Like this document? Why not share!

- Math foldables ebook by The Math Magazine 1337 views
- Notebook foldables ebook by The Math Magazine 850 views
- Origami math ebook 48pgs by The Math Magazine 1494 views
- Foldables by Jennifer Evans 5025 views
- Math connects course 2 notebook fol... by The Math Magazine 2089 views
- 2013 09 sp_maths_sa2_04_solved by Yagya Malik 2225 views

1,924

Published on

Interactive Notebook Foldables, Organizers and Templates

License: CC Attribution-ShareAlike License

No Downloads

Total Views

1,924

On Slideshare

0

From Embeds

0

Number of Embeds

2

Shares

0

Downloads

0

Comments

0

Likes

6

No embeds

No notes for slide

- 1. Contributing AuthorDinah ZikeConsultantDouglas Fisher, Ph.D.Professor of Language and Literacy EducationSan Diego State UniversitySan Diego, CA®
- 2. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may bereproduced or distributed in any form or by any means, or stored in a database or retrieval system, withoutthe prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storageor transmission, or broadcast for distance learning.Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027Printed in the United States of America.ISBN: 978-0-07-890238-3 Math Connects: Concepts, Skills, and Problem Solving, Course 3MHID: 0-07-890238-X Noteables™: Interactive Study Notebook with Foldables®1 2 3 4 5 6 7 8 9 10 009 17 16 15 14 13 12 11 10 09 08
- 3. Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ContentsFoldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . . . 21-1 A Plan for Problem Solving. . . . . . . . . . . 41-2 Variables, Expressions, and Properties . . 61-3 Integers and Absolute Value . . . . . . . . . 91-4 Adding Integers. . . . . . . . . . . . . . . . . . . 121-5 Subtracting Integers . . . . . . . . . . . . . . . 161-6 Multiplying and Dividing Integers. . . . . 181-7 Writing Equations . . . . . . . . . . . . . . . . . 211-8 Problem-Solving Investigation:Work Backward . . . . . . . . . . . . . . . . . . . 231-9 Solving Addition and SubtractionEquations . . . . . . . . . . . . . . . . . . . . . . . 241-10 Solving Multiplication andDivision Equations. . . . . . . . . . . . . . . . . 26Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . . 332-1 Rational Numbers . . . . . . . . . . . . . . . . . 352-2 Comparing and OrderingRational Numbers . . . . . . . . . . . . . . . . . 382-3 Multiplying Positive andNegative Fractions. . . . . . . . . . . . . . . . . 402-4 Dividing Positive and NegativeFractions. . . . . . . . . . . . . . . . . . . . . . . . . 422-5 Adding and SubtractingLike Fractions. . . . . . . . . . . . . . . . . . . . . 452-6 Adding and Subtracting UnlikeFractions. . . . . . . . . . . . . . . . . . . . . . . . . 472-7 Solving Equations with RationalNumbers. . . . . . . . . . . . . . . . . . . . . . . . . 492-8 Problem-Solving Investigation:Look for a Pattern . . . . . . . . . . . . . . . . 512-9 Powers and Exponents . . . . . . . . . . . . . 522-10 Scientific Notation. . . . . . . . . . . . . . . . . 54Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . . 623-1 Square Roots . . . . . . . . . . . . . . . . . . . . . 643-2 Estimating Square Roots. . . . . . . . . . . . 663-3 Problem-Solving Investigation:Use a Venn Diagram . . . . . . . . . . . . . . . 683-4 The Real Number System . . . . . . . . . . . 693-5 The Pythagorean Theorem . . . . . . . . . . 723-6 Using the Pythagorean Theorem . . . . . 753-7 Geometry: Distance on theCoordinate Plane. . . . . . . . . . . . . . . . . . 77Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . . 854-1 Ratios and Rates . . . . . . . . . . . . . . . . . . 874-2 Proportional and NonproportionalRelationships . . . . . . . . . . . . . . . . . . . . . 894-3 Rate of Change . . . . . . . . . . . . . . . . . . . 914-4 Constant Rate of Change . . . . . . . . . . . 944-5 Solving Proportions . . . . . . . . . . . . . . . 974-6 Problem-solving Investigation:Draw a Diagram . . . . . . . . . . . . . . . . . . 994-7 Similar Polygons . . . . . . . . . . . . . . . . . 1004-8 Dilations. . . . . . . . . . . . . . . . . . . . . . . . 1034-9 Indirect Measurement. . . . . . . . . . . . . 1054-10 Scale Drawings and Models . . . . . . . . 108Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 110Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 1165-1 Ratios and Percents . . . . . . . . . . . . . . . 1185-2 Comparing Fractions, Decimals,and Percents . . . . . . . . . . . . . . . . . . . . 1205-3 Algebra: The Percent Proportion . . . . 1235-4 Finding Percents Mentally . . . . . . . . . 1255-5 Problem-Solving Investigation:Reasonable Answers . . . . . . . . . . . . . . 1275-6 Percent and Estimation. . . . . . . . . . . . 1285-7 Algebra: The Percent Equation . . . . . 1315-8 Percent of Change. . . . . . . . . . . . . . . . 1335-9 Simple Interest. . . . . . . . . . . . . . . . . . . 137Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 139Foldables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 1446-1 Line and Angle Relationships . . . . . . . 1466-2 Problem-Solving Investigation:Use Logical Reasoning. . . . . . . . . . . . . 1496-3 Polygons and Angles. . . . . . . . . . . . . . 1506-4 Congruent Polygons . . . . . . . . . . . . . . 1526-5 Symmetry . . . . . . . . . . . . . . . . . . . . . . . 1546-6 Reflections . . . . . . . . . . . . . . . . . . . . . . 1566-7 Translations . . . . . . . . . . . . . . . . . . . . . 159Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 162Math Connects, Course 3 iii
- 4. Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ContentsFoldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 1677-1 Circumference and Area of Circles. . . 1697-2 Problem-Solving Investigation:Solve a Simpler Problem . . . . . . . . . . . 1717-3 Area of Composite Figures . . . . . . . . . 1727-4 Three-Dimensional Figures . . . . . . . . . 1747-5 Volume of Prisms and Cylinders . . . . . 1777-6 Volume of Pyramids and Cones . . . . . 1807-7 Surface Area of Prisms andCylinders. . . . . . . . . . . . . . . . . . . . . . . . 1827-8 Surface Area of Pyramids . . . . . . . . . . 1857-9 Similar Solids . . . . . . . . . . . . . . . . . . . . 187Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 190Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 1968-1 Simplifying Algebraic Expressions . . . 1978-2 Solving Two-Step Equations . . . . . . . . 2008-3 Writing Two-Step Equations. . . . . . . . 2038-4 Solving Equations with Variableson Each Side. . . . . . . . . . . . . . . . . . . . . 2068-5 Problem-Solving Investigation:Guess and Check . . . . . . . . . . . . . . . . . 2088-6 Inequalities . . . . . . . . . . . . . . . . . . . . . 2098-7 Solving Inequalities by Addingor Subtracting . . . . . . . . . . . . . . . . . . . 2128-8 Solving Inequalities by Multiplyingor Dividing . . . . . . . . . . . . . . . . . . . . . . 214Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 216Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 2219-1 Sequences . . . . . . . . . . . . . . . . . . . . . . 2239-2 Functions . . . . . . . . . . . . . . . . . . . . . . . 2269-3 Representing Linear Functions . . . . . . 2299-4 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . 2339-5 Direct Variation . . . . . . . . . . . . . . . . . . 2369-6 Slope-Intercept Form . . . . . . . . . . . . . 2399-7 Systems of Equations . . . . . . . . . . . . . 2419-8 Problem-Solving Investigation:Use a Graph . . . . . . . . . . . . . . . . . . . . . 2449-9 Scatter Plots . . . . . . . . . . . . . . . . . . . . . 245Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 248Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 25410-1 Linear and Nonlinear Functions . . . . . 25510-2 Graphing Quadratic Functions . . . . . . 25810-3 Problem-Solving Investigation:Make a Model . . . . . . . . . . . . . . . . . . . 26010-4 Graphing Cubic Functions. . . . . . . . . . 26110-5 Multiplying Monomials. . . . . . . . . . . . 26410-6 Dividing Monomials . . . . . . . . . . . . . . 26610-7 Powers of Monomials . . . . . . . . . . . . . 26910-8 Roots of Monomials . . . . . . . . . . . . . . 271Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 273Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 27811-1 Problem-Solving Investigation:Make a Table . . . . . . . . . . . . . . . . . . . . 28011-2 Histograms. . . . . . . . . . . . . . . . . . . . . . 28111-3 Circle Graphs . . . . . . . . . . . . . . . . . . . . 28411-4 Measures of Central Tendencyand Range . . . . . . . . . . . . . . . . . . . . . . 28811-5 Measures of Variation. . . . . . . . . . . . . 29111-6 Box-and-Whisker Plots . . . . . . . . . . . . 29411-7 Stem-and-Leaf Plots . . . . . . . . . . . . . . 29711-8 Select an Appropriate Display . . . . . . 301Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 303Foldables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307Vocabulary Builder. . . . . . . . . . . . . . . . . . . . . 30812-1 Counting Outcomes . . . . . . . . . . . . . . 31012-2 Probability of Compound Events . . . . 31312-3 Experimental andTheoretical Probability . . . . . . . . . . . . 31612-4 Problem-Solving Investigation:Act It Out . . . . . . . . . . . . . . . . . . . . . . . 32012-5 Using Sampling to Predict. . . . . . . . . . 321Study Guide . . . . . . . . . . . . . . . . . . . . . . . . . . 324iv Math Connects, Course 3
- 5. Math Connects, Course 3 vCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Organizing Your FoldablesHave students make this Foldable to help themorganize and store their chapter Foldables.Begin with one sheet 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.Reading and Taking Notes As you read and study each chapter, recordnotes in your chapter Foldable. Then store your chapter Foldables insidethis Foldable organizer.
- 6. ®Chapter3Math Connects, Course 3 61Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3 Real Numbers andthe Pythagorean TheoremUse 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 two sheets of 81_2" by 11" notebookpaper.Fold one in half fromtop to bottom. Cutalong fold from edgesto margin.Fold the other sheetin half from topto bottom. Cut alongfold between margins.Insert ﬁrst sheetthrough secondsheet and align folds.Label each page with Chapter 3Real Numbersand thePythagoreanTheorema lesson number and title.NOTE-TAKING TIP: When you take notes, clarifyterms, record concepts, and write examples foreach lesson. You may also want to list ways inwhich the new concepts can be used in yourdaily life.061-083_CH03_881084.indd 61 11/19/07 12:58:46 PM62 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3BUILD YOUR VOCABULARYThis 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 orExampleabscissa[ab-SIH-suh]conversecoordinate planehypotenuseirrational numberlegsordered pairordinate[OR-din-it]originperfect square061-083_CH03_881084.indd 62 11/19/07 12:58:47 PMvi Math Connects, Course 3This note-taking guide is designed to help you succeed inMath Connects, Course 3. Each chapter includes:The Chapter Openercontains instructions andillustrations on how tomake a Foldable that willhelp you to organizeyour notes.Copyright©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.
- 7. Math Connects, Course 3 75Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–6 Using the Pythagorean TheoremEXAMPLE Use the Pythagorean TheoremRAMPS A ramp to a newlyconstructed building mustbe built according to theguidelines stated in theAmericans with DisabilitiesAct. If the ramp is 24.1feet long and the top ofthe ramp is 2 feet off theground, how far is the bottomof the ramp from the baseof the building?Notice the problem involves a right triangle. Use thePythagorean Theorem.24.12= a2+ 22 Replace c with 24.1 andb with 2.= a2+ Evaluate 24.12and 22.- = a2= - Subtract from each side.= a2Simplify.= a Deﬁnition of square root≈ a Simplify.The end of the ramp is about from the base ofthe building.Check Your Progress If a truck ramp is 32 feet long andthe top of the ramp is 10 feet off the ground, how far is the endof the ramp from the truck?MAIN IDEA• Solve problems usingthe PythagoreanTheorem.ORGANIZE ITOn Lesson 3-6 of yourFoldable, explain thePythagorean Theorem inyour own words and givean example of how itmight be used in areal-life situation.Chapter 3Real Numbersand thePythagoreanTheorem®061-083_CH03_881084.indd 75 11/19/07 12:58:52 PMMath Connects, Course 3 viiFPO - will bereplaced withnew page 65, ifneeded.3–1Math Connects, Course 3 65Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Find each square root.a. √64b. - 25_144c. ±√2.25EXAMPLE Use an Equation to Solve a ProblemMUSIC The art work of the square picture in a compactdisc case is approximately 14,161 mm2 in area. Find thelength of each side of the square.The area is equal to the square of the length of a side.Let A = the area and let s = the length of the side A = s214,161 = s2Write the equation.= √s2Take the square root of each side.The length of a side of a compact disc case is aboutmillimeters since distance cannot be negative.Check Your Progress A piece of art is a square picture thatis approximately 11,025 square inches in area. Find the lengthof each side of the square picture.ORGANIZE ITOn Lesson 3-1 of yourFoldable, explain howto ﬁnd the square rootof a number and give anexample.Chapter 3Real Numbersand thePythagoreanTheorem®HOMEWORKASSIGNMENTPage(s):Exercises:061-083_CH03_881084.indd 65 11/19/07 12:58:47 PMCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Examples parallel theexamples in your textbook.Check Your Progressexercises allow you tosolve similar exerciseson your own.Lessons cover the content ofthe lessons in your textbook.As your teacher discusses eachexample, follow along andcomplete the fill-in boxes.Take notes as appropriate.Foldables featurereminds you totake notes in yourFoldable.80 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R3STUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD 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 toglencoe.comYou can use your completedVocabulary Builder(pages 62–63) to help you solvethe puzzle.3-1Square RootsComplete each sentence.1. The principle square root is the square rootof a number.2. To solve an equation in which one side of the square is a squaredterm, you can take the of each side of theequation.Find each square root.3. √900 4. -√36_495. -√625 6. √25_1213-2Estimating Square RootsDetermine between which two consecutive whole numberseach value is located.7. √23 8. √599. √27 10. √18061-083_CH03_881084.indd 80 11/19/07 12:58:54 PMBringing It All TogetherStudy Guide reviewsthe main ideas and keyconcepts from each lesson.
- 8. Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.NOTE-TAKING TIPSviii Math Connects, Course 3Your notes are a reminder of what you learned in class. Taking good notes canhelp students 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.
- 9. ®Chapter1Math Connects, Course 3 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 plain piece of 11" × 17" paper.Fold the paper in sixths lengthwiseOpen and Fold a 4" tab along theshort side. Then fold the rest in half.Label Draw lines along the folds and labelas shown.NOTE-TAKING TIP: When taking notes, it may behelpful to explain each idea in words and give oneor more examples.Algebra: Integers
- 10. 2 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R1BUILD YOUR VOCABULARYThis 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 orExampleabsolute valueadditive inversealgebraalgebraic expression[AL-juh-BRAY-ihk]conjecturecoordinatecounterexampledeﬁne a variableequation[ih-KWAY-zhuhn]evaluateinequality
- 11. Math Connects, Course 3 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDeﬁnitionDescription orExampleinteger[IHN-tih-juhr]inverse operationsnegative numbernumerical expressionoppositesorder of operationspositive numberpowerspropertysolutionsolvevariable
- 12. 4 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–1EXAMPLES Use the Four-Step PlanHOME IMPROVEMENT The Vorhees family plans to paintthe walls in their family room. They need to cover 512square feet with two coats of paint. If a 1-gallon can ofpaint covers 220 square feet, how many 1-gallon cans ofpaint do they need?UNDERSTAND Since they will be using coats of paint,we must the area to be painted.PLAN They will be covering × squarefeet or square feet. Next, divideby to determine how manycans of paint are needed.SOLVE ÷ =CHECK Since they will purchase a whole numberof cans of paint, round to .They will need to purchase cans of paint.Check Your Progress Jocelyn plans to paint her bedroom.She needs to cover 400 square feet with three coats of paint.If a 1-gallon can of paint covers 350 square feet, how many1-gallon cans of paint does she need?Some problem solving strategies require you to make anor conjecture.BUILD YOUR VOCABULARY (pages 2–3)MAIN IDEA• Solve problems usingthe four-step plan.ORGANIZE ITSummarize the four-stepproblem-solving planin words and symbols.Include an example ofhow you have used thisplan to solve a problem.®A Plan for Problem Solving
- 13. 1–1Math Connects, Course 3 5Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. GEOGRAPHY Study the table. The ﬁve largest states intotal area, which includes land and water, are shown.Of the ﬁve states shown, which one has the smallestarea of water?Largest States in AreaState Land Area (mi2) Total Area (mi2)Alaska 570,374 615,230Texas 261,914 267,277California 155,973 158,869Montana 145,556 147,046New Mexico 121,364 121,598Source: U.S. Census BureauUNDERSTAND What do you know? You are given the total areaand the land area for ﬁve states. What are youtrying to ﬁnd? You need to ﬁnd the water area.PLAN To determine the water area,the from thefor each state.SOLVE Alaska = 615,230 - 570,374 =Texas = 267,277 - 261,914 =California = 158,869 - 155,973 =Montana = 147,046 - 145,556 =New Mexico = 121,598 - 121,364 =CHECK Compare the water area for each state todetermine which state has the least water area.has the least water area withsquare miles.Check Your Progress Refer to Example 2. How many timeslarger is the land area of Alaska than the land area of Montana?HOMEWORKASSIGNMENTPage(s):Exercises:REMEMBER ITAlways check tomake sure your answeris reasonable. You cansolve the problem againif you think your answeris not correct.
- 14. 6 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A variable is a , usually a letter, used torepresent a .An algebraic expression contains a , anumber, and at least one symbol.When you substitute a number for the , analgebraic expression becomes a numerical expression.To evaluate an expression means to ﬁnd itsvalue.To avoid confusion, mathematicians have agreed on acalled the order of operations.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLES Evaluate Algebraic ExpressionsEvaluate each expression if q = 5, r = 6, and s = 3.4(r - s)24(r - s)2= 4( - )2Replace with 6 andwith 3.= 4( )2Perform operations in theﬁrst.= 4 Evaluate the .= Simplify.MAIN IDEA• Evaluate expressionsand identify properties.1–2 Variables, Expressions, and PropertiesKEY CONCEPTOrder of Operations1. Do all operationswithin groupingsymbols ﬁrst; startwith the innermostgrouping symbols.2. Evaluate all powersbefore otheroperations.3. Multiply and dividein order from left toright.4. Add and subtract inorder from left toright.
- 15. 1–2Math Connects, Course 3 7Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Expressions such as 72and 23are called powers andrepresent repeated .BUILD YOUR VOCABULARY (pages 2–3)q2- 4r - 1q2- 4r - 1 = - 4 - 1 Replace with 5 andwith 6.Evaluate beforeother operations..Add and subtract in orderfrom left to right..= - 4(6) - 1= 25 - - 1= -=6q_5sThe fraction bar is a grouping symbol. Evaluate the expressionsin the numerator and denominator separately before dividing.6q_5s=6 (5)_5 (3)Replace with 5 and with 3.= 30_15Do all ﬁrst.= .Check Your Progress Evaluate each expression.a. 2(a + b)2 if a = 3 and b = 2b. b2+ 3c - 5 if b = 4 and c = 2c. 3s_q + 4if q = 2 and s = 42
- 16. 1–28 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The branch of mathematics that involveswith variables is called algebra.Properties are sentences that are true forany numbers.A counterexample is an example that shows that aconjecture is .BUILD YOUR VOCABULARY (pages 2–3)REMEMBER ITCommutativePropertya + b = b + aa · b = b · aAssociative Propertya + (b + c) = (a + b) + ca · (b · c) = (a · b) · cDistributive Propertya(b + c) = ab + aca(b - c) = ab - acIdentity Propertya + 0 = aa · 1 = aEXAMPLES Identify PropertiesName the property shown by 12 · 1 = 12.Multiplying by 1 does not change the number.This is the Property of Multiplication.Check Your Progress Name the property shown by3 · 2 = 2 · 3.EXAMPLES Find a CounterexampleState whether the following conjecture is true or false.If false, provide a counter example.The sum of an odd number and an even number isalways odd.This conjecture is .Check Your Progress State whether the followingconjecture is true or false. If false, provide a counterexample.Division of whole numbers is associative.HOMEWORKASSIGNMENTPage(s):Exercises:
- 17. Math Connects, Course 3 9Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 1–3 Integers and Absolute ValuesA negative number is a number than zero.numbers, positive numbers, andare members of the set of integers.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Compare Two IntegersReplace the with < or > to make -2 -1 atrue sentence.The number line shows that -2 is than -1, since itlies to the of -1. So, write -2 -1.Check Your Progress Replace each with < or > tomake a true sentence.a. -2 2b. -4 -6The that corresponds to a iscalled the coordinate of that point.A sentence that two different numbersor quantities is called an inequality.BUILD YOUR VOCABULARY (pages 2–3)MAIN IDEA• Compare and orderintegers and ﬁndabsolute value.
- 18. 1–310 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The absolute value of a number is the distance thenumber is from on the number line.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLES Expressions with Absolute ValueEvaluate each expression.REMEMBER ITThe absolute valueof a number is not thesame as the opposite ofa number. Rememberthat the absolute valueof a number cannot benegative.⎪5⎥ - ⎪5⎥The graph of 5 is units from 0 on the number line.So, ⎪5⎥ = . Then subtract 5 units.Thus, ⎪ 5⎥ - ⎪5⎥ =⎪6⎥ - ⎪-5⎥⎪6⎥ - ⎪-5⎥ = -⎪-5⎥ The absolute value of 6 is .= 6 - ⎪-5⎥ == Simplify.Evaluate ⎪6 - 9⎥ - ⎪5 - 3⎥ .⎪6 - 9⎥ - ⎪5 - 3⎥ = ⎪ ⎥- ⎪ ⎥ Simplify the absolutevalue expressions.= - ⎪2⎥ The absolute value of-3 is .= 3 - The absolute value of2 is .= Simplify.
- 19. 1–3Math Connects, Course 3 11Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Evaluate ⎪x⎥ + 13 if x = -4.⎪x⎥ + 13 = ⎪ ⎥+ 13 Replace x with .= + 13 ⎪-4⎥ == Simplify.Check Your Progress Evaluate each expression.a. ⎪-3⎥ - ⎪3⎥ b. ⎪9⎥ - ⎪-6 ⎥ c. ⎪4 - 7⎥ - ⎪11 - 6⎥d. Evaluate ⎪x⎥ + 7 if x = -2.HOMEWORKASSIGNMENTPage(s):Exercises:
- 20. 12 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–4EXAMPLE Add Integers with the Same SignAdd -8 + (-4).Use a number line.Start at zero.Move units to the left.From there, move 4 units .So, -8 + (-4) = .Check Your Progress Add using a number lineor counters.KEY CONCEPTAdding Integers withthe Same Sign To addintegers with the samesign, add their absolutevalues. Give the result thesame sign as the integers.a. -3 + (-6)b. -13 + (-12)Adding IntegersMAIN IDEA• Add integers.
- 21. 1–4Math Connects, Course 3 13Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Add Integers with Different SignsORGANIZE ITExplain and giveexamples of how to addintegers with the samesign and how to addintegers with a differentsigns.®Find 4 + (-6).Use a number line.Start at .Move 4 units .From there, move units left.So, 4 + (-6) = .Find -5 + 9.Use a number line.Start at .Move units .From there, move units left .So, -5 + 9 = .KEY CONCEPTSAdding Integers withDifferent Signs To addintegers with differentsigns, subtract theirabsolute values. Givethe result the same signas the integer with thegreater absolute value.Find -33 + 16.-33 + 16 = To ﬁnd -33 + 16, subtract⎪16⎥ from ⎪-33⎥.The sum isbecause ⎪-33⎥ > ⎪16⎥.
- 22. 1–414 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Add.a. 3 + (-5)b. -6 + 8c. 25 + (-15)Two numbers with the same butdifferent signs are called opposites.An integer and its are also calledadditive inverses.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Add Three or More IntegersFind 2 + (-5) + (-3).2 + (-5) + (-3) = 2 + [ + (-3)] Associative Property= 2 + Order of operations= Simplify.
- 23. 1–4Math Connects, Course 3 15Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find each sum.a. 3 + (-6) + (-2) b. -10 + 5 + 10 + 7EXAMPLE Add Three or More IntegersSTOCKS An investor owns 50 shares in a video-gamemanufacturer. A broker purchases 30 shares more forthe client on Tuesday. On Friday, the investor asks thebroker to sell 65 shares. How many shares of this stockwill the client own after these trades are completed?Selling a stock decreases the number of shares, so the integerfor selling is .Purchasing new stock increases the number of shares, so theinteger for buying is .Add these integers to the starting number of shares to ﬁnd thenew number of shares.50 + + ( )= (50 + )+ ( ) Associative Property= + (-65) 50 + == Simplify.Check Your Progress MONEY Jaime gets an allowanceof $5. She spends $2 on video games and $1 on lunch. Her bestfriend repays a $2 loan and she buys a $3 pair of socks. Howmuch money does Jaime have left?HOMEWORKASSIGNMENTPage(s):Exercises:
- 24. 16 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–5 Subtracting IntegersEXAMPLES Subtract a Positive IntegerFind 2 - 6.2 - 6 = 2 + (-6) To subtract 6, add .= Add.Find -7 - 5.-7 - 5 = 7 (-5) To subtract , add -5.= -12 Add.KEY CONCEPTSubtracting IntegersTo subtract an integer,add its opposite oradditive inverse.EXAMPLES Subtract a Negative IntegerFind 11 - (-8).11 - (-8) = + 8 To subtract -8, add .= Add.WEATHER The overnight temperature at a researchstation in Antarctica was -13°C, but the temperaturerose to 2°C during the day, what was the differencebetween the temperatures?2 - (-13) = 2 To subtract -13, .= 15 Add.The difference between the temperatures was .Check Your Progress Subtract.ORGANIZE ITRecord in your Foldablehow to subtract integers.Be sure to includeexamples.®a. 3 - 7 b. -6 - 2c. 15 - (-3) d. -7 - (-11)MAIN IDEA• Subtract integers.
- 25. 1–5Math Connects, Course 3 17Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Evaluate Algebraic ExpressionsEvaluate each expression if p = 6, q = -3, and r = -7.12 - r12 - r = 12 - Replace r with .= 12 + To subtract add .= Add.q - p2q - p = -3 - (6)2 Replace q with andp with .= -3 + To subtract , add .= Add.Check Your Progress Evaluate each expression ifa = 3, b = -6, and c = 2.a. 10 - c b. b - aWRITE ITExplain why -b does notnecessarily mean that thevalue of -b is negative.HOMEWORKASSIGNMENTPage(s):Exercises:
- 26. 18 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Multiplying and Dividing IntegersEXAMPLE Multiply Integers with Different SignsFind 8(-4).8(-4) =The factors have signs. The product is.EXAMPLE Multiply Integers with the Same SignFind -12(-12).-12(-12) =The factors have the sign. The productis .EXAMPLE Multiply More Than Two IntegersFind 6(-2)(-4).6(-2)(-4) = [6(-2)] Property= -12 6(-2) == -12(-4) =Check Your Progress Multiply.a. 6(-3) b. -2(6)c. -8(-8) d. 5(-3)(-2)1–6MAIN IDEA• Multiply and divideintegers.KEY CONCEPTSMultiplying Two IntegersThe product of twointegers with differentsigns is negative.The product of twointegers with the samesign is positive.Dividing Integers Thequotient of two integerswith different signs isnegative.The quotient of twointegers with the samesign is positive.REMEMBER ITDecide on the signof the product beforemultiplying. If thenumber of negativesis even the product ispositive. If the numberof negatives is odd theproduct is negative.
- 27. 1–6Math Connects, Course 3 19Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Divide IntegersFind 30 ÷ (-5).30 ÷ -5 =The dividend and the divisor have signs.The quotient is .Check Your Progress Divide.a. 36 ÷ (-6) b. -30_-5EXAMPLE Evaluate Algebraic ExpressionsEvaluate -3x - (-4y) if x = -10 and y = -4.3x - (-4y)= 3( )- [-4( )] Replace x withand y with .= - 3(-10) =-4(-4) == -30 + To subtract , add.= Add.Check Your Progress Evaluate 2a - (-3b) if a = -6 andb = -4.ORGANIZE ITDescribe why theproduct or quotient oftwo integers with thesame sign is positiveand the product orquotient of two integerswith different signs isnegative.®
- 28. 1–620 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Find the Mean of a Set of IntegersGOLF Justin scored the following points for a roundof nine holes of golf. Find Justin’s average score forthe round.Hole 1 2 3 4 5 6 7 8 9Score +4 +3 0 -1 +2 -1 +2 +1 -1To ﬁnd the mean of a set of numbers, ﬁnd the sum of thenumbers. Then divide the result by how many numbers thereare in the set.4 + 3 + 0 + (-1) + 2 + (-1) + 2 + 1 + (-1)________9= __9= 1Justin’s average score was .Check Your Progress Average Low TemperaturesMonth Temp. (°C)Jan. -20Feb. -15March -5April 10May 25June 31July 41Aug. 38Sept. 34Oct. 19Nov. 3Dec. -15The table shows a set of recordlow temperatures. Find themean (average) of all12 temperatures.HOMEWORKASSIGNMENTPage(s):Exercises:
- 29. Math Connects, Course 3 21Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 1–7 Writing EquationsA mathematical sentence that contains ansign (=) is called an equation. When you choosea variable and an unknown quantity for the variable torepresent, this is called deﬁning the variable.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Write an Algebraic EquationCONSUMER ISSUES The cost of a book purchased onlineplus $5 shipping and handling comes to a total of $29.Write an equation to model this situation.Words The price of a book plus $5 shipping is $29.Variable Let b represent the price of the book.The priceof a book plus $5 shipping is $29.Equation + = 29The equation is .Check Your Progress Write the price of a toy plus $6shipping is $35 as an algebraic equation.EXAMPLE Write an Equation to Solve a ProblemNUTRITION A box of oatmeal contains 10 individualpackages. If the box contains 30 grams of ﬁber, writean equation to ﬁnd the amount of ﬁber in one packageof oatmeal.Words Ten packages of oatmeal contain 30 grams of ﬁber.Variable Let f represent the grams of ﬁber per package.Ten packages 30 gramsof oatmeal contain of ﬁber.Equation = 30The equation is .MAIN IDEA• Write algebraicequations from verbalsentences and problemsituations.REMEMBER ITIt is often helpful toselect letters that caneasily be connectedto the quantity theyrepresent. For example,age = a.
- 30. 1–722 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress A particular box of cookies contains10 servings. If the box contains 1,200 Calories, write anequation to ﬁnd the number of Calories in one serving ofcookies.EXAMPLETEST EXAMPLE The eighth grade has $35 less inits treasury than the seventh grade has. Given s, thenumber of dollars in the seventh-grade treasury, whichequation can be used to ﬁnd e, the number of dollars inthe eighth-grade treasury?A e = 35 - sB e = s - 35C e = s ÷ 35D e = 35sRead the ItemThe phrase $35 less . . . than the seventh grade indicates.Solve the ItemThe amount of moneyin the eighth-gradetreasury isthe amount of money inthe seventh-gradetreasury less $35.e = s - 35The solution is .Check Your Progress MULTIPLE CHOICE Helena andher friends ordered 3 bags of popcorn and 4 drinks from thesnack stand. Which equation could be used to ﬁnd c, the totalcost if p represents the cost of a bag of popcorn and d representsthe cost of a drink?F c = 7(p + d) H c = 3p + 4dG c = 7(p - d) J c = 7p + 7dExplain why it isimportant to read a wordproblem more than oncebefore attempting tosolve it.REVIEW ITHOMEWORKASSIGNMENTPage(s):Exercises:
- 31. Math Connects, Course 3 23Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 1–8 Problem-Solving Investigation:Work BackwardEXAMPLESCHEDULING Wendie is meeting some friends for amovie and a dinner. She needs to be ﬁnished with dinnerby 7:30 P.M. to make it home by 8:00 P.M. The movie runsfor 90 minutes, and she wants to have at least 1 hour fordinner. If it takes 20 minutes to get from the theater tothe restaurant, what is the latest starting time she canchoose for the movie she wants to see?UNDERSTAND You know what time Wendie needs tohead home. You know the time it takesfor each event. You need to determinePLAN Start with the and workbackward.SOLVE Finish dinner 7:30 P.M.Go back 1 hour for dinner.Go back for travel. 6:10 P.M.Go back 90 minutes for the movie.CHECK Assume the movie starts at Workfoward, adding the time for each event.The latest starting time for the movie isCheck Your Progress SHOPPING Mia spent $9.50 ata fruit stand, then spent three times that amount at thegrocery store. She had $7.80 left. How much money did shehave initially?MAIN IDEA• Solve problems byworking backward.HOMEWORKASSIGNMENTPage(s):Exercises:
- 32. 24 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1–9 Solving Addition and Subtraction EquationsWhen you solve an equation, you are trying to ﬁnd thevalues of the variable that makes the equation .A solution is the value of the variable that makes thevariable .BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Solve an Addition EquationKEY CONCEPTSSubtraction Property ofEquality If you subtractthe same number fromeach side of an equation,the two sides remainequal.Addition Property ofEquality If you add thesame number to eachside of an equation, thetwo sides remain equal.Solve 7 = 15 + c.METHOD 1 Vertical Method7 = 15 + c Write the equation.7 = 15 + c Subtract from each side._______-15 = -15= c 7 - 15 = ; 15 - 15 =METHOD 2 Horizontal Method7 = 15 + c Write the equation.7 - = 15 + c - Subtract from each side.= c 7 - 15 = ; and- 15 = 0Check Your Progress Solve 6 = 11 + a.MAIN IDEA• Solve equations usingthe Subtraction andAddition Properties ofEquality.
- 33. 1–9Math Connects, Course 3 25Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Addition and subtraction are called inverse operationsbecause they “undo” each other.BUILD YOUR VOCABULARY (pages 2–3)EXAMPLE Solve an Addition EquationOCEANOGRAPHY At high tide, the top of a coralformation is 2 feet above the surface of the water.This represents a change of -6 feet from the height ofthe coral at low tide. Write and solve an equation todetermine h, the height of the coral at low tide.WordsVariableEquationThe height at low tide plus the change is theheight at high tide.Let h represent the height at low tide.h + (-6) = 2h + -6 = 2 Write the equation.h + (-6) - = 2 - Subtract from eachside.h = Simplify.The height of the coral at low tide is 8 feet.EXAMPLE Solve a Subtraction EquationSolve -5 = z - 16.Use the horizontal method.-5 = z - 16 Write the equation.-5 + = z - 16 + Add to each side.= z -16 + 16 = and+ 16 = 11.Check Your Progress Solve -6 = x - 12.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITCompare how to solvean equation involvingwhole numbers andan equation involvingintegers.®
- 34. 26 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Solve a Multiplication EquationSolve 7z = -49.7z = -49 Write the equation.7z__= -49__ each side by .z = 7 ÷ 7 = , -49 ÷ 7 == Identity Property; 1z =EXAMPLE Solve a Division EquationSolve c_9= -6.c_9= -6 Write the equation.c_9= -6 Multiply each side by .c = -6 =EXAMPLE Use an Equation to Solve a ProblemSURVEYING English mathematician Edmund Gunterlived around 1600. He invented the chain, which wasused as a unit of measure for land and deeds. One chainequals 66 feet. If the south side of a property measures330 feet, how many chains long is it?WordsVariableEquationOne chain equals 66 feet.Let c = the number of chains in feet.Measurement 66 times theof property is number of chains330 =1–10 Solving Multiplication and Division EquationsMAIN IDEA• Solve equations byusing the Divisionand MultiplicationProperties of Equality.KEY CONCEPTSDivision Property ofEquality If you divideeach side of an equationby the same nonzeronumber, the two sidesremain equal.Multiplication Propertyof Equality If youmultiply each side of anequation by the samenumber, the two sidesremain equal.
- 35. 1–10Math Connects, Course 3 27Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Solve the equation.330 = 66c Write the equation.330__ = 66c__ Divide each side by .= 330 ÷ =The number of chains in 330 feet is .Check Your Progressa. Solve 8a = -64. b. Solve x_5= -10.c. Most horses are measured in hands. One hand equals4 inches. If a horse measures 60 inches, how manyhands is it?ORGANIZE ITOn your Foldable table,explain how to solvemultiplication equationsusing the multiplicationproperties of equality.®HOMEWORKASSIGNMENTPage(s):Exercises:
- 36. 28 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERC H A P T E R1STUDY GUIDE® VOCABULARYPUZZLEMAKERBUILD 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 you solvethe puzzle.1-1A Plan for Problem SolvingUse the four step plan to solve the problem.1. Lisa plans to redecorate her bedroom. Each wall is 120 squarefeet. Three walls need a single coat of paint and the fourth wallneeds a double coat. If each can of paint will cover 200 square feet,how many gallons of paint does Lisa need?1-2Variables, Expressions, and Properties2. Number the operations in the correct order for simplifying2 + 4 (9 - 6 ÷ 3).addition subtractionmultiplication division3. Describe how the expressions 2 + 5 and 5 + 2 are different.Then determine whether the two expressions are equal to eachother. If the expressions are equal, name the property that saysthey are equal.
- 37. Math Connects, Course 3 29Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BRINGING IT ALL TOGETHER1-3Integers and Absolute ValuesComplete each sentence with either left or right to make a truesentence. Then write a statement comparing the two numberswith either <, or >.4. -45 lies to the of 0 on a number line.5. 72 lies to the of 0 on a number line.6. -3 lies to the of -95 on a number line.7. 6 lies to the of -7 on a number line.1-4Adding IntegersDetermine whether you add or subtract the absolute values ofthe numbers to ﬁnd the sum. Give reasons for your answers.8. 4 + 89. -3 + 510. 9 + (-12)11. -23 + (-16)1-5Subtracting IntegersRewrite each difference as a sum. Then ﬁnd the sum.12. 2 - 913. -3 - 814. 10 - (-12)15. -5 - (-16)
- 38. 30 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 BRINGING IT ALL TOGETHER1-6Multiplying and Dividing IntegersFind each product or quotient.16. 9(-2) 17. -6(-7)18. 12 ÷ (-4) 19. -35 ÷ (-7)1-7Writing EquationsDetermine whether each situation requires addition,subtraction, multiplication or division.20. Find the difference in the cost of a gallon of premium gasoline andthe cost of a gallon of regular gasoline.21. Find the ﬂight time after the time has been increased by 15minutes.1-8Problem Solving Investigation: Work Backward22. LOANS Alonso bought supplies for a camping trip. He has about$2 left. He spent $15.98 at the grocery store, then spent $21.91 atthe sporting goods store. He also spent a third of his money for adeposit on the campsite. About how much money did Alonso haveoriginally?1-9Solving Addition and Subtraction EquationsSolve each equation.23. x + 6 = 9 24. s - 5 = 14 25. 11 + m = 331-10Solving Multiplication and Division EquationsSolve each equation.26. 8r = 32 27. 3 = x_728. -9 = -9g
- 39. Math Connects, Course 3 31Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ChecklistC H A P T E R1Student Signature Parent/Guardian SignatureTeacher SignatureARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.I completed the review of all or most lessons without using mynotes or asking for help.• You are probably ready for the Chapter Test.• You may want take the Chapter 1 Practice Test onpage 79 of your textbook as a ﬁnal check.I used my Foldable or Study Notebook to complete the review ofall or most lessons.• You should complete the Chapter 1 Study Guide and Review onpages 74–78 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 79 of your textbook.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 Foldable.• Then complete the Chapter 1 Study Guide and Review onpages 74–78 of your textbook.• If you are unsure of any concepts or skills, refer back to the speciﬁclesson(s).• You may also want to take the Chapter 1 Practice Test onpage 79 of your textbook.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 1.
- 40. ®32 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R2Use 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.Place 5 sheets of paper3_4inch apart.Roll up bottom edges.All tabs should be thesame size.Staple along the fold.Label the tabs with the2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numberslesson numbers.NOTE-TAKING TIP: As you study a lesson, writedown questions you have, comments andreactions, short summaries of the lesson, and keypoints that are highlighted and underlined.Algebra: Rational Numbers
- 41. Chapter2Math Connects, Course 3 33Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R2BUILD YOUR VOCABULARYThis 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 orExamplebar notationbasedimensional analysisexponentlike fractionsmultiplicative inverses(continued on the next page)
- 42. 34 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDeﬁnitionDescription orExamplepowerrational numberreciprocalsrepeating decimalscientiﬁc notationterminating decimalunlike fractions
- 43. Math Connects, Course 3 35Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 2–1 Rational NumbersA rational number is any number that can be expressed inthe form a_bwhere a and b are and b ≠ 0.A decimal like 0.0625 is a terminating decimal becausethe division ends, or terminates, when theis 0.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Write a Fraction as a DecimalKEY CONCEPTRational NumbersA rational number isany number that can beexpressed in the forma_b, where a and b areintegers and b ≠ 0.Write 3_16as a decimal.3_16means 3 16.0.187516 3.0000 Divide 3 by 16.__16140__128120__11280__80 Division ends when the is 0.0You can also use a calculator.The fraction 3_16can be written as .Check Your Progress Write 1_16as a decimal.MAIN IDEA• Express rationalnumbers as decimalsand decimals asfractions.
- 44. 2–136 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.A like 1.6666 . . . is called a repeating decimal.Since it is not possible to show all of the , youcan use bar notation to show that the 6 .BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Write a Mixed Number as a DecimalWRITE ITExplain how you decidewhere the bar is placedwhen you use barnotation for a repeatingdecimal.Write -3 2_11as a decimal.You can write -3 2_11as -35_11or 35_-11. To change -3 2_11to adecimal, ﬁnd or .-11 35.0000__-3320__-1190__-8820__-1190__-882 The remainder after each step is 2 or 9.The mixed number -3 2_11can be written as.Check Your Progress Write 51_9as a decimal.ORGANIZE ITUnder the tab forLesson 2–1, explain inyour own words how toexpress rational numbersas decimals and decimalsas fractions.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
- 45. 2–1Math Connects, Course 3 37Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Write a Terminating Decimal as a FractionWrite 0.32 as a fraction.0.32 = 32__ 0.32 is 32 .= Simplify. Divide by the greatestcommon factor of 32 and 100, .The decimal 0.32 can be written as .Check Your Progress Write 0.16 as a fraction.EXAMPLE Write a Repeating Decimal as a FractionALGEBRA Write 2.−7 as a mixed number.Let N = 2.−7 or 2.777 . . . . Then 10N = .Multiply N by because 1 digit repeats.Subtract N = 2.777 . . . to eliminate the part,0.777 . . . .10N = 27.777 . . .________-1N = 2.777 . . . N = 1N= 25 10N - 1N == Divide each side by .N = Simplify.Check Your Progress Write 1.−7 as a mixed number.HOMEWORKASSIGNMENTPage(s):Exercises:
- 46. 38 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Compare Positive Rational NumbersReplace with <, >, or = to make 3_78_13atrue sentence.Write as fractions with the same denominator.For 3_7and 8_13, the least common denominator is 91.3_7=3 ·__7 ·= _918_13=8 ·__13 ·= _91Since _91< _91, 3_78_13.EXAMPLE Compare Using DecimalsReplace with <, >, or = to make 0.7 7_11atrue sentence.0.7 7_11Express 7_11as a decimal.In the tenths place, 7 > 6.So, 0.7 7_11.Check Your Progress Replace each with <, >, or = tomake a true sentence.a. 2_33_5b. 4_90.5Comparing and Ordering Rational Numbers2–2MAIN IDEACompare and orderrational numbers.ORGANIZE ITUnder the tab forLesson 2–2, explain howyou can compare twonumbers by expressingthem as decimals andcomparing the decimals.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
- 47. 2–2Math Connects, Course 3 39Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Order Rational NumbersCHEMISTRY The values forSubstanceDensity(g/cm3)aluminum 2.7beryllium 1.87brick 14_5crown glass 21_4fused silica 2.−2marble 23_5nylon 1.1pyrex glass 2.32rubber neoprene 1.−3Source: CRC Handbook of Chemistryand Physicsthe approximate densitiesof various substances areshown in the table. Orderthe densities from leastto greatest.Write each fraction asa decimal.14_5=21_4=23_5=From the least to the greatest, the densities are1.1, 1.−3, 14_5, 1.87, 2.−2, 21_4, 2.32, 23_5, and 2.7. So, the isthe least dense, and is the most dense.Check Your Progress CoasterRide Time(min)Big Dipper 13_4Double Loop 1.5Mind Eraser 1.8Serial Thriller 2 1_12X-Flight 2.−3The ride times for ﬁveamusement parkattractions are shown inthe table. Order the lengthsfrom least to greatest.HOMEWORKASSIGNMENTPage(s):Exercises:REMEMBER ITOn a number line,a number to the leftis always less than anumber to the right.
- 48. 40 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.MAIN IDEA• Multiply positive andnegative fractions.Multiplying Positive and Negative Fractions2–3Dimensional analysis is the process of including units ofwhen you .BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Multiply FractionsKEY CONCEPTMultiply FractionsTo multiply fractions,multiply the numeratorsand multiply thedenominators.Find 3_7· 8_9. Write in simplest form.3_7· 8_9= 31_7· 8_93Divide 3 and 9 by their GCF, .= ___Multiply the numerators.Multiply the denominators.= 8_21Simplify.EXAMPLE Multiply Negative FractionsFind -3_4· 7_12. Write in simplest form.-3_4· 7_12= -31_4· 7_124Divide -3 and 12 by their GCF, .= ___Multiply the numerators.Multiply the denominators.= -_ The factors have different signs,so the product is negative.EXAMPLE Multiply Mixed NumbersFind 31_5· 13_4. Write in simplest form.31_5· 13_4= · 31_5= , 13_4=
- 49. 2–3Math Connects, Course 3 41Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.= 164_5· 7_41Divide 16 and 4 by theirGCF, .= ___5 · 1Multiply the numerators.Multiply the denominators.= , or 5 Simplify.Check Your Progress Multiply. Write in simplest form.a. - 2_15· 5_9b. 32_5· 22_9EXAMPLEVOLUNTEER WORK Last summer the 7th gradersperformed a total of 250 hours of community service.If the 8th graders spent 11_5this much time volunteering,how many hours of community service did the 8thgraders perform?The 8 graders spent 11_5times the amount of time as the7th graders on community service.6_5· 250 = ·=1,500_5orThe 8th graders did of community servicelast summer.Check Your Progress VOLUNTEER WORK Lastsummer the 5th graders performed a total of 150 hoursof community service. If the 6th graders spent 11_3thismuch time volunteering, how many hours of communityservice did the 6th graders perform?HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITUnder the tab forLesson 2–3, explain inyour own words howto multiply rationalnumbers.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
- 50. 42 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Two numbers whose product is one are multiplicativeinverses.The numbers 4 and 1_4areor reciprocals of each other.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Find a Multiplicative InverseKEY CONCEPTSInverse Property ofMultiplication Theproduct of a rationalnumber and itsmultiplicative inverse is 1.Dividing FractionsTo divide by a fraction,multiply by itsmultiplicative inverse.Write the multiplicative inverse of -24_7.-24_7= Write -24_7as an improper fraction.Since -18_7 (- 7_18)= , the multiplicative inverseof -24_7is .Check Your Progressa. Write the multiplicative inverse of -15_6.EXAMPLE Divide Negative FractionsFind 2_7÷ -8_9. Write in simplest form.2_7÷ -8_9= 2_7· Multiply by the multiplicativeinverse of -8_9which is .= 21_7· 9_84Divide 2 and 8 by their GCF, .= The fractions have different signs,so the quotient is negative.MAIN IDEA• Divide positive andnegative fractions.Dividing Positive and Negative Fractions2–4ORGANIZE ITOn the tab for Lesson2–4, explain in your ownwords how to dividerational numbers.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
- 51. 2–4Math Connects, Course 3 43Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Divide Mixed NumbersFind 31_4÷ (-21_8). Write in simplest form.31_4÷ (-21_8)= ÷ ( ) 31_4= ,-21_8== · (- 8_17) The multiplicativeinverse of is - 8_17.= 13_41· (- 82_17) Divide 4 and 8 by theirGCF, .= -26_17or Simplify.Check Your Progress Find each quotient. Write insimplest form.a. -3_5÷ 9_10b. 21_3÷ (-11_9)WRITE ITExplain how you woulddivide a fraction by awhole number.
- 52. 2–444 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLEPAINTING It took the ﬁve members of the Johnson family101_2days to paint the 7 rooms in their house. At thisrate, how long will it take the four members of the Reyesfamily to complete a similar task in their house?If persons of the Johnson family each workeddays, the project required 5 × 101_2person-days of work. Dividethis number by persons to ﬁnd the number of days it willtake the Reyes family to complete their task.5 101_2person-days ÷ 4=5 × 101_2person-days____1× 1__4 personsMultiply by themultiplicative inverseof 4, which is .= 52.5_4or Simplify.It will take the Reyes family days to complete asimilar painting task in their house.Check Your Progress DECORATING Six students spent31_2hours decorating the school gym for a dance. How longwould it take 8 students to decorate the gym in the same way?HOMEWORKASSIGNMENTPage(s):Exercises:
- 53. Math Connects, Course 3 45Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Adding and Subtracting Like FractionsFractions with like are calledlike fractions.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLE Add Like FractionsFind 3_16+ (-15_16). Write in simplest form.3_16+ (- 15_16 )=+ ( )____16Add the numerators.The denominatorsare the same.= -12_16or Simplify.EXAMPLE Subtract Like FractionsKEY CONCEPTSAdding Like FractionsTo add fractions withlike denominators, addthe numerators andwrite the sum over thedenominator.Subtracting LikeFractions To subtractfractions with likedenominators, subtractthe numerators and writethe difference over thedenominator.Find -7_10- 9_10. Write in simplest form.- 7_10- 9_10= ___10Subtract the numerators.The denominatorsare the same.= -16_10or Rename -16_10as -1 6_10or .Check Your Progress Find each difference. Write insimplest form.a. 2_9+ (-8_9) b. -7_8- 5_82–5MAIN IDEA• Add and subtractfractions with likedenominators.
- 54. 2–546 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLE Add Mixed NumbersFind 25_8+ 61_8. Write in simplest form.25_8+ 61_8= ( + )+ (5_8+ 1_8 ) Add the whole numbersand fractions separately.= +5 + 1_8Add the numerators.= or Simplify.EXAMPLE Subtract Mixed NumbersHEIGHTS In the United States, the average heightof a 9-year-old girl is 534_5inches. The average height of a16-year-old girl is 641_5inches. How much does anaverage girl grow from age 9 to age 16?641_5- 534_5= __5- __5Write the mixed numbersas improper fractions.=-____5Subtract the numerators.The denominators arethe same.= 52_5or Rename 52_5as .The average girl grows inches from age 9 to age 16.Check Your Progressa. Find 3 3_10+ 4 1_10. Write in simplest form.b. Ainsley was 421_7inches tall when she was 4 years old. Whenshe was 10 years old, she was 503_7inches tall. How much didshe grow between the ages of 4 and 10?ORGANIZE ITUnder the tab forLesson 2–5, recordmodels illustrating theaddition and subtractionof like fractions.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®HOMEWORKASSIGNMENTPage(s):Exercises:
- 55. Math Connects, Course 3 47Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Adding and Subtracting Unlike Fractions2–6Fractions with denominators are calledunlike fractions.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLES Add and Subtract Unlike FractionsAdd or subtract. Write in simplest form.5_8+ (-3_4)5_8+ (-3_4)= 5_8+ (-3_4)· The LCD is 2 · 2 · 2 or 8.= + Rename the fractionsusing the LCD.= Add the numerators.= Simplify.-7_96- (-15_128)- 7_96- (- 15_128)= - 7_96· + · 3_396 = 2 · 3, 128 = 2 .The LCD is 27· 3 or .= _384+ _384Rename using the LCD.=-28 + 45__ Add the numerators.= _384Simplify.MAIN IDEA• Add and subtractfractions with unlikedenominators.KEY CONCEPTAdding and SubtractingUnlike Fractions To ﬁndthe sum or difference oftwo fractions with unlikedenominators, renamethe fractions with acommon denominator.Then add or subtract andsimplify, if necessary.
- 56. 2–648 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Check Your Progress Add or subtract. Write insimplest form.a. 5_6+ (-2_3) b. - 7_12- (- 4_15)EXAMPLE Add Mixed NumbersFind -41_8+ 2 5_12. Write in simplest form.-41_8+ 2 5_12= +Write the mixed numbersas fractions.= -33_8· 3_3+ 29_12· 2_2The LCD is 2 · 2 · 2 · 3or .= +Rename each fractionusing the LCD.= ____24Add the numerators.= or -1 Simplify.Check Your Progress Find -51_6+ 35_8. Write insimplest form.HOMEWORKASSIGNMENTPage(s):Exercises:ORGANIZE ITUnder the tab forLesson 2–6, record thedifferences betweenadding and subtractinglike and unlike fractions.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
- 57. Math Connects, Course 3 49Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 2–7 Solving Equations with Rational NumbersEXAMPLES Solve by Using Addition or SubtractionSolve g + 2.84 = 3.62.g + = 3.62 Write the equation.g + 2.84 - = 3.62 - Subtract fromeach side.g = Simplify.Solve -4_5= s - 2_3.-4_5= s - 2_3Write the equation.-4_5+ = s - 2_3+ Add to each side.-4_5+ = s Simplify.+ 10_15= s Rename each fractionusing the LCD.= s Simplify.EXAMPLES Solve by Using Multiplication or DivisionSolve 7_11c = -21.7_11c = -21 Write the equation.( 7_11c)= (-21) Multiply each side by .c = Simplify.MAIN IDEA• Solve equationsinvolving rationalnumbers.ORGANIZE ITUnder the tab forLesson 2–7, summarizein your own words whatyou have learned aboutsolving equations withrational numbers.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
- 58. 2–750 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Solve 9.7t = -67.9.9.7t = -67.9 Write the equation.9.7t__ = -67.9__ Divide each side by .t = Simplify.Check Your Progress Solve each equation.a. h + 2.65 = 5.73 b. -2_5= x - 3_4.c. 3_5x = -27 d. 3.4t = -27.2EXAMPLE Write an Equation to Solve a ProblemPHYSICS You can determine the rate an object istraveling by dividing the distance it travels by the timeit takes to cover the distance (r = d_t ). If an object travelsat a rate of 14.3 meters per second for 17 seconds, howfar does it travel?r = d_t14.3 = d__ Write the equation.(14.3) = 17(d__) Multiply each side by .= d Simplify.Check Your Progress If an object travels at a rate of73 miles per hour for 5.2 hours, how far does it travel?What is a mathematicalsentence containingequals sign called?(Lesson 1–7)REVIEW ITHOMEWORKASSIGNMENTPage(s):Exercises:
- 59. Math Connects, Course 3 51Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 2–8 Problem-Solving Investigation:Look for a PatternEXAMPLEINTEREST The table below shows the amount ofinterest $3,000 would earn after 7 years at variousinterest rates. How much interest would $3,000 earnat 6 percent interest?Interest Rate(%)Interest Earned($)1 $2102 $4203 $6304 $8405 $1,050UNDERSTAND You know the amount of interest earned atinterest rates of 1%, 2%, 3%, 4%, 5%, and6%. You want to know the amount of interestearned at 6%.PLAN Look for a pattern in the amounts of interestearned. Then continue the pattern to ﬁnd theamount of interest earned at a rate of .SOLVE For each increase in interest rate, the amountof interest earned increases by $210. So foran interest rate of 6%, the amount of interestearned would be $1,050 + $210 = .CHECK Check your pattern to make sure the answeris correct.Check Your Progress INTEREST The table belowshows the amount of interest $5,000 would earn after 3 yearsat various interest rates. How much interest would $5,000 earnat 7 percent interest?Interest Rate(%)Interest Earned($)1 $1502 $3003 $4504 $6005 $750MAIN IDEA• Look for a pattern tosolve problems.HOMEWORKASSIGNMENTPage(s):Exercises:
- 60. 52 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The base is the number that is .The exponent tells how many times the isused as a .The number that is expressed using an iscalled a power.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLES Write Expressions Using PowersWrite 1_3· 1_3· 1_3· 7 · 7 using exponents.1_3· 1_3· 1_3· 7 · 7 = · Associative Property= Deﬁnition ofexponentsWrite p · p · p · q · p · q · q using exponents.p · p · p · q · p · q · q= p · p · p · p · q · q · q Property= (p · p · p · p) · (q · q · q) Property= · Deﬁnition of exponentsCheck Your Progress Write each expressionusing exponents.a. 2 · 2 · 2 · 2 · 5 · 5 · 5 b. x · y · x · x · y · y · y2–9 Powers and ExponentsMAIN IDEA• Use powers andexponents inexpressions.KEY CONCEPTZero and NegativeExponents Any nonzeronumber to the zeropower is 1. Any nonzeronumber to the negativen power is 1 divided bythe number to the nthpower.
- 61. 2–9Math Connects, Course 3 53Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Evaluate PowersEvaluate (3_4)5.(3_4)5= Deﬁnition of exponents= 243_1,024Simplify.Evaluate 3-7.3-7= 1__ Deﬁnition of negative exponents= 1__ Simplify.ALGEBRA Evaluate x3· y5if x = 4 and y = 2.x3· y5=3·5Replace x with andy with .= ( )· ( )Write the powers as products.= 64 · 32 Simplify.= Simplify.Check Your Progress Evaluate each expression.a. (3_5)3b. 2-5c. Evaluate x2· y4if x = 3 and y = 4.ORGANIZE ITOn the tab forLesson 2–9, comparehow to evaluate anexpression with positiveexponents and one withnegative exponents.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®HOMEWORKASSIGNMENTPage(s):Exercises:
- 62. 54 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.2–10 Scientiﬁc NotationA number is expressed in scientiﬁc notation when it iswritten as a of a factor and aof 10.BUILD YOUR VOCABULARY (pages 33–34)EXAMPLES Express Numbers in Standard Form9.62 × 105in standard form.9.62 × 105= 962000 The decimal place movesplaces to the right.=Write 2.85 × 10-6in standard form.2.85 × 10-6= 0.00000285 The decimal point moves 6places to the left.=Check Your Progress Write each number instandard form.a. 5.32 × 104b. 3.81 × 10-4MAIN IDEA• Express numbers inscientiﬁc notation.KEY CONCEPTScientiﬁc NotationA number is expressedin scientiﬁc notationwhen it is written as theproduct of a factor anda power of 10. The factormust be greater than orequal to 1 and lessthan 10.
- 63. 2–10Math Connects, Course 3 55Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLES Write Numbers in Scientiﬁc NotationWrite -931,500,000 in scientiﬁc notation.-931500000 = -9.315 × 100,000,000 The decimal point moves8 places.= The exponent is positive.Write 0.00443 in scientiﬁc notation.0.00443 = × 0.001 The decimal point movesplaces.= 4.43 × The exponent is .EXAMPLE Compare Numbers in Scientiﬁc NotationPLANETS The following Planet Radius (km)Earth 6.38 × 103Jupiter 7.14 × 104Mars 3.40 × 103Mercury 2.44 × 103Neptune 2.43 × 104Saturn 6.0 × 104Uranus 2.54 × 104Venus 6.05 × 103Source: CRC Handbook of Chemistryand Physicstable lists the averageradius at the equator forplanets in our solar system.Order the planets accordingto radius from largest tosmallest.First order the numbersaccording to their exponents.Then order the numbers withthe same exponents bycomparing the factors.STEP 1× 1046.38 × 1032.43 × 1043.40 × 1036.0 × 104> 2.44 × 1032.54 × 104× 103Jupiter, Neptune,Saturn, UranusEarth, Mars,Mercury, VenusORGANIZE ITUnder the tab forLesson 2–10, collectand record examplesof numbers youencounter in your dailylife and write them inscientiﬁc notation.2-72-82-102-92-62-52-42-32-1, 2-2Algebra:Rational Numbers®
- 64. 2–1056 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.STEP 27.14 × 104> 6.0 × 104> 2.54 × 104> 2.43 × 1046.38 × 103> 6.05 × 103> 3.40 × 103> 2.44 × 103The order from largest to smallest is , Saturn,Uranus, Neptune, Earth, Venus, Mars, and .Check Your Progress Write each number inscientiﬁc notation.a. 35,600,000 b. 0.000653c. The table lists the mass forPlanetMass(in tons)Mercury 3.64 × 1020Venus 5.37 × 1021Earth 6.58 × 1021Mars 7.08 × 1020Jupiter 2.09 × 1024Saturn 6.25 × 1023Uranus 9.57 × 1023Neptune 1.13 × 1023Source: NASAeach of the planets in oursolar system. Order theplanets according to massfrom largest to smallest.Jupiter Saturn Uranus NeptuneEarth Venus Mars MercuryHOMEWORKASSIGNMENTPage(s):Exercises:
- 65. Math Connects, Course 3 57Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.BRINGING IT ALL TOGETHERSTUDY GUIDE® VOCABULARYPUZZLEMAKERBUILD 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 33–34) to help you solvethe puzzle.2-1Rational NumbersWrite each fraction or mixed number as a decimal.1. -3_42. 31_63. -72_5Write each decimal as a fraction or mixed number in simplest form.4. 9.5 5. 0.6 6. 8.1252-2Comparing and Ordering Rational NumbersUse <, >, or = to make each sentence true.7. -4_5-2_38. 4.4 42_59. 2.93 2.93Graph each pair of rational numbers on a number line.10. 1_5, 1_311. -4_5, - 9_10C H A P T E R2
- 66. 58 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 BRINGING IT ALL TOGETHER2-3Multiplying Positive and Negative FractionsComplete each sentence.12. The greatest common factor of two numbers is thenumber that is a of both numbers.13. Numerators and denominators are by theirgreatest common factors to the fraction.Multiply. Write in simplest form.14. - 7_12· 3_415. 42_3· 51_82-4Dividing Positive and Negative FractionsWrite the multiplicative inverse for each mixed number.16. 21_517. -13_818. 34_7Complete the sentence.19. To divide by a , multiply by itsinverse.20. To a number by 21_5, multiply by 5_11.2-5Adding and Subtracting Like FractionsDetermine whether each pair of fractions are like fractions.21. 3_5, 3_722. 5_8, 7_823. 4_7, -5_724. 5_9, -2_3Add or subtract. Write in simplest form.25. 5_9- 2_926. 5_8+ 7_827. 4_7- 5_7
- 67. Math Connects, Course 3 59Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 BRINGING IT ALL TOGETHER2-6Adding and Subtracting Unlike FractionsAdd or subtract. Write in simplest form.28. 5_8- 7_1229. 3_5+ 3_730. -2_3+ 5_92-7Solving Equations with Rational NumbersMatch the method of solving with the appropriate equation.31. 25a = 3.75 a. Subtract 3_5from each side.b. Multiply each side by 5_3.c. Subtract 3.75 from each side.d. Add 1.25 to each side.e. Divide each side by 25.32. 3_5m = 7_1033. r - 1.25 = 4.534. 3_5+ f = 1_22-8Problem Solving Investigation: Look for a Pattern35. LIFE SCIENCE The table shows OutsideTemperature(˚C)Flashes perMinute16 820 924 1128 14about how many times a ﬁreﬂyﬂashes at different temperatures.About how many times will aﬁreﬂy ﬂash when thetemperature is 36°C?2-9Powers and ExponentsEvaluate each expression.36. 5437. 6338. 282-10Scientiﬁc NotationWrite each number in scientiﬁc notation.39. 8,790,000 40. 0.0000125
- 68. Checklist60 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.ARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study are given witheach item.I completed the review of all or most lessons without using my notesor asking for help.• You are probably ready for the Chapter Test.• You may want take the Chapter 2 Practice Test onpage 139 of your textbook as a ﬁnal check.I used my Foldable or Study Notebook to complete the review ofall or most lessons.• You should complete the Chapter 2 Study Guide and Review onpages 134–138 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 139 of your text book.I asked for help from someone else to complete the review of all ormost lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 2 Foldable.• Then complete the Chapter 2 Study Guide and Review on pages134–138 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 139 of your textbook.C H A P T E R2Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 2.Student Signature Parent/Guardian SignatureTeacher Signature
- 69. ®Chapter3Math Connects, Course 3 61Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3 Real Numbers andthe Pythagorean TheoremUse 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 two sheets of 81_2" by 11" notebookpaper.Fold one in half fromtop to bottom. Cutalong fold from edgesto margin.Fold the other sheetin half from topto bottom. Cut alongfold between margins.Insert ﬁrst sheetthrough secondsheet and align folds.Label each page with Chapter 3Real Numbersand thePythagoreanTheorema lesson number and title.NOTE-TAKING TIP: When you take notes, clarifyterms, record concepts, and write examples foreach lesson. You may also want to list ways inwhich the new concepts can be used in yourdaily life.
- 70. 62 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.C H A P T E R3UILD YOUR VOCABULARYThis 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 orExampleabscissa[ab-SIH-suh]conversecoordinate planehypotenuseirrational numberlegsordered pairordinate[OR-din-it]originperfect square
- 71. Math Connects, Course 3 63Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDeﬁnitionDescription orExamplePythagorean Theoremquadrantsradical signreal numbersquare rootx-axisx-coordinatey-axisy-coordinate
- 72. 64 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–1 Square RootsNumbers such as 1, 4, 9, and 25 are called perfect squaresbecause they are squares of numbers.The of squaring a number is ﬁnding asquare root.The symbol √⎯⎯ is called a radical sign and is used toindicate the positive .BUILD YOUR VOCABULARY (pages 62–63)EXAMPLES Find Square RootsKEY CONCEPTSquare Root A squareroot of a number is oneof its two equal factors.Find each square root.√81√81 indicates the square root of 81.Since = 81, √81 = .- 16_81- 16_81indicates the square root of 16_81.Since = 16_81, - 16_81= .±√1.44±√1.44 indicates bothsquare roots of 1.44.Since = 1.44 and = 1.44, ±√1.44 = ±1.2,or .MAIN IDEA• Find square roots ofperfect squares.
- 73. 3–1Math Connects, Course 3 65Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your Progress Find each square root.a. √64b. - 25_144c. ±√2.25EXAMPLE Use an Equation to Solve a ProblemMUSIC The art work of the square picture in a compactdisc case is approximately 14,161 mm2 in area. Find thelength of each side of the square.The area is equal to the square of the length of a side.Let A = the area and let s = the length of the side A = s214,161 = s2Write the equation.= √s2Take the square root of each side.The length of a side of a compact disc case is aboutmillimeters since distance cannot be negative.Check Your Progress A piece of art is a square picture thatis approximately 11,025 square inches in area. Find the lengthof each side of the square picture.ORGANIZE ITOn Lesson 3-1 of yourFoldable, explain howto ﬁnd the square rootof a number and give anexample.Chapter 3Real Numbersand thePythagoreanTheorem®HOMEWORKASSIGNMENTPage(s):Exercises:
- 74. 66 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Estimating Square RootsEXAMPLES Estimate Square RootsEstimate √54 to the nearest whole number.The ﬁrst perfect square less than 54 is .The ﬁrst perfect square greater than 54 is .49 < 54 < 64 Write an inequality.< 54 < 49 = and 64 =√72< √54 < √82Take the square root ofeach number.7 < √54 < 8 Simplify.So, √54 is between and . Since 54 is closer to 49than 64, the best whole number estimate for √54 is .Estimate √41.3 to the nearest whole number.• The ﬁrst perfect square less than 41.3 is 36.• The ﬁrst perfect square greater than 41.3 is 49.Plot each square rooton a number line.Then plot √41.3 .36 < 41.3 < 49 Write an inequality.< 41.3 < 36 = and 49 =√62< √41.3 < √72Find the square root of each number.< √41.3 < Simplify.So, √41.3 is between and . Since 41.3 is closer to 36than 49, the best whole number estimate for √41.3 is .MAIN IDEA• Estimate square roots.3–2
- 75. 3–2Math Connects, Course 3 67Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Estimate Square RootsFINANCE If you were to invest $100 in a bank account fortwo years, your investment would earn interest dailyand be worth more when you withdrew it. If you had$120 after two years, the interest rate, written as adecimal, would be found using the expression(√120 - 10)___10.Estimate the value.First estimate the value of √120.100 < 120 < 121 and areperfect squares.102< 120 < 112100 = and 121 =< √120 < Take the square root of each number.Since 120 is closer to than 100, the best wholenumber estimate for √120 is . Use this to evaluatethe expression.(√120 - 10)___10=( - 10)___10orThe approximate interest rate is 0.10 or .Check Your Progressa. Estimate √65 to the nearest whole number.b. If you were to invest $100 in a bank account for two years,your money would earn interest daily and be worth morewhen you withdrew it. If you had $250 after two years, theinterest rate, written as a decimal, would be found using theexpression(√150 - 10)___10. Estimate this value.ORGANIZE ITOn Lesson 3-2 of yourFoldable, explain how toestimate square roots.Chapter 3Real Numbersand thePythagoreanTheorem®HOMEWORKASSIGNMENTPage(s):Exercises:
- 76. 68 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–3 Problem-Solving Investigation:Use a Venn DiagramEXAMPLELANGUAGES Of the 40 foreign exchange studentsattending a middle school, 20 speak French, 23speak Spanish, and 22 speak Italian. Nine studentsspeak French and Spanish, but not Italian. Sixstudents speak French and Italian, but not Spanish.Ten students speak Spanish and Italian, but not French.Only 4 students speak all three languages. Use a Venndiagram to ﬁnd how many exchange students do notspeak any of these languages.UNDERSTAND You know how many students speak each ofthe different languages. You want to organizethe information.PLAN Make a VennDiagram to organizethe information.SOLVE Since 4 studentsspeak all threelanguages, place athree in the sectionthat represents allthree languages.Fill in the othersections as appropriate.Add the numbers in each region of the diagram:1 + 9 + 6 + 4 + 10 + 2 =Since there are 40 exchange studentsaltogether, 40 - 32 = of them do notspeak French, Spanish, or Italian.CHECK Check each circle to see if the appropriatenumber of students is represented.Check Your Progress SPORTS Of the 30 students in Mr.Hall’s gym class, 14 play basketball, 9 play soccer, and 11 playvolleyball. Three students play basketball and soccer, but notvolleyball. One student plays soccer and volleyball, but notbasketball. Six students play basketball and volleyball, butnot soccer. Only 2 students play all three sports. Use a Venndiagram to ﬁnd how many students in the class do not play anyof these sports.1 09426 10French SpanishItalianHOMEWORKASSIGNMENTPage(s):Exercises:MAIN IDEA• Use a Venn diagram tosolve problems.
- 77. Math Connects, Course 3 69Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 3–4 The Real Number SystemNumbers that are not are calledirrational numbers.The set of rational numbers and the set ofnumbers together make up the set of real numbers.BUILD YOUR VOCABULARY (pages 62–63)EXAMPLES Classify NumbersName all sets of numbers to which each real numberbelongs.0.090909 . . .The decimal ends in a pattern.It is a number because it is equivalent to .√25Since √25 = , it is a number, an, and a rational number.-√12Since the decimal does not repeat or , it isan number.Check Your Progress Name all sets of numbers towhich each real number belongs.a. 0.1010101010...b. √64c. √13MAIN IDEA• Identify and classifynumbers in the realnumber system.KEY CONCEPTIrrational Number Anirrational number is anumber that cannot beexpressed as a_b, wherea and b are integersand b ≠ 0.
- 78. 3–470 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLES Graph Real NumbersEstimate √8 and -√2 to the nearest tenth. Thengraph √8 and -√2 on a number line.Use a calculator to determine the approximate decimal values.√8 ≈-√2 ≈Locate these points on a number line.0123 1 2 3√8 ≈ and -√2 ≈ .Check Your Progress Estimate √3 and -√6 to the nearesttenth. Then graph √3 and -√6 on a number line.EXAMPLES Compare Real NumbersReplace each with <, >, or = to make a true sentence.37_8√15Write each number as a decimal.37_8= √15 =Since is greater than ,37_8= √15.ORGANIZE ITOn Lesson 3-4 of yourFoldable, summarize theproperties of the realnumber system.Chapter 3Real Numbersand thePythagoreanTheorem®REMEMBER ITAlways simplifynumbers beforeclassifying them.
- 79. 3–4Math Connects, Course 3 71Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 3.−2 √10.4Write √10.4 as a decimal.√10.4 ≈Since 3.−2 is than 3.224903099...,3.−2 √10.4.Check Your Progress Replace each with <, >, or = tomake a true sentence.a. 33_8√14 b. 1.−5 √2.25EXAMPLEBASEBALL The time in seconds that it takes an object tofall d feet is 0.25√d. How many seconds would it take fora baseball that is hit 250 feet straight up in the air to fallfrom its highest point to the ground?Use a calculator to approximate the time it will take for thebaseball to fall to the ground.0.25 √d = 0.25 Replace d with .≈ 3.95 or about Use a calculator.It will take about for the baseball to fall tothe ground.Check Your Progress The time in seconds that it takes anobject to fall d feet is 0.25√d. How many seconds would it takefor a baseball that is hit 450 feet straight up in the air to fallfrom its highest point to the ground?HOMEWORKASSIGNMENTPage(s):Exercises:WRITE ITExplain why you candetermine that -√2 isless than 1.2 withoutcomputation.
- 80. 72 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3–5 The Pythagorean TheoremA right triangle is a triangle with one right angle of 90°.The sides that form the right angle are called legs.The hypotenuse is the side opposite the right angle.The Pythagorean Theorem describes the relationshipbetween the lengths of the legs and the hypotenuse forany right triangle.BUILD YOUR VOCABULARY (pages 62–63)EXAMPLES Find the Length of a SideWrite an equation you could use to ﬁnd the length of themissing side of the right triangle. Then ﬁnd the missinglength. Round to the nearest tenth if necessary.12 in.16 in.cc2= a2+ b2Pythagorean Theoremc2= 122+ Replace a with and b with .c2= + Evaluate 122and 162.c2= Add 144 and 256.c = ±√400 Deﬁnition of square rootc = or Simplify.The equation has two solutions, and .However, the length of a side must be positive. So, thehypotenuse is inches long.MAIN IDEA• Use the PythagoreanTheorem.KEY CONCEPTPythagorean TheoremIn a right triangle, thesquare of the length ofthe hypotenuse is equalto the sum of the squaresof the lengths of the legs.
- 81. 3–5Math Connects, Course 3 73Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. Check Your ProgressWrite an equation you could use to ﬁnd the length of themissing side of the right triangle. Then ﬁnd the missing length.Round to the nearest tenth if necessary.8 cm15 cmcEXAMPLE Find the Length of a SideThe hypotenuse of a right triangle is 33 centimeterslong and one of its legs is 28 centimeters. What is a, thelength of the other leg?c2= a2+ b2Pythagorean Theorem2= a2+2Replace the variables.1,089 = a2+ 784 Evaluate each power.- = a2+ - Subtract.= a2Simplify.± √305 = a Deﬁnition of square root= a Use a calculator.The length of the other leg is about centimeters.Check Your Progress The hypotenuse of a right triangle is26 centimeters long and one of its legs is 17 centimeters. Findthe length of the other leg.ORGANIZE ITOn Lesson 3-5 of yourFoldable, explain howto use the PythagoreanTheorem to ﬁnd themissing length of a sideof a right triangle.Chapter 3Real Numbersand thePythagoreanTheorem®REMEMBER ITThe longest side of aright triangle is thehypotenuse. Therefore, crepresents the length ofthe longest side.
- 82. 3–574 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.If you the parts of the Pythagorean Theorem,you have formed its converse.BUILD YOUR VOCABULARY (pages 62–63)EXAMPLE Identify a Right TriangleThe measures of three sides of a triangle are 24 inches,7 inches, and 25 inches. Determine whether the triangleis a right triangle.c2= a2+ b2Pythagorean Theorem25272+ 242c = 25, a = 7, b = 24625 + 576 Evaluate 252, 72, and 242.= 625 Simplify. The triangle is a right triangle.Check Your ProgressThe measures of three sides of a triangle are 13 inches,5 inches, and 12 inches. Determine whether the triangleis a right triangle.HOMEWORKASSIGNMENTPage(s):Exercises:KEY CONCEPTConverse of thePythagorean TheoremIf the sides of a trianglehave lengths a, b, and cunits such thatc2= a2+ b2, thenthe triangle is a righttriangle.
- 83. Math Connects, Course 3 75Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. 3–6 Using the Pythagorean TheoremEXAMPLE Use the Pythagorean TheoremRAMPS A ramp to a newlyconstructed building mustbe built according to theguidelines stated in theAmericans with DisabilitiesAct. If the ramp is 24.1feet long and the top ofthe ramp is 2 feet off theground, how far is the bottomof the ramp from the baseof the building?Notice the problem involves a right triangle. Use thePythagorean Theorem.24.12= a2+ 22 Replace c with 24.1 andb with 2.= a2+ Evaluate 24.12and 22.- = a2= - Subtract from each side.= a2Simplify.= a Deﬁnition of square root≈ a Simplify.The end of the ramp is about from the base ofthe building.Check Your Progress If a truck ramp is 32 feet long andthe top of the ramp is 10 feet off the ground, how far is the endof the ramp from the truck?MAIN IDEA• Solve problems usingthe PythagoreanTheorem.ORGANIZE ITOn Lesson 3-6 of yourFoldable, explain thePythagorean Theorem inyour own words and givean example of how itmight be used in areal-life situation.Chapter 3Real Numbersand thePythagoreanTheorem®
- 84. 3–676 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.EXAMPLETEST EXAMPLE The cross-sectionof a camping tent is shown. Find thewidth of the base of the tent.A 6 ft C 10 ftB 8 ft D 12 ftRead the ItemFrom the diagram, you know that the tent forms two congruentright triangles.Solve the ItemUse the Pythagorean Theorem.c2= a2+ b2Pythagorean Theorem= a2+ c = , b == a2+ Evaluate 102and 82.100 - 64 = a2+ 64 - 64 Subtract 64 from each side.= a2Simplify.= a Deﬁnition of square root= a SimplifyThe width of the base of the tent is a + a or + =feet. Therefore, choice is correct.Check Your Progress32 ft12 ftr rMULTIPLE CHOICE Thediagram shows the cross-section of a roof. How longis each rafter, r?F 15 ft G 18 ft H 20 ft J 22 ftHOMEWORKASSIGNMENTPage(s):Exercises:
- 85. Math Connects, Course 3 77Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Geometry: Distance on the Coordinate PlaneA coordinate plane is formed by two number lines thatform right angles and intersect at their points.The point of intersection of the two number lines is theorigin.The number line is the y-axis.The number line is the x-axis.The number lines separate the coordinate plane intosections called quadrants.Any point on the coordinate plane can be graphed by usingan ordered pair of numbers.The number in the ordered pair is called thex-coordinate.The number of an ordered pair is they-coordinate.Another name for the is abscissa.Another name for the is ordinate.BUILD YOUR VOCABULARY (pages 62–63)EXAMPLE Name an Ordered PairName the ordered pair for point A.• Start at the origin.• Move right to ﬁnd theof point A, which is .(continued on the next page)3–7yxAMAIN IDEAS• Graph rational numberson the coordinateplane.• Find the distancebetween points on thecoordinate plane.ORGANIZE ITOn Lesson 3-7 of yourFoldable, explain inwriting how to useordered pairs to ﬁnd thedistance between twopoints.Chapter 3Real Numbersand thePythagoreanTheorem®
- 86. 3–778 Math Connects, Course 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.• Move up to ﬁnd the ,which is .So, the ordered pair for point A is .Check Your Progress Name the orderedyxApair for point A.EXAMPLES Graphing Ordered PairsGraph and label each point on the same coordinateplane.J(-3, 2.75)• Start at and moveunits to the .Then move units.• Draw a dot and label it.K(4, -11_4)• Start at and move units to the .Then move units.• Draw a dot and label it .Check Your Progress yxOGraph and label eachpoint on the samecoordinate plane.a. J(-2.5, 3.5)b. K(2, -21_2)yxK 4, 1J( 3, 2.75)14)(
- 87. 3–7Math Connects, Course 3 79Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc. EXAMPLE Find the Distance on the Coordinate PlaneGraph the ordered pairs (0, -6)and (5, -1). Then ﬁnd the distancebetween the points.Let c = distance between the two points, a = 5, and b = 5.c2= a2+ b2Pythagorean Theoremc2= + Replace a with and b with .c2= + =√c2= Deﬁnition ofc = Simplify.The points are about apart.Check Your Progress Graph the ordered pairs (0, -3) and( 2, -6). Then ﬁnd the distance between the points.REMEMBER ITYou can use thePythagorean Theoremto ﬁnd the distancebetween two points ona coordinate plane.xyO(5, 1)(0, 6)yxOHOMEWORKASSIGNMENTPage(s):Exercises:

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment