Chapter1.5
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This document provides examples and explanations for adding and subtracting integers. It discusses subtracting a positive or negative integer by adding the opposite integer. Additional examples apply integer operations to real-world contexts like architecture and aviation. Practice problems at the end ask students to subtract integers and evaluate expressions with integer variables.
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Msm1 fl ch11_01
The document is a math lesson on integers that includes examples and explanations of positive and negative numbers, opposites, integers, and absolute value. It provides practice problems identifying positive and negative numbers in real world contexts, graphing integers on a number line, and finding the absolute value of integers using a number line. The lesson concludes with a quiz reviewing these concepts.
Division of Polynomials.pptx
The document discusses polynomial division and related concepts. It defines polynomial expressions and covers the algorithms for long division and synthetic division of polynomials. It also introduces the factor theorem and remainder theorem, which relate the factors and remainder of a polynomial division to evaluating the polynomial at specific values. The document provides examples of applying these techniques to divide polynomials and determine factors and remainders.
ppt math6 qt3-wk3.pptx
The document provides instructions on subtracting integers. It explains:
1) To subtract integers, transform the subtraction into addition by keeping the first number and changing the second number's sign.
2) Examples are provided of subtracting integers with different signs and the same sign.
3) A multi-step word problem is worked out as an example of subtracting integers.
Class Presentation Math 1
This document contains notes from a 7th grade math class covering topics like subtracting integers, multiplying integers, and solving algebraic equations. Key points covered include: when subtracting integers, you add the opposite; when multiplying integers with the same sign the product is positive, and with different signs the product is negative; and to solve equations, you perform the same operation to both sides until the variable is isolated on one side.
Class Presentation Math 1
This document contains notes from a 7th grade math class covering topics like subtracting integers, multiplying integers, and solving algebraic equations. Key points covered include: when subtracting integers, you add the opposite; when multiplying integers with the same sign the product is positive, and with different signs the product is negative; and to solve equations, you perform the same operation to both sides until the variable is isolated on one side.
AFS Math 2
This document contains notes from a 7th grade math class covering topics like subtracting integers, multiplying integers, and solving algebraic equations. Key points covered include: when subtracting integers, you add the opposite; when multiplying integers with the same sign the product is positive, and with different signs the product is negative; and to solve equations, you perform the same operation to both sides until the variable is isolated on one side.
GMAT | Quant Basics | MBA Classes
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Simple Equations I
This document discusses solving one-step linear equations using addition and subtraction. It defines key terms like equations, solutions, and isolating variables. It explains that when transforming equations, the same operations must be applied to both sides to maintain equivalence. Inverse operations like addition and subtraction can isolate variables. Examples show how to isolate variables using addition or subtraction and solve equations. Students are then prompted to solve practice equations on their own. The document also discusses using equations to solve real-world problems, like finding a person's maximum heart rate based on their age.
GraphTransformations.pptx
1. This document discusses graph transformations of functions, including translations, stretches, and reflections. It provides rules for how modifications inside and outside the function f(x) will affect the x-values and y-values of the graph.
2. Examples are given of applying transformation rules to specific points on a graph and determining the new coordinates. The document also demonstrates sketching a transformed graph using key points.
3. An exercise section provides multiple choice and short answer questions to test understanding of describing transformations and finding coordinates of transformed points.
Msm1 fl ch11_04
The document provides examples and explanations for adding integers on a number line and in expressions. It includes warm-up problems, examples of writing integer addition modeled on number lines, evaluating integer expressions, and an application problem about plane altitude relative to sea level using integer addition. The document is a lesson on adding integers with examples to practice the skill.
Ejercicios resueltos de analisis matematico 1
The document describes the logarithmic differentiation method used to derive functions where the exponent is a variable. It explains the steps: take the natural log of both sides, apply logarithm properties, derive both terms, isolate the function, and substitute back in. Examples are provided and solved, such as deriving y=xx, y=sen(x)(x3+6x), and y=ln x3 + 5x2cos(x). Related activities are summarized with solutions to practice problems applying this method.
Sequence function
The document defines key concepts related to sequences and series. It explains that a sequence is an ordered list of numbers with a specific pattern or rule. A sequence function is a function whose domain is the set of natural numbers. Terms are the individual numbers in a sequence. Finite sequences have a set number of terms while infinite sequences continue without end. Partial sums refer to adding a specific number of terms. Sigma notation compactly represents the sum of terms in a sequence. The document also introduces the principle of mathematical induction as a method to prove that statements are true for all natural numbers.
Chapter3.4
This document provides examples of solving linear equations with one variable. It begins with examples of solving equations with the variable on both sides, including subtracting like terms to isolate the variable. It then gives examples of solving more complex multi-step equations, showing the process of combining like terms and using properties of equality. Finally, it provides a word problem example involving costs for flower bouquets with different variables representing fees and costs per item.
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3 3 i can add and subtract decimals
This document provides instructions and examples for adding and subtracting decimals. It explains the basic steps of lining up the decimal point and filling in missing places with zeros before adding or subtracting. When subtracting across zeros, it notes to borrow from the first non-zero digit if needed. Several examples show evaluating decimal expressions by substituting values for variables and performing the indicated operations. The document concludes with a quiz to assess understanding of adding and subtracting decimals.
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This document provides examples of multiplying and dividing integers. For multiplying integers, the examples show multiplying a negative number times a positive number results in a negative product, and multiplying two negative numbers results in a positive product. For dividing integers, the examples demonstrate that when dividing a negative number by a positive number the result is negative, and when dividing a positive number by a negative number the result is negative.
New week 6
This document outlines the daily schedule and assignments for a pre-algebra class over the course of a week. It includes instructions to have homework on desks, complete warm-ups, discuss previous homework, do assignments from textbooks and workbooks, take a quiz, play an integer product game, and complete a mathematical reflection. The schedule is detailed for Monday through Friday with different assignments and activities each day.
New week 5
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The document contains summaries of pre-algebra warm ups and lessons for four days of the week. It includes tasks to complete tables, find differences, identify numbers between given values, calculate new scores, and make charts. It also lists homework assignments and materials needed for the lessons.
New week 3
This document contains summaries of daily lessons and activities for a Pre-Algebra class over the course of a week. It includes warm-up problems, learning objectives, homework assignments, quizzes, and vocabulary terms. The class focuses on topics like using chip models to represent addition and subtraction, ordering numbers, properties of rational numbers, and extending addition to rational numbers.
Newweek2
The document provides information about a pre-algebra class that covers topics like the number line and rational numbers. It includes warm-up problems, homework assignments, and discussions of investigations into extending the number line and using it to represent number sentences for changes in temperature. The class materials are aimed at helping students understand rational numbers and how to use the number line to compare numbers and represent number sentences.
10.3
This document provides examples of using quadratic functions in intercept form. It demonstrates how to identify the x-intercepts from the function, graph the function by plotting intercepts and the vertex, write a function given intercepts and a point, and model a real-world scenario like a dolphin's leap using a quadratic function. Key aspects covered include the intercept form equation, finding the vertex and axis of symmetry, and completing the steps to graph or write a quadratic function based on given information.
New week 1
The document provides information about a pre-algebra class, including:
1) Instructions for students to write down their homework, review class expectations, and get out notebooks.
2) Details about classroom rules and expectations for students.
3) An overview of the upcoming unit on operations with integers which will cover comparing and ordering numbers on a number line.
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This document contains a multi-part math problem about using similar triangles to estimate heights and distances. Part A asks students to use similar triangles to find the height of a building from given measurements. Part B asks students to use the mirror method with their group to estimate the height of an object and provide their measurements and explanation. Part C compares the estimates from Parts A and B and asks if they seem reasonable. Follow-up questions involve pooling the class data and comparing estimates from the two methods.
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The document contains instructions and information about using similar triangles to estimate heights and distances that are difficult to measure directly. It discusses using shadows and mirrors to form similar triangles and estimate heights of objects. Measurements are taken of shadows, mirrors, and distances that allow heights to be calculated through properties of similar triangles. Students work through examples estimating heights of buildings using these methods.
11.6
This document provides an example of how to use the work formula to solve problems involving work done at a steady rate. It gives the formula for work rate as the amount of a job completed in a given time. It then works through two examples - one calculating the time for two people to complete a job together, and another multiple choice problem calculating the time for one person to complete a job alone based on work rates.
11.5
This document discusses solving rational equations by using the cross product property. It provides three examples of solving rational equations:
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2) Solving a rational equation with rational expressions on both sides. The solution appears to be 2, but it is an extraneous solution.
3) Solving a rational equation by factoring the denominators to find the least common denominator (LCD).
11.4
1) To add or subtract rational expressions with the same or different denominators, we first find the least common denominator (LCD), which is the least common multiple of the denominators.
2) We then rewrite the rational expressions with the LCD as the common denominator before adding or subtracting the numerators.
3) Once the rational expressions have been rewritten with the same denominator, we can perform the addition or subtraction operation as we would with numerical fractions.
New week 8
Raphael wants to make enlarged posters of his advertisement to display at a sale. He has an 8.5" by 11" ad and wants to enlarge it as much as possible using the copy machines at his local copy shop, which can enlarge documents between 50-200% and have paper sizes of 8.5" by 11", 11" by 14", and 11" by 17". The best option would be to use the 11" by 17" paper and enlarge the ad 150% to make it a similar, larger poster without trimming off the edges of the paper.
11.1
This document provides examples of direct and inverse variation, including how to identify, graph, and write equations for direct and inverse variation relationships. It also contains examples of solving work problems using inverse variation.
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- Direct variation is when y=kx and inverse variation is when y=k/x, where k is the constant of variation.
- Example 1 shows how to identify if an equation represents direct, inverse, or neither type of variation.
- Examples 2 and 3 demonstrate how to graph inverse variation equations.
- Examples 4, 5, and 6 show how to write inverse variation equations from tables of data or real-world context and solve problems using inverse variation equations.
New week 6
This document provides instructions and materials for a math lesson on similarity and scale factors. It includes examples of similar figures with questions about their side lengths, scale factors, and areas. It also discusses how police use measurements and similar figures to determine characteristics like a criminal's height from surveillance photos. Students are asked to use a photo of a teacher holding an object of known size to calculate the teacher's height, and to explain how police may have used a similar technique to determine a robber's height from a store surveillance photo.
9.9
The document provides examples of factoring polynomials completely. It begins by outlining guidelines for factoring polynomials completely, such as factoring out the greatest common monomial factor, looking for differences of squares or perfect square trinomials, and factoring trinomials and polynomials with four terms by grouping. It then works through examples of factoring various polynomials completely by applying these guidelines. These include factoring trinomials, solving a polynomial equation, and solving a multi-step problem involving factoring a polynomial to find dimensions.
9.8
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Chapter1.5
- 1. Holt CA Course 2 Warm Up California Standards Lesson Presentation Preview
- 2. Warm Up Add. 1. –7 + 2 4. –6 + (–28) 2. –12 + (–9) 5. 104 + (–87) 3. 32 + (–19) 6. –18 + (–24) – 5 – 34 17 – 42 – 21 13
- 3. NS1.2 Add, subtract , multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. NS2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers. California Standards
- 4. When you subtract a positive integer, the difference is less than the original number. Therefore, you move to the left on the number line. To subtract a negative integer, you move to the right . You can also subtract an integer by adding its opposite. You can then use the rules for addition of integers.
- 5. Additional Example 1: Subtracting Integers A. –7 – 4 – 7 – 4 = –7 + (–4) B. 8 – (–5) 8 – (–5) = 8 + 5 C. –6 – (–3) – 6 – (–3) = –6 + 3 = –11 = 13 = –3 Add the opposite of 4. Add the opposite of –5. Add the opposite of –3. Same sign; use the sign of the integers. Same sign; use the sign of the integers. 6 > 3; use the sign of 6. Subtract.
- 6. Check It Out! Example 1 A. 3 – (–6) 3 – (–6) = 3 + 6 B. –4 – 1 – 4 – 1 = –4 + (–1) C. –7 – (–8) – 7 – (–8) = –7 + 8 = 9 = –5 = 1 Add the opposite of –6. Add the opposite of 1. Add the opposite of –8. Same signs; use the sign of the integers. Same sign; use the sign of the integers. 8 > 7; use the sign of 8. Subtract.
- 7. – 9 – y for y = –4 – 9 + 4 – 5 Evaluate the expression for the given value of the variable. – 9 – y – 9 – (–4) Substitute –4 for y. Add the opposite of –4. 9 > 4; use the sign of 9. Additional Example 2A: Evaluating Expressions with Integers
- 8. n – 6 for n = –2 n – 6 – 2 – 6 Substitute –2 for n. Evaluate the expression for the given value of the variable. – 2 + (–6) – 8 Add the opposite of 6. Same sign; use the sign of the integers. Additional Example 2B: Evaluating Expressions with Integers
- 9. |8 – j | + |–2| for j = –6 |8 – j| + |–2 | |8 – (–6) | + |–2| Substitute –6 for j. Evaluate the expression for the given value of the variable. |14| + |–2| 14 + 2 Add the opposite of –6. 8 + 6 = 14. Additional Example 2C: Evaluating Expressions with Integers |8 + 6| + |–2| The absolute value of 14 is 14, and the absolute value of –2 is 2. Add. 16
- 10. – 5 – r for r = –2 – 5 + 2 – 3 Evaluate the expression for the given value of the variable. – 5 – r – 5 – (–2) Substitute –2 for r. Add the opposite of –2. 5 > 2; use the sign of 5. Check It Out! Example 2A
- 11. a – 7 for a = –9 a – 7 – 9 – 7 Substitute –9 for a. Evaluate the expression for the given value of the variable. – 9 + (–7) – 16 Add the opposite of 7. Same sign; use the sign of the integers. Check It Out! Example 2B
- 12. |11 – m | + 7 for m = –3 |11 – m| + 7 |11 – (–3) | + 7 Substitute –3 for m. Evaluate the expression for the given value of the variable. |14| + 7 14 + 7 Add the opposite of –3. 11 + 3 = 14. Check It Out! Example 2C |11 + 3| + 7 The absolute value of 14 is 14. Add. 21
- 13. The top of the Sears Tower, in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top? Additional Example 3: Architecture Application 1454 – (–43) Subtract the lowest level from the top. 1454 + 43 Add the opposite of –43. 1497 Same sign; use the sign of the integers. It is 1497 feet from the lowest level to the top.
- 14. The distance from the high dive to the swimming pool is 10 feet. The pool is 12 feet deep. What is the total distance from the high dive to the bottom of the pool? Check It Out! Example 3 10 – (–12) Subtract the depth of the pool from the height of the high dive. 10 + 12 Add the opposite of –12. 22 Same sign; use the sign of the integers. It is 22 feet from the diving board to the bottom of the pool.
- 15. Lesson Quiz Subtract. 1. –6 – (–4) – 2 – 6 9 2. –3 – 3 3. 4 – (–5) Evaluate each expression for the given value of the variable. 4. 9 – s for s = –5 14 5. –4 – w + 5 for w = 21 – 20 6. Suretta is flying in an airplane and rises an additional 20 feet. Then she descends 190 feet toward the ground. How far below her original height did Suretta go? 170 feet