a = 3.6 Write the equation.9a_ = 3.6_ Divide each side by .a = Simplify.5–8MAIN IDEA• Solve equationscontaining rationalnumbers.Which properties allowyou to add or subtractthe same number fromeach side of an equation?(Lesson 3–3)REVIEW IT
  • 133. 5–8Glencoe Pre-Algebra 125Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Solve by Using MultiplicationSolve -3_5t = -6.-3_5t = -6 Write the equation.(-3_5t)= (-6) Multiply each side by .= Simplify.Check Your Progress Solve.a. -6m = -4.8 b. -5_8a = -10EXAMPLECEREAL Torrey eats 5_6cup of cereal each morning andanother 2_3cup as a snack after school. If one box ofcereal contains 10 cups of cereal, how many days willthe box last?The amount of cereal that Torrey eats each day is5_6+ 2_3= 5_6+ = or 11_2cups. 11_2cups per day timesthe number of days equals 10 cups of cereal. If d represents thenumber of days, then d = .11_2d = 10 Write the equation.d = 10Rename 11_2as animproper fraction.(3_2)d = (10) Multiply each side by .d = or about Simplify.The box of cereal will last approximately 61_2days.Check Your Progress Each morning Michael buys acappuccino for $4.50 and each afternoon he buys a regularcoffee for $1.25. If he put aside $30 to buy coffee drinks, howmany days will the money last?ORGANIZE ITUnder the tab forLesson 5–8, write anequation involvingfractions that can besolved using division.Solve your problem.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 134. 126 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Measures of Central TendencyEXAMPLE Find the Mean, Median, and Modea. MOVIES The revenue of the 10 highest grossingmovies as of 2004 are given in the table. Find themean, median, and mode of the revenues.Top 10 Movie Revenues(millions of $)436 249373 187371 176279 173261 163mean = sum of revenues____number of movies=436 + 373 + 371 + 279 + 261 + 249 + 187 + 176 + 173 + 163__________= __ orThe mean revenue isTo find the median, order the numbers from least to greatest.163, 173, 176, 187, 249, 261, 279, 371, 373, 436median = ___ =The median revenue is .There is because each number in the setoccurs .5–9MAIN IDEAS• Use the mean, median,and mode as measuresof central tendency.• Choose an appropriatemeasure of centraltendency andrecognize measuresof statistics.KEY CONCEPTSMeasures of CentralTendencymean the sum of thedata divided by thenumber of items in thedata setmedian the middlenumber of the ordereddata, or the mean of themiddle two numbersmode the number ornumbers that occur mostoften
  • 135. 5–9Glencoe Pre-Algebra 127Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. b. OLYMPICS The line plot shows the number of goldmedals earned by each country that participated inthe 2002 Winter Olympic games in Salt Lake City,Utah. Find the mean, median, and mode for the goldmedals won.2 310 54 6 7 8 9 10 11 12 13ϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫ ϫ ϫ ϫϫSource: Time Almanacmean =6(0) + 3(1) + 5(2) + 3(3) + 3(4) + 2(6) + 1(10) + 1(11) + 1(12)_________25= 3.16There are numbers. The median number is the middlein an ordered data list. The median is . The numberoccurs most frequently in the set of data. The modeis .Check Your Progressa. TEST SCORES The test scores for a class of nine studentsare 85, 93, 78, 99, 62, 83, 90, 75, and 85. Find the mean,median, and mode of the test scores.b. FAMILIES A survey3 421 65 7 8 9 10ϫ ϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫϫof school-age childrenshows the family sizesdisplayed in the lineplot. Find the mean,median, and mode.ORGANIZE ITUnder the tab forLesson 5–9, explain thedifferences betweenmean, median, andmode.
  • 136. 5–9128 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETEST EXAMPLE The monthly salaries for the employeesat Bob’s Book Store are: $1290, $1400, $1400, $1600, $2650.Which measure of central tendency should Bob’s BookStore’s manager use to show new employees that thesalaries are high?A mode B median C mean D cannot be determinedRead the Test ItemTo find which measure of central tendency to use, find the, , and of the dataand select the greatest measure.Solve the Test ItemMean:Mode:Median:The is the highest measure, so the answer is .Check Your Progress TEST EXAMPLE The number ofhours spent exercising each week by women are: 1, 6, 4, 2, 1,and 8. Which measure of central tendency should a person useto show that women do not spend enough time exercising?A mode B median C mean D cannot be determinedHOMEWORKASSIGNMENTPage(s):Exercises:
  • 137. Glencoe Pre-Algebra 129Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R5STUDY GUIDEVOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 5 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 5, go to:glencoe.comYou can use your completedVocabulary Builder(pages 104–105) to help yousolve the puzzle.5-1Fractions as DecimalsWrite each fraction or mixed number as a decimal. Use a bar toshow a repeating decimal.1. 5_62. 7_83. -4 1_11Replace each with <, >, or = to make a true sentence.4. -5.43 -5.62 5. 4_59_116. 0.76 23_295-2Rational NumbersWrite each decimal as a fraction or mixed number insimplest form.7. 0.62 8. 3.48 9. 1.−75-3Multiplying Rational NumbersFind each product. Write in simplest form.10. 3_5 (-2_3 ) 11. - 4_15 (-55_6 ) 12.p_15· 3_p2
  • 138. 130 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 5 BRINGING IT ALL TOGETHER5-4Dividing Rational NumbersFind each quotient. Write in simplest form.13. 2_9÷ (1_8) 14. - 3_11÷ ( 7_22) 15. 5pq_t÷ 6q_t16. Holly is wallpapering her kitchen. How many 81_2feet lengthsof wallpaper can she cut from a roll of wallpaper that is591_2feet long?5-5Adding and Subtracting Like FractionsFind each sum or difference. Write in simplest form.17. 3_10+ 6_1018. - 3_11- ( 9_11 ) 19. -3 7_18m + 5 5_18m5-6Least Common MultipleFind the least common multiple (LCM) of each set ofnumbers of monomials.20. 12, 42 21. 8, 12, 18 22. 14, 63Find the least common denominator (LCD) of each pair offractions.23. 5_6, 7_1524. 11_18, 23_3225. 1_6xy, 7_9y5-7Adding and Subtracting Unlike FractionsFind each sum or difference. Write in simplest form.26. 4_7+ 2_527. 5_8- 9_2028. 61_9- 4 5_12
  • 139. Glencoe Pre-Algebra 131Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 5 BRINGING IT ALL TOGETHER5-8Solving Equations with Rational NumbersMatch each equation with the appropriate first step of itssolution.29. y - 6 = 11.8 a. Multiply each side by 6.b. Add 6 to each side.c. Subtract 6 from each side.d. Divide each side by -6.e. Multiply each side by -6.30. 6 + x = -931. c_6= 1_232. -1_6p = -1_633. Dividing by a fraction is the same as multiplying by the.5-9Measures of Central TendencyFind the mean, median, and mode for each set of data.If necessary, round to the nearest tenth.34. 6, 8, 12, 7, 6, 11, 2035. 9.2, 9.7, 8.6, 9.8, 9.9, 8.9, 9.0, 8.536. Which measure of central tendency is most affected by anextreme value?
  • 140. Checklist132 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R5Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 5 Practice Test onpage 285 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 5 Study Guide and Reviewon pages 281–284 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 5 Practice Test on page 285.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 5 Foldables.• Then complete the Chapter 5 Study Guide and Review onpages 281–284 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 5 Practice Test onpage 285.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 5.
  • 141. Chapter6Glencoe Pre-Algebra 133Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R6Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with a piece of lined paper.Fold in thirdslengthwise.Draw lines along Decimal PercentFractionfolds and labelas shown.NOTE-TAKING TIP: When you take notes, recordreal-life examples of how you can use fractions,decimals, and percent, such as telling time andmaking change.Ratio, Proportion, and Percent
  • 142. 134 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R6This is an alphabetical list of new vocabulary terms you will learn in Chapter 6.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebiased sampleconstant ofproportionalitycross productsdiscountnonproportionalpercentpercent equationpercent of changepercent proportionBUILD YOUR VOCABULARY
  • 143. Glencoe Pre-Algebra 135Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 6 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplepopulationproportionproportionalrateratiosamplescalescale drawing orscale modelscale factorsimple interestunbiased sampleunit rate
  • 144. 136 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.6–1 Ratios and RatesA ratio is a of two numbers by.A rate is a of twohaving different kinds of units.When a rate is simplified so that it has a denominator of, it is called a unit rate.BUILD YOUR VOCABULARY (pages 134–135)EXAMPLE Write Ratios as FractionsExpress the ratio 10 roses out of 12 flowers as a fractionin simplest form.10_12= Divide the numerator and denominator by the, .The ratio of roses to flowers is to . This means thatfor every flowers, of them are roses.EXAMPLE Write Ratios as FractionsExpress the ratio 21 inches to 2 yards as a fraction insimplest form.21 inches__2 yards= 21 inches___inchesConvert yards to inches.=inches___inchesDivide the numerator anddenominator by the , .Written in simplest form, the ratio is .MAIN IDEAS• Write ratios as fractionsin simplest form.• Determine unit rates.What does it mean for afraction to be in simplestform? (Lesson 4-4)REVIEW IT
  • 145. 6–1Glencoe Pre-Algebra 137Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Express each ratio as a fractionin simplest form.a. 8 golden retrievers b. 4 feet to 18 inchesout of 12 dogsEXAMPLE Compare Unit RatesSHOPPING A 12-oz bottle of cleaner costs $4.50. A 16-ozbottle of cleaner costs $6.56. Which costs less per ounce?Find and compare the unit rates of the bottles.$4.50__12 ounces= __1 ounce$6.56__16 ounces= __1 ounceThe bottle has the lower .EXAMPLE Convert RatesANIMALS A snail moved 30 feet in 2 hours. How manyinches per minute did the snail move?You need to convert feet to inches and hours to minutes.30 ft_2 hr= 30 ft_2 hr· 12 in._1 ft÷ 60 min__1 hr= 30 ft_2 hr· 12 in._1 ft· Write the reciprocal of 60 min__1 hr.= =Divide thecommonfactorsand units.Simplify.Check Your Progressa. SHOPPING A 6-pack of a soft drink costs $1.50. A 12-packof a soft drink costs $2.76. Which pack costs less per can?b. JOGGING Dave jogs 2 miles in 22 minutes. How many feetper second is this?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 146. 138 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.6–2 Proportional and NonproportionalRelationshipsRatios and rates that are constant are .relationships contain ratios or ratesthat are not constant.BUILD YOUR VOCABULARY (pages 134–135)EXAMPLE Identify Proportional RelationshipsDetermine whether the set of numbers in each table isproportional.a.Baseballs 1 2 3 4Cost (dollars) 2 3 4 5Write the ratio of to for eachnumber of baseballs in simplest form.1_22_33_44_5The rates are , so the number of baseballs isto the cost.b.Time (seconds) 1 2 3 4Distance (inches) 4 8 12 16Write the ratio of to for eachtime in simplest form.1_42_8= 1_43_12= 1_44_16= 1_4The rates are , so time is to thedistance.MAIN IDEAS• Identify proportionaland nonproportionalrelationships in tablesand graphs.• Describe a proportionalrelationship using anequation.
  • 147. 6–2Glencoe Pre-Algebra 139Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Determine whether the set ofnumbers in each table is proportional.a.Chaperones 1 2 3 4Students 15 30 45 60b.Number of Classes 1 2 3 4Cost (dollars) 12 22 30 38EXAMPLEWORK Nina charges $5 for each day of pet sitting. Writean equation relating the cost of pet sitting to the numberof days. What would be the cost of pet sitting for 4 days?Determine the between thecost and number of days.cost_day= $5WordsVariablesEquationThe cost is times the number of days.Let c = cost and d = number of days.c = 5d Write the equation= 5( ) Replace with the number of days.= Multiply.The cost of pet sitting for 4 days is .Check Your Progress WORK Robert gets paid $15 foreach yard he mows. Write an equation relating the amount hegets paid to the number of yards he mows. What would be thetotal amount paid for mowing 8 yards?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 148. 140 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Using ProportionsA proportion is a statement of of two .In the proportion a_b= c_d, the ad and cb arecalled the cross products of the proportion.BUILD YOUR VOCABULARY (pages 134–135)EXAMPLE Solve ProportionsSolve each proportion.a. c_36= 9_15c_36= 9_15c · 15 = 36 · 9 Cross products= Multiply.= Divide.c =b. 16_v = 4.8_1.516_v = 4.8_1.516 · 1.5 = v · 4.8 Cross products= Multiply.= Divide.= vCheck Your Progress Solve each proportion.a. x_12= 3_8b. 5_m = 3_4.26–3MAIN IDEAS• Solve proportions.• Use proportions tosolve real-worldproblems.KEY CONCEPTSProportion A proportionis an equation statingthat two ratios are equal.Property of ProportionsThe cross products of aproportion are equal.
  • 149. 6–3Glencoe Pre-Algebra 141Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLEARCHITECTURE An architect builds a model of a buildingbefore the actual building is built. The model is 8 inchestall and the actual building will be 22 feet tall. Themodel is 20 inches wide. Find the width of the actualbuilding.Write and solve a proportion using ratios that compare actualheight to model height.actual height___model height= actual width___model width= Write a proportion.= Cross products= Multiply.= Divide.= w Simplify.The actual width of the building is .Check Your Progress A model of a jet airplane has a lengthof 9 inches and a wingspan of 6 inches. Find the wingspan ofthe actual plane if the length is 120 feet.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 150. 142 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Scale Drawings and ModelsA scale drawing or scale model is used to represent anobject that is too or too to be drawn orbuilt at actual size.The of a length on a scale drawing or model tothe corresponding length on the real object is called thescale factor.BUILD YOUR VOCABULARY (page 135)EXAMPLE Find Actual MeasurementsMAP A map has a scale of 1 inch = 8 miles. Two townsare 3.25 inches apart on the map. What is the actualdistance between the two towns?METHOD 1 Let x represent the actual distance between thetwo towns. Write and solve a proportion.map distanceactual distance1 inch__8 miles= inches__milesmap distanceactual distance=Find the crossproducts.x = Simplify.The actual distance between the two towns is .METHOD 2 The actual distance is proportional to the distanceon the scale drawing with a ratio .Find the scale factor.1 inch__8 miles= Convert 8 miles to inches.The scale factor is . So, the actual distanceis times the map distance.6–4MAIN IDEAS• Use scale drawings.• Construct scaledrawings.REMEMBER ITWhen finding thescale factor, be sure touse the same units ofmeasure.
  • 151. 6–4Glencoe Pre-Algebra 143Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. a = 506,880m Write the equation.= 506,880( )or Simplify.The actual distance is 1,647,360 inches or .Check Your Progress A scale drawing of a new house has ascale of 1 inch = 4 feet. The height of the living room ceiling is2.75 inches on the scale drawing. What is the actual height ofthe ceiling?EXAMPLE Determine the ScaleMODEL CAR A model car is 4 inches long. The actual caris 12 feet long. What is the scale of the model?model lengthactual length4 inches__12 feet=model lengthactual length=Find the crossproducts.= Simplify.=Divide each sideby 4.x =The scale is .Check Your Progress A model log cabin is 12 incheshigh. The actual log cabin is 42 feet high. What is the scaleof the model?
  • 152. 6–4144 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Construct a Scale DrawingPATIO DESIGN Sheila is designing a patio that is 16 feetlong and 14 feet wide. Make a scale drawing of the patio.Use a scale of 0.5 inch = 4 feet.Step 1 Find the measure of the patio’s length on the drawing.drawing lengthactual length0.5 inch__4 feet= x inches__16 feetdrawing lengthactual length0.5 · 16 = 4 · x Cross products8 = 4x Simplify.= x Divide.On the drawing, the length is inches.Step 2 Find the measure of the patio’s width on the drawing.drawing lengthactual length0.5 inch__4 feet= w inches__14 feetdrawing widthactual width0.5 · 14 = 4 · w Cross products7 = 4w Simplify.= w Divide.On the drawing, the width is or 13_4inches.Step 3 Make the scaledrawing. Use 1_4-inchgrid paper.Check Your Progress GARDENING A garden is 18 feetlong and 14 feet wide. Make a scale drawing of the garden. Usea scale of 0.5 inch = 4 feet.WRITE ITWhat two numbers doyou need to constructa scale drawing of anobject?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 153. Glencoe Pre-Algebra 145Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Fractions, Decimals, and PercentsA percent is a ratio that compares a number to 100.BUILD YOUR VOCABULARY (page 134)EXAMPLE Percents as FractionsExpress each percent as a fraction in simplest form.a. 60% = 60_100b. 104% = 104_100= = orc. 0.3% = 0.3_100d. 561_4% =561_4_100= 0.3_100· = 561_4÷= = 2259_4· 1_1004orEXAMPLE Fractions as PercentsExpress each fraction as a percent.a. 19_20= or b. 8_5= orCheck Your ProgressExpress each percent as a fraction in simplest form.a. 35% b. 160%c. 0.8% d. 321_2%Express each fraction as a percent.e. 17_25f. 14_10MAIN IDEAS• Express percents asfractions and vice versa.• Express percents asdecimals and vice versa.6–5KEY CONCEPTSPercents and DecimalsTo write a percent as adecimal, divide by 100and remove the percentsymbol.To write a decimal asa percent, multiply by100 and add the percentsymbol.
  • 154. 6–5146 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Percents as DecimalsExpress each percent as a decimal.Divide by 100 and remove the %.a. 60% = 60% = b. 2% = 02% =c. 658% = 6.58 = d. 0.4% = 00.4 =EXAMPLE Decimals as PercentsExpress each decimal as a percent.Multiply by 100 and add the %.a. 0.4 = 0.40 = b. 0.05 = 0.05 =EXAMPLE Fractions as PercentsExpress each fraction as a percent. Round to thenearest tenth percent, if necessary.a. 5_8= 0.625 = b. 1_3= 0.333… ≈c. 9_1000= 0.009 = d. 23_14≈ 1.643 =Check Your ProgressExpress each percent as a decimal.a. 84% b. 7%c. 302% d. 0.9%Express each decimal as a percent.e. 0.84 f. 0.01Express each fraction as a percent. Round to thenearest tenth percent, if necessary.g. 3_8h. 5_12i. 13_1000j. 21_17ORGANIZE ITUnder each tab of yourFoldable, describe areal-life situation whereit would be helpful toconvert to a fraction,decimal, or percent.Decimal PercentFraction
  • 155. 6–5Glencoe Pre-Algebra 147Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Compare NumbersBAKERY A baker said that 25% of his customers buy onlybread and 2_5of his customers buy only cookies. Whichgroup is larger?Write as a percent. Then compare with .2_5= or>Since is greater than , the group of customersthat buy only is larger.Check Your Progress SCHOOL The school principalstates that 3_8of the students are involved in instrumentalmusic while 42% are involved in vocal music. Which group islarger?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 156. 148 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Using the Percent ProportionIn a percent proportion, one of the numbers, called thepart, is being to the ,called the base, or whole.BUILD YOUR VOCABULARY (page 134)EXAMPLE Find the Percenta. Twenty is what percent of 25?Twenty is being compared to 25. So, is the part andis the whole. Let n represent the .= n_100Write the percent proportion.= Find the cross products.= n Simplify.So, 20 is of 25.b. What percent of 8 is 12?Twelve is being compared to 8. So, is the part andis the whole. Let n represent the .= n_100Write the percent proportion.= Find the cross products.= n Simplify.So, of 8 is 12.6–6MAIN IDEA• Use the percentproportion tosolve problems.KEY CONCEPTPercent Proportionpart__whole=percent__100
  • 157. 6–6Glencoe Pre-Algebra 149Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find the PartWhat number is 8.8% of 20?The percent is , and the whole is .Let n represent the .n__ = __100Write the percent proportion.= Find the cross products.n = Simplify.So, 8.8% of 20 is .EXAMPLE Find the WholeSeventy is 28% of what number?The percent is and the part is .Let n represent the .__n= __100Write the percent proportion.= Find the cross products.= n Simplify.So, 70 is 28% of .Check Your Progress Use the percent proportion tosolve each problem. Round to the nearest tenth.a. Twelve is what percent of 40?
  • 158. 6–6150 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.b. What percent of 20 is 35?c. What number is 42.5% of 90?d. Ninety is 24% of what number?EXAMPLE Apply the Percent ProportionTENNIS From the years 1999 through 2005, SerenaWilliams won the U.S. Open Tennis Championshipstwo times and Wimbledon two times. What percent ofboth tournaments combined during those years wasSerena Williams the women’s champion? Round to thenearest tenth.The part is and the whole is . Let n representthe percent.= n_100· 100 = · n= n= Divide each side by .≈ n Simplify.Check Your Progress BAKE SALE At the school bakesale, 23 chocolate chip cookies, 18 oatmeal raisin cookies, and7 peanut butter cookies were sold. If the sale started with atotal of 90 cookies, what percent of the cookies were sold?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 159. Glencoe Pre-Algebra 151Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Finding Percents MentallyEXAMPLE Find Percent of a Number MentallyFind the percent of each number mentally.a. 50% of 4650% of 46 = of 46 Think: 50% = .= Think: of 46 is .So, 50% of 46 is .b. 25% of 8825% of 88 = of 88 Think: 25% = .= Think: of 88 is .So, 25% of 88 is .c. 70% of 11070% of 110 = of 110 Think: 70% = .= Think: of 110 is .So, 70% of 110 is .Check Your Progress Find the percent of eachnumber mentally.a. 50% of 82 b. 25% of 36 c. 80% of 606–7MAIN IDEAS• Compute mentally withpercents.• Estimate with percents.ORGANIZE ITUnder the percents tabof your Foldable, writethe percent-fractionequivalents foundon page 327 of yourtextbook.Decimal PercentFraction
  • 160. 6–7152 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Estimate Percentsa. Estimate 22% of 494.22% is about or .494 is about .of is .So, 22% of 494 is about .b. Estimate 1_4% of 1219.1_4% = 1_4× . 1219 is about .of is .So, 1_4% of 1219 is about × or .c. Estimate 155% of 38.155% means about for every 100or about for every 10.38 has about tens.× = .So, 155% of 38 is about .Check Your Progress Estimate.a. 38% of 400b. 1_5% of 2482c. 183% of 93HOMEWORKASSIGNMENTPage(s):Exercises:
  • 161. Glencoe Pre-Algebra 153Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Using Percent EquationsThe percent equation is an equivalent form of thepercent in which the percent is writtenas a decimal.BUILD YOUR VOCABULARY (page 134)EXAMPLE Find the PartFind 38% of 22.The percent is and the whole is . You need to findthe . Let n represent the part.n = Write 38% as the decimal .n = Simplify.So, 38% of 22 is .EXAMPLE Find the Percent19 is what percent of 25?You know that the whole is and the part is .Let n represent the percent.= n( )= n Divide each side by .= n Simplify.So, 19 is of 25.Check Your Progressa. Find 64% of 48. b. 8 is what percent of 25?6–8MAIN IDEAS• Solve percent problemsusing percentequations.• Solve real-life problemsinvolving discount andinterest.REMEMBER ITTo determinewhether your answeris reasonable, estimatebefore finding the exactanswer.
  • 162. 6–8154 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find the Whole84 is 16% of what number?You know that the part is and the percent is .Let n represent the whole.= n Write 16% as the decimal .__0.16= __0.16Divide each side by .= n Simplify.So, 84 is 16% of .Check Your Progress 315 is 42% of what number?Discount is the amount by which the regular price of anitem is reduced.BUILD YOUR VOCABULARY (page 134)EXAMPLE Find DiscountJEWELRY The regular price of a ring is $495. It is on saleat a 20% discount. What is the sale price of the ring?METHOD 1First, use the percent equation to find 20% of 495. Let drepresent the discount.d = The whole is and thepercent is .d = Simplify.Then, find the sale price.495 - = Subtract the discount fromthe original price.The sale price is .
  • 163. 6–8Glencoe Pre-Algebra 155Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. METHOD 2A discount of 20% means the ring will cost -or of the original price. Use the percent equation tofind 80% of 495. Let s represent the sale price.s = 0.80(495) The whole is and the percentis .s = The sale price of the ring will be .Check Your Progress RETAIL The regular price of astereo system is $1295. The system is on sale at a 15% discount.Find the sale price of the stereo system.Simple interest is the amount of money paid or earned forthe use of money.BUILD YOUR VOCABULARY (page 135)EXAMPLE Apply Simple Interest FormulaBANKING Suppose you invest $2000 at an annual interestrate of 4.5%. How long will it take for it to earn $495 ininterest?I = prt Simple interest formula495 = 2000(0.045)t I = 495, p = 2000, r = 0.045= Simplify.= Divide each side by .= t Simplify.It will take years to earn $495.Check Your Progress BANKING Suppose you invest$3500 at an annual interest rate of 6.25%. How long will it takefor it to earn $875?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 164. 156 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Percent of ChangeA percent of change tells the an amounthas increased or decreased in relation to theamount.BUILD YOUR VOCABULARY (page 134)EXAMPLE Find Percent of ChangeFind the percent of change from 325 to 390.Step 1 Subtract to find the amount of change.- = new amount - originalamountStep 2 percent of change =amount of change____original amount= = orThe percent of change from 325 to 390 is .EXAMPLE Find Percent of IncreaseTUITION In 1965, when John entered college, the tuitionper year was $7500. In 2000, when his daughter wentto the same school, the tuition was $25,500. Find thepercent of change.Step 1 Subtract to find the amount of change.- =Step 2 percent of change =amount of change____original tuition= = orThe percent of change is .6–9MAIN IDEAS• Find percent ofincrease.• Find percent ofdecrease.
  • 165. 6–9Glencoe Pre-Algebra 157Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progressa. Find the percent of change from 84 to 105.b. TEXTBOOKS In 1990, the price of a textbook was $38.In 2000, the price of the same textbook was $81. Find thepercent of change.EXAMPLE Find Percent of DecreaseCLOTHING A $110 sweater is on sale for $88. What is thepercent of change?Step 1 Subtract to find the amount of change.- = sale price - original priceStep 2 percent of change =amount of change____original price= = orThe percent of change is . In this case, the percent ofchange is a percent of .Check Your Progress SHOES A $145 pair of tennis shoesis on sale for $105. What is the percent of change?ORGANIZE ITOn the back of yourFoldable, describe howto find a percent ofincrease and a percentof decrease.Decimal PercentFractionHOMEWORKASSIGNMENTPage(s):Exercises:
  • 166. 158 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Using Sampling to PredictA subgroup or subset of a population used to representthe whole is a called a .An sample is a random sample that isrepresentative of a larger sample.A sample is a sample that is notrepresentative of the population.BUILD YOUR VOCABULARY (pages 134–135)EXAMPLE Identify and Describe SampleIdentify the sample as biased or unbiased and describeits type.a. Mr. Ackermen needs several volunteers to collecthomework before each class. He randomly calls out acolor and whoever is wearing that color is chosen.Since the population is alland they are selected randomly from students wearing acertain color, the sample is anb. A hardware store wants feedback on their productsand service. They include a telephone number oneach receipt so customers can voluntarily call andparticipate.Since the customers at this particular store probably preferthis store’s products and service, the sample is .The sample is a since onlycustomers of this store are given the chance to participate inthe survey. It is also asince only those who want to participate will respond.6–10MAIN IDEAS• Identify varioussampling techniques.• Determine the validityof a sample and predictthe actions of a largergroup.
  • 167. 6–10Glencoe Pre-Algebra 159Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Identify the sample as biased orunbiased and describe its type.a. To determine peoples favorite snack food, the first tencustomers leaving a candy store are surveyed.b. To determine 5 students to be class volunteers for the day,each student in the class is given a number. A computer isused to randomly select 5 numbers and the students withthose numbers are chosen as the class volunteers.EXAMPLE Using Sampling to Predicta. SPORTS Miss Newman surveyed every tenth studentin the hallway to see which sport they preferredwatching. 44% preferred football, 28% basketball,20% soccer, and 8% tennis. Is this sampling methodvalid? If so, out of 560 students in the entire school,how many would you expect to say they preferredwatching basketball?This is ansince Miss Newman selected students according to a specific. So, this sampling method is .Since 28% of those surveyed preferred watching, to find how many would say theypreferred watching basketball in the entire school, findof .WordsVariableEquationWhat number is of ?Let n =n =(continued on the next page)
  • 168. 6–10160 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.n == Multiply.So, you would expect about students prefer watching.b. MUSIC A middle school planned to play music duringlunch. To determine what type of music studentspreferred, 25 students with MP3 players wererandomly surveyed and asked what type of music theypreferred. Sixteen said they preferred country music.Is this sampling method valid? If so, how many of the535 students in the school would you expect to prefercountry music?This is a samplesince only students were askedto respond. Also, only (25 out of 535) of thestudents were surveyed. Therefore, this sampling methodwill not produce an and predictionof the type of music students prefer.Check Your Progressa. COLORS To determine favorite colors, students wearingeither blue or red were surveyed. 32% preferred blue, 29%red, 23% yellow, and 16% green. Is this sampling methodvalid? If so, out of the 450 students in the entire school, howmany would you expect to say they prefer red?b. TELEVISIONS Jason surveyed every fifth classmate tofind out how many televisions each had in their home. 63%responded that they had three or more televisions in theirhome. Is this sampling method valid? If so, how many of the845 students in the school should Jason expect to have threeor more televisions in their home?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 169. Glencoe Pre-Algebra 161Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R6VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 6 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 6, go to:glencoe.comYou can use your completedVocabulary Builder(pages 134–135) to help yousolve the puzzle.6-1Ratios and RatesUnderline the correct term or phrase to fill the blank in eachsentence.1. A is a ratio of two measurements havingdifferent kinds of units. (fraction, unit, rate)2. A unit rate has a of 1. (numerator, denominator,simplest form)3. A ratio is a comparison of two numbers by .(addition, multiplication, division)4. Express the ratio 16 novels out of 40 books as a fractionin simplest form.6-2Proportional and Nonproportional RelationshipsDetermine whether the set of numbers in each table areproportional.5. Number of Guests 6 7 8 9 10Cost (dollars) 42 49 56 63 706. Number of hours 1 2 4 6 7Price (dollars) 14 23 41 59 68STUDY GUIDE
  • 170. 162 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 6 BRINGING IT ALL TOGETHER6-3Using ProportionsSolve each proportion.7. 8_45= 1.6_x 8.y_12= 1.6_49. 5_24= z_726-4Scale Drawings and Models10. A swimming pool is 36 feet long and 15 feet wide. Make a scaledrawing of the pool that has a scale of 1_4in. = 3 ft.11. The right arm of the Statue of Libertyis 42 feet long. A scale model of thestatue has a 3-inch long right arm.What is the scale of the model?6-5Fractions, Decimals, and PercentsUnderline the greatest number in each set.12. {4_7, 45%, 0.42, 5 out of 8} 13. { 2_11, 11%, 0.17, 1 out of 12}6-6Using the Percent Proportion14. 11 is 20% of what number?15. What is 36% of 75?16. 18 is what percent of 60?6-7Finding Percents MentallyEstimate.17. 2_3% of 155 18. 147% of 78 19. 84% of 31
  • 171. Glencoe Pre-Algebra 163Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 6 BRINGING IT ALL TOGETHER6-8Using Percent EquationsSolve each problem using the percent equation.20. 7 is what percent of 25? 21. What is 40.4% of 50?22. 32 is 5% of what number? 23. Find 140% of 75.24. A CD player is on sale at a 20% discount. If it normally sellsfor $49.95, what is the sale price?25. What is the annual interest rate if $2800 is invested for4 years and $364 in interest is earned?6-9Percent of Change26. A $775 computer is marked down to $620.Find the percent of change.27. Refer to the table shown. Which school School 1994 2004Oakwood 672 702Jefferson 433 459Marshall 764 780had the smallest percent of increase inthe number of students from 1994 to2004?6-10Using Sampling to Predict28. COOKIES The students in the life skills class took asurvey during lunch time about the type of cookies theyshould make for the bake sale. They randomly surveyeda total of 67 students and their results are shown in thetable. Is this sampling method valid? If so, how manyof the cookies should be peanut butter if they make 800cookies? Explain your reasoning.Type NumberChocolate Chip 29Peanut butter 15Chocolate 12Sugar 11
  • 172. Checklist164 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R6Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 6.Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 6 Practice Test onpage 353 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 6 Study Guide and Reviewon pages 348–352 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 6 Practice Test onpage 353.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 6 Foldables.• Then complete the Chapter 6 Study Guide and Review onpages 348–352 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 6 Practice Test onpage 353.ARE YOU READY FORTHE CHAPTER TEST?
  • 173. Chapter7Glencoe Pre-Algebra 165Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R7Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with an 11" × 17" sheet of paper.Fold the short sidesso they meet in themiddle.Fold the topto the bottom.Open and cutalong second foldto make four tabs.Staple a sheet ofgrid paper inside.Add axes as shown.(ϩ, ϩ)(Ϫ, ϩ)y(Ϫ, Ϫ)O(ϩ, Ϫ)xLabel the quadrantson the tabs.NOTE-TAKING TIP: When you take notes, listen orread for main ideas. Then record those ideas forfuture reference.Functions and Graphing
  • 174. 166 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R7BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 7.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleconstant ofvariation[VEHR-ee-Ay-shuhn]constant rate of changedirect variationfunctionline of fitlinear equation[LINH-ee-uhr]
  • 175. Glencoe Pre-Algebra 167Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 7 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplelinear relationshipsrate of changeslopeslope-intercept form[IHNT-uhr-sehpt]vertical line testy-intercept
  • 176. 168 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A function is a special relation in which each memberof the domain is paired with exactly one member inthe range.BUILD YOUR VOCABULARY (page 166)EXAMPLE Ordered Pairs and Tables as FunctionsDetermine whether each relation is a function. Explain.a. {(-3, -3), (-1, -1), (0, 0), (-1, 1), (3, 3)}; -1 in the domain is paired with both andin the .b. x 7 6 5 2 -3 -6y 2 4 6 4 2 -2, each x value is pairedwith y value.Check Your Progress Determine whether eachrelation is a function. Explain.a. {(2, 5), (4, -1), (3, 1), (6, 0), (-2, -2)}b. x 3 1 -1 -3 1 -5y 5 4 3 -4 2 1EXAMPLE Use a Graph to Identify FunctionsDetermine whether the graphxyOis a function. Explain., it passes the .FunctionsMAIN IDEAS• Determine whetherrelations are functions.• Use functions todescribe relationshipsbetween twoquantities.7–1REMEMBER ITIf any vertical linedrawn on the graphof a relation passesthrough no more thanone point on the graph,then the relation is afunction. This is avertical line test.
  • 177. 7–1Glencoe Pre-Algebra 169Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress DetermineyxOwhether the graph is a function. Explain.EXAMPLEBUSINESS The table Number of Hours Number of Boxes0 010 300020 600030 9000shows the number ofboxes made.a. Do these data represent a function? Explain.; for each 10 hours, only ofboxes is made.b. Describe how box production is related to hoursof operation.As the number of hours , the number ofboxes produced .Check Your ProgressBUSINESS The tableNumber of Hours Number of Boxes5 12010 24015 36020 480shows the numberof chairs made.a. Do these data represent a function? Explain.b. Describe how chair production is related to hours ofoperation.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITIn your notes, draw agraph of a relation thatis a function and agraph of a relation thatis not a function. Explainwhy the second relationis not a function.(ϩ, ϩ)(Ϫ, ϩ)y(Ϫ, Ϫ)O(ϩ, Ϫ)x
  • 178. 170 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.7–2 Representing Linear FunctionsA linear equation in two variables is an equation in whichthe appear in terms andneither variable contains an other than 1.BUILD YOUR VOCABULARY (page 166)EXAMPLE Use a Table of Ordered PairsFind four solutions of y = 4x + 3.Choose four values for x. Then substitute each value into theequation to solve for y.x y = 4x + 3 y (x, y)0 y = 4 + 31 y = 4 + 32 y = 4 + 33 y = 4 + 3Four solutions are , , , and .Check Your Progress Find four solutions of y = 2x - 4.MAIN IDEAS• Solve linear equationswith two variables.• Graph linear equationsusing ordered pairs.ORGANIZE ITIn your notes, write alinear equation, thenexplain how to solve itusing the four stepsfor finding solutionsof equations.(ϩ, ϩ)(Ϫ, ϩ)y(Ϫ, Ϫ)O(ϩ, Ϫ)x
  • 179. 7–2Glencoe Pre-Algebra 171Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Solve an Equation for yBUSINESS At a local software company, Level 1employees x earn $48,000 and Level 2 employees yearn $24,000. Find four solutions of 48,000x + 24,000y= 216,000 to determine how many employees at eachlevel the company can hire for $216,000.48,000x + 24,000y = 216,000 Write theequation.24,000y = 216,000 - Subtractfrom eachside.24,000y__ =216,000__ -48,000x__ Divide eachside by.y = Simplify.Choose four x values and substitute them into .x y = 9 - 2x y (x, y)0 y = 9 - 21 y = 9 - 22 y = 9 - 23 y = 9 - 2(0, ) 0 Level 1, Level 2(1, ) 1 Level 1, Level 2(2, ) 2 Level 1, Level 2(3, ) 3 Level 1, Level 2The company can hire 0 Level 1 and Level 2 employees,1 Level 1 and Level 2 employees, 2 Level 1 andLevel 2 employees, or 3 Level 1 and Level 2 employees.
  • 180. 7–2172 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress BOOKS At a local bookstore,hardbacks are on sale for $6 and paperbacks are on sale for$3. Bob has $42 to spend on books. Find four solutions todetermine how many books of each type Bob can buy withhis $42.EXAMPLE Graph a Linear EquationGraph y = x - 3 by plotting ordered pairs.First, find ordered pair solutions.x y = x - 3 y (x, y)-1 y = - 30 y = - 31 y = - 32 y = - 3Plot these ordered pairs and drawxyOa line through them. The line is acomplete graph of the function.Check Your ProgressGraph y = 5 - x by plotting ordered pairs.yxOHOMEWORKASSIGNMENTPage(s):Exercises:What are the signs ofthe x and y coordinatesin the four quadrants ofthe coordinate plane?(Lesson 2–6)REVIEW IT
  • 181. Glencoe Pre-Algebra 173Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A in one with respect toanother quantity is called the rate of change.BUILD YOUR VOCABULARY (page 167)EXAMPLESCHOOL The graph showsxyNumber of WeeksQuizScores10 2 3 4 5706050809073768187 89Jared’s quiz scores for thefirst five weeks after hejoined a study group. Findthe rate of change fromWeek 2 to Week 5.= ___≈change in quiz scorechange in timeSo, the expected rate of change in quiz scores is an increase ofabout per week.Check Your ProgressSUMMER CAMP The graph showsEnrollment2003001000400Year321 5413020423634562the number of campers enrolledat a summer camp during its firstfive years of operation. Find therate of change from Year 2 toYear 5.MAIN IDEAS• Find rates of change.• Solve problemsinvolving ratesof change.Rate of Change7–3
  • 182. 7–3174 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Compare Rates of ChangeINCOME The table showsYearIncome ($)Milers Joneses2001 49,000 50,0002002 51,000 52,0002003 52,500 54,5002004 55,000 57,000the yearly incomes of twofamilies. Compare the ratesof change.Milers’ rate of change =change in y__change in x== orJones’ rate of change =change in y__change in x== orThe income of the JonesesDollars(thousands)$0$48$50$52$54$56$58Year20012002200320042005JonesesMilersincreases at a faster ratethan the income of the Milers.Check Your ProgressYearIncome ($)Longs Greens1998 45,000 43,0001999 48,000 46,0002000 51,500 49,5002001 55,000 54,000INCOME The table shows theyearly incomes of two families.Compare the rates of change.
  • 183. 7–3Glencoe Pre-Algebra 175Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Negative Rate of ChangeCOOKIES Natalie sold 100 cookies in 5 hours. The graphbelow shows the relationship between the hours spentselling and the number of cookies that remained. Findthe rate of change.rate of change = _____= ___= __=So, the rate of change is ,or a decrease of for every .Check Your ProgressSPENDING The table showsWeeks, x Amount ($), y1 4502 2253 1804 105the amount of money in Garrett’ssavings during several weeks.Find the rate of change.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 184. 176 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.have straight line graphs.BUILD YOUR VOCABULARY (pages 166–167)EXAMPLE Use a Graph to Find a Constant Rate of ChangeSOCCER The graph showsYen’s soccer goals for theten-week season. Find theconstant rate of change fromWeek 2 to Week 8. Describewhat the rate means.Choose any two points on the lineand find the rate of change betweenthem. We will use the points at (2, 1) and (8, 5).week 2, 1 goal week 8, 5 goalsrate of change =change in goals___change in time= __=The rate of change goals per week means that Yen scoredgoals every weeks.Check Your ProgressSCHOOL The graph shows thenumber of students at LincolnElementary school. Find the constantrate of change from 2002 to 2005.Describe what the rate means.MAIN IDEAS• Identify proportionaland nonproportionalrelationships by findinga constant rate ofchange.• Solve problemsinvolving directvariation.Constant Rate of Change and Direct Variation7–4
  • 185. 7–4Glencoe Pre-Algebra 177Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Use Graphs to IdentifyProportional Linear RelationshipsJOGGING The distance that a Time(min)Distance(mi)x y15 1230 2245 3060 34jogger runs is recorded in thetable. Determine if there is aproportional linear relationshipbetween the time and distance.To determine if the quantities areproportional, finddistance y__time xfor pointson the graph.12_15= 22_30= 30_45= 34_60=Since the ratio distance__timeis not the same for every pair of values,the distance run is to the time.Check Your ProgressWORK The table shows the amountTime (hr) Amount ($)x y1 82 143 184 20Sam was paid for doing various jobsfor his neighbors. Determine if thereis a proportional linear relationshipbetween the time and amount paid.A special type of linear equation that describes constantrate of change is a .The constant of variation is the , or, in the equation y = kx,represented by k.BUILD YOUR VOCABULARY (pages 166–167)
  • 186. 7–4178 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Use Direct Variation to Solve ProblemsLANDSCAPING As it is beingTime (min) Hole Depth (in.)x y10 820 1530 2440 31dug, the depth of a wide holefor a backyard pond isrecorded in a table.a. Write an equation thatrelates time and hole depth.Step 1 Find the value of kusing the equation y = kx.Choose any point in the table. Then solve for .y = kx Direct Variation= k( ) Replace y with and x with .= k Simplify.Step 2 Use to write an equation.y = kx Direct VariationReplace k with .b. Predict how long it will take to dig a depth of36 inches.y = 0.8x Write the direct variation equation.= 0.8x Replace y with .= x Divide.It will take to dig a hole.Check Your ProgressWAGES Kelly recorded the hoursTime (hr) Amount ($)x y2 14.504 29.006 43.508 58.00she worked and the amount shewas paid in a table.a. Write an equation that relates timeand amount paid.b. Predict how much Kelly will get paidfor working 5 hours.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 187. Glencoe Pre-Algebra 179Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Slope describes the of a line. It is the ratioof the rise, or the change, to the run, or thechange.BUILD YOUR VOCABULARY (page 167)EXAMPLE Use a Graph to Find SlopeFind the slope of each line.a. yxO(0, 1)(1, 4)m =y2 - y1__x2 - x1Definition of slopem = __m = or(x1, y1) = (0, 1)(x2, y2) = (1, 4)The slope is .b. yxO(3, 1)(Ϫ3, 3)m =y2 - y1__x2 - x1Definition of slopem = __m = or(x1, y1) = (3, 1)(x2, y2) = (-3, 3)The slope is .MAIN IDEA• Find the slope of a line.KEY CONCEPTSlope The slope m ofa line passing throughpoints (x1, y1) and(x2, y2) is the ratioof the difference iny-coordinates to thecorrespondingdifference inx-coordinates.Slope7–5
  • 188. 7–5180 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Positive and Negative SlopesFind the slope of the line that passes through each pairof points.a. B(2, 7), C(-3, -2)m =y2 - y1__x2 - x1Definition of slopem = ___ (x1, y1) = (2, 7),(x2, y2) = (-3, -2)m =b. F(-5, 1), G(-3, -6)m =y2 - y1__x2 - x1Definition of slopem = ___ (x1, y1) = (2, 7),(x2, y2) = (-3, -2)m =Check Your Progress Find the slope of each line.a. yxO(1, 4)(Ϫ2, Ϫ3)b. yxO(5, Ϫ1)(Ϫ2, 4)ORGANIZE ITIn your notes, write asample equation foreach slope: positive,negative, zero, andundefined. Then grapheach equation and writeits slope.(ϩ, ϩ)(Ϫ, ϩ)y(Ϫ, Ϫ)O(ϩ, Ϫ)x
  • 189. 7–5Glencoe Pre-Algebra 181Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Zero and Undefined SlopesFind the slope of each line.a. yxO(2, Ϫ3)(Ϫ3, Ϫ3)m =y2 - y1__x2 - x1m = ___m = or(x1, y1) = (-3, -3)Definition of slopeb. yxO(2, Ϫ2)(2, 3)m =y2 - y1__x2 - x1m = ___m = The slope is .(x1, y1) = (-3, -3)(x2, y2) = (2, -3)Definition of slopeCheck Your Progress Find the slope of each line.a. yxO(4, 3)(Ϫ1, 3)b. yxO(Ϫ3, 4)(Ϫ3, Ϫ2)(x2, y2) = (2, -3)
  • 190. 182 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.An equation written in the form y = mx + b, where m is theslope and b is the y-intercept, is in slope-intercept form.BUILD YOUR VOCABULARY (page 167)EXAMPLE Find the Slope and y-InterceptState the slope and the y-intercept of the graphof y = 1_2x + 3.y = 1_2x + 3y = mx + bWrite the equation in the form y = mx + b.The slope is . The y-intercept is .EXAMPLE Write the Equation in Slope-Intercept FormState the slope and the y-intercept of the graphof -4x + 5y = -10.-4x + 5y = -10 Write the equation.-4x + 5y + 4x = -10 + 4x Add 4x to each side.= Simplify.y = Divide each side by .y = Slope-intercept formThe slope is , and the y-intercept is .Check Your Progress State the slope and they-intercept of the graph of each line.a. y = 2x - 7 b. -5x + y = 17–6MAIN IDEAS• Determine slopes andy-intercepts of lines.• Graph linear equationsusing the slope andy-intercept.Slope-Intercept Form
  • 191. 7–6Glencoe Pre-Algebra 183Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Graph an EquationGraph y = -3x + 9 using the slope and y-intercept.Step 1 Find the slope and y-intercept.slope = y-intercept =Step 2 Graph the y-intercept point at .Step 3 Write the slope as .Use it to locate a second point on the line.m = _ ____Another point on the line is at .change in x:change in y:Step 4 Draw a line through the two yxO 2Ϫ4Ϫ6Ϫ86824Ϫ4Ϫ64 6 8(0, 9)(1, 6)y ϭ Ϫ3x ϩ 9points.Check Your Progress Graph y = 2_3x + 4 using the slopeand y-intercept.yxOORGANIZE ITIn your notes, writean example of a linearequation in slope-intercept form. Graphthe equation using itsslope and y-intercept andlist the steps involved.(ϩ, ϩ)(Ϫ, ϩ)y(Ϫ, Ϫ)O(ϩ, Ϫ)xWRITE ITWhat are the two waysto interpret a negativeslope when graphing anequation?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 192. 184 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.7–7 Writing Linear EquationsEXAMPLE Write Equations From Slope and y-InterceptWrite an equation in slope-intercept form for the linehaving slope of -1_4and a y-intercept of 7.y = mx + b Slope-intercept formy = -1_4x + 7 Replace m with and b with .EXAMPLE Write an Equation From a GraphWrite an equation in slope-intercept yO xform for the line graphed.The y-intercept is . From ,you can go up unit and to theone unit to another point onthe line. So, the slope is .y = mx + b Slope-intercept formy = x + Replace m with and b with .y = Simplify.Check Your Progressa. Write an equation in slope-intercept form for the linehaving slope of -3 and a y-intercept of -5.b. Write an equation in slope-intercept yxOform for the line graphed.MAIN IDEAS• Write equationsgiven the slope andy-intercept, a graph,a table, or two points.
  • 193. 7–7Glencoe Pre-Algebra 185Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Write an Equation to Make a PredictionBUSINESS The owners of the Good Times eaterysurveyed their customers to find out where they lived.They learned that for each 5-mile radius from theirrestaurant, 30 fewer people visited them. They had150 patrons in the area immediately surrounding thediner. Predict the number of customers who lived20 miles away.Make a table ofDistance x Patrons y0 1505 12010 90ordered pairs.Step 1 Find the slope m.m =change in y__change in x==Step 2 Find the y-intercept b.(x, y) = (distance, patrons)= (0, )When the distance is within ,there are .Step 3 Write the equation.y = mx + b Slope-intercept formy = x + 150 Replace m with andb with .Step 4 Substitute the distance of miles.y = -6x + 150 Write the equation.= -6( )+ 150 Replace x with .= Simplify.So, the diner had 30 patrons that lived miles away.
  • 194. 7–7186 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress WEATHER Attendance at anoutdoor sporting event is affected by the temperature outside.When the outside temperature is 0°F, the attendance is 12people. For every increase in temperature of 20 degrees, theattendance increases by 100 people. Predict the attendanceif the temperature is 60°F.EXAMPLE Write an Equation Given Two PointsWrite an equation for the line that passes through(7, 0) and (6, 3).Step 1 Find the slope m.m =y2 - y1__x2 - x1Definition of slopem = __ or(x1, y1) = (7, 0)(x2, y2) = (6, 3)Step 2 Find the y-intercept b. Use the slope and thecoordinates of either point.y = mx + b Slope-intercept form= Replace m with , x with, and y with .= b Simplify.Step 3 Substitute the slope and y-intercept.y = mx + b Slope-intercept formy = Replace m with and bwith .Check Your Progress Write an equation for the line thatpasses through (4, -2) and (-2, -14).ORGANIZE ITIn your notes, write twopoints, find the equationof the line that passesthrough them, and graphthe line.(ϩ, ϩ)(Ϫ, ϩ)y(Ϫ, Ϫ)O(ϩ, Ϫ)x
  • 195. 7–7Glencoe Pre-Algebra 187Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Write an Equation From a TableUse the table of values x y-2 16-1 100 41 -2to write an equation inslope-intercept form.Step 1 Find the slope m. Usethe coordinates of anytwo points.m =y2 - y1__x2 - x1Definition of slopem = ___ or(x1, y1) = (-2, 16)(x2, y2) = (-1, 10)Step 2 Find the y-intercept b. Use the slope and thecoordinates of either point.y = mx + b Slope-intercept form= + b Replace m with , y with, and x with .= b Simplify.Step 3 Substitute the slope and y-intercept.y = mx + b Slope-intercept formy = + Replace m with , andb with .Check Your ProgressUse the table of values to write an x y-6 4-3 23 -26 -4equation in slope-intercept form.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 196. 188 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A line of fit is a line that is very to most of thedata points.BUILD YOUR VOCABULARY (page 166)EXAMPLE Make Predictions from a Line of FitAGRICULTURE The table shows the amount of land in theU.S. farms from 1980 to 2000.YearLand(million acres)1980 10391985 10121990 9861995 9632000 943a. Make a scatter plot and draw the line of fit forthe data.Draw a line that best fits the data.YearAmountofLand(millionacres)80859095000510900950100010500b. Use the line of fit to predict the amount of land inthe year 2010.Extend the line so that you can find the y value for an xvalue of . The y value for is about .So, a prediction for the amount of farm land in 2010 isapproximately million acres.7–8 Prediction EquationsMAIN IDEAS• Draw lines of fit forsets of data.• Use lines of fit to makepredictions about data.REMEMBER ITA line of fit is onlyan estimation. Differentlines with differentslopes can be drawn toapproximate the data.
  • 197. 7–8Glencoe Pre-Algebra 189Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your ProgressRETAIL The table shows theYearNumber ofLaptops Sold1998 2151999 2982000 3952001 430number of laptop computerssold at a local computer storefrom 1998 to 2001.a. Make a scatter plot and draw aline of fit for the data.yx199820002002100300500700LaptopsSoldYearb. Use the line of fit to predict the number of laptops sold in theyear 2003.EXAMPLE Make Predictions from an EquationINTERNET The scatter plot3530252015105YearU.S.HouseholdswithInternetAccess(millions)’94 ’95 ’96 ’97 ’98 ’99 ’0040shows the number of U.S.households (millions) withInternet access.a. Write an equation in slope-intercept form for the lineof fit.Step 1Select two points on the line and find the slope. Noticethat the two points on the line of fit are not originaldata points.m =y2 - y1__x2 - x1Definition of slopem = ____(x1, y1) = (1995, 10)(x2, y2) = (2000, 37)m =WRITE ITDoes a line of fit alwaysgive a good prediction?Explain.
  • 198. 7–8190 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Step 2 Next, find the y-intercept.y = mx + b Slope-intercept form= + b (x, y) = (2000, 37),and m = .= b Simplify.Step 3 Write the equation.y = mx + b Slope-intercept formy = m = , b =b. Predict the number of U.S. households that will haveInternet in the year 2010.y = Write the equation for theline of fit.y = Replace x with .y = Simplify.A prediction for the number of U.S. households that willhave Internet in the year 2010 is about .Check Your ProgressTEMPERATURE The scatter plot yx10002000300040001000200300HeatingBill($)Square Footageshows the heating bill for themonth of January for differentsize houses.a. Write an equation in slope-interceptform for the line of fit.b. Predict the heating bill for a house that is 4100 square feetin size.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 199. Glencoe Pre-Algebra 191Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R7STUDY GUIDEVOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 7 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 7, go to:glencoe.comYou can use your completedVocabulary Builder(pages 166–167) to help yousolve the puzzle.7-1FunctionsDetermine whether each relation is a function.1. {(2, 5), (3, 7), (-2, 5), (1, 8)} 2. {(-1, 1), (3, 4), (2, 2), (-1, 5)}3. The table shows how age affects the value of one Age(years)Value0 $15001 $12002 $8003 $300type of computer. Is the relation a function?Describe how age is related to value.7-2Representing Linear FunctionsFind four solutions of each equation. Show eachsolution as ordered pairs.4. y = x + 1 5. y = 5x - 4The equation y = 3.28x describes the approximatenumber of feet y in x meters.6. Describe what the solution (5, 16.4) means.7. About how many feet is a 200 meter dash?
  • 200. 192 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 7 BRINGING IT ALL TOGETHER8. Graph the equation y = 4x - 3 yxOby plotting ordered pairs.7-3Rate of Change9. SCHOOL The table shows the growthYear Enrollment2003 2022004 2192005 2432006 260in student enrollment of the freshmanclasses at Washington High School. Findthe rate of change from 2003 to 2005.10. POOLS The graph shows the relationshipbetween the amount of time it takes todrain a child’s pool and the amount of waterthat is remaining. Find the rate of change.7-4Constant Rate of Change and Direct Variation11. WALNUTS The cost of walnuts varies directly with the number ofpounds bought. Three pounds cost $9.75. Write an equation thatrelates the weight and the cost of walnuts. Then predict the cost of8.5 pounds of walnuts.7-5SlopeFind the slope of the line that passes through each pairof points.12. A(2, 3) and B(1, 1) 13. S(6, -5) and T(4, 1)
  • 201. Glencoe Pre-Algebra 193Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 7 BRINGING IT ALL TOGETHER7-6Slope-Intercept FormState the slope and y-intercept, then graph each equation.14. y = 2x - 1 15. 4x + 2y = 5yxOyxO7-7Writing Linear EquationsWrite an equation in slope-intercept form for each line.16. slope = -3, y-intercept = 717. slope = 5_8, y-intercept = 018. Write an equation in slope-interceptform for the line passing through(-3, 4) and (1, 2).7-8Prediction EquationsThe table shows the number of digitalYearSales(millions)1999 1.82000 3.62001 5.92002 6.72003 9.2**Projected in Nov. 2003Digital Photography Reviewcameras sold in Japan.19. Make a scatter plot and draw a line of fit.Then predict how many digital cameraswill be sold in Japan in 2008.NumberSold(millions)46208Years Since 1998321 54Digital Cameras Soldin Japan
  • 202. Checklist194 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R7Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 7 Practice Test onpage 413 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 7 Study Guide and Reviewon pages 408–412 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 7 Practice Test onpage 413.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 7 Foldable.• Then complete the Chapter 7 Study Guide and Review onpages 408–412 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 7 Practice Test onpage 413.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 7.
  • 203. Chapter8Glencoe Pre-Algebra 195Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R8Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 81_2" × 11" of notebook paper.Fold in halflengthwise.Fold in thirds andthen fold each thirdin half.Open. Cut one sidealong the folds tomake tabs.Label each tab with 8-18-28-38-48-58-6the lesson numberas shown.NOTE-TAKING TIP: Write down questions that youhave about what you are reading in the lesson.Then record the answer to each question as youstudy the lesson.Equations and Inequalities
  • 204. 196 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BUILD YOUR VOCABULARYC H A P T E R8This is an alphabetical list of new vocabulary terms you will learn in Chapter 8.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleidentityinequality[IHN-ih-KWAHL-uht-ee]null or empty set[NUHL]
  • 205. Glencoe Pre-Algebra 197Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 8–1 Solving Equations with Variables on Each SideEXAMPLE Equations with Variables on Each SideSolve 5x + 12 = 2x.5x + 12 = 2x Write the equation.5x - + 12 = 2x - Subtract from each side.= Simplify.= x Mentally divide each side by .Check Your Progress Solve 7x = 5x + 6.EXAMPLE Equations with Variables on Each SideSolve 7x + 3 = 2x + 23.7x + 3 = 2x + 23 Write the equation.7x - + 3 = 2x - + 23 Subtract from eachside.= 23 Simplify.- = 23 - Subtract from eachside.= Simplify.x = Mentally divide.Check Your Progress Solve each equation.a. 4x + 15 = 2x - 7 b. 2.4 - 3m = 6.4m - 8.88MAIN IDEA• Solve equations withvariables on each side.ORGANIZE ITAs you read throughLesson 8-1, write downone or more questionsyou have behind the 8-1tab of your Foldable. Asyou study the lesson,take notes, and recordinformation that answersyour questions.8-18-28-38-48-58-6
  • 206. 8–1198 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLECAR RENTAL A car rental agency has two plans. UnderPlan A, a car rents for $80 plus $20 each day. UnderPlan B, a car rents for $120 plus $15 a day. What numberof days results in the same cost?Let d represent the number of days.plus per day equals + per day== Write the equation.80 + 20d - = 120 + 15d - Subtract fromeach side.80 + 5d = 120 Simplify.80 + 5d - = 120 - Subtract fromeach side.5d = 40 Simplify.= Divide each sideby .= Simplify.If you rent the car for days, the cost is the same forboth plans.Check Your Progress CELL PHONES A cell phoneprovider offers two plans. Under Plan A, the monthly cost is$20 with a cost of $0.35 per minute. Under Plan B, the monthlycost is $35 with a cost of $0.15 per minute. What number ofminutes results in the same cost?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 207. Glencoe Pre-Algebra 199Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 8–2 Solving Equations with Grouping SymbolsEXAMPLE Solve Equations with ParenthesesSolve 3h = 5(h - 2).3h = 5(h - 2) Write the equation.3h = - Property3h = Simplify.3h - = Subtract from eachside.= Simplify.h = Simplify.Ths solution is .EXAMPLE No SolutionSolve 4x - 0.3 = 4x + 0.9.4x - 0.3 = 4x + 0.9 Write the equation.4x - - 0.3 = 4x - + 0.9 Subtract from eachside.= Simplify.The sentence is true. So, the solution set is .Check Your Progress Solve each equation.a. 4t = 7(t - 3) b. 16 + 1.3m = -12 + 1.3mMAIN IDEAS• Solve equations thatinvolve groupingsymbols.• Identify equations thathave no solution oran infinite number ofsolutions.ORGANIZE ITAs you read throughLesson 8-2, write downone or more questionsyou have behind the 8-2tab of your Foldable. Asyou study the lesson,take notes, and recordinformation that answersyour questions.8-18-28-38-48-58-6
  • 208. 8–2200 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.An equation that is for every value of theis called an identity.BUILD YOUR VOCABULARY (page 196)EXAMPLES All Numbers as SolutionsSolve 3(4x - 2) + 15 = 12x + 9.3(4x - 2) + 15 = 12x + 9 Write the equation.+ 15 = 12x + 9 Distributive Property= 12x + 9 Simplify.= Subtract from each side.= Mentally divide each side by .The sentence is true. The solution setis .Check Your Progress Solve 10a - 9 = 5(2a - 3) + 6.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 209. Glencoe Pre-Algebra 201Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A mathematical sentence that contains or iscalled an inequality.BUILD YOUR VOCABULARY (page 196)EXAMPLE Write InequalitiesWrite an inequality for each sentence.a. Your height is greater than 52 inches.Variable: Let h represent .Inequality:b. Your speed is less than or equal to 62 miles per hour.Variable: Let s represent .Inequality:Check Your Progress Write an inequality for eachsentence.a. Your height is less than 48 inches.b. Your age is greater than 12 years.c. Your weight is less than or equal to 120 pounds.d. Your speed is greater than or equal to 35.8–3MAIN IDEAS• Write inequalities.• Graph inequalities.ORGANIZE ITAs you read throughLesson 8-3, write downone or more questionsyou have behind the 8-3tab of your Foldable. Asyou study the lesson,take notes, and recordinformation that answersyour questions.8-18-28-38-48-58-6Inequalities
  • 210. 8–3202 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Determine Truth of an InequalityFor the given value, state whether the inequality is trueor false.a. s - 9 < 4, s = 6- 9 4 Replace s with .< 4 Simplify.The sentence is .b. 14 ≤ a_3+ 1, a = 3614 ≤ _3+ 1 Replace a with .14 + 1 Simplify.14 Simplify.The sentence is .Check Your Progress For the given value, statewhether each inequality is true or false.a. 12 - m > 7, m = 5b. 20_x + 3 ≤ 6, x = 10WRITE ITDescribe one way toremember the differencebetween the > symboland the ≥ symbol.
  • 211. 8–3Glencoe Pre-Algebra 203Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Graph Inequalitiesa. Graph x > 10.12111098The open circle means the number 10 is .b. Graph x ≥ 10.12111098The closed circle means the number 10 is .c. Graph x < 10.12111098The open circle means the number 10 is .Check Your Progress Graph each inequality.a. x < 31 432 5b. x > 31 432 5c. x ≥ 31 432 5EXAMPLE Write an InequalityWrite the inequality for the graph.Ϫ40 Ϫ39 Ϫ38 Ϫ37 Ϫ36A closed circle is on -38, so the point -38 is inthe graph. The arrow points to the , sothe graph includes all numbers than or-38. That is, .Check Your Progress Write the inequality for the graph.Ϫ10 Ϫ9 Ϫ5Ϫ6Ϫ7Ϫ8HOMEWORKASSIGNMENTPage(s):Exercises:
  • 212. 204 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Solve an Inequality Using SubtractionSolve y + 5 > 11.y + 5 > 11 Write the inequality.y + 5 - > 11 - Subtract 5 from each side.> Simplify.EXAMPLE Solve an Inequality Using AdditionSolve -21 ≥ d - 8.-21 ≥ d - 8 Write the inequality.-21 + ≥ d - 8 + Add to each side.≥ Simplify.EXAMPLE Graph Solutions of InequalitiesSolve h - 11_2< 5. Graph the solution on a number line.h - 11_2< 5 Write the inequality.h - 11_2+ < 5 + Add to each side.< Simplify.87654Place at . Draw a line and arrow tothe .Solving Inequalities by Adding or Subtracting8–4MAIN IDEA• Solve inequalities byusing the Addition andSubtraction Propertiesof Inequality.KEY CONCEPTAddition and SubtractionProperties When youadd or subtract the samenumber from each sideof an inequality, theinequality remains true.
  • 213. 8–4Glencoe Pre-Algebra 205Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Solve each equation.a. x + 9 < 13b. m + 8 < -2c. Solve x - 3_4≥ 1_2. Graph the solution on a number line.Ϫ1 0 4321ORGANIZE ITAs you read throughLesson 8-4, write downquestions you havebehind the 8-4 tabof your Foldable. Asyou study the lesson,take notes, and recordinformation that answersyour questions.8-18-28-38-48-58-6HOMEWORKASSIGNMENTPage(s):Exercises:
  • 214. 206 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Solving Inequalities by Multiplying or Dividing8–5EXAMPLE Multiply or Divide by a Positive Numbera. Solve 9x ≤ 54.9x ≤ 54 Write the inequality.9x_ ≤ 54_ Divide each side by .≤ Simplify.b. Solve d_9> 4.d_9> 4 Write the inequality.9(d_9 )> (4) Multiply each side by .> Simplify.Check Your Progress Solve each inequality.a. 3x > 21 b. 6 ≤p_3EXAMPLETEST EXAMPLE Martha earns $9 per hour working fora fast-food restaurant. Which inequality can be used tofind how many hours she must work in a week to earn atleast $117?A 9x < 117 C 9x > 117B 9x ≥ 117 D 9x ≤ 117Let x represent the number of hours worked.Amount earnedper hour timesnumberof hoursis atleastamount earnedeach weekThe inequality is So, the answer is .MAIN IDEAS• Solve inequalities bymultiplying or dividingby a positive number.• Solve inequalities bymultiplying or dividingby a negative number.KEY CONCEPTMultiplication andDivision PropertiesWhen you multiply ordivide each side of aninequality by the sameor positive number, theinequality remains true.ORGANIZE ITAs you study the lesson,take notes, and recordinformation aboutsolving inequalities.8-18-28-38-48-58-6
  • 215. 8–5Glencoe Pre-Algebra 207Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress TEST EXAMPLE Ed earns $6 perhour working at the library. Write an inequality that can beused to find how many hours he must work in a week to earnmore than $100?A 6x < 100 C 6x ≤ 100B 6x ≥ 100 D 6x > 100EXAMPLE Multiply or Divide by a Negative NumberSolve each inequality and check your solution. Thengraph the solution on a number line.a. x_-5≥ 7x_-5≥ 7 Write the inequality.( x_-5) ≤ (7) Multiply each side byand reverse the symbol.x ≤ Ϫ37 Ϫ36 Ϫ35 Ϫ34 Ϫ33b. -9x < -27 Write the inequality.-9x__ > -27__ Divide each side byand reverse the symbol.x > 54321Check Your Progress Solve each inequality and checkyour solution. Then graph the solution on a number line.a. x_-3> 6Ϫ20 Ϫ19 Ϫ15Ϫ16Ϫ17Ϫ18b. -5x ≤ -405 6 10987KEY CONCEPTMultiplication andDivision PropertiesWhen you multiply ordivide each side of aninequality by the samenegative number, theinequality symbol mustbe reversed for theinequality to remain true.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 216. 208 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Solve a Two-Step InequalitySolve 5x + 13 > 83. Graph the solution on a number line.5x + 13 > 83 Write the inequality.5x + 13 - > 83 - Subtract from each side.> Simplify.> Divide each side by .>Check Your Progress Solve 3x - 9 < 18. Graph thesolution on a number line.6 7 111098EXAMPLE Reverse the Inequality SymbolSolve 7 - 4a ≤ 23 - 2a. Graph the solution on anumber line.7 - 4a ≤ 23 - 2a Write the inequality.7 - 4a + ≤ 23 - 2a + Add to each side.≤ Simplify.≤ Subtract from each side.≤ Simplify.≥ Divide each side byand change ≤ to ≥.a ≥ Ϫ8Ϫ9 Ϫ7 Ϫ6Ϫ10Solving Multi-Step Inequalities8–6MAIN IDEA• Solve inequalities thatinvolve more than oneoperation.ORGANIZE ITAs you read throughLesson 8-6, write downquestions you havebehind the 8-6 tab ofyour Foldable. As youstudy the lesson, takenotes, and recordinformation thatanswers your questions.8-18-28-38-48-58-6
  • 217. 8–6Glencoe Pre-Algebra 209Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Solve 8 + 2x < 5x - 7. Graph thesolution on a number line.2 3 87654EXAMPLERUNNING José wants to run a 10K marathon. Refer toGet Ready for the Lesson in the text. If the length of hiscurrent daily runs is 2 kilometers, how many kilometersshould he increase his daily run to have enoughendurance for the race?Let d represent the increase in the number of milesJosé should run.Words 3 times 2 kilometers plus amount of increase isgreater than or equal to desired distance.Inequality≥ Write the equation≥ Distributive Property≥ Subtract fromeach side.≥ Simplify.≥Divide each sideby .≥ Simplify.Jose should increase his daily run by at least kilometerseach day.Check Your Progress A person weighing 168 pounds hasa 7-pound backpack. If three times the weight of your backpackand its contents should be less than your body weight, what isthe maximum weight for the contents of the pack?ORGANIZE ITUnder the tab forLesson 8-6, write anexample of an inequalitythat requires two stepsto solve. Label each stepwith the operation beingundone.8-18-28-38-48-58-6HOMEWORKASSIGNMENTPage(s):Exercises:
  • 218. 210 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R8STUDY GUIDEVOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 8 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 8, go to:glencoe.comYou can use your completedVocabulary Builder(page 196) to help yousolve the puzzle.8-1Solving Equations with Variables on Each SideNumber the steps in the correct order for solving the equation2x + 4 = 4x - 8. Some steps may be used more than once.1. Simplify. 2. Subtract 2x from each side.3. Write the equation. 4. Add 8 to each side.5. Divide each side by 2.8-2Solving Equations with Grouping Symbols6. The perimeter of a rectangle is 74 inches. Find the dimensions andthe area if the length is 5 inches shorter than twice the widths.8-3InequalitiesFor each of the following phrases, write the correspondinginequality symbol in the blank. Use <, >, ≤, or ≥.7. is greater than 8. is less than or equal to9. Write an inequality for the sentence: Seven less than a number is atleast 15.
  • 219. Glencoe Pre-Algebra 211Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 8 BRINGING IT ALL TOGETHER8-4Solving Inequalities by Adding or Subtracting10. Is 6 a solution for the inequality 17 + x > 23? Explain.Solve each inequality. Then graph the solution on anumber line.11. b + 6 < 19 4 5 6 7 8 9 10 11 12 13 14 1512. 21 > n + 27 Ϫ8 Ϫ7 Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 313. -8 ≤ -15 + x Ϫ1 0 1 2 3 4 5 6 7 8 9 108-5Solving Inequalities by Multiplying or DividingMatch each inequality with its graph.14. 2x ≥ 615. x_-3> -116. 12x < -3617. -3x < -98-6Solving Multi-Step InequalitiesUnderline the correct term or phrase to complete eachstatement.18. Remember to (reverse, delete) the inequality symbol whenmultiplying or dividing both sides of the inequality by anegative number.19. To check the solution x > 14, you should try a number (smaller,greater) than 14 in the original inequality.Solve each inequality. Graph the solution on a number line.20. x_2+ 7 < 6 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 421. 3(p + 2) ≤ 2(2p + 7.5) Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4a.Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4b.Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4c.Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4d.Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4e.Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4
  • 220. Checklist212 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R8Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 8 Practice Test onpage 455 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 8 Study Guide and Reviewon pages 451–454 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 8 Practice Test onpage 455.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 8 Foldables.• Then complete the Chapter 8 Study Guide and Review onpages 451–454 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 8 Practice Test onpage 455.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 8.ARE YOU READY FORTHE CHAPTER TEST?
  • 221. Chapter9Glencoe Pre-Algebra 213Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R9Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with three plain sheets of 81_2" × 11" paper.Fold to make a triangle.Cut off extra paper.Repeat Step 1 twice.You now have threesquares.Stack the three squaresand staple along the fold.Label each sectionRightTriangleswith a topic.NOTE-TAKING TIP: A visual (graph, diagram,picture, chart) can present information in aconcise, easy-to-study format. Clearly label yourvisuals and write captions when needed.Real Numbers and Right Triangles
  • 222. 214 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R9BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 9.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleacute angleacute trianglecongruent[kuhn-GROO-uhnt]Distance Formulaequilateral triangle[EE-kwuh-LAT-uh-ruhl]hypotenuse[hy-PAHT-uhn-noos]indirect measurementirrational numbersisosceles triangle[eye-SAHS-uh-LEEZ]line segment
  • 223. Glencoe Pre-Algebra 215Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 9 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleobtuse angle[ahb-TOOS]obtuse triangleperfect squarePythagorean Theorem[puh-THAG-uh-REE-uhn]radical signreal numbersright angleright trianglescalene triangle[SKAY-LEEN]similar figuressquare rootstraight angletrianglevertex
  • 224. 216 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.9–1 Squares and Square RootsA radical sign, √ , is used to thesquare root.BUILD YOUR VOCABULARY (page 215)EXAMPLE Find Square RootsFind each square root.a. √64 indicates the square root of 64.Since = 64, √64 = .b. -√121 indicates the square root of 121.Since = 121, -√121 = .c. ±√4 indicates both square roots of 4. Since 22= ,√4 = and -√4 = .d. √z2indicates the positive square root of z2.√z2=EXAMPLE Find Square Roots with a CalculatorUse a calculator to find each square root to thenearest tenth.a. √222nd  √  22 ENTER Use a calculator.√22 ≈ Round to thenearest tenth.b. -√319(–) 2nd  √  319 ENTER Use acalculator.-√319 ≈ Round to thenearest tenth.MAIN IDEAS• Find squares andsquare roots.• Estimate square roots.KEY CONCEPTSquare Root A squareroot of a number is oneof its two equal factors.
  • 225. 9–1Glencoe Pre-Algebra 217Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find each square root.a. √25 b. -√144c. ±√16 d. √t2Use a calculator to find each square root to thenearest tenth.d. √71 e. -√38EXAMPLE Estimate Square RootsORGANIZE ITUnder the tab forLesson 9-1, list and thenestimate three squareroots to the nearestwhole number.RightTrianglesEstimate √22 to the nearest whole number.• The first perfect square less than 22 is 16.• The first perfect square greater than 22 is 25.• Plot each square root on a number line.The square root of √22 is between the whole numbersand . Since 22 is closer to than , you canexpect that √22 is closer to than .Check Your Progress Estimate each square root to thenearest whole number.a. √54 b. -√152
  • 226. 9–1218 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLESKYSCRAPER The tallest building in Houston, Texasis the JP Morgan Chase Tower, standing at 1002 feettall. Use the Real-World Link in the text to determineabout how far a person can see from the top floor on aclear day.D = 1.22 × Write the formula.= 1.22 × Replace A with .= Evaluate the square root first.Then multiply.On a clear day, the light will be visible from about.Check Your Progress SKYSCRAPER A skyscraperstands 378 feet high. On a clear day, about how far could anindividual standing on the roof of the skyscraper see? Roundto the nearest tenth.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 227. Glencoe Pre-Algebra 219Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The Real Number SystemThe set of numbers and the set ofnumbers together make up the set of real numbers.BUILD YOUR VOCABULARY (pages 214–215)EXAMPLE Classify Real NumbersName all of the sets of numbers to which each realnumber belongs.a. 0.2−−46 This repeating decimal is a numberbecause it is equivalent to .b. √225 Since √225 = , this number is ac. -72_6Since -72_6= , this number is anand a .d. 14_4Since 14_4= , this number is a.Check Your Progress Name all of the sets of numbersto which each real number belongs.a. 0.−−−380b. -√81c. 45_9d. 19_4MAIN IDEAS• Identify and comparenumbers in the realnumber system.• Solve equations byfinding square roots.KEY CONCEPTIrrational Number Anirrational number is anumber that cannot beexpressed as a_b, where aand b are integers and bdoes not equal 0.9–2
  • 228. 9–2220 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Compare Real Numbers on a Number LineReplace with <, >, or = to make √125 117_8a truestatement.Express each number as a . Thenthe numbers.√125 =117_8=11.0 11.2 11.4 11.6 11.8 12.0Since √125 is to the of 117_8, √125 117_8.Check Your Progress Replace with <, >, or = tomake √61 73_4a true statement.EXAMPLE Solve EquationsSolve w2= 169. Round to the nearest tenth, if necessary.w2= 169 Write the equation.= Take the squareroot of each side.w = or w = Find the positiveand negativesquare root.w = or w =Check Your Progress Solve m2= 81. Round to the nearesttenth, if necessary.ORGANIZE ITUnder the tab forLesson 9-2, explain howto compare real numberson a number line. Be sureto include an example.RightTrianglesHOMEWORKASSIGNMENTPage(s):Exercises:
  • 229. Glencoe Pre-Algebra 221Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.TrianglesEXAMPLE Use Ratios to Find Angle MeasuresALGEBRA The measures of the angles of a certaintriangle are the ratio 2:3:5. What are the measuresof the angles?Let represent the measure of one angle, themeasure of a second angle, and the measure of thethird angle.= 180 The sum of the measures is 180.= 180 Combine like terms.= Divide each side by .x = Simplify.2x = 2( )or , 3x = 3( )or , and5x = 5( )or .The measures of the angles are , , and .Check Your Progressa. Find the value of x in MNO. MN82˚41˚x˚Ob. The measures of the angles of a certain triangle are in theratio 3:5:7. What are the measures of the angles?9–3MAIN IDEAS• Find the missing anglemeasure of a triangle.• Classify trianglesby properties andattributes.KEY CONCEPTAngles of a Triangle Thesum of the measures ofthe angles of a triangleis 180°.
  • 230. 9–3222 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Classify AnglesClassify each angle as acute, obtuse, right, or straight.a.K ML25˚b.STR115˚m∠KLM . m∠RST .So, ∠RST is .So, ∠KLM is .Check Your Progress Classify each angle as acute,obtuse, right, or straight.a. b.HGIEXAMPLE Classify TrianglesClassify the triangle by its angles and by its sides.60˚ 60˚60˚Angles All angles are .Sides All sides are .The triangle is an triangle.Check Your Progress Classify each triangle by itsangles and by its sides.a. 130˚20˚30˚b. 60˚ 60˚60˚KEY CONCEPTClassify Triangles by theirAngles and by their SidesAcute Triangle A trianglewith all acute angles.Obtuse Triangle Atriangle with one obtuseangle.Right Triangle A trianglewith one right angle.Scalene TriangleA triangle with nocongruent sides.Isosceles TriangleA triangle with at leasttwo sides congruent.Equilateral TriangleA triangle with all sidescongruent.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 231. Glencoe Pre-Algebra 223Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.In a right triangle, the side opposite the angle isthe hypotenuse.If you know the lengths of two of a righttriangle, you can use the Pythagorean Theorem to find thelength of the side. This is called solving a righttriangle.BUILD YOUR VOCABULARY (pages 214–215)EXAMPLE Find the Length of the HypotenuseFind the length of the hypotenuse of the right triangle.c ft21 ft20 ftc2= a2+ b2Pythagorean Theoremc2=2+2Replace a with and b with .c2= + Evaluate and .c2= Add and .c2= Take the of eachside.c = The length is .Check Your Progress Find the length3 m4 mc mof the hypotenuse of the right triangle.MAIN IDEAS• Use the PythagoreanTheorem to find thelength of a side of aright triangle.• Use the converse of thePythagorean Theoremto determine whethera triangle is a righttriangle.KEY CONCEPTPythagorean TheoremIf a triangle is a righttriangle, then the squareof the length of thehypotenuse is equal tothe sum of the squares ofthe lengths of the legs.The Pythagorean Theorem9–4
  • 232. 9–4224 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Solve a Right TriangleFind the length of the leg of the right triangle to thenearest tenth.c2= a2+ b2Pythagorean Theoremb m11 m8 m2=2+ b2Replace c withand a with .= + b2Evaluate and .= b2Subtract 64 from each side.= √b2Take the of each side.2nd  √  ENTERThe length of the leg is about .EXAMPLE Use the Pythagorean TheoremTEST EXAMPLE A building is 10 feet tall. A ladder ispositioned against the building so that the base of theladder is 3 feet from the building. About how many feetlong is the ladder?A 10.0 ft C 12.4 ft3 ft10 ftB 10.4 ft D 14.9 ftc2= a2+ b2Pythagorean Theoremc2=2+2Replace a withand b with .c2= + Evaluate and .c2= Simplify.√c2= √109 Take the of each side.c ≈ Round to the nearest tenth.The ladder is about tall. The answer is .ORGANIZE ITUnder the tab for thePythagorean Theorem,write the PythagoreanTheorem. Then draw aright triangle and labelthe sides a, b, and c asused in the theorem.RightTriangles
  • 233. 9–19–4Glencoe Pre-Algebra 225Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progressa. Find the length of the leg of thea in.15 in.8 in.right triangle.b. TEST EXAMPLE An 18-foot ladder is placed against abuilding which is 14 feet tall. About how far is the base ofthe ladder from the building?A 11.3 ft B 11.0 ft C 10.5 ft D 10.2 ftEXAMPLE Identify a Right TriangleThe measures of three sides of a triangle are 48 feet,60 feet, and 78 feet. Determine whether the triangleis a right triangle.c2= a2+ b2Pythagorean Theorem2 2+2Replace a with , b with, and c with .+ Evaluate.Simplify.The triangle a right triangle.Check Your Progress The measures of three sides ofa triangle are 42 inches, 61 inches, 84 inches. Determinewhether the triangle is a right triangle.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 234. 226 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The Distance FormulaEXAMPLE Use the Distance FormulaFind the distance between M(8, 4) and N(-6, -2). Roundto the nearest tenth, if necessary.d = √(x2 - x1)2+ (y2 - y1)2Distance FormulaMN =(x1, y1) = (8, 4),(x2, y2) = (26, 22)MN = Simplify.MN = Evaluate and.MN = Add and .MN ≈The distance between points M and N is about .Check Your Progress Find the distance between A(-4, 5)and B(3, -9). Round to the nearest tenth, if necessary.EXAMPLE Use the Distance Formula to Solve a ProblemGEOMETRY Find the perimeter of yO xY (Ϫ2, 4)X (Ϫ5, 1)Z (Ϫ3, Ϫ3)XYZ to the nearest tenth.First, use the DistanceFormula to find the lengthof each side of the triangle.Distance Formula:MAIN IDEA• Use the DistanceFormula to determinelengths on a coordinateplane.KEY CONCEPTDistance Formula Thedistance d between twopoints with coordinates(x1, y1) and (x2, y2), isgiven by d =√(x2 - x1)2 + (y2 - y1)2.9–5
  • 235. 9–5Glencoe Pre-Algebra 227Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Side−−XY: X(-5, 1), Y(-2, 4)XY =(x1, y1) = (-5, 1),(x2, y2) = (-2, 4)XY = Simplify.XY = Simplify.Side−−YZ: Y(-2, 4), Z(-3, -3)YZ =(x1, y1) = (-2, 4),(x2, y2) = (-3, -3)YZ = Simplify.YZ = Simplify.Side−−ZX: Z(-3, -3), X(-5, 1)ZX =(x1, y1) = (-3, -3),(x2, y2) = (-5, 1)ZX = Simplify.ZX = Simplify.The perimeter is + + or about.Check Your Progress Find the yxO(2, 5)(Ϫ3, 1)(4, Ϫ2)ABCperimeter of ABC to the nearest tenth.WRITE ITWhich point should beused for (y2 - y1) inthe distance formula?Explain.
  • 236. 9–5228 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLESOCCER Nikki kicks a ball from a position that is2 yards behind the goal line and 4 yards from thesideline (-2, 4). The ball lands 8 yards past the goalline and 2 yards from the same sideline (8, 2). Whatdistance, to the nearest tenth, was the ball kicked?Let d = the distance the ball was kicked. Use the distanceformula.d = √(x2 - x1)2+ (y2 - y1)2Distance Formulad = (x1, y1) = (-2, 4),(x2, y2) = (8, 2)d = Add.d = Simplify.d = ≈The ball was kicked a distance of about yards.Check Your Progress LANDSCAPING Geneva setup a coordinate system with units of feet to plan the positionof two trees she wants to plant. She plans to put one tree at(-3, -4) and one at (5, 2). How far apart will the trees be?Round to the nearest tenth.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITWrite the DistanceFormula under the tabfor this topic. Illustratethe formula.RightTriangles
  • 237. Glencoe Pre-Algebra 229Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 9–1 Similar Figures and Indirect MeasurementFigures that have the same but notnecessarily the same size are called similar figures.BUILD YOUR VOCABULARY (page 215)EXAMPLE Find Measures of Similar FiguresThe figures are similar.Find the missing measures.The corresponding sidesBAC D1233NMO Px3are .MO_AC= OP_CDWrite a proportion.= MO = , AC = ,OP = , CD == Find the cross products.= Simplify.= x Divide each side by .The value of x is .Check Your Progress A DE FB C8 in.4 in.6 in.x in.The figures are similar. Find themissing measure.9–6MAIN IDEAS• Identify correspondingparts and find missingmeasures of similarfigures.• Solve problemsinvolving indirectmeasurement usingsimilar triangles.KEY CONCEPTCorresponding Parts ofSimilar Figures If twofigures are similar, thenthe corresponding angleshave the same measureand the correspondingsides are proportional.Draw anexample of similar figuresin your notes. Label thecorresponding sides andangles.
  • 238. 9–6230 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Use Indirect MeasurementMAPS A surveyor wants to find the distance RS acrossthe lake. He constructs PQT similar to PRS andmeasures the distances as shown. What is the distanceacross the lake?PSRTQ25 m60 m12 m x= Write a .= Substitution= Find the .= Simplify.= x Divide each side by .The distance across the lake is .Check Your Progress In the figure, MNO is similar toQPO. Find the distance across the park.MNO PQ8 miPark3 mi5 mix miHOMEWORKASSIGNMENTPage(s):Exercises:
  • 239. Glencoe Pre-Algebra 231Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R9STUDY GUIDEVOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 9 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 9, go to:glencoe.comYou can use your completedVocabulary Builder(pages 214–215) to help yousolve the puzzle.9-1Squares and Square RootsFind each square root, if possible.1. √361 2. √-196 3. -√441Estimate each square root to the nearest whole number.Do not use a calculator.4. √120 5. √150 6. -√709-2The Real Number SystemUnderline the correct term to complete each sentence.7. Numbers with decimals that (are, are not) repeating orterminating are irrational numbers.8. All square roots (are, are not) irrational numbers.9. Irrational numbers (are, are not) real numbers.Name all of the sets of numbers to which each real numberbelongs. Let N = natural numbers, W = whole numbers,Z = integers, Q = rational numbers, and I = irrational numbers.10. -49 11. √48 12. 11Solve each equation. Round to the nearest tenth, if necessary.13. b2= 225 14. 2z2= 88
  • 240. 232 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 9 BRINGING IT ALL TOGETHER9-3TrianglesFind the value of x in the triangle. Then classify thetriangle as acute, right, or obtuse.15.80˚35˚x16.50˚x17. The measures of the angles of a triangle are in the ratio 3:4:5.What is the measure of each angle?9-4The Pythagorean TheoremIf c is the measure of the hypotenuse, find each missingmeasure. Round to the nearest tenth, if necessary.18. a = 12, b = ?, c = 37 19. a = ?, b = 6, c = 1620. The length of the sides of a triangle are 10, 24, and 26. Determinewhether the triangle is a right triangle.
  • 241. Glencoe Pre-Algebra 233Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 9 BRINGING IT ALL TOGETHER9-5The Distance FormulaFind the distance between each pair of points. Round to thenearest tenth, if necessary.21. J(8, -3), K(5, 1) 22. P(-3, 7), Q(4, 2)23. S(2, 4), T(0, -2) 24. C(-5, -1), D(3, -4)9-6Similar Figures and Indirect MeasurementFor Questions 25 and 26, use the trianglesat the right. PQR ∼ UVW.25. Name an angle with the same measureas ∠W.26. Find the value of x.27. In the figure at the right, the triangles aresimilar. How far is the waterfall from thegrove of redwood trees?PQRVU W32.5x83 mi1.5 miWaterfallx mi12 miTrailheadRedwood GrovePond
  • 242. Checklist234 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R9Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 9 Practice Test onpage 507 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 9 Study Guide and Reviewon pages 503–506 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 9 Practice Test onpage 507.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 9 Foldable.• Then complete the Chapter 9 Study Guide and Review onpages 503–506 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 9 Practice Test onpage 507.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 9.
  • 243. Chapter10Glencoe Pre-Algebra 235Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R10 Two-Dimensional FiguresUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with four plain sheets of 11" × 17"paper, eight index cards, and glue.Fold in halfwidthwise.Fold the bottomto form a pocket.Glue the edges.Repeat three times.Then glue all fourpieces togetherto form a booklet.Label each pocket.MonkeylikeTriangles TrapezoidsPlace an index cardin each pocket.NOTE-TAKING TIP: To help you organize data,create study cards when taking notes, recordingand defining vocabulary words, and explainingconcepts.
  • 244. 236 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R10BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 10.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleadjacent angles[uh-JAY-suhnt]circlecircumference[suhr-KUHMP-fuhrnts]complementary angles[kahm-pluh-MEHN-tuh-ree]congruent[kuhn-GROO-uhnt]corresponding partsdiagonaldiameterdilationparallel lines
  • 245. Glencoe Pre-Algebra 237Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 10 BRINGING IT ALL TOGETHERVocabulary TermFoundon PageDefinitionDescription orExampleperpendicular linesπ (pi)polygonquadrilateral[KWAH-druh-LA-tuh-ruhl]radiusreflectionsupplementary angles[SUH-pluh-MEHN-tuh-ree]transformationtranslationtransversalvertical angles
  • 246. 238 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10–1Two lines in a plane that never intersect are parallel lines.A line that two parallel lines is calleda transversal.When two lines intersect, they form two pairs ofangles called vertical angles.When two angles have the same , share a commonside, and do not overlap, they are adjacent angles.If the sum of the measures of two angles is , theangles are complementary.If the sum of the measures of two angles is , theangles are supplementary.Lines that to form a areperpendicular lines.BUILD YOUR VOCABULARY (pages 236–237)EXAMPLE Find Measures of AnglesIn the figure, m n and s and t31471191215101314162568m nstare transversals. If m∠7 = 123°,find m∠2 and m∠8.Since ∠7 and ∠2 are alternateangles, they are .So, m∠2 = .Since ∠7 and ∠8 are angles,they are . So, m∠8 = .MAIN IDEAS• Identify therelationships of anglesformed by two parallellines and a transversal.• Identify therelationships ofvertical, adjacent,complementary, andsupplementary angles.Line and Angle RelationshipsKEY CONCEPTParallel Lines Cut bya Transversal If twoparallel lines are cut bya transversal, then thefollowing pairs of anglesare congruent.• Corresponding anglesare congruent.• Alternate interiorangles are congruent.• Alternate exteriorangles are congruent.
  • 247. 10–1Glencoe Pre-Algebra 239Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress In the figure in Example 1, m nand s and t are transversals. If m∠4 = 57°, find m∠5 and m∠1.EXAMPLELEG LIFTS Kian does leg lifts each morning. For eachrepetition he lifts his legs 35 degrees off the ground.What is the measure of the angle formed by his bodyand legs in this position?The angles are .= Write the equation.m∠x + 35 = 180 Subtract from each side.m∠x = Simplify.The angle formed by his body and legs is .Check Your Progress SEWING Linda cuts a piece ofmaterial from the corner at a 35° angle. What is the measureof the other angle formed by the cut?EXAMPLE Find Measures of AnglesAngles PQR and STU are supplementary. If m∠PQR =x - 15 and m∠STU = x - 65, find the measure of eachangle.Step 1 Find the value of x.m∠PQR + m∠STU = Supplementary angles(x - 15) + (x - 65) = Substitution- = Combine like terms.= Add to each side.x = Divide each side by .KEY CONCEPTNames of SpecialAngles The eight anglesformed by parallel linesand a transversal havespecial names.• Interior angles• Exterior angles• Alternate interiorangles• Alternate exteriorangles• Correspondingangles
  • 248. 10–2240 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Step 2 Replace x with to find the measure of each angle.m∠PQR = x - 15= - 15 orm∠STU = x - 65= - 65 orCheck Your Progress Angles ABC and DEF arecomplementary. If m∠ABC = x + 12 and m∠DEF = 2x - 9,find the measure of each angle.EXAMPLETRANSPORTATION A road crosses railroad tracks atan angle as shown. If m∠1 = 131°, find m∠6 and m∠5.Since and ∠5 are corresponding angles,1 24 35 68 7they are congruent. So, m∠5 = .Since and ∠6 are supplementary angles,the sum of their measures is 180°;180 - = . So, m∠6 = .Check Your Progress TRANSPORTATION Main Streetcrosses Broadway Boulevard and Maple Avenue at an angleas shown. If m∠1 = 48°, find m∠3 and m∠4.WRITE ITWhat is the differencebetween complementaryangles andsupplementary angles?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 249. Glencoe Pre-Algebra 241Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 10–2Figures that have the same and arecongruent.The parts of congruent triangles that arecorresponding parts.BUILD YOUR VOCABULARY (page 236)EXAMPLE Name Corresponding PartsName the correspondingF I GD HEparts in the congruenttriangles shown. Thencomplete the congruencestatement.Corresponding Angles DEF ?∠D , ∠E , ∠FCorresponding Sides−−−DE ,−−−DF ,−−EFOne congruence statement is .Check Your Progress Name the corresponding parts inthe congruent triangles shown. Then complete the congruencestatement.ACBDEFABC ?MAIN IDEA• Identify congruenttriangles andcorresponding partsof congruent triangles.KEY CONCEPTCorresponding Partsof Congruent TrianglesIf two triangles arecongruent, theircorresponding sides arecongruent and theircorresponding anglesare congruent.Congruent Triangles
  • 250. 10–2242 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.What do we call atriangle with at leasttwo congruent sides?Three congruent sides?(Lesson 9-3)REVIEW ITEXAMPLE Identify Congruent TrianglesDetermine whether the trianglesNM ON R QM O PPQ Rshown are congruent. If so, namethe corresponding parts andwrite a congruence statement.EXPLORE The drawing shows which angles are congruentand the lengths of all sides.PLAN Note which segments have the same length andwhich angles are congruent. Write correspondingvertices in the same order.SOLVE Angles: The arcs indicate that ∠M ,∠N , and ∠O .Sides: The slash marks indicate that−−−MN ,−−−NO , and−−−MO .Since all pairs of corresponding angles and sides are, the two triangles are .One congruence statement is .CHECK Draw MNO and QPR so that they arein the same . Then comparethe angles and sides.Check Your Progress Determine whether the trianglesshown are congruent. If so, name the corresponding parts andwrite a congruence statement.A B X ZCY
  • 251. 10–2Glencoe Pre-Algebra 243Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Find Missing MeasuresCONSTRUCTION A brace is used to support a tabletop.In the figure, ABC DEF.B C F EA D50˚2 fta. What is the measure of ∠F?∠F and ∠C are angles. So, they are. Since m∠C = , m∠F = .b. What is the length of−−DF?−−−DF corresponds to . So,−−−DF and are. Since AC = , DF = .Check Your Progress In the figure, ABC DEF.C FA DB E44˚22 in.a. What is the measure of ∠B?b. What the length of EF?
  • 252. 244 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10–3 Transformations on the Coordinate PlaneA movement of a geometric figure is a transformation.In a translation, you a figure from one positionto another without turning it.In a reflection, you a figure over a line.In a dilation, you enlarge or reduce a figure by a scale factor.BUILD YOUR VOCABULARY (pages 236–237)EXAMPLE Translation in a Coordinate PlaneTriangle ABC is shown on the coordinate plane. Findthe coordinates of the vertices of the image of ABCtranslated 4 units right and 5 units down.A A(-7, 2), B(-5, -5), C(1, 0)xyOB A(1, 12), B(3, 5), C(9, 10)C A(-7, 12), B(-5, 5), C(1, 10)D A(1, 2), B(3, -5), C(9, 0)This translation can be written asthe ordered pair .To find the coordinates of the translatedimage, add to each x-coordinateand add to each y-coordinate.vertex 4 right, 5 down translationA (-3, 7) + AB(-1, 0) + BC(5, 5) + CThe coordinates of the vertices of ABC are A ,B , and C . So, the answer is .MAIN IDEA• Draw translations,reflections, anddilations on acoordinate plane.KEY CONCEPTTranslationStep 1 Describe thetranslation usingan ordered pair.Step 2 Add thecoordinates ofthe ordered pairto the coordinatesof the originalpoint.
  • 253. 10–3Glencoe Pre-Algebra 245Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your ProgressTEST EXAMPLE Triangle DEFxyOis shown on the coordinate plane.Find the coordinates of the verticesof the image of DEF translated3 units left and 2 units up.A D(-4, 3), E(-6, -1), F(1, -6)B D(2, 3), E(0, -1), F(7, -6)C D(-4, 7), E(-6, 3), F(1, -2)D D(2, 7), E(0, 3), F(7, -2)EXAMPLE Reflection in a Coordinate PlaneThe vertices of a figure are M(-8, 6), N(5, 9), O(2, 1), andP(-10, 3). Graph the figure and the image of the figureafter a reflection over the y-axis.To find the coordinates of the vertices of the image after areflection over the y-axis, multiply the x-coordinate byand use the same y-coordinate.vertex reflectionM(-8, 6) MN(5, 9) NO(2, 1) OP(-10, 3) PThe coordinates of the verticesxxyOO 44 88Ϫ4Ϫ444Ϫ8of the reflected figure areM , N ,O , and P .KEY CONCEPTReflection• To reflect a pointover the x-axis, usethe same x-coordinateand multiply they-coordinate by -1.• To reflect a pointover the y-axis, usethe same y-coordinateand multiply thex-coordinate by -1.
  • 254. 10–3246 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress ThexyOvertices of a figure are Q(-2, 4),R(-3, 1), S(3, -2), and T(4, 3).Graph the figure and theimage of the figure after areflection over the y-axis.EXAMPLE Dilations in a Coordinate PlaneA polygon has vertices A(-1, 1), B(1, 1), and C(1, 2).Graph the polygon and the image of the polygon after adilation centered on the origin with a scale factor of 3.To dilate the polygon,yxOthe coordinates of each vertex by .A(-1, 1)B(1, 1)C(1, 2)The coordinates of the dilated image are , ,and .Check Your Progress A figure has vertices A(2, -2),B(4, 6), C(-4, 4), and D(-6, -2). Graph the figure and theimage of the figure after a dilation centered at the origin witha scale factor of 1_2.yxOKEY CONCEPTDilationSuppose k is the scalefactor of a dilation.• If k > 1, the dilation isan enlargement.• If 0 < k < 1, thedilation is a reduction.• If k = 1, the dilationis congruent to theoriginal figure.
  • 255. Glencoe Pre-Algebra 247Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 10–4 QuadrilateralsA quadrilateral is a closed figure with sidesand vertices.BUILD YOUR VOCABULARY (page 237)EXAMPLE Find Angle MeasuresFind the value of x. Then find75˚110˚Q TSRx˚4x˚each missing angle measure.WordsVariableEquationThe sum of the measures of the anglesis 360°.Let m∠Q, m∠R, m∠S, and m∠T represent themeasures of the angles.m∠Q + m∠R + m∠S + m∠T =m∠Q + m∠R + m∠S + m∠T = Angles of aquadrilateral75 + 4x + 110 + x = Substitution+ = Combinelike terms.+ - = - Subtract.= 175 Simplify.x = Divide.The value of x is .So, m∠T = and m∠R = or .MAIN IDEAS• Find the missingangle measures of aquadrilateral.• Classify quadrilaterals.KEY CONCEPTAngles of aQuadrilateral The sumof the measures of theangles of a quadrilateralis 360°.
  • 256. 10–4248 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find40˚120˚Bx˚4x˚CADthe value of x. Then find eachmissing angle measure.EXAMPLE Classify QuadrilateralsClassify each quadrilateral using the name that bestdescribes it.a.The quadrilateral has of. It is a trapezoid.b.The quadrilateral has ofand . It is a .Check Your Progress Classify each quadrilateral usingthe name that best describes it.a.b.ORGANIZE ITOn your Quadrilateralsindex card, drawthree examples ofquadrilaterals, anddescribe how to findthe sum of the measuresof the angles in aquadrilateral.MonkeylikeTriangles TrapezoidsHOMEWORKASSIGNMENTPage(s):Exercises:
  • 257. Glencoe Pre-Algebra 249Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 10–5 PolygonsA polygon is a simple, closed figure formed by consecutive.A diagonal is a line segment in a polygon that twononconsecutive .BUILD YOUR VOCABULARY (pages 236–237)EXAMPLE Classify PolygonsClassify each polygon.a.This polygon has sides. It is a .b.This polygon has sides. It is a .Check Your Progress Classify each polygon.a. b.MAIN IDEAS• Classify polygons.• Determine the sumof the measures of theinterior and exteriorangles of a polygon.ORGANIZE ITOn your index card forpolygons, draw severalpolygons and label themwith their name andnumber of sides.MonkeylikeTriangles Trapezoids
  • 258. 10–5250 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Measures of Interior AnglesFind the sum of the measures of the interior anglesof a quadrilateral.A quadrilateral has sides. Therefore, n = .(n - 2)180 = Replace n with .= or Simplify.The sum of the measures of the interior angles ofa quadrilateral is .Check Your Progress Find the sum of the measures of theinterior angles of a pentagon.EXAMPLE Find Angle Measures of a Regular PolygonTRAFFIC SIGNS A stop sign is a regular octagon. Whatis the measure of one interior angle in a stop sign?Step 1 Find the sum of the measures of the angles.An octagon has 8 sides. Therefore, n = .(n - 2)180 = Replace n with .= or Simplify.The sum of the measures of the interior angles is .Step 2 Divide the sum by 8 to find the measure of one angle.÷ 8 =So, the measure of one interior angle in a stop sign is .Check Your Progress A picnic table in the park is a regularhexagon. What is the measure of one interior angle in thepicnic table?HOMEWORKASSIGNMENTPage(s):Exercises:KEY CONCEPTInterior Angles of aPolygon If a polygonhas n sides, then n - 2triangles are formed.The sum of the degreemeasures of the interiorangles of the polygon is(n - 2)180.
  • 259. Glencoe Pre-Algebra 251Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 10–6 Area: Parallelograms, Triangles, and TrapezoidsEXAMPLE Find Areas of ParallelogramsFind the area of each parallelogram.a.3m3mThe base is .The height is .A = bh Area of a parallelogram= b = , h == Multiply.The area is .b.6.2 in.4.3 in.The base is .The height is .A = bh Area of a parallelogram= b = , h == Multiply.The area is .Check Your Progress Find the area of eachparallelogram.a.4 cm3 cmb.1.3 ft1.51.5 ftMAIN IDEAS• Find area ofparallelograms.• Find the areasof triangles andtrapezoids.KEY CONCEPTArea of a ParallelogramIf a parallelogram hasa base of b units and aheight of h units, thenthe area A is bh squareunits.
  • 260. 10–6252 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find Areas of TrianglesFind the area of each triangle.a.4 m3 m The base is .The height is .A = 1_2bh Area of a triangle= b = , h == Multiply.The area of the triangle is .b.6.4 f3.9 ftThe base is .The height is .A = 1_2bh Area of a triangle= b = , h == Multiply.The area of the triangle is .Check Your Progress Find the area of each triangle.a.15 in.12 in.b.5.2 cm3.6 cmORGANIZE ITAdd diagrams, labels,and area formulas tothe index cards forparallelograms, triangles,and trapezoids in yourFoldable.MonkeylikeTriangles TrapezoidsKEY CONCEPTArea of a Triangle If atriangle has a base ofb units and a height ofh units, then the area Ais 1_2bh square units.
  • 261. 10–6Glencoe Pre-Algebra 253Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find Area of a TrapezoidFind the area of the trapezoid.The height is . 6 m5 m147 m12The bases are and .A = Area of aA = h = , a = , andb =A = Add.A = Divide out the common factors.A = or Simplify.The area of the trapezoid is .Check Your Progress Find the area of the trapezoid.6 ft2 ft5 ftKEY CONCEPTArea of a Trapezoid Ifa trapezoid has basesof a units and b unitsand a height of h units,then the area A of thetrapezoid is 1_2h(a + b)square units.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 262. 254 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.10–7 Circles: Circumference and AreaThe distance across the circle through its isits diameter.The distance from the to any point on thecircle is its radius.The of the circumference of a circle to theof the circle is always equal to 3.1415926 . . . ,represented by the Greek letter π (pi).BUILD YOUR VOCABULARY (pages 236–237)EXAMPLE Find the Circumference of a CircleFind the circumference of each circle to the nearesttenth.a.12 in.C = πd Circumference of a circleC = Replace d with .C = Simplify. This is the exactcircumference.Using a calculator, you find that the circumference is about.b.7.1 mC = 2πd Circumference of a circleC = Replace r with .C = Simplify. Use a calculator.The circumference is about .MAIN IDEAS• Find circumferenceof circles.• Find area of circles.KEY CONCEPTCircumference of a CircleThe circumference ofa circle is equal to itsdiameter times π, or 2times its radius times π.
  • 263. 10–7Glencoe Pre-Algebra 255Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find the circumference of eachcircle to the nearest tenth.a.4 ftb.1.6 cmEXAMPLELANDSCAPING A landscaper has a tree whose roots forma ball-shaped bulb with a circumference of 110 inches.What is the minimum circumference that the landscaperwill have to dig the hole in order to plant the tree?Use the formula for the circumference of a circle to findthe diameter.C = πd Circumference of a circle= π · d Replace C with .= d Divide each side by .≈ Simplify. Use a calculator.The diameter of the hole should be at least .Check Your Progress SWIMMING POOL A circularswimming pool has a circumference of 24 feet. Matt must swimacross the diameter of the pool. How far will Matt swim?
  • 264. 10–7256 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find Areas of CirclesFind the area of each circle. Round to the nearest tenth.a.11 ftA = πr2Area of a circleA = Replace r with .A = Evaluate .A ≈ Use a calculator.The area is about .b.8.3 cmA = πr2Area of a circleA = Replace r with .A = Evaluate .A ≈ Use a calculator.The area is about .Check Your Progress Find the area of each circle.Round to the nearest tenth.a.7 mb.10.4 in.KEY CONCEPTArea of a Circle The areaof a circle is equal to πtimes the square of itsradius.Add a diagramof a circle to your Circlesindex card. Label thecenter, diameter, radiusand circumference. Thenwrite the formulas forthe circumference andarea of a circle.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 265. Glencoe Pre-Algebra 257Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 10–8 Area: Composite FiguresEXAMPLE Find Area of Composite FiguresFind the area of the figure to thenearest tenth.Separate the figure into a triangle, square,2 in.2 in.2 in.2 in.4 in.and a quarter-circle. Then find the sum ofthe areas of the figures.Area of SquareA = bh Area of a squareA = or b = h =Area of TriangleA = 1_2bh Area of a triangleA = or b = , h =Area of Quarter-circleA = 1_4πr2Area of a quarter-circleA = r =The area of the figure is + + or aboutsquare inches.Check Your Progress Find the area of the figure to thenearest tenth.4 cm3 cm10 cmMAIN IDEA• Find the area ofcomposite figures.What is the differencebetween πr2and (πr)2?(Lesson 4-2)REVIEW IT
  • 266. 10–8258 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLECARPETING Carpeting costs $2 per 14 ft10 ft12 ft3 ft3 ftsquare foot. How much will it cost tocarpet the area shown?Step 1 Find the area to be carpeted.Area of RectangleA = bh Area of a rectangleA = or b = , h =Area of SquareA = bh Area of a squareA = or b = h =Area of TriangleA = 1_2bh Area of a triangleA = or b = , h =The area to be carpeted is + + orsquare feet.Step 2 Find the cost of the carpeting.× =So, it will cost to carpet the area.Check Your Progress 6 ft29 ft10 ftPAINTING One gallonof paint is advertised tocover 100 square feet ofwall surface. About howmany gallons will be neededto paint the wall shown atthe right?ORGANIZE ITOn your CompositeFigures index card,describe how to findthe area of a compositefigure.MonkeylikeTriangles Trapezoids
  • 267. Glencoe Pre-Algebra 259Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R10STUDY GUIDEVOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 10 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 10, go to:glencoe.comYou can use your completedVocabulary Builder(pages 236–237) to help yousolve the puzzle.10-1Line and Angle RelationshipsComplete.1. Two angles are if the sum of theirmeasures is 90°.2. When two lines intersect, they form two pairs of opposite anglescalled .In the figure at the right, m and p is a transversal. mpᐉ1 5678234If m∠5 = 96°, find the measure of each angle.3. ∠2 4. ∠3 5. ∠810-2Congruent TrianglesIn the figure shown, the triangles are congruent.Complete each congruence statement.6. ∠J 7.−−−JHK H S TJ R8.−−−HK 9. ∠K10. ∠H 11.−−KJ
  • 268. 260 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 10 BRINGING IT ALL TOGETHER10-3Transformations on the Coordinate Plane12. Suppose the figure graphed is reflected over yxOACDBthe y-axis. Find the coordinates of thevertices after the reflection.13. A figure has the vertices P(4, -2), Q(3, -4),R(1, -4), S(2, -1). Find the coordinatesof the vertices of the figure after a dilationcentered on the origin with a scale factor of 3.10-4QuadrilateralsMatch each description with a quadrilateral.a. squareb. trapezoidc. rectangled. rhombus14. a parallelogram with four congruent sides andfour right angles15. one pair of opposite sides is parallel16. a parallelogram with four congruent sides17. In quadrilateral EFGH, m∠E = 90°, m∠F = 120°, andm∠G = 70°. Find m∠H.10-5PolygonsFind the sum of the measures of the interior angles of eachpolygon.18. decagon 19. heptagon 20. 15-gonFind the measure of an interior angle of each polygon.21. regular octagon 22. regular nonagon
  • 269. Glencoe Pre-Algebra 261Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 10 BRINGING IT ALL TOGETHER10-6Area: Parallelograms, Triangles, and TrapezoidsFind the area of each figure described.23. triangle: base, 6 ft; height, 4 ft24. parallelogram: base, 13 m; height, 7 m25. trapezoid: height, 4 cm; bases, 3 cm and 9 cm10-7Circles: Circumference and AreaComplete.26. The distance around a circle is called the .27. The is the distance across a circle through its center.Find the circumference and area of each circle. Round to thenearest tenth.28.7 in.29.11 m1210-8Area: Composite FiguresFind the area of each figure. Round to the nearest tenth, if necessary.30. 3 cm6 cm2.5 cm11 cm2 cm31.8.6 in.13.4 in.3.1 in.
  • 270. Checklist262 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 10 Practice Test onpage 569 of your textbook as a final check.I used my Foldable or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 10 Study Guide and Reviewon pages 564–568 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 10 Practice Test onpage 569.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 10 Foldable.• Then complete the Chapter 10 Study Guide and Review onpages 564–568 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 10 Practice Test onpage 569.C H A P T E R10Visit glencoe.com toaccess your textbook,more examples, self-checkquizzes, and practice teststo help you study theconcepts in Chapter 10.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher Signature
  • 271. Chapter11Glencoe Pre-Algebra 263Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R11Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a plain piece of 11" x 17" paper.Fold the paperin thirdslengthwise.Fold a 2" tabalong the shortside. Then foldthe rest in fourths.Draw lines alongCh.11VolumePrismsCylindersPyramidsConesSurfaceAreafolds and labelas shown.NOTE-TAKING TIP: When taking notes, use a tableto make comparisons about the new material.Determine what will be compared, decide whatstandards will be used, and then use what isknown to find similarities and differences.Three-Dimensional Figures
  • 272. 264 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R11BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 11.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebaseconecylinder[SIH-luhn-duhr]edgefacelateral[LA-tuh-ruhl] arealateral facenetplanepolyhedron[pah-lee-HEE-druhn]
  • 273. Glencoe Pre-Algebra 265Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 11 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleprismpyramidsimilar solidsslant heightsolidspheresurface areavertexvolume
  • 274. 266 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.11–1A plane is a two-dimensional surface that extendsin all directions.Intersecting planes can formfigures or solids. A polyhedron is a solid with flat surfacesthat are .In a polyhedron, an edge is where two planes intersectin a . A face is a surface. A vertex is whereor more planes in a point.A prism is a polyhedron with two , congruentfaces called bases.A pyramid is a polyhedron with one base that is anypolygon. Its other faces are .BUILD YOUR VOCABULARY (pages 264–265)EXAMPLE Identify SolidsIdentify each solid. Name the bases, faces, edges,and vertices.a.GH JNKPLMThis figure has two parallel congruent bases that are, GHJK and LMNP, so it is a.Three-Dimensional FiguresMAIN IDEAS• Identify three-dimensional figures.• Draw various viewsof three-dimensionalfigures.KEY CONCEPTPolyhedronstriangular prismrectangular prismtriangular pyramidrectangular pyramid
  • 275. 11–1Glencoe Pre-Algebra 267Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.faces:edges:vertices:b. GEFDThis figure has one base, DEF, so it is a.faces:edges:vertices:Check Your Progress Identify the solid. Name thebases, faces, edges, and vertices.a. AC DBEb. HGLP NK JMREMEMBER ITIn a rectangularprism, any two parallelrectangles are bases,and any face is a basein a triangular pyramid.Bases do not have tobe on the bottom of afigure.
  • 276. 11–1268 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEARCHITECTURE An architect’ssketch shows the plans for anew skyscraper. Each unit onthe drawing represents 80 feet.a. Draw a top view and find thearea of the ground floor.The drawing is two rectangles,a 4 × 6 and a 2 × 1, so the actualdimensions are 4(80) × 6(80) plusor 2(80) × 1(80) or 320 feet × 480 feetplus 160 feet × 80 feet. To find the area add the areasof the two rectangles. A = +or .The area of the groundfloor is .b. Draw a top-count view of the building.Using the top view from part a,write the number of levelsfor each unit of the building.c. How many floors are in the skyscraperif each floor is 16 feet high?You can see from the side view andtop-count view that the height of thebuilding is 7 units.total height: 7 units × 80 feet per unit= 560 feet number of floors:÷=Check Your ProgressARCHITECTURE An architect’ssketch shows the plans for a newoffice building. Draw a top viewand find the area of the ground floor.Then find the number of floors inthe office building if each floor is15 feet high.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 277. Glencoe Pre-Algebra 269Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Volume: Prisms and CylindersVolume is the of occupied bya solid region.BUILD YOUR VOCABULARY (page 265)EXAMPLE Volume of a Rectangular PrismFind the volume of16 cm8 cm 25 cmthe prism.V = Bh Formula for volume of a prism= The base is a ,so B = .= = 25, = 16, = 8= Simplify.The volume is cubic centimeters.EXAMPLE Volume of a Triangular PrismFind the volume of the3 in.2 in.5 in.triangular prism.V = Bh Formula for volume of a prism= B = area of base or .= The of the prism is .= Simplify.The volume is cubic inches.MAIN IDEAS• Find volumes of prisms.• Find volumes of circularcylinders.KEY CONCEPTVolume of a PrismThe volume V of a prismis the area of the base Btimes the height h.11–2
  • 278. 11–2270 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find the volume of each prism.a.6 ft2.5 ft3 ftb.5 ft1.5 ft4 ftEXAMPLE Height of a PrismBAKING Baking Cake batter is poured into a pan that isa rectangular prism whose base is an 8-inch square base.If the cake batter occupies 192 cubic inches, what will bethe height of the batter?V = Bh Formula for volume of a prismV = · w · h Formula for volume of arectangular prism= Replace V with ,with , and w with .= Simplify.= h Divide each side by .The height of the batter is .Check Your ProgressSWIMMING POOLS A swimming pool is filled with 960 cubicfeet of water. The pool is a rectangular prism 20 feet long and12 feet wide and is the same depth throughout. Find the depthof the water.
  • 279. 11–2Glencoe Pre-Algebra 271Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A cylinder is a whose bases are congruent,parallel , connected with a side.BUILD YOUR VOCABULARY (page 264)EXAMPLE Volume of a CylinderFind the volume of each cylinder.Round to the nearest tenth.a.7 ft14 ftV = Formula for volumeof a= Replace r withand h with .≈ Simplify.The volume is about cubic feet.b. diameter of base 10 m, height 2 mSince the diameter is , the radius is .V = πr2h Formula for volume of a cylinder= Replace r withand h with .≈ Simplify.Check Your Progress Find the volume of eachcylinder. Round to the nearest tenth.a.7 in.4 in. b. diameter of base 8 cm,height 6 cmHOMEWORKASSIGNMENTPage(s):Exercises:KEY CONCEPTVolume of a CylinderThe volume V of acylinder with radius r isthe area of the base Btimes the height h.Write theformulas for the volumeof a prism and thevolume of a cylinder inyour table.
  • 280. 272 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.11–3 Volume: Pyramids, Cones, and SpheresEXAMPLE Volumes of PyramidsFind the volume of the pyramid.15 in.15 in.12 in.If necessary, round to thenearest tenth.V = 1_3Bh Formula for volumeof a pyramid= Replace B with · .= The height is inches.= Simplify.The volume is cubic inches.A cone is a three-dimensional figure with onebase. A curved surface connects the base and the vertex.BUILD YOUR VOCABULARY (page 264)EXAMPLE Volume of a ConeFind the volume of the cone. 8 m5.5 mRound to the nearest tenth.V = 1_3πr2h Formula for volume of a cone= r = and h = .≈ Simplify.The volume is cubic meters.MAIN IDEAS• Find volumes ofpyramids.• Find volumes of conesand spheres.KEY CONCEPTSVolume of a PyramidThe volume V of apyramid is one-third thearea of the base B timesthe height h.Volume of a ConeThe volume V of a conewith radius r is one-thirdthe area of the base Btimes the height h.Write theseformulas in your table.
  • 281. 11–3Glencoe Pre-Algebra 273Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find the volume of each solid.Round to the nearest tenth.a.8 in.6 in.7 in.b.6.2 in.10.5 in.EXAMPLE Volume of a SphereFind the volume of the sphere.Round to the nearest tenth.V = Formula for volume ofa sphere.= Replace r with .≈ Simplify.The volume of the sphere is about .Check Your ProgressFind the volume of the sphere.Round to the nearest tenth.
  • 282. 11–3274 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLELANDSCAPING When mulch was dumped from a truck, itformed a cone-shaped mound with a diameter of 15 feetand a height of 8 feet.a. What is the volume of the mulch?V = 1_3πr2h Formula for volume of a cone= r = , h = .≈ cubic feetb. How many square feet can be covered with this mulchif 1 cubic foot covers 4 square feet of ground?ft2of ground = mulch ×of ground____mulch= of groundCheck Your Progress PLAYGROUND A load of woodchips for a playground was dumped and formed a cone-shaped mound with a diameter of 10 feet and a heightof 6 feet.a. What is the volume of the wood chips?b. A person shoveling the wood chips removes them at a rate of2 ft3every minute. How long does it take for the load of woodchips to be completely removed?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 283. Glencoe Pre-Algebra 275Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The surface area of a three-dimensional figure is theof the of all of theof the figure.BUILD YOUR VOCABULARY (page 265)EXAMPLE Surface Area of PrismsFind the lateral and surface area of the rectangularprism.a.21 cm34 cm4 cmFind the lateral area. Find the surface area.L = Ph S = L + 2B= (2 + 2w)(h) = L + 2 w= ( )( ) = + 2= =b.20 m 3 m16 m12 mThe lateral area is made up of the areas of the lateral faces.L = Ph Write the formula.= Substitution.= Simplify.Find the surface area.S = L + 2B Write the formula.= L + 2(1_2bh) B = 1_2bh (area of triangle)= + 2(1_2) Substitution= Simplify.11–4 Surface Area: Prisms and CylindersMAIN IDEAS• Find the lateral areaand surface areas ofprisms.• Find the lateral areaand surface areas ofcylinders.KEY CONCEPTSurface Area ofRectangular PrismsThe surface area S of arectangular prism withlength l, width w, andheight h is the sum of theareas of the faces.
  • 284. 11–4276 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find the lateral area and surfacearea of each prism.a.14 in.5 in.8 in.b.5 ft7 ft4 ft3 ftEXAMPLE Surface Area of a CylinderFind the lateral area and surface8 m5 marea of the cylinder. Roundto the nearest tenth.Lateral Area Surface AreaL = 2πrh S = L + 2πr2= == =≈ =Check Your Progress21 in.8.2 in.Find the lateral area and surfacearea of the cylinder. Round tothe nearest tenth.KEY CONCEPTSurface Area of CylindersThe surface area S of acylinder with height hand radius r is the areaof the two bases plusthe area of the curvedsurface.Write theformulas for the surfacearea of a prism and thesurface area of a cylinderin your table.
  • 285. 11–4Glencoe Pre-Algebra 277Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLECEREALS A company packages its cereal in arectangular prism that is 2.5 inches by 7 inches by12 inches. It is considering packaging it in a cylinder-shaped container having a 6-inch diameter and a heightof 7.5 inches. Which uses the least amount of packaging?Surface Area of Rectangular PrismLateral Area Area of BasesS = += += +=Surface Area of CylinderLateral Area Area of BasesS = += += +=Since , theuses less packaging.Check Your Progress CANDY A candy company isdeciding between two types of packaging for its gumballs.The first option is a rectangular prism that is 6 inches by4 inches by 1.5 inches. The second option is a cylinderhaving a radius of 2 inches and a height of 5 inches. Whichoption requires less packaging?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 286. 278 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The or height of eachis called the slant height.The of the of the lateral faces is thelateral area of a pyramid.BUILD YOUR VOCABULARY (pages 264–265)EXAMPLE Surface Area of a PyramidFind the surface area of the square pyramid.8 ft8.9 ftFind the lateral area and the base area.Area of each lateral faceL = 4(1_2)bh Area of 4 triangles= Replace b withand h with .= Simplify.Then find the surface area. The base of the pyramidis a square.S = L + B Write the formula.= L + The area of a square is .= Substitution= Simplify.11–5 Surface Area: Pyramids and ConesMAIN IDEAS• Find the surface areasof pyramids.• Find surface areas ofcones.WRITE ITIf the base of a pyramidis a regular polygon,what do you know aboutits lateral faces?
  • 287. 11–5Glencoe Pre-Algebra 279Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find the surface3 m5.5 marea of the square pyramid.EXAMPLE Surface Area of a ConeFind the surface area10 ft3.5 ftof the cone. Round tothe nearest tenth.S = πr + πr2Formula for surface area ofa coneS = + Replace withand with .S ≈ square feet Simplify.The surface area is about square feet.Check Your Progress Find the surface14.6 cm8.2 cmarea of the cone. Round to the nearest tenth.KEY CONCEPTSurface Area of a ConeThe surface area S of acone with slant heightand radius r is the lateralarea plus the area ofthe base.Write theformulas for the surfacearea of a pyramid andthe surface area of acone in your table.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 288. 280 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Two solids are similar solids if they have the sameand their corresponding measuresare .BUILD YOUR VOCABULARY (page 265)EXAMPLE Identify Similar SolidsDetermine whether the6 m4 m7.5 m12 mpair of solids is similar.Write a proportion comparingradii and heights.Find the cross products.Simplify.The radii and heights are proportional, so thecylinders are similar.Check Your Progress Determine whether the pairof solids is similar.6 in.15 in.2 in.5 in.7.5 in.3 in.11–6 Similar SolidsMAIN IDEAS• Identify similar solids.• Solve problemsinvolving similar solids.
  • 289. 11–6Glencoe Pre-Algebra 281Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find Missing MeasuresThe cylinders shown are similar. Find the radiusof cylinder A.Cylinder B6 cm8 cm4.5 cmCylinder Axradius of cylinder A____radius of cylinder B= _____= Substitute the knownvalues.x = 8( ) Find the crossproducts.= Simplify.x = Divide each side by.The radius of cylinder A is centimeters.Check Your Progress The rectangular prisms below aresimilar. Find the height of prism B.10 in. 15 in.BA4 in.6 in.x in.3 in.
  • 290. 11–6282 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEDOLLHOUSE A small model of a fish tank for Eva’sdollhouse is built on a scale of 1 cm to 5 in. and has avolume of 24 cm3. What is the volume of the actualfish tank?You know the scale factor a_bis and the volume of themodel is . Since the volumes have a ratio of (a_b)3and a_b= , replace a with and b with in (a_b)3.volume of model____volume of fish tank= (a_b)3Write the ratio of volumes.= Replace a withand b with .= Simplify.The volume of the fish tank is times the volumeof the model.=Check Your Progress TRAINS A scale model of a railroadboxcar is built on a scale of 1 inch to 50 inches and has avolume of 72 cubic inches. What is the volume of the actualboxcar?HOMEWORKASSIGNMENTPage(s):Exercises:KEY CONCEPTRatios of Similar SolidsIf two solids are similarwith a scale factor ofa_b, then the surface areashave a ratio of a2_b2andthe volumes have aratio of a3_b3.
  • 291. Glencoe Pre-Algebra 283Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R11STUDY GUIDEVOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 11 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 11, go to:glencoe.comYou can use your completedVocabulary Builder(pages 264–265) to help yousolve the puzzle.11-1Three-Dimensional Figures1. Identify the solid. Name the faces, JMLKedges, and vertices.State whether each sentence is true or false. If false, replacethe underlined word to make a true sentence.2. A ____pyramid is a solid with two bases.3. Intersecting ___lines form three-dimensional figurescalled solids.11-2Volume: Prisms and CylindersFind the volume of each prism or cylinder. Round to thenearest tenth if necessary.4.6 in.4 in. 5.4.8 m5.3 m6.1 m
  • 292. 284 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 11 BRINGING IT ALL TOGETHER11-3Volume: Pyramids, Cones, and SpheresFind the volume of each solid. Round to the nearest tenth ifnecessary.6. cone: diameter 14 ft, height 11 ft7. square pyramid: length 4.5 m, height 6.8 m11-4Surface Area: Prisms and CylindersFind the lateral area and surface area of each solid.Round to the nearest tenth if necessary.8.6.5 ft4 ft 9.6 cm10 cm12 cm8 cm11-5Surface Area: Pyramids and ConesFind the surface area of each solid. Round to the nearesttenth if necessary.10.3 ft in.6 ft3411. 3.2 m.2.4 m.2.4 m.12. square pyramid: base side lengths 5 in., slant height 8 in.
  • 293. Glencoe Pre-Algebra 285Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 11 BRINGING IT ALL TOGETHER11-6Similar SolidsDetermine whether each pair of solids is similar.13.2 m8 m4 m3 m6 m2 m3 m3 m14. 1 ft2.1 ft3 ft6.3 ftFind the missing measure for the pair of similar solids.15. 20 cm50 cm35 cmx80 cm32 cm
  • 294. Checklist286 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R11Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 11 Practice Test onpage 619 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 11 Study Guide and Reviewon pages 615–618 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 11 Practice Test onpage 619.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 11 Foldables.• Then complete the Chapter 11 Study Guide and Review onpages 615–618 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 11 Practice Test onpage 619.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 11.ARE YOU READY FORTHE CHAPTER TEST?
  • 295. Chapter12Glencoe Pre-Algebra 287Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R12 More Statistics and ProbabilityUse the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with a piece of notebook paper.Fold lengthwiseto the holes.Cut along the topline and then cut10 tabs.Label the lessonnumbers andtitles as shown.NOTE-TAKING TIP: When taking notes onstatistics, include your own statistical examples asyou write down concepts and definitions. This willhelp you to better understand statistics.
  • 296. 288 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R12BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 12.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleback-to-backstem-and-leaf plotbox-and-whisker plotcombinationcomposite eventsdependent eventsexperimentalprobabilityFundamentalCounting Principlehistogramindependent eventsinterquartile range[in-tuhr-kwawr-tyl]measures of variation
  • 297. Glencoe Pre-Algebra 289Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 12 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplemutually exclusiveeventsoutcomesoutlierspermutation[puhr-myoo-tay-shuhn]probabilityquartilesrangesample spacesimple eventstem-and-leaf plottheoretical probabilitytree diagramupper and lowerquartiles
  • 298. 290 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.12–1 Stem-and-Leaf PlotsIn a stem-and-leaf plot, numerical data are listed inascending or descending .Stem Leaf5 1 2 3 66 0 57 1 6|0 = 60The place value of the data is used for thestems. The place value forms the leaves.BUILD YOUR VOCABULARY (page 289)EXAMPLE Draw a Stem-and-Leaf PlotFOOD Display the dataPeanuts Harvest, 2001State Amount (lb)Alabama 2400Florida 2800Georgia 2800New Mexico 2400North Carolina 2900Oklahoma 2200South Carolina 2900Texas 2600Virginia 3000in a stem-and-leaf plotwith or without the useof technology.Step 1 Find the leastand the greatestnumber. Thenidentify thegreatest placevalue digit ineach number.2200The least numberhas in theplace.3000The greatest numberhas in theplace.MAIN IDEAS• Display data instem-and-leaf plots.• Interpret data instem-and-leaf plots.ORGANIZE ITWrite a description of astem-and-leaf plot underthe tab for this lesson.
  • 299. 12–1Glencoe Pre-Algebra 291Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Step 2 Draw a vertical line and write the stems andto the left of the line.Step 3 Write the leaves to the right of the line, with thecorresponding stem.Step 4 Rearrange the leaves so they are ordered fromleast to greatest. Then include a key.Stem Leaf2 4 = 2400 lbCheck Your Progress Displaythe speeds 65, 72, 59, 68, 75,70, 68, 64, 67, 69, 72, and 55given in miles per hour in astem-and-leaf plot.EXAMPLE Interpret DataVOTING The stem-and-leaf plot lists the percent ofpeople in each state in 2004 that were born in Mexico,rounded to the nearest whole number.Stem Leaf0 0 0 0 1 1 2 2 3 40 4 5 5 6 6 8 8 81 0 1 4 4 72 1 2 3 83 1 2 3 5 5 9 94 0 1 2 3 3 3 4 6 85 2 6 66 4 67 4 31 = 31%a. Which interval contains the most percentages?Most of the data occurs in the interval.b. What is the greatest percent of people living in oneU.S. state that were born in Mexico?The greatest percent is .What are the mean, themedian, and the mode ofa set data? (Lesson 5–9)REVIEW IT
  • 300. 12–1292 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.c. What is the median percent of people living in oneU.S. state that were born in Mexico?The median in this case is the mean of the middle twonumbers or .Check Your Progress Stem Leaf0 0 51 0 2 2 5 8 8 82 0 0 0 4 4 5 5 5 53 0 0 2 2 2 4 4 5 5 6 64 0 2 4 4 5 5 5 5 8 8 9 95 0 0 2 5 = $25ALLOWANCES Thestem-and-leaf plotlists the amount ofallowance studentsare given each month.a. In which interval do most of the monthly allowances occur?b. What is the greatest monthly allowance given?c. What is the median monthly allowance given?Two sets of data can be using a back-to-backstem-and-leaf plot. The leaves for one set of data are onone side of the and the leaves for the otherset of data are on the other side.BUILD YOUR VOCABULARY (page 288)EXAMPLEAGRICULTURE The yearly California Florida7 1 48 4 2 0 0 2 42 1 32 3 = 23 2 0 = 20million lb million lbproduction of honey inCalifornia and Florida isshown for the years 2000to 2004, in millions of pounds.Source: USDAa. Which state produces more honey?; it produces between and millionpounds per year.
  • 301. 12–1Glencoe Pre-Algebra 293Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. b. Which state has the most varied production? Explain.; the data are more spread out.Check Your Progress EXAMS The exam score earnedon the first test in a particular class is shown for maleand female students.Male Female8 2 69 6 4 7 4 8 8 97 4 2 2 0 8 1 3 4 8 96 5 3 9 2 5 92 8 = 82 7 4 = 74a. Which group of students had the higher test scores?b. Which group of students had more varied test scores?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 302. 294 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Measures of VariationMeasures of variation are used to describe theof the data.The range of a set of data is the betweenthe greatest and the least values of the set.The quartiles are the values that divide a set of data intoequal parts.The of the lower half of a set of data is thelower quartile.The median of the of a set of data is theupper quartile.BUILD YOUR VOCABULARY (page 289)EXAMPLE RangeFind the range of each set of data.a. {$79, $42, $38, $51, $63, $91}The greatest value is , and the least value is .So, the range is - or .b. Stem Leaf3 3 3 5 7 7 84 0 3 3 4 95 4 93 5 = 35The greatest value is and the least value is .So, the range is - or .12–2MAIN IDEAS• Find measures ofvariation.• Use measures ofvariation to interpretand compare data.WRITE ITWhat does the rangedescribe about a set ofdata?
  • 303. 12–2Glencoe Pre-Algebra 295Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find the range of each setof data.a. {14, 37, 82, 45, 24, 10, 75} b. Stem Leaf5 2 3 5 5 96 4 8 97 0 1 8 96 8 = 68EXAMPLE Interquartile Range and OutliersFind the interquartile range and any outliers for{2, 49, 17, 14, 14, 22, 15, 32, 24, 25}.Step 1 List the data from least to greatest. Then findthe median.Step 2 Find the upper and lower quartiles.lower half upper half2 14 14 15 17 22 24 25 32 49median = orThe interquartile range is - or .Step 3 Find the limits for the outliers.Multiply the interquartile× 1.5 = range, , by 1.5.14 - = Subtract from thelower quartile.+ 25 = Add 16.5 to the upper quartile.The limits for the outliers are and .There are no values less than . One value,, is greater than . So, is an outlier.KEY CONCEPTSInterquartile RangeThe interquartile range isthe range of the middlehalf of a set of data. It isthe difference betweenthe upper quartile andthe lower quartile.Outliers Data that aremore than 1.5 times thevalue of the interquartilerange beyond thequartiles.
  • 304. 12–2296 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find the interquartile range foreach set of data.a. {52, 74, 98, 80, 63, 84, 77}b. {12, 18, 25, 31, 23, 19, 16, 22, 28, 32}EXAMPLELAND USE The urban land in certain western andeastern states is listed below as the percent of eachstate’s total land, rounded to the nearest percent.Western States Eastern States1 1 1 1 1 0 0 03 2 2 2 1 1 1 0 3 3 4 5 6 6 85 4 4 0 8 9 9 9 9 9 91 1 3 3 4 4 52 3 6 72 0 = 2% 3 5 2 7 = 27%Source: U.S. Census Bureaua. What is the median percent of urban land use foreach region?The median percent of urban land use for the western statesis . The median percent of urban land use for theeastern states is .b. Compare the range for each set of data.The range for the west is - or ,and the range for the east is - or .The percents of urban land used in the vary more.ORGANIZE ITExplain the differencebetween the range andthe interquartile range ofa set of data under thetab for Lesson 12–2.
  • 305. 12–2Glencoe Pre-Algebra 297Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress FITNESS The hours per weekspent exercising for teenagers and people in theirtwenties are listed in the stem-and-leaf plot.Teens Twenties5 4 2 0 0 0 4 6 7 97 3 1 0 2 2 51 2 0 3 4 5 83 1 = 13 hr 1 5 = 15 hra. What is the median time spent exercising for each group?b. Compare the range for each set of data.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 306. 298 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Box-and-Whisker PlotsA box-and-whisker plot a set of data intousing the median and quartiles. A box isdrawn around the , and whiskersextend from each quartile to the data points.BUILD YOUR VOCABULARY (page 288)EXAMPLE Draw a Box-and-Whisker PlotJOBS The projected number of employees in 2008 in thefastest-growing occupations is shown. Display the datain a box-and-whisker plot.Fastest-Growing JobsOccupationJobs(1000s)OccupationJobs(1000s)Computer Engineer 622 Desktop Publishing 44Computer Support 869 Paralegal/Legal Assistant 220Systems Analyst 1194 Home Health Aide 1179Database Administrator 155 Medical Assistant 398Source: U.S. Census BureauStep 1 Find the and number.Then draw a number line that covers theof the data.Step 2 Find the , the extremes, and the upperand lower . Mark these points above thenumber line.Step 3 Draw a box and the whiskers.12–3MAIN IDEAS• Display data in a box-and-whisker plot.• Interpret data in a box-and-whisker plot.REMEMBER ITThe median doesnot necessarily dividethe box in half. Dataclustered toward onequartile will shift themedian in its direction.0 150 300 450 600 750 900 10501200
  • 307. 12–3Glencoe Pre-Algebra 299Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress TRAVEL The data listed belowrepresents the time, in minutes, required for students to travelfrom home to school each day. Display the data in a box-and-whisker plot.14 32 7 45 18 22 26 9 4 18 150 10 20 30 40 50EXAMPLEWEATHER The box-and-whisker plot below shows theaverage percent of sunny days per year for selectedcities in each state.20 30 40 50 60 70 80 90Source: U.S. Census Bureaua. Half of the selected cities have an average percent ofsunny days under what percent?Half of the selected cities have an average percent of sunnydays under .b. What does the length of the box in the box-and-whisker plot tell about the data?The length of the box is . This tells us that the datavalues are .Check Your Progress CLOTHES The box-and-whiskerplot below shows the average amount spent per monthon clothing.0 50 100 150 200 250 300a. What is the smallest amount spent per month on clothing?b. Half of the monthly expenditures on clothing are under whatamount?ORGANIZE ITWrite a description ofa box-and-whisker plotunder the tab for thislesson.
  • 308. 12–3300 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.c. What does the length of the box-and-whisker plot tell aboutthe data?EXAMPLETREES The average maximum height, in feet, forselected evergreen trees and deciduous trees isdisplayed. How do the heights of evergreen treescompare with the heights of deciduous trees?DeciduousTreesEvergreenTrees0 25 50 75 100Source: ohioline.osu.eduMost deciduous trees range in height between andfeet. However, some are as tall as feet. Mostevergreen trees range in height between and feet.However, some are as tall as feet. Most evergreen treesare than most deciduous trees.Check Your Progress GAS MILEAGE The average gasmileage, in miles per gallon, for selected compact cars andsedans is displayed. How do the gas mileages of compact carscompare with the gas mileages for sedans?0 10 20 30 40 50Compact carsSedansHOMEWORKASSIGNMENTPage(s):Exercises:
  • 309. Glencoe Pre-Algebra 301Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.HistogramsA histogram uses to display numerical data thathave been organized into intervals.BUILD YOUR VOCABULARY (page 288)EXAMPLE Draw a HistogramTOURISM The frequency Overseas TravelersNumber ofVistors(1000s)Tally Frequency0–1000 91001–2000 22001–3000 13001–40004001–5000 25001–6000 1Source: U.S. Department of Commercetable shows the numberof overseas visitors tothe top 15 U.S. cities in2004. Display the datain a histogram.Step 1 Draw and label ahorizontal andvertical axis.Includea .Step 2 Show the intervalsfrom the frequencytable on theaxisand an interval of 1on theaxis.Step 3 For each interval, draw abar whose height is givenby the .12–4MAIN IDEAS• Display data in ahistogram.• Interpret data in ahistogram.WRITE ITWhat type of data does ahistogram display?
  • 310. 12–4302 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Daily CustomersNumber ofCustomersTally Frequency0–49 650–99 12100–149 9150–199 3SHOPPING The frequencytable shows the number ofdaily customers a new grocerystore has during its first 30days in business. Display thedata in a histogram.EXAMPLE Interpret DataELEVATIONS Use thehistogram.a. How many statesHighest Elevations in U.S.Elevation (meters)NumberofStates05101520250–12501251–25002501–37503751–50005001–6250have highest pointswith elevations atleast 3751 meters?Since states have elevations in the 3751–5000 rangeand 2 states have elevations in the range,+ or states have highest points withelevations at least 3751 meters.b. Is it possible to tell the height of the tallest point?No, you can only tell that the highest point is betweenand meters.ORGANIZE ITDescribe how to displaydata in a histogramunder the tab for thislesson.
  • 311. 12–4Glencoe Pre-Algebra 303Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Use this histogram.Drivers’ SpeedsSpeedNumberofDrivers642013570–7980–8960–6950–5940–49a. How many drivers had a speed of at least 70 miles per hour?b. Is it possible to tell the lowest speed driven?EXAMPLEEMPLOYMENT Use the histograms.TradeNumber of Employees(thousands)NumberofStates4045302010051525350–10001001–20002001–30003001–40004001–5000ServicesNumber of Employees(thousands)NumberofStates4045302010051525350–10001001–20002001–30003001–40004001–5000Which business sector has more states with between1,001,000 and 3,000,000 employees?By comparing the graphs, you find that hasmore states with between 1,001,000 and 3,000,000 employees.
  • 312. 12–4304 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Use the histograms that showweekly dining expenses.East CoastCost ($)NumberofPeople642013560–7980–9940–5920–390–19West CoastDining Out ExpensesCost ($)NumberofPeople642013560–7980–9940–5920–390–19Which coast has more people spending at least $60 weekly?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 313. Glencoe Pre-Algebra 305Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Selecting an Appropriate DisplayEXAMPLE Select an Appropriate Displaya. DESSERT Danielle took a survey of her classmates’preferences for desserts. Danielle’s survey revealedthat 46% of her classmates like pie, 32% like icecream, 9% like cake, 7% like candy, and 6% don’t havea preference. How could Danielle best display theresults of her survey? Then make the display with orwithout the use of technology.Awould compare theparts of the data tothe .b. LACROSSE Juan compares the heights of the playerson two lacrosse teams. Juan’s team has the followingplayers with heights, in inches: 61, 60, 58, 59, 57, 67, 58,60, 60, 65, 61, and 61. The rival team has the followingplayers with heights, in inches: 62, 70, 65, 60, 60, 58, 66,63, 61, 57, 67, and 64. What is an appropriate displayfor the data? Make the display.A would condenseand the data.Check Your Progressa. SPORTS Out of 40 athletessurveyed, 12 play basketballand 18 play soccer. Of thoseathletes who play either sport,5 play both sports. Select anappropriate type of display forthis situation. Then make thedisplay with or without theuse of technology.12–5MAIN IDEA• Select an appropriatedisplay for a set ofdata.
  • 314. 12–5306 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.b. TEST SCORES Ms. Slater compares the scores of thestudents in her two math classes. The morning math classearned the following scores on the last test: 98, 82, 76, 94,65, 82, 78, 98, 86, 93, 74, 96, 73, 87, and 81. The afternoonmath class earned the following scores: 86, 93, 75, 89,100, 84, 86, 97, 64, 95, 92, 85, 79, 90, and 85. Select anappropriate type of display for this situation. Then make thedisplay with or without the using technology.EXAMPLEWhich graph would best represent the data if you wantto show relationships among sets of data?A line graph C bar graphB Venn diagram D circle graphYou can eliminate choice becausecompare parts of the data to the whole. Choicedisplays frequencies of data in categories and choiceshows change over time. Even though andshow relationships among similar typesof data, show relationships amongdifferent types of data. So, the answer is .Check Your Progress TEST EXAMPLE Which graphwould best represent the data if you want to show how manytimes each number occurs in the data?A box-and-whisker plot C line graphB line plot D bar graphHOMEWORKASSIGNMENTPage(s):Exercises:
  • 315. Glencoe Pre-Algebra 307Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Misleading GraphsEXAMPLE Misleading GraphsFOOD The graphs show the decrease in the priceof lemons.Price of LemonsGraph AYearDollarperPound1.601.401.201.000.800.60098 99 00 01 02 03 04Price of LemonsGraph BYearDollarperPound1.601.401.201.000.800.60098 00 02 04a. Why do the graphs look different?The scales differ.b. Which graph appears to show a more rapid decreasein the price of lemons after 2002? Explain.Graph B; the slope of the line from tois steeper in Graph B.Check Your Progress The graphs show the increase inattendance at a public elementary school.School AttendanceGraph A10020030040020022001 2003 2004 2005School AttendanceGraph B20040060080020022001 2003 2004 2005StudentsYearStudentsYeara. Why do the graphs look different?12–6MAIN IDEAS• Recognize when graphsare misleading.• Evaluate predictionsand conclusions basedon data analysis.REMEMBER ITCarefully read thelabels and the scaleswhen interpreting agraph.
  • 316. 12–6308 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.b. Which graph appears to show a more rapid increase inattendance between 1997 and 1998? Explain.EXAMPLE Misleading Bar GraphsINTERNET The graph shows Internet Users (%)AgePercent60504020018–24 25–34 35–44 45–54 55–64 65–up10.735.154.853.853.358.7the percent of Internet usein different age groups.According to the graph,more 18- to 24-year-oldsare using the Internetthan the other age groups.Determine whether thisstatement is accurate.Justify your reasoning., the statement is . Even though the18–24 age groups have ,the other age groups andthus .Check Your Progress Daily HighTemperatures80–9950–7920–490–19NumberofDaysTemperature (°F)8070504020100TEMPERATURE The graph showsthe daily high temperatures for theprevious six months. According tothe graph, there were less than twiceas many days 50° to 79° than therewere days 80° to 99°. Determinewhether this statement is accurate.Justify your reasoning.ORGANIZE ITUnder the Lesson 12-6tab, draw an exampleof a misleading graph,and explain why it ismisleadingHOMEWORKASSIGNMENTPage(s):Exercises:
  • 317. Glencoe Pre-Algebra 309Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Simple ProbabilityEXAMPLE Find ProbabilitySuppose a number cube is rolled. What is the probabilityof rolling a 4 or a 5?There are numbers that are a 4 or a 5.There are 6 possible outcomes: 1, 2, 3, 4, 5, and 6.P(4 or 5) = number of favorable outcomes______number of possible outcomes= or orEXAMPLE Find ProbabilitySuppose that two number cubes are rolled. Find theprobability of rolling two identical numbers.Make a table 1 2 3 4 5 61 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)showing thesample spacewhen rolling twonumber cubes.P(two identical numbers) = or or .Check Your Progressa. Suppose a number cube is rolled. What is the probability ofrolling a number that is divisible by 3?b. Suppose that two number cubes are rolled. Find theprobability of rolling two numbers whose sum is 8.12–7MAIN IDEAS• Find the probability ofsimple events.• Use a sample to predictthe actions of a largergroup.KEY CONCEPTProbability Theprobability of an eventis a ratio that comparesthe number of favorableoutcomes to the numberof possible outcomes.
  • 318. 12–7310 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Experimental probability is what actually occurs whenconducting a probability experiment. Theoreticalprobability is what should occur.BUILD YOUR VOCABULARY (pages 288–289)EXAMPLE Find Experimental ProbabilityA coin was tossed 40 times and heads came up 18 times.Find the experimental probability of getting tails forthis experiment.number of times tails occur_____number of possible outcomes= or or .Check Your Progress Brian is shooting baskets with abasketball. He makes 13 shots and misses 9 shots. Determinethe experimental probability of Brian making a shot.EXAMPLE Make a PredictionSPORTS Miss Newman surveyed her class to see whichsport they preferred watching. 44% preferred football,28% basketball, 20% soccer, and 8% tennis. Out of 560students in the entire school, how many would youexpect to say they prefer watching basketball?partwholea_560= 28_100percent100 · a = 560 · 28=a =About students say they prefer watching basketball.Check Your Progress The students in an art class weresurveyed about their favorite color. 32% preferred blue, 29%preferred red, 23% preferred yellow, and 16% preferred green.Out of 450 students in the entire school, how many would youexpect to say they prefer red?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 319. Glencoe Pre-Algebra 311Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Counting OutcomesA tree diagram is a diagram used to show the total numberof possible outcomes.BUILD YOUR VOCABULARY (page 289)EXAMPLE Use a Tree Diagram to Count OutcomesGREETING CARDS A greeting-card maker offers threebirthday greeting in four possible colors as shown in thetable below. Draw a tree diagram to find the number ofcards that can be made from three greeting choices andfour color choices.You can draw a diagram Greeting ColorHumorous BlueTraditional GreenRomantic OrangeRedto find the number ofpossible cards.blue (B) T,Bgreen (G) T,Gorange (O) T,Ored (R) T,Rblue (B) R,Bgreen (G) R,Gorange (O) R,Ored (R) R,RH,BH,GH,OH,RHumorous (H)(T)Romantic (R)Greeting ColorThere are possible cards.12–8MAIN IDEAS• Use tree diagramsor the FundamentalCounting Principle tocount outcomes.• Use the FundamentalCounting Principle tofind the probability ofan event.What is the name forthe set of all possibleoutcomes of a probabilityevent? (Lesson 12-7)REVIEW IT
  • 320. 12–8312 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Use the Fundamental Counting PrincipleCELL PHONES A cell phone company offers 3 paymentplans, 4 styles of phones, and 6 decorative phone wraps.How many phone options are available?Use the Fundamental Counting Principle.The numberof types ofpayment plans timesthe numberof stylesof phonesThe numberof decorativewrapsThe numberof possibleoutcomes.times equals× × =There are possible phone options.Check Your Progressa. An ice cream parlor offers a special on one-scoop sundaeswith one topping. The ice cream parlor has 5 different flavorsof ice cream and three different choices for toppings. Howmany different sundaes can be made?b. A sandwich shop offers 4 choices for bread, 5 choices formeat, and 3 choices for cheese. If a customer can make onechoice from each category, how many different sandwichescan be made?KEY CONCEPTFundamental CountingPrinciple If event M canoccur in m ways and isfollowed by event N thatcan occur in n ways, thenthe event M followedby N can occur in m · nways.Explain how todetermine the number ofpossible outcomes usinga tree diagram and theFundamental CountingPrinciple.
  • 321. 12–8Glencoe Pre-Algebra 313Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find Probabilitiesa. Henry rolls a number cube and tosses a coin. What isthe probability that he will roll a 3 and toss heads?First find the number of outcomes.There are possible outcomes. There is one outcome thathas a 3 and a head.P(3 and head) = number of favorable outcomes______number of possible outcomes=The probability that Henry will roll a 3 and toss headsis .b. What is the probability of winning a raffle where thewinning number is made up of 6 numbers from 1 to 50chosen at random? Assume all numbers are eligibleeach draw.First, find the number of possible outcomes. Use theFundamental Counting Principle.The total number of outcomes is × × ×× × or 15,625,000,000.There is 1 winning number. So, the probability of winningwith 1 ticket is .Check Your Progressa. Bob rolls a number cube b. What is the probability ofand tosses a coin. What winning a lottery where theis the probability that he winning number is made upwill roll an odd number of 5 numbers from 1 to 20and toss tails? chosen at random? Assumeall numbers are eligibleeach draw.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 322. 314 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Permutations and CombinationsAn or listing in which isimportant is called a permutation.BUILD YOUR VOCABULARY (page 289)EXAMPLE Use a PermutationTRAVEL The Reyes family will visit a complex of themeparks during their summer vacation. They have a four-day pass good at one park per day. They can choose fromseven parks.a. How many different ways can they arrange theirvacation schedule?The order in which they visit the parks is important. Thisarrangement is a permutation.parks Choose .P(7, 4) ==choices for the 1st daychoices for the 2nd daychoices for the 3rd daychoices for the 4th dayThere are possible arrangements.b. How many five-digit numbers can be made from thedigits 2, 4, 5, 8, and 9 if each digit is used only once?choices for the 1st digitchoices remain for the 2nd digitchoices remain for the 3rd digitchoices remain for the 4th digitchoice remains for the 5th digitP(5, 5) = =There are numbers that can be made.12–9MAIN IDEAS• Use permutations.• Use combinations.REMEMBER ITThe first factor in apermutation is thenumber of things youare choosing from.
  • 323. 12–9Glencoe Pre-Algebra 315Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progressa. How may ways can five runners be arranged on a three-person relay team?b. How many six-digit numbers can be made from the digits 1,2, 3, 4, 5, and 6 if each digit is used only once?An arrangement or in which is notimportant is called a combination.BUILD YOUR VOCABULARY (page 288)EXAMPLE Use a Combinationa. HATS How many ways can a window dresser choosetwo hats out of a fedora, a bowler, and a sombrero?Since order is not important, this arrangement is acombination.First, list all of the permutations of the types of hats takenat a time. Then cross off arrangements that arethe same as another one.There are ways to choose two hats from threepossible hats.b. PENS How many ways can a customer choose twopens from a purple, orange, green, red, and black pen?Since order is not important, this arrangement is acombination.First, list all of the permutations of the types of pens takenat a time. Then cross off arrangements that arethe same as another one.There are ways to choose two pens from fivepossible pens.ORGANIZE ITExplain the differencebetween a permutationand a combination underthe Lesson 12-8 tab.
  • 324. 12–9316 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress How many ways can two shirts beselected from a display having a red shirt, a blue shirt, a greenshirt, and a white shirt?EXAMPLETENNIS The players listed are Thomas CarlAger JackBrian SethKyle Pedroplaying singles in a tennistournament. If each playerplays every other player once,what is the probability that Kyleplays in the first match?Kyle playing Ager is the same as playing ,so this is a .Find the combination of people taken at a time. Thenfind how many matches involve Kyle.C( , )= or There are ways tochoose people to play.Kyle plays each person once during the tournament. If thereare other people, Kyle is involved in games.So the probability that Kyle plays in the first match is 7_28or 1_4.Check Your ProgressVOLLEYBALL The teams Huskers BroncosGators WavesCougars Red StormWild Cats LionsBadgers Bearcatslisted are playing in a volleyballtournament. If each team playsevery other team once, what isthe probability that the Lionsplay in the first game?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 325. Glencoe Pre-Algebra 317Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Probability of Composite EventsA composite event consists of simpleevents.In independent events, the outcome of one event does notthe outcome of a second event.BUILD YOUR VOCABULARY (page 288)EXAMPLE Probability of Independent EventsGAMES In a popular number cube game, the highestpossible score in a single turn is a roll of five of a kind.After rolling one five of a kind, every other five of a kindyou roll earns 100 points. What is the probability ofrolling two five of a kinds in a row?The events are since each roll does not affectthe outcome of the next roll.There are ways to roll five of a kind.There are 65or ways to roll five dice. So, theprobability of rolling five of a kind on a toss of the numbercubes is or .P(two five of a kind)= P(five of a kind on first roll) · P(five of a kind on second roll)= ·=12–10MAIN IDEAS• Find the probabilityof independent anddependent events.• Find the probabilityof mutually exclusiveevents.KEY CONCEPTProbability of TwoIndependent EventsThe probability of twoindependent events isfound by multiplying theprobability of the firstevent by the probabilityof the second event.
  • 326. 12–10318 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find the probability of rollingdoubles four times in a row when rolling a pair of numbercubes.If the of one event the outcomeof a second event, the events are called dependent events.If two events happen at the ,they are said to be mutually exclusive.BUILD YOUR VOCABULARY (pages 288–289)EXAMPLE Probability of Dependent EventsCLOTHES Charlie’s clothes closet contains 3 blueshirts, 10 white shirts, and 7 striped shirts. What is theprobability that Charlie will reach in and randomlyselect a white shirt followed by a striped shirt?P(white shirt and striped shirt) = ·= orThe probability Charlie will select a white shirt followed by astriped shirt is .Check Your Progress COOKIES A plate has 6 chocolatechip cookies, 4 peanut butter cookies, and 5 sugar cookies.What is the probability of randomly selecting a chocolate chipcookie followed by a sugar cookie?10 of 20 shirtsare white.7 of 19remainingshirts arestriped.KEY CONCEPTProbability of TwoDependent EventsIf two events, A and Bare dependent, thenthe probability ofboth events occurringis the product of theprobability of A and theprobability of B after Aoccurs.
  • 327. 12–10Glencoe Pre-Algebra 319Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Probability of Mutually Exclusive EventsCARDS You draw a card from a standard deck of playingcards. What is the probability that the card will be ablack nine or any heart?The events are because the card cannot be both a black nine and a heart at the same time.P(black nine or heart) = P( )+ P( )= +=The probability that the card will be a black nine or any heartis .Check Your Progress CARDS You draw a card from astandard deck of playing cards. What is the probability that thecard will be a club or a red face card?KEY CONCEPTProbability of TwoMutually ExclusiveEventsThe probability of oneor the other of twomutually exclusiveevents can be found byadding the probabilityof the first event to theprobability of thesecond event.Under the12–10 tab, explain whenyou would use each ofthe three probabilityformulas defined in thislesson.HOMEWORKASSIGNMENTPage(s):Exercises:
  • 328. 320 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R12STUDY GUIDEVOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 12 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 12, go to:glencoe.comYou can use your completedVocabulary Builder(pages 288–289) to help yousolve the puzzle.12-1Stem-and-Leaf PlotsUse the table at the right. Home runs hit by AmericanLeague Leaders in 2002Chavez 34Delgado 33Giambi 41Ordóñez 38Palmeiro 43Rodríguez 57Soriano 39Tejeda 34Thome 52Source: mlb.com1. Display the data set ina stem-and-leaf plot.2. In which interval do most ofthe players fall?12-2Measures of VariationFind the range, interquartile range, and any outliers for eachset of data.3. {42, 22, 59, 82, 15, 37, 71, 24}4. Stem Leaf1 3 72 2 3 83 1 4 6 7 1 3 = 135. Stem Leaf7 0 2 4 7 88 0 2 79 3 6 7 0 = 70
  • 329. Glencoe Pre-Algebra 321Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 12 BRINGING IT ALL TOGETHER12-3Box-and-Whisker PlotsDraw a box-and-whisker plot for each set of data.6. 24, 40, 22, 15, 52, 46, 31, 22, 3610 20 30 40 50 607. 342, 264, 289, 272, 245, 316, 331, 249, 270, 261240 260 280 300 320 340For exercises 8 and 9, use the box-and-whisker plot shown.8. What is the warmestlowest recordedtemperature?9. What percent of the temperatures range from 0°C to -40°C?12-4HistogramsFor Exercises 10–12, use the frequency table shown.10. Display the data in a histogram.11. How many people were surveyed?12. How many people surveyed saw no more than 8 movies?Ϫ60 Ϫ50 Ϫ40 Ϫ30 Ϫ20 Ϫ10Lowest Recorded Temperature (°C) in the USMovies Seen in the Last 12 MonthsMovies Tally Frequency1–4 95–8 159–12 2213–16 5
  • 330. 322 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 12 BRINGING IT ALL TOGETHER12-5Selecting an Appropriate DisplayOLYMPICS The table shows the winning times for the Men’sMarathon during the Summer Olympic Games from 1928 to 2004Year 1928 1932 1936 1948 1952 1956 1960 1964 1968Time (min) 153 152 149 155 143 145 135 132 140Year 1972 1976 1980 1984 1988 1992 1996 2000 2004Time (min) 132 130 131 129 131 133 133 130 131Source: olympic.org13. Which graph best represents the data if you want to show changeover a period of time?12-6Misleading Statistics14. Which graph gives the impression that the top-selling 2003album sold far more units than any other in the top five?2003 Top Five Selling AlbumsGraph AA B C D EUnitsSold(millions)Album765432003 Top Five Selling AlbumsGraph BA B C D EUnitsSold(millions)Album765432112-7Simple Probability15. A box contains 7 black, 10 blue, 5 green, and8 red pens. One pen is selected at random.Find the probability that it is not green.16. Refer to the graph. Out of a group Leisure-time favorites12%19%29%Family timeTV watchingReadingSource: USA Todayof 3500 people, how many wouldyou expect to say that family timeis their favorite leisure-time activity?
  • 331. Glencoe Pre-Algebra 323Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 12 BRINGING IT ALL TOGETHER12-8Counting OutcomesFind the number of possible outcomes for each situation.19. One part of a test has 7 true-false questions.20. A bicycle is made with a choice of two seats, three frames, and fivecolors.21. What is the probability of rolling exactly one 6 when two numbercubes are rolled?12-9Permutations and CombinationsTell whether each situation is a permutation or combination.Then solve.22. How many ways can you choose 4 books from 15 on a shelf?23. How many 4-digit numbers can you write using the digits 1, 2,3, and 4 exactly once in each number?12-10Probability of Compound EventsFor Exercises 24 and 25, pens are drawn from a bag containing6 red, 8 black, and 4 blue pens. Label each situation as independent,dependent, or mutually exclusive events. Then find each probability.24. drawing a red pen, which is replaced, followed by a blue pen25. drawing a black pen or a blue pen26. What is P(A and B) if P(A) = 1_6, P(B) = 2_3, P(B following A) = 4_5,and A and B are dependent?
  • 332. Checklist324 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureC H A P T E R12Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 12 Practice Test onpage 695 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 12 Study Guide and Reviewon pages 690–694 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 12 Practice Test onpage 695.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 12 Foldables.• Then complete the Chapter 12 Study Guide and Review onpages 690–694 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 12 Practice Test onpage 695.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 12.
  • 333. Chapter13Glencoe Pre-Algebra 325Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R13Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 11" × 17" paper.Fold the shortsides towardthe middle.Fold the topto the bottom.Open. Cut alongthe second foldto make four tabs.Label each ofϫϩ ϪFunctionsthe tabs as shown.NOTE-TAKING TIP: When taking notes, writeclean and concise explanations. Someone who isunfamiliar with the math concepts should be ableto read your explanations and learn from them.Polynomials and Nonlinear Functions
  • 334. 326 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R13BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 13.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplebinomial[by-NOH-mee-uhl]cubic function[KYOO-bihk]degree
  • 335. Glencoe Pre-Algebra 327Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 13 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplenonlinear functionpolynomial[PAHL-uh-NOH-mee-uhl]quadratic function[kwah-DRAT-ink]trinomial[try-NOH-mee-uhl]
  • 336. 328 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.13–1An that contains one or moreis called a polynomial.A polynomial with is called a binomial,and a polynomial with is called atrinomial.The degree of a monomial is the of theof its variables.BUILD YOUR VOCABULARY (pages 326–327)EXAMPLE Classify PolynomialsDetermine whether each expression is a polynomial. If itis, classify it as a monomial, binomial, or trinomial.a. -2_xThe expression a polynomial because -2_x has avariable in the .b. x2- 12This a polynomial because it is the differenceof two . There are two terms, so it is a.Check Your Progress Determine whether eachexpression is a polynomial. If it is, classify it as amonomial, binomial, or trinomial.a. x3+ 3x2+ 8b. √x + 5MAIN IDEAS• Identify and classifypolynomials.• Find the degree of apolynomial.PolynomialsREMEMBER ITWhen classifyingpolynomials, first writeall expressions insimplest form.
  • 337. 13–1Glencoe Pre-Algebra 329Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Degree of a Monomial or PolynomialFind the degree of each polynomial.a. -10w4The variable w has degree , so the degree of-10w4is .b. 8x3y7z x3has a degree of , y7has a degree of ,and z has a degree of . The degree of8x3y7z is + + or .c. a2b5- 4term degreea2b54The greatest degree is .So, the degree of thepolynomial is .d. 2x2y2+ 7xy6term degree2x2y27xy6The greatest degree is .So, the degree of thepolynomial is .Check Your Progress Find the degree of eachpolynomial.a. 5m3b. -3ab2c5c. x3y3+ 4x4y d. -3mn4- 7HOMEWORKASSIGNMENTPage(s):Exercises:
  • 338. 330 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Add Polynomialsa. Find (9w - 4) + (w + 5).METHOD 1 Add vertically.9w - 4_______(+) w + 5 Align like terms.Add.METHOD 2 Add horizontally.(9w - 4) + (w + 5)= + Associative andCommutative Properties=The sum is .b. Find (6x2- 3x + 1) + (-x2+ x - 1).METHOD 1 Add vertically.6x2- 3x + 1__________(+) -x2+ x - 1 Align like terms.Add.METHOD 2 Add horizontally.(6x2- 3x + 1) + (-x2+ x - 1)= + +Write theexpression.Group liketerms.= Simplify.The sum is .MAIN IDEAS• Add polynomials.13–2ORGANIZE ITWrite an example ofadding two polynomialswith two or three termseach under the “+” tab.ϫϩ ϪFunctionsAdding Polynomials
  • 339. 13–2Glencoe Pre-Algebra 331Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find each sum.a. (5b + 2) + (3b - 6)b. (3m2- 5m + 9) + (-5m2+ 3m - 7)EXAMPLEGEOMETRY The length of a rectangle is 3x 2+ 2x - 5 unitsand the width is 8x - 1 units.a. Find the perimeter.P =Formula for theperimeter of arectangle.P = 2 + 2Replace withandw with .P = Distributive PropertyP = Simplify.The perimeter is .b. Find the perimeter of the rectangle if x = 3.P = Write the equation for theperimeter.P = 6( )2+ 20( )- 12 Replace x with .P = Simplify.The perimeter of the rectangle is when x = 3.Check Your Progress GEOMETRY The width of arectangle is 2w2+ 3w + 4 units and the width is 6w - 3 units.Find the perimeter. Then find the length when w = 5.Identify the like terms inthe expression6x + 5 + 3y - 4 - 2x.(Lesson 3–2)REVIEW ITHOMEWORKASSIGNMENTPage(s):Exercises:
  • 340. 332 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Subtract Polynomialsa. Find (7a + 4) - (9a + 2).7a + 4______(-) 9a + 2 Align like terms.Subtract.b. Find (8b2+ 6) - (3b2+ 6b + 1).8b2+ 6_________(-) 3b2+ 6b + 1 Align like terms.Subtract.Check Your Progress Find each difference.a. (2x + 9) - (5x - 4) b. (5k2+ 3k - 4) - (2k2+ 1)EXAMPLE Subtract Using the Additive Inversea. Find (4x - 8) - (3x + 9).The additive inverse of 3x + 9 is (-1)(3x - 9) or .(4x - 8) - (3x - 9)= (4x - 8) + Add the additive inverse.= Group like terms.= Simplify.b. Find (7ab + 2b2) - (3a2+ ab + b2).The additive inverse of 3a2+ ab + b2is(-1)(3a2+ ab + b2) or .13–3 Subtracting PolynomialsORGANIZE ITWrite an exampleof subtracting twopolynomials with two orthree terms each underthe “-” tab.ϫϩ ϪFunctionsMAIN IDEAS• Subtract polynomials.
  • 341. 13–3Glencoe Pre-Algebra 333Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Align the like terms and add the additive inverse.7ab + 2b27ab + 2b2__________(-) 3a2+ ab + b2(+)___________Check Your Progress Find each difference.a. (8c - 3) - (-2c + 4) b. (-3xy - 4y2) - (2x2- 8xy + 2y2)EXAMPLEALLOWANCE Nguyen receives a monthly allowance fromhis parents of 2x + 5. Susan receives an allowance ofx + 6. For both, x represents the number of chores eachcompleted. When x ≥ 2, Nguyen earns more than Susan.How much more does he earn?difference in allowance when x ≥ 2= allowance - allowance= Substitution= Add the additive inverse.= Group like terms.= Simplify.Nguyen earns in allowance when x ≥ 2.Check Your Progress PROFIT The ABC Company’s costsare given by 3x + 200 where x = the number of items produced.The revenue is given by 5x. Find the profit, which is thedifference between the revenue and the cost.HOMEWORKASSIGNMENTPage(s):Exercises:WRITE ITExplain when youmight use a placeholderwhen subtracting twopolynomials.
  • 342. 334 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Product of a Monomial and a Polynomiala. Find -8(3x + 2).-8(3x + 2) = + Distributive Property= Simplify.b. Find (6x - 1)(-2x).(6x - 1)(-2x) = 6x - 1 Distributive Property= Simplify.Check Your Progress Find each product.a. 3(-5m - 2)b. (4p - 8)(-3p)EXAMPLE Product of a Monomial and a PolynomialFind 4b(-a2+ 5ab + 2b2).4b(-a2+ 5ab + 2b2)= Distributive Property= Simplify.Check Your Progress Find -3x(2x2- 4xy + 3y2).MAIN IDEAS• Multiply a polynomialby a monomial.ORGANIZE ITWrite an example ofmultiplying a monomialby a polynomial withtwo or three termsunder the “×” tabϫϩ ϪFunctionsMultiplying a Polynomial by a Monomial13–4
  • 343. 13–4Glencoe Pre-Algebra 335Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLETEST EXAMPLE The length of a dog run is 4 feet morethan three times its width. The perimeter of the dog runis 56 feet. What are the dimensions of the dog run?A 8 ft by 20 ft C 3 ft by 56 ftB 10 ft by 12 ft D 6 ft by 22 ftLet w represent the width of the dog run. Thenrepresents the length. Write an equation.Perimeter equals twice the sum of thelength and width.P = 2 ( + w)P = 2( + w) Write the equation.56 = P = 56, =56 = Combine like terms.56 = Distributive Property= Subtract from each side.= Divide each side by .The width of the dog run is and the length isor . The answer is .Check Your Progress TEST EXAMPLE The length of agarden is four more than twice its width. The perimeter of thegarden is 44 feet. What are the dimensions of the garden?A 6 ft by 12 ft C 12 ft by 16 ftB 6 ft by 16 ft D 8 ft by 12 ftWRITE ITHow do you determinethe degree of apolynomial?HOMEWORKASSIGNMENTPage(s):Exercises:
  • 344. 336 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.13–5 Linear and Nonlinear FunctionsA nonlinear function is a function whose graph is aline.BUILD YOUR VOCABULARY (page 327)EXAMPLE Identify Functions Using GraphsDetermine whether each graph represents a linear ornonlinear function.a. yO xThe graph is a line,so it represents afunction.b. yO xThe graph is a , not aline, so it representsa function.Check Your Progress Determine whether each graphrepresents a linear or nonlinear function.a. yO xb. yO xMAIN IDEAS• Determine whethera function is linear ornonlinear.Why is the equationy = 2x2+ 3 a function?(Lesson 7–1)REVIEW IT
  • 345. 13–5Glencoe Pre-Algebra 337Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Identify Functions Using EquationsDetermine whether each equation represents a linear ornonlinear function.a. y = -5x - 4This equation represents a function because it iswritten in the form .b. y = 2x2+ 3This equation is because x is raised to theand the equation cannot be written inthe form .Check Your Progress Determine whether eachequation represents a linear or nonlinear function.a. y = 2_x + 6b. 2x + y = 4EXAMPLE Identify Functions Using TablesDetermine whether each table represents a linear ornonlinear function.a.x y2 254 176 98 1+ 2+ 2+ 2- 8- 8- 8b.x y5 28 411 814 16+ 3+ 3+ 3+ 2+ 4+ 8As x increases by , As x increases by ,y increases by aamount each time. So, this isa function.y decreases by .So, this is afunction.ORGANIZE ITWrite an example of alinear function and anexample of a nonlinearfunction under theFunctions tab.ϫϩ ϪFunctions
  • 346. 13–5338 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Determine whether each tablerepresents a linear or nonlinear function.a.x y3 105 117 139 16b.x y10 49 78 107 13EXAMPLE Describe a Linear FunctionWhich of the following is a linear function?a. y =1_x+ 3The independent variable has an exponent of .b. y = -9xThe independent variable has an exponent of .c. y = x(x - 5)The independent variable has an exponent of .d. 32 = 2x2+ 3yThe independent variable has an exponent of .The linear function is .Check Your Progress Which of the following is a linearfunction?a. y = x2+ 3b. xy = -5c. 5x - y = 1d. y = 1_4x3HOMEWORKASSIGNMENTPage(s):Exercises:
  • 347. Glencoe Pre-Algebra 339Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 13–6 Graphing Quadratic and Cubic FunctionsEXAMPLE Graph Quadratic Functionsa. Graph y = -2x2.Make a table of values, plot the , andconnect the points with a .x -2x2(x, y)-1.5 -2(-1.5)2= 4.5-1 -2(-1)2= (-1, -2)0.5 -2(0.5)2= (-0.5)-0.5 -2(-0.5)2= (-0.5, -0.5)0 -2(0)2=1 -2(1)2= (1, -2)1.5 -2(1.5)2= -4.5Oxyb. Graph y = -x2- 3.Make a table of values, plot the ordered pairs, and connectthe points with a curve.x -x2- 3 (x, y)-2 -(-2)2- 3 =-1 -(-1)2- 3 = (-1, -4)0 -(0)2- 3 = -31 -(1)2- 3 = -42 -(2)2- 3 = (2, -7)O xyMAIN IDEAS• Graph quadraticfunctions.• Graph cubic functions.REMEMBER ITWhen substitutingvalues for x in a function,consider using decimalvalues if necessary to findpoints that are closertogether.
  • 348. 13–6340 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Graph each function.a. y = -x2Oxyb. y = 3x2- 8OxyEXAMPLE Graph Cubic FunctionsGraph y = -x3_2.xyOx -x3_2(x, y)-2 -(-2)3_2= 4 (-2, 4)-1 -(-1)3_2= 0.50 -(0)3_2=1 -(1)3_2= -0.5 (1, -0.5)2 -(2)3_2=ORGANIZE ITUnder the Functions tab,write an example of aquadratic function andan example of a cubicfunction. Then grapheach function.ϫϩ ϪFunctions
  • 349. 13–6Glencoe Pre-Algebra 341Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Graph y = x3- 3.xyOHOMEWORKASSIGNMENTPage(s):Exercises:
  • 350. 342 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R13STUDY GUIDEVOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 13 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 13, go to:glencoe.comYou can use your completedVocabulary Builder(pages 326–327) to help yousolve the puzzle.13-1PolynomialsDetermine whether each expression is a polynomial. If it is,classify it as a monomial, binomial, or trinomial.1. 5m - 3 2. 5_c + c23. 7 - 3y - 4y3Find the degree of each polynomial.4. pq 5. 144 6. x4+ x - 513-2Adding PolynomialsFind each sum.7. (4y - 17) + (2y + 3) 8. (9b2+ 4b - 15) + (-3b2+ 8)13-3Subtracting PolynomialsFind each difference.9. (6x + 11y) - (10x - 2y) 10. x2+ 9xy - 12y__________(-) 2xy - y
  • 351. Glencoe Pre-Algebra 343Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 13 BRINGING IT ALL TOGETHER13-4Multiplying a Polynomial by a MonomialFind each product.11. 4(3q - 2) 12. (3y + 8)x 13. 7a(2a2- 3b)13-5Linear and Nonlinear FunctionsDetermine whether each graph, equation, or table representsa linear or nonlinear function. Explain.14. yO x15. yO x16. y = 5_x + 317.x y-3 9-1 10 01 118.x y-12 -3-10 -2-8 -1-6 013-6Graphing Quadratic and Cubic FunctionsGraph each function.19. y = -2x2+ 4 20. y = 0.5x3- 2yO xyO x
  • 352. Checklist344 Glencoe Pre-AlgebraCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Student Signature Parent/Guardian SignatureTeacher SignatureVisit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 13.C H A P T E R13Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 13 Practice Test onpage 735 of your textbook as a final check.I used my Foldable or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 13 Study Guide and Reviewon pages 732–734 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 13 Practice Test onpage 735.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 13 Foldable.• Then complete the Chapter 13 Study Guide and Review onpages 732–734 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 13 Practice Test onpage 735.