Prealgebra: An Applied Approach [6 ed.] 1133365450, 9781133365457

Table of contents :
Cover
IFC
Ask the Authors!
Title
Statement
Copyright
Brief Contents
Contents
Preface
Take AIM and Succeed!
Index of Applications
Ch A: AIM for Success
Objectives
Focus on Success
Prep Test
Section A.1 How to Succeed in This Course
Section A.2 How to Use This Text to Succeed in this Course
Ch 1: Whole Numbers
Objectives
Focus on Success
Prep Test
Section 1.1 Introduction to Whole Numbers
Section 1.2 Addition and Subtraction of Whole Numbers
Section 1.3 Multiplication and Division of Whole Numbers
Section 1.4 Solving Equations with Whole Numbers
Section 1.5 The Order of Operations Agreement
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Test
Ch 2: Integers
Objectives
Focus on Success
Prep Test
Section 2.1 Introduction to Integers
Section 2.2 Addition and Subtraction of Integers
Section 2.3 Multiplication and Division of Integers
Section 2.4 Solving Equations with Integers
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Test
Cumulative Review Exercises
Ch 3: Fractions
Objectives
Focus on Success
Prep Test
Section 3.1 Least Common Multiple and Greatest Common Factor
Section 3.2 Introduction to Fractions
Section 3.3 Multiplication and Division of Fractions
Section 3.4 Addition and Subtraction of Fractions
Section 3.5 Solving Equations with Fractions
Section 3.6 Exponents, Complex Fractions, and the Order of Operations Agreement
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test
Cumulative Review Exercises
Ch 4: Decimals and Real Numbers
Objectives
Focus on Success
Prep Test
Section 4.1 Introduction to Decimals
Section 4.2 Addition and Subtraction of Decimals
Section 4.3 Multiplication and Division of Decimals
Section 4.4 Solving Equations with Decimals
Section 4.5 Radical Expressions
Section 4.6 Real Numbers
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Test
Cumulative Review Exercises
Ch 5: Variable Expressions
Objectives
Focus on Success
Prep Test
Section 5.1 Properties of Real Numbers
Section 5.2 Variable Expressions in Simplest Form
Section 5.3 Addition and Subtraction of Polynomials
Section 5.4 Multiplication of Monomials
Section 5.5 Multiplication of Polynomials
Section 5.6 Division of Monomials
Section 5.7 Verbal Expressions and Variable Expressions
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Test
Cumulative Review Exercises
Ch 6: First-Degree Equations
Objectives
Focus on Success
Prep Test
Section 6.1 Equations of the Form x + a = b and ax = b
Section 6.2 Equations of the Form ax + b = c
Section 6.3 General First-Degree Equations
Section 6.4 Translating Sentences into Equations
Section 6.5 The Rectangular Coordinate System
Section 6.6 Graphs of Straight Lines
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Test
Cumulative Review Exercises
Ch 7: Measurement and Proportion
Objectives
Focus on Success
Prep Test
Section 7.1 The Metric System of Measurement
Section 7.2 Ratios and Rates
Section 7.3 The U.S. Customary System of Measurement
Section 7.4 Proportions
Section 7.5 Direct and Inverse Variation
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Test
Cumulative Review Exercises
Ch 8: Percent
Objectives
Focus on Success
Prep Test
Section 8.1 Percent
Section 8.2 The Basic Percent Equation
Section 8.3 Percent Increase and Percent Decrease
Section 8.4 Markup and Discount
Section 8.5 Simple Interest
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Test
Cumulative Review Exercises
Ch 9: Geometry
Objectives
Focus on Success
Prep Test
Section 9.1 Introduction to Geometry
Section 9.2 Plane Geometric Figures
Section 9.3 Triangles
Section 9.4 Solids
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Test
Cumulative Review Exercises
Ch 10: Statistics and Probability
Objectives
Focus on Success
Prep Test
Section 10.1 Organizing Data
Section 10.2 Statistical Measures
Section 10.3 Introduction to Probability
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Test
Cumulative Review Exercises
Final Exam
Solutions to "You Try It"
Answers to Selected Exercises
Glossary
Index
Table of Geometric Formulas and Properties
IBC

Citation preview

Take AIM and Succeed! Aufmann Interactive Method

AIM

The Aufmann Interactive Method (AIM) is a proven learning system that has helped thousands of students master concepts and achieve results. 493 To follow the aim, step through the HOW TO examples that are provided and then work through In most cases, the percent is written as a decimal before the basic percent equation is / YOU TRY IT the matched EXAMPLE solved. However, some percents are pairs. more easily written as a fraction than as a decimal. SECTION 8.2    The Basic PercenT equaTion

For example,

1 1 33 % 5 3 3

2 2 66 % 5 3 3

2 1 16 % 5 3 6

1 5 83 % 5 3 6

In HOW TO 2, the percent is written as a fraction rather than as a decimal. How to 2

What is 33 13 % of 90?

Percent # base 5 amount

Use the basic percent equation. Percent 5

3313% 5 13, base 5 90, amount 5 SolutionS to “You trY it”

n

S23

33 13 % of 90 is 30. You Try It 4 Strategy

Solution





You Try It 3

You Try It 4 You Try It 5

You Try It 6

30 5 n

Interactive

cent equation. Percent 5 n, base 5 40, The resistance is 0.125 ohm. n 5 0.625 5 62.5% 120namount 96 5 25 The proportion ratio, writSolve for n25 is 62.5% of 40. by dividing each method side of is based on writing two ratios . One ratio 5is the percent 120 Percent 120 #amount the equation ten by 120. Solution 5 amount as percent . The second ratio is the amount-to-base ratio, written as base 100 base . These two # You Try It 3 ratios form the proportion n 5 0.8 n 40 5 25 33% means 33 out of 100. Strategy To find the base, use the basic percent 40n 25 33 out of every 100 Americans carry balances percent amount Write the decimal as a percent. 25 n 5 80% 40 5 40 1 up to $10,000 on their credit cards. equation. Percent100 5 16 % 5 , base 5 n, base 3 correctly. 6 answered 80%8 “You of the questions n 5 0.625 5 62.5% Solutions You to Chapter Try It” amount 5 15 1 1 110 25 is 62.5% of 40. The proportion method can be illustrated by a diagram. The rectangle at the left is divided 110% 5 110a b5a b51 # base 5 amount Solution Percent Percent 100 100 10 SecTIon 8.1Amount into two parts. On the left-hand side, the whole rectangle is represented by 100 and the You Try It 3 1 part by the # n percent. 100 Try It 1 Base 33% means 33 out of 100. 5 15 On the right-hand side, the whole rectangle is represented by the base You 110% 5 11010.012 5 1.10 Strategy To find the base, use the basic percent and the6 part by the amount. The ratio of the percent to 100 is equal to the ratio of the 33 out of every 100 Americans carry balances 1 2 1 amount base. #6 1 1 1 100 1 up to $10,000 on their credit cards. 6 # tonthe 5 15 equation. Percent 5 16 % 5 , base 5 n, 6 33 % 5 33 a b5 a b 3 6 65457_Ch08_481-532.indd 7/25/12 11:29 AM 3 3 100 3 493 100 When solving a percent problem using the basic percent equation, we first have to identify n 5 90 amount 5 15 1 110 and the 1 amount. The same is true 100 1 the percent, the base, when solving a percent problem 2 You Try It 2 110% 5 110a b5a b51 5 5 # base 5 amount Solution ercent the 16using % of 90 is 15. 100 100 method. 10 Remember that the proportion the base usually Pfollows word of. 300 3 3 1 # n 5 15 1 2 1 10% 5 110 0.01 5 1.10 You Try It 4 Percent 5 25, base 5 n, amount 5 8 0.8% 5 0.810.012 5 0.008 6 How to 5 What is 32% of 85? 25 8 1 #6 5 1 1 1n 100 1 6 # n 5 15 percent amount 5 5 500 3 100 6 5 You Try It 3 33 % 5 33 5 a b a b Use the proportion method. 5 1100%2 5 % 5 71 % 100 base 100 3 25 #3n 5 100 # 8 3 100 7 7 7 7 n 5 90 Look 32 n 25n 5 800 100 1at the diagram at the left. 2012 Cengage Learning. All Rights Reserved. May 32% not be copied, in 5 whole in part.5 Due to electronic third party content may be2 suppressed from5the eBook and/or eChapter(s). Editorial review has n scanned, 5or duplicated, 5 800 Percent 32,orbase 85, amountrights, 5 n some 5 Copyright 14 14 deemed that any 1400 25n 85 rights restrictions require it. 16 at % of 90 is 15. does not materially affect the overall300 Cengage Learning reserves the right to remove additional content any time100 if subsequent 3 1100%2 5 suppressed 1 5 5 % < content 155.6% learning 5 experience. 3 25 25 9 9 9 9 100 32 85

Solutions to Chapter 8 “You Try It”

You Try It 2

1# 90 5 n 3

3 3 300 SolutionS to “You trY it” S23 You Try It 7 5 1100%2 5 % 5 60% 5 5 5 To find the resistance: The three elements of the basic percent equation are the percent, the base, and the amount. SECTION 8.2    The Basic PercenT equaTion 60% of consumers have a rewards credit card. 495 c Write the basic inverse variation equation, If any two elements of the basic percent equation are given, the third element can be replace the variables by the given values, and found. You Try It 4 3 3 300 0.038 5 0.0381100%2 You Try It 8 solve for k. You Try It 7 5 1100%2 5 % 5 60% To find the resistance: 5 3.8% 5 5 5 Strategy c Write the inverse variation equation, replacIn HOW TO 1 and HOW TO 2, the unknown was the amount. In HOW TO 3 below, the ExamplE 3 yOu Try ing k by its value. Substitute 0.02 for the IT 3 60% of consumers have a rewards credit card. c W rite the basic inverse variation equation, unknown SecTIon 8.2is the percent. In HOW TO 4, the unknown is the base. diameter and solve for the resistance. replace the variables by the given values, and 60 is 2.5% what? 16 23 % of what is 15? YouofTry It 1 0.038 5 0.0381100%2 You Try It 8 k solve for k. R 5 2 Strategy to 3 To find the amount, use the basic percent 5 3.8% Your solution 20 is what percent of 32? d Solution How c Write the inverse variation equation, replac2 2 k Use the basic percent ing equation. k by its value. Substitute 0.02 for the # base 5 amount the equation. Percent 5 66 % 5 , Use basic percent equation. Percent         •     R 5 0.5 when  d 5 0.01. 0.5 5 SecTIon 8.2 3 3 10.012 2 diameter and solve for the resistance. Percent 5 2.5% 5 5 45, amount 5 n 5 20 5 0.025, Percent 5base n,base base 5n,32, amount You Try It 1n # 32 5 20 k k amount 5 60         •  Solve for k. 0.5 5 # base 5 amount Solution R P5 Solution ercent 0.0001 2 20 Strategy 32n To find the amount, use the basic percent for n by ddividing each side of 5 2 Percent # base Solve 5 amount 0.00005 5 k 2 2 32 32 equation by 32. k 1452 5 n # n the 0.025 5 60 equation. Percent 5 66 % 5 , 3         •   R 5 0.5 when  d 5 0.01. 0.5 5 0.00005 2 3 3 10.012 n 5 0.625 R 5 60 30 5 n 0.025n d2 base 5 45, amount 5 n 5 k2as a percent. 0.025 0.025 Write the decimal n 5 62.5% •   Solve for k.         0.00005 0.530 is 66 5 % of 45. Solution Percent # base 5 amount         •  d 5 0.02 R 5 0.0001 3 n 20 5 is 2400 10.022 2 62.5%5ofk32. 2 0 .00005 0.00005         •  Solve for R. 1452 5 n 60 is 2.5% 2400. YouofTry It 2 R 5 3 0.00005 Solution on p. S23 0.0004 Strategy R T5 o find the percent, use the basic per 30 5 n R 5 0.125 d2 Apply tHe concept cent equation. Percent 5 n, base 5 40, 2 0.00005 The resistance is 0.125 ohm. What percent of 30 is 66 5 25   96 You correctly the ques-% of 45.     of •  the d 5120 0.02questions on an exam. Ramount 5 answered 2 3   OBJECTIVE B Solution 10.022 # base tions did answer correctly? Percent 5 amount you To solve percent problems using proportions # 40  5 0.00005 n 25 #       •   Solve for R. You Try It 2 Use the basic Percent base 5 amount R 5 percent equation. Problems can be solved using the basic percent equation can also be solved using 40nthat 25 0.0004 Strategy n # 120 T5 o find the percent, use the basic per 5 Percent 5 base 5 96 96 R n, 5proportions. 0.125540120, amount 40

For extra support, you can find the complete solutions to problems in the back of the text. the YOU TRY IT

SecTIon 8.1 You Try It 1

Aufmann





Method

Ask the Authors! We have taught math for many years. During that time, we have had students ask us a number of questions about mathematics and this course. Here you find some of the questions we have been asked most often, starting with the big one.

Dick Aufmann

Joanne Lockwood

Why do I have to take this course?

You may have heard that “Math is everywhere.” That is probably a slight exaggeration, but math does find its way into many disciplines. There are obvious places like engineering, science, and medicine. There are other disciplines such as business, social science, and political science where math may be less obvious but still essential. If you are going to be an artist, writer, or musician, the direct connection to math may be even less obvious. Even so, as art historians who have studied the Mona Lisa have shown, there is a connection to math. But, suppose you find these reasons not all that compelling. There is still a reason to learn basic math skills: You will be a better consumer and be able to make better financial choices for you and your family. For instance, is it better to buy a car or lease a car? Math can provide an answer.

I find math difficult. Why is that? It is true that some people, even very smart people,

find math difficult. Some of this can be traced to previous math experiences. If your basic skills are lacking, it is more difficult to understand the math in a new math course. Some of the difficulty can be attributed to the ideas and concepts in math. They can be quite challenging to learn. Nonetheless, most of us can learn and understand the ideas in the math courses that are required for graduation. If you want math to be less difficult, practice. When you have finished practicing, practice some more. Ask an athlete, actor, singer, dancer, artist, doctor, skateboarder, or (name a profession) what it takes to become successful and the one common characteristic they all share is that they practiced—a lot.

Why is math important? As we mentioned earlier, math is found in many fields of study. There are, however, other reasons to take a math course. Primary among these reasons is to become a better problem solver. Math can help you learn critical thinking skills. It can help you develop a logical plan to solve a problem. Math can help you see relationships between ideas and to identify patterns. When employers are asked what they look for in a new employee, being a problem solver is one of the highest ranked criteria.

What do I need to do to pass this course? The most important thing you must do is to know and understand the requirements outlined by your instructor. These requirements are usually given to you in a syllabus. Once you know what is required, you can chart a course of action. Set time aside to study and do homework. If possible, choose your classes so that you have a free hour after your math class. Use this time to review your lecture notes, rework examples given by the instructor, and begin your homework. All of us eventually need help, so know where you can get assistance with this class. This means knowing your instructor’s office hours, the hours of the math help center, and how to access available online resources. And finally, do not get behind. Try to do some math EVERY day, even if it is for only 20 minutes.

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

6

edition

Prealgebra An Applied Approach

Richard N. Aufmann Palomar College

Joanne S. Lockwood Nashua Community College

Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States

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This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest.

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Prealgebra: An Applied Approach, Sixth Edition Richard N. Aufmann, Joanne S. Lockwood Senior Publisher: Charlie Van Wagner Acquisitions Editor: Marc Bove Developmental Editor: Danielle Derbenti Assistant Editor: Lauren Crosby Editorial Assistant: Jennifer Cordoba Media Editors: Heleny Wong, Guanglei Zhang Brand Manager: Gordon Lee Marketing Communications Manager: Jason LaChapelle Content Project Manager: Cheryll Linthicum Art Director: Vernon Boes Manufacturing Planner: Becky Cross

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Printed in the United States of America 1  2  3  4  5  6  7  16  15  14  13  12

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Brief Contents

A 1 2 3 4 5 6 7 8 9 10

AIM for Success  AIM-1 Whole Numbers  1 Integers  85 Fractions  145 Decimals and Real Numbers  229 Variable Expressions  307 First-Degree Equations  371 Measurement and Proportion  431 Percent  481 Geometry  533 Statistics and Probability  601

Final Exam 647 Solutions to “You Try It”  S1 Answers to Selected Exercises  A1 Glossary  G1 Index  I1

v Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

vii



Contents

CHAPTER

A

AIM for Success

AIM-1

This important chapter outlines some study skills that are used by students who have been successful in this course. Topics include how to stay motivated, making a commitment to succeed, how to manage your time, and preparing for and taking tests. There is a complete guide to the textbook and how to use its features to become a successful student.

CHAPTER

1

Whole Numbers

1

PREP TEST ​ ​1 SECTION 1.1

A To identify the order relation between two numbers ​ ​2







C To round a whole number to a given place value ​ ​5



D To solve application problems and use statistical graphs ​ ​7

SECTION 1.2

B T  o write whole numbers in words, in standard form, and in expanded form ​ ​3

A To add whole numbers ​ ​18





B To subtract whole numbers ​ ​24



C To solve application problems and use formulas ​ ​28

CHECK YOUR PROGRESS ​ ​40 SECTION 1.3

A To multiply whole numbers ​ ​41







C To divide whole numbers ​ ​48



D To factor numbers and find the prime factorization of numbers ​ ​53



E To solve application problems and use formulas ​ ​55

SECTION 1.4



SECTION 1.5

B To simplify expressions that contain exponents ​ ​46

A To solve equations ​ ​67 B To solve application problems and use formulas ​ ​69 A T  o use the Order of Operations Agreement to simplify expressions ​ ​73

CHAPTER 1 SUMMARY ​ ​77 CONCEPT 1 REVIEW EXERCISES ​ ​81 CHAPTER 1 TEST ​ ​83

vii Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

viii

c o n t e n t s

CHAPTER

2

Integers

85

PREP TEST ​ ​85 SECTION 2.1

A To identify the order relation between two integers ​ ​86







C To evaluate expressions that contain the absolute value symbol ​ ​89



D To solve application problems ​ ​90

SECTION 2.2

B To find the opposite of a number ​ ​88

A To add integers ​ ​98





B To subtract integers ​ ​102



C To solve application problems and use formulas ​ ​106

CHECK YOUR PROGRESS ​ ​114 SECTION 2.3

A To multiply integers ​ ​115







C To solve application problems ​ ​120

SECTION 2.4



SECTION 2.5

B To divide integers ​ ​117

A To solve equations ​ ​127 B To solve application problems and use formulas ​ ​129 A T  o use the Order of Operations Agreement to simplify expressions ​ ​133

CHAPTER 2 SUMMARY ​ ​137 CHAPTER 2 REVIEW EXERCISES ​ ​139 CHAPTER 2 TEST ​ ​141 CUMULATIVE REVIEW EXERCISES ​ ​143

CHAPTER

3

Fractions

145

PREP TEST ​ ​145 SECTION 3.1

A To find the least common multiple (LCM) ​ ​146







C To solve application problems ​ ​148

SECTION 3.2

B To find the greatest common factor (GCF) ​ ​147

A T  o write proper fractions, improper fractions, and mixed numbers ​ ​153







C To identify the order relations between two fractions ​ ​158



D To solve application problems ​ ​160

SECTION 3.3

B To write equivalent fractions ​ ​156

A To multiply fractions ​ ​167





B To divide fractions ​ ​172



C To solve application problems and use formulas ​ ​175

CHECK YOUR PROGRESS ​ ​185

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

ix

c o n t e n t s

SECTION 3.4

A To add fractions ​ ​186







C To solve application problems ​ ​194

SECTION 3.5



SECTION 3.6

B To subtract fractions ​ ​190

A To solve equations ​ ​203 B To solve application problems and use formulas ​ ​205 A To simplify exponential expressions ​ ​210





B To simplify complex fractions ​ ​211



C T  o use the Order of Operations Agreement to simplify expressions ​ ​214

CHAPTER 3 SUMMARY ​ ​220 CHAPTER 3 REVIEW EXERCISES ​ ​223 CHAPTER 3 TEST ​ ​225 CUMULATIVE REVIEW EXERCISES ​ ​227

CHAPTER

4

Decimals and Real Numbers

229

PREP TEST ​ ​229 SECTION 4.1

A To write decimals in standard form and in words ​ ​230







C To round a decimal to a given place value ​ ​233



D To solve application problems ​ ​235

SECTION 4.2



SECTION 4.3

B To identify the order relation between two decimals ​ ​232

A To add and subtract decimals ​ ​240 B To solve application problems and use formulas ​ ​243 A To multiply decimals ​ ​251





B To divide decimals ​ ​254



C T  o convert between decimals and fractions and to identify the order relation between a decimal and a fraction ​ ​258



D To solve application problems and use formulas ​ ​261

CHECK YOUR PROGRESS ​ ​271 SECTION 4.4



SECTION 4.5

A To solve equations ​ ​272 B To solve application problems ​ ​273 A To find the square root of a perfect square ​ ​276







C To solve application problems and use formulas ​ ​281

SECTION 4.6

B To find the square root of a whole number ​ ​279

A To graph real numbers on the number line ​ ​287





B To graph inequalities on the number line ​ ​290



C To solve application problems ​ ​292

CHAPTER 4 SUMMARY ​ ​298 CHAPTER 4 REVIEW EXERCISES ​ ​301 CHAPTER 4 TEST ​ ​303 CUMULATIVE REVIEW EXERCISES ​ ​305

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

x

c o n t e n t s

CHAPTER

5

Variable Expressions

307

PREP TEST ​ ​307 SECTION 5.1



SECTION 5.2



SECTION 5.3

A To apply the Properties of Real Numbers ​ ​308 B To use the Distributive Property ​ ​311 A To add like terms of a variable expression ​ ​318 B To simplify general variable expressions ​ ​320 A To add polynomials ​ ​326





B To subtract polynomials ​ ​327



C To solve application problems ​ ​329

CHECK YOUR PROGRESS ​ ​335 SECTION 5.4



SECTION 5.5



SECTION 5.6



SECTION 5.7

A To multiply monomials ​ ​336 B To simplify powers of monomials ​ ​338 A To multiply a polynomial by a monomial ​ ​342 B To multiply two binomials ​ ​343 A To divide monomials ​ ​346 B To write numbers in scientific notation ​ ​349 A To translate verbal expressions into variable expressions ​ ​354





B T  o translate verbal expressions into variable expressions and then simplify ​ ​356



C To solve application problems ​ ​357

CHAPTER 5 SUMMARY ​ ​362 CHAPTER 5 REVIEW EXERCISES ​ ​365 CHAPTER 5 TEST ​ ​367 CUMULATIVE REVIEW EXERCISES ​ ​369

CHAPTER

6

First-Degree Equations

371

PREP TEST ​ ​371 SECTION 6.1



SECTION 6.2



SECTION 6.3

A To solve equations of the form x ​1 ​a ​5 ​b ​ ​372 B To solve equations of the form ax ​5 ​b ​ ​375 A To solve equations of the form ax ​1 ​b ​5 ​c ​ ​380 B To solve application problems using formulas ​ ​381 A To solve equations of the form ax ​1 ​b ​5 ​cx ​1 ​d ​ ​386





B To solve equations containing parentheses ​ ​387



C To solve application problems using formulas ​ ​389

CHECK YOUR PROGRESS ​ ​394

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

xi

c o n t e n t s

SECTION 6.4



SECTION 6.5



SECTION 6.6



A To translate a sentence into an equation and solve ​ ​395 B To solve application problems ​ ​397 A To graph points in a rectangular coordinate system ​ ​403 B To solve application problems using scatter diagrams ​ ​405 A To determine solutions of linear equations in two variables ​ ​412 B To graph equations of the form y ​5 ​mx ​1 ​b ​ ​414

CHAPTER 6 SUMMARY ​ ​423 CHAPTER 6 REVIEW EXERCISES ​ ​425 CHAPTER 6 TEST ​ ​427 CUMULATIVE REVIEW EXERCISES ​ ​429

CHAPTER

7

Measurement and Proportion

431

PREP TEST ​ ​431 SECTION 7.1

A To use units of measurement in the metric system ​ ​432

SECTION 7.2

A To write ratios and rates ​ ​440

SECTION 7.3

A To use units of measurement in the U.S. Customary System ​ ​444





B To solve application problems ​ ​446



C To convert between U.S. Customary units and metric units ​ ​448

CHECK YOUR PROGRESS ​ ​455 SECTION 7.4



SECTION 7.5



A To solve proportions ​ ​456 B To solve application problems using proportions ​ ​458 A To solve direct variation problems ​ ​465 B To solve inverse variation problems ​ ​467

CHAPTER 7 SUMMARY ​ ​473 CHAPTER 7 REVIEW EXERCISES ​ ​475 CHAPTER 7 TEST ​ ​477 CUMULATIVE REVIEW EXERCISES ​ ​479

CHAPTER

8

Percent

481

PREP TEST ​ ​481 SECTION 8.1



SECTION 8.2

A To write percents as decimals or fractions ​ ​482 B To write fractions and decimals as percents ​ ​484 A To use the basic percent equation ​ ​491







C To solve application problems ​ ​497

SECTION 8.3



B To solve percent problems using proportions ​ ​495

A To solve percent increase problems ​ ​507 B To solve percent decrease problems ​ ​508

CHECK YOUR PROGRESS ​ ​512 Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

xii

c o n t e n t s

SECTION 8.4



SECTION 8.5

A To solve markup problems ​ ​513 B To solve discount problems ​ ​515 A To solve simple interest problems ​ ​520

CHAPTER 8 SUMMARY ​ ​525 CHAPTER 8 REVIEW EXERCISES ​ ​527 CHAPTER 8 TEST ​ ​529 CUMULATIVE REVIEW EXERCISES ​ ​531

CHAPTER

9

Geometry

533

PREP TEST ​ ​533 SECTION 9.1

A To solve problems involving lines and angles ​ ​534







C To solve problems involving the angles of a triangle ​ ​542

SECTION 9.2



B T  o solve problems involving angles formed by intersecting lines ​ ​539

A To find the perimeter of plane geometric figures ​ ​551 B To find the area of plane geometric figures ​ ​556

CHECK YOUR PROGRESS ​ ​569 SECTION 9.3

A T  o find the unknown side of a right triangle by using the Pythagorean Theorem ​ ​570







C To determine whether two triangles are congruent ​ ​574

SECTION 9.4



B To solve similar triangles ​ ​572

A To find the volume of geometric solids ​ ​581 B To find the surface area of geometric solids ​ ​584

CHAPTER 9 SUMMARY ​ ​592 CHAPTER 9 REVIEW EXERCISES ​ ​595 CHAPTER 9 TEST ​ ​597 CUMULATIVE REVIEW EXERCISES ​ ​599

CHAPTER

10

Statistics and Probability

601

PREP TEST ​ ​601 SECTION 10.1 A To make frequency distributions ​ ​602



B To read histograms ​ ​604



C To read frequency polygons ​ ​605

SECTION 10.2 A To determine the mean, median, and mode of a distribution ​ ​611



B To draw a box-and-whiskers plot ​ ​615



C To calculate the standard deviation of a distribution ​ ​616

CHECK YOUR PROGRESS ​ ​624

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

c o n t e n t s

xiii

SECTION 10.3 A To determine the probability of simple events ​ ​625



B To determine the odds of an event ​ ​629

CHAPTER 10 SUMMARY ​ ​638 CHAPTER 10 REVIEW EXERCISES ​ ​641 CHAPTER 10 TEST ​ ​643 CUMULATIVE REVIEW EXERCISES ​ ​645

Final exam ​ ​647 Solutions to “You Try It” ​ ​S1 Answers to selected exercises ​ ​A1 Glossary ​ ​G1 Index ​ ​I1

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Preface

A

mong the many questions we ask when we begin the process of revising a textbook, the most important is, “How can we improve the learning experience for the student?” We find answers to this question in a variety of ways, but most commonly by talking to students and instructors and by evaluating the written feedback we receive from instructors. Bearing this feedback in mind, our ultimate goal as we set out to create the sixth edition of Prealgebra: An Applied Approach was to provide students with more materials to help them better understand the underlying concepts presented in this course. As a result, we have made the following changes to the new edition. New to this edition is the Focus on Success vignette that appears at the beginning of each chapter. Focus on Success offers practical tips for improving study habits and performance on tests and exams. We now include an Apply the Concept box within the objectives that teach addition, subtraction, multiplication, and division. The arithmetic operation is applied to a real-world situation so that students can relate the operation to their everyday lives. For example, multiplication of whole numbers is applied to determining the total number of cans of soda in eight six-packs of soda. HOW TO examples offer detailed instructions for solving a variety of problems. The definition and key concept boxes have been enhanced in this edition; they now include examples to show how the general case translates to specific cases. In each exercise set, the first group of exercises is now titled Concept Check. The Concept Check exercises focus on the concepts that lie behind the skills developed in the section. We consider an understanding of these concepts essential to a student’s success in mastering the skills required to complete the exercises that follow. In the News exercises are application exercises found within most exercise sets. These exercises are based on newsworthy data and are drawn from current events. Every chapter contains Check Your Progress exercises. This feature appears approximately mid-chapter and tests students’ understanding of the concepts presented to that point in the chapter. We trust that the new and enhanced features of the sixth edition will help students more successfully engage with the content. By narrowing the gap between the concrete and the abstract, between the real world and the theoretical, students should more plainly see that mastering the skills and topics presented is well within their reach and well worth the effort.

New to This Edition • • • • •

Apply the Concept boxes are provided within objectives that teach arithmetic operations. Concept Check exercises appear at the beginning of each exercise set. Enhanced definition and key concept boxes now include examples that illustrate how the general case applies to specific cases. The Focus on Success feature at the beginning of each chapter offers practical guidance to help students develop positive study habits. Check Your Progress exercises appear approximately mid-chapter and test students’ understanding of the concepts presented up to that point in the chapter.

xv Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

xvi

Preface

• • • • • •

• •

HOW TO examples offer detailed explanations of problem-solving techniques. Tips for Success now appear in every chapter. In the News articles within the exercise sets relate the math skills being learned to current events. Application problems throughout the text have been updated. Projects or Group Activities are now included at the end of each exercise set. Chapter A, AIM for Success, now appears as the first chapter of the text. This chapter describes skills used by students who have been successful in this course. Topics include how to stay motivated, making a commitment to success, time management, and how to prepare for and take tests. A guide to the textbook is included to help students use its features effectively. More annotations have been added to the worked Examples, to more effectively explain the steps of the solutions. Many of the Chapter Summaries have been expanded to include more entries and more descriptive explanations.

Organizational Changes We have made the following changes in order to improve the effectiveness of the textbook and enhance the student’s learning experience. •

• •

•

•

• •

• •

In Section 2.1, the introduction to positive and negative numbers has been rewritten. The material is now easier for the student to understand, which will result in a better start to the semester! The introduction to Objective 3.3A has been reorganized and streamlined. In Section 5.1, the presentation of the Properties of Real Numbers has been reorganized. Additional examples of each property are provided. The new format makes it easier for students to understand and apply the concepts. Section 5.4 now includes more detailed examples of each Rule for Simplifying Exponential Expressions. Section 5.6 provides more detailed examples of the Rule for Dividing Exponential Expressions, the Definition of Zero as an Exponent, and the Definition of Negative Exponents. In Section 5.7, the table for translating verbal phrases into mathematical expressions has been expanded to include more of the verbal phrases students will encounter in application problems. The design is more prominent, and the table is easier to use as a reference. Objectives 6.2B and 6.3C now provide a wider range of application problems that make use of first-degree equations. The exposition in Section 6.6 has been expanded to provide more explanation and more annotated examples on the important topic of graphing linear equations in two variables. Section 7.1 contains a new introduction to the metric system. Chapter 8, Percent, has been revised substantially. In Section 8.1, the exposition was increased from two to four pages to provide a slower and more descriptive introduction to the crucial topic of percent. More examples are given in the exposition, and additional numbered Examples and You Try Its provide students with the exposure they need to understand the concepts. Two pages have been added to the Section 8.1 exercise set. The expanded exercise set provides more basic, concept-driven exercises; more application problems to help students un-

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

P r e f a c e

•

•

•

xvii

derstand how percent is used in the real world; and more practice in writing percents as fractions and decimals and in writing fractions and decimals as percents. The topic of the basic percent equation is presented in Section 8.2. In the new edition, the exposition is two pages longer, for a slower, more detailed introduction to solving percent problems. Three pages have been added to the Section 8.3 exercise set to provide students with more practice in solving percent problems. There are more hands-on exercises; for example, the student is asked to shade a given percent of a grid and circle a given percent of a number of objects. Objective 10.2B has been expanded to provide students with more examples of, and practice with, determining the five values that make up a box-and-whiskers plot. In Objective 10.2C, the flow and display of the material has been improved. Students will find it easier to follow the steps involved in calculating standard deviation.

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Take AIM and Succeed! An Objective-Based Approach Prealgebra: An Applied Approach is organized around a carefully constructed hierarchy of objectives. This “objective-based” approach provides an integrated learning path that enables you to find resources such as assessment tools (both within the text and online), videos, tutorials, and additional exercises for each Integers objective in the text.

1

Integers

SECTIOn 2.1

A To identify the order relation between two integers B To find the opposite of a number C To evaluate expressions that contain the absolute value symbol D To solve application problems SECTIOn 2.2

A To add integers B To subtract integers C To solve application problems and use formulas

2

Focus on Success

2

SECTIOn 2.1

A To identify the order relation between two integers B To find the opposite of a number C To evaluate expressions that contain the absolute value symbol Focus on Success D To solve application problems

Each Chapter Opener outlines the learning OBJECTIVES that appear in each section of the chapter. The list of objectives serves OBJECTIVES as a resource to guide you in your study and review of the topics.

SECTIOn 2.3

Taking the PREP TEST for each chapter will help you determine which topics you need to study more carefully and which topics you need only review. The ANSWERS to the PREP TEST provide references to the OBJECTIVES on which the exercises are based.

OBJECTIVES

2

Have you formed SECTIOn 2.2 or are you part of a study group? Remember that a study A To add integers group can be a great way to stay focused B To subtract integers on succeeding in this course. You can C To solve application support each other, get help and offer problems and use formulas help on homework, and prepare for tests SECTIOn 2.3Homework Time, page together. (See AAIM-5.) To multiply integers

B To divide integers C To solve application problems

Have you formed or are you part of a study group? Remember that a study group can be a great way to stay focused on succeeding in this course. You can support each other, get help and offer help on homework, and prepare for tests together. (See Homework Time, page AIM-5.)

Prep Test

© iStockphoto.com/CEFutcher

Are you ready to succeed in this chapter? Take the Prep Test below to find out if you are ready to learn the new material.

SECTIOn 2.4

Answers to selected exercises A3 A To solvePrep equations Test © iStockphoto.com/CEFutche r 1. Place the correct symbol, , or ., between the two numbers. B To solve application problems and use formulas 54 45 Are you ready to succeed in this chapter? Take the Prep Test below Chapter 1 test SECTIOn 2.5 It 4] 2.  16,000 Exampleto 10]learn   3. the 4029 [1.2B; HOW TO 11]   4.  x 4y3 [1.3B; You Try It 7]   find  out if you[1.3B; are ready new material. SECTIOn 2.4 1.  329,700 [1.3A; You Tryto Order of 9]   7.  7177 , 7717 [1.1A; 2. What from 4 to 6]8 on 5.  Yes [1.2A; Example 5] A  To 6.  use 3000 the [1.1C; Example Exampleis3]the  distance 8.  8490 [1.1B; Example   the number line? A To solve equations Operations Agreement to , 9.  three hundred eighty-two thousand four [1.1B; Example   10.  the 2000two [1.2A; Example 1]   11.  11,008 [1.3A; HOW TO 1]   1. Placenine thehundred correct symbol, or ., 5] between numbers. B To solve application expressions problems and12.  use2,400,000 formulas [1.3A; Examplesimplify 2]   13.  1, 2, 4, 23, 46, 92 [1.3D; HOW TO 16]   14.  24 # 3 # 5 [1.3D; Example 18]   For Exercises 3 to 6, add, subtract, multiply, or divide. 45 Commutative Property of Addition [1.2A; Example 2]   17.  897 [1.3C; Example 15]   15.  30,866 [1.2B; Example 9]  5416.  The

A To multiply integers B To divide integers C To solve application problems

SECTIOn 2.5

1 8193 3. 7654 A To use the Order What is the Example distance3]from 4 to7 8[1.2A; on the number 21.  of 44 [1.4A; HOW TO 3] 2.   22.  56 [1.5A;   23.  Example 2] line?   24.  78 [1.4B; Example 3]   Operations Agreement to 25.  720 [1.3A; HOW TO 5]   26.  The balance in your account after making the purchase is $556. [1.2C; Example 11]   simplify expressions 18.  26 [1.5A; Example 2]

  19.  Girls grow the most between birth and age 1. [1.2B; Example 8]

  20.  51 [1.4A; HOW TO 2]

 

4. 6097 For  Exercises 3 to 6, add, multiply, or divide. 27a.  The perimeter is 96 cm. b.  The area is 576 cm .subtract, [1.3E; HOW TO 19, HOW TO 21] 2   2318 2

28.  The diver’s monthly take-home pay is $4456. [1.2C; Example 11]   29.  There are 465 million more registered users on Facebook than on 3. 7654 1 8193 Twitter. [1.2C; Example 11]   30.  The commission earned is $1440. [1.3E; Example 21] 3   56 5. 472 HAPTER 2    Integers 92The valueCper 31.  share of the fund is $11. [1.3E; Example 22]

4. 6097 2 2318

6. 144 4 24

5. 472 3 56 2.1  EXERCISES

Answers to Chapter 2 Selected Exercises 6. 144 4 24

prep test

Concept Check

7. Solve: 1 9 [1.2A] 1.  54 . 45 [1.1A]   2.  4 units [1.1A] 22  5 3. y15,847 8.  5 [1.4A]   9.  $172 [1.2C]   10.  31 [1.5A]

3

In every section, an OBJECTIVE STATEMENT introduces each new topic of discussion. Videos are available for each objective.

7. Solve: 22 5 y 1 9

8.   Solve: 5 60   4.  3779 [1.2B] 5.  26,43212b [1.3A]   6.  6 [1.3C]

7. 13 [1.4A]

8. Solve: 12b 5 60   1. Fill in the blank with left or right. 9. What is the price of a scooter that cost a business $129 and has a markup seCtion 2.1 a. On a number line, the number 28 is to the of the number 23. of $43? Use the formula P   5 C 1 M, where P is the price of a product 1a.  left   b.  right   3.  negative;   5. of absolute valuethat   cost 7.  a business 9. Whatpositive is the price a scooter $129 and has a3markup b. On a number line, the number 0 is to the of the number 24. −6 −5 −4 −3 −2consumer, −1 0 1 2 C 4 the 5 6 cost paid by the store for the product, and M is the is of $43? Use the formula P 5 C 1 M, where Ptoisathe price of a  product   11.  9.  −6 −5 −4 −3 −2 −1 0 1 2to3a consumer, 4 5 6 C is the−6cost paid by −1 the store and M is the −5 −4 −3 −2 0 1 for 2markup. 3the4 product, 5 6   15.  1   17.  21   19.  3   21.  A is 24. C is 22.   23.  A is 27. D is 24. 13.  markup.   2. −6 F−5 ill in the blank with , or .. −4 −3 −2 −1 0 1 2 3 4 5 6 18 2131 2 62,2 101 1 12 4 4 # 32   27.  3 . 27   29.  242 , 27 2   31.  53 . 246   33.  10. . 25 251 Simplify: , 210. 220   35.  25.  22 a. On a number line, 21 is to the right of 210, so 21 18 2 10. 23, Simplify: 1912  443.  4 #210, 32 27, 25, 4, 12   45a.  Never true   b.  Sometimes true 37.  22,On a number line, 25 is to the left of 2, so 25 0, 3   39.  25, 1, 4   41.  24,620, 5, 27, b. 2.

65457_Ch02_085-144.indd 85

c.  Sometimes true   d.  Always true   47.  245   49.  88   51.  2n   53.  d 55. the opposite of negative thirteen C Hof AP T E R 2p     I 59.  n t efive g e plus r s negative ten   61.  negative fourteen minus negative three   63.  negative thirteen minus eight   86the opposite 57.  negative 65.  m plus negative n   67.  7   69.  246   71.  73   73.  z   number. The opposite of a 75.  2p 77. Negative 79. 4 81. 9 85 83. 11 85. 12   3. The opposite of a positive number is a 87.  23 negative number is a   89.  227   91.  25   93.  241 number.   95.  293   97.  10 99. 8 101. 6 103. 0 212 0 . 0 8 0 105. 0 6 0 , 0 13 0 s e c t i o n 107.  0 21 0 , 0 217 0   109.  0 x 0 5 0 2x 0   111.  2 0 6 0 , 2142, 0 27 0 , 21292   113.  29, 2 0 27 0 , 2152, 0 4 0   115.  2 0 10 0 , 2 0 28 0 , 21222, 21232, 0 5 0   117.  The USPS loss as a negative number is 2329,000,000.   119.  The loss was greater during the first quarter.   121a.  The predicted earnings per share for Mycopen in 2015 are 227¢.   4. Ipredicted n the expression 8 (22), the first 2 and the second b.   The earnings per 2 share for Mycopen in sign is read as 2017 are 240¢.   123.  Yes, Mycopen is predicted to have a profit in 2018.   7/25/12 11:23 AM 125.  The stock that showed the least net change 2 sign is read as . is Stock B.   127.  The wind chill factor is 29°F.   129.  The cooling power is 235°F.   65457_Ch02_085-144.indd 85 131.  A temperature of 230°F with a 5-mile-per-hour wind would feel colder than a temperature of 220°F with a 10-mile-per-hour wind.   133.  211   135.  26, 25, 24, 23, 22, 21, 0, 1, 2, 3, 4, 5, 6   137a.  22 and 6   b.  22 and 8   139.  Answers will vary.   11, OBJECTIVE A To identify the order relation between two integers

2.1

Introduction to Integers

0 25 0 5 5 is read “the of negative five is   5.   The equation seCtion 2.2 five.” In Chapter zero andminus numbers zero were 1.  the same; negative   3.  Negative; negative 1,  only 5.  Negative;   7. greater (25)  than 9.  211   11.  discussed. 25 13. In 8 this15.chapter, 24 17. 22 are214 introduced. “7 230 degrees 37. below “$50 in41. 228 Tips Success 19.  29 for   21.  1   23.  215  numbers 25.  0   less 27. than 221 zero   29.  31. 19Phrases 33. such 25 as35. 9 zero,” 39. 212 1272 sea level”The refer less than zero.with Japan and Mexico is Before a new  47.  11 debt,” 43.  213 you   begin 45.  218   49. and 1  “20 51. feet x 1below   53a.  totaltoofnumbers the U.S. balance of trade chapter, you should 2$126,500,000,000. b. The of the U.S. balance of trade with and Mexico is 2$94,900,000,000. 0 2ytake 0 for y 0 2yCanada 0 5total 26.   6.  Evaluate time of to the review c. some total U.S. balance of trade with Japan and China is 2$333,200,000,000.   55.  5   57.  22   59.  211   61.  217   The a. Replace y with . 5 0 2 1262 0 previously learned skills. One 63.  The Addition Property of Zero Numbers   65.  Thegreater Associative of Addition   67.  0numbers.   69.  18 Numbers   71.  No less   73.  75. No thanProperty zero are called positive thanYeszero are way doThe opposite of 26 is 6. this is to complete Sometimes tob. 77.  true   79.  Always true   81.  23   83.  213 5  085.  7 0  87.  0 89. 217 91. 23 93. 12 95. 27 called negative numbers. the Prep Test. See page 97.    99.  267   101.  26   103.  215   105.  The difference between the highest and lowest temperatures ever recorded in South 2106 This c. test The absolute value of 6 is 6. 5 85. focuses on the

4

Section exercises are keyed to OBJECTIVE STATEMENTS.

America is 82°C.   will 107.  109. 11 111. 0 113. 2138 115. 26 117. 13 119. 28 121. 5 123. 2 125. 26 particular skills that be29 127.  12  for129.  23 chapter.   131.  18   133.  Yes   135.  No   137.  Yes 139. Sometimes true required the new 141a.  The difference in elevation between Mt. Aconcagua and Death Valley is 7046 m.   b.  The difference in elevation between Mt. Kilimanjaro A positive number can be indicated by placing a plus sign (1) in front of the number. and Assal is 6051 m.   143.  Europe has the smallest difference between highest and lowest elevations.     Lake OBJECTIVE A To identify the order relation between two integers For example, we can write 14 instead of 4. Both 14 and 4 represent “positive 4.” Usually, 145.  The difference between the average temperatures at 12,000 ft and 40,000 ft is 86°.   147.  The golfer’s score relative to par is 23.   Point of Interest however, the plus sign isinomitted and it ison understood thatwas the107°F. number  isb. a The positive number. 149a.  Themanuscripts difference between the high and low temperatures the Unites States April 2, 2010, difference between the Chinese Graph the number on the number line. high andfrom low temperatures dating about 250 b.c.in the contiguous 48 states on April 2, 2010, was 100°F.   151.  The distance is 19 units.   153.  willrecorded vary. Possible answers include 21 and 26, 22 and 25, and 23 and   7. Answers 25 8. 24. 21 contain the first

A negative number is indicated by placing a negative sign (2) in front of the number. use of negative numbers. However, it was not −2 until late0 1 number −5 −4 −3 −1 2 3 4 21 5 is 6 read −6 −5 −4 −3 −2 −1 two,” and0so1on.2 3 4 5 6     −6Unless   “negative one,” 22 is read   “negative otherwise noted, all content on this page is © Cengage Learning. in the fourteenth century that mathematicians generally accepted 9. 26 these numbers. 10. 22

The

The number line can be extended to the left of zero to show negative numbers.

   

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

65457_em-ans_A01-A26.indd 3

11. x, for x 5 5

xviii    PREFACE

   

   

−7

−6

  −5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

  −4

−3

−2

−1

0

1

2

12. x, for x 5 0

3

4

5

6

7

7/25/12 11:38 AM

−6 −5 −4 −3 −2 −1 0 1 The 2 3integers 4 5 6 are  

13. x, for x 5 24

85

−5.−4 −2 −1 0 1 to2 the 3 right 4 5 of 6 zero . . . , 24, 23, 22, 21, 0,  1, 2, −6 3, 4, . . −3 . The integers are the positive integers. The integers to the left of zero are the negative integers. Zero is an integer, but it is neither positive nor negative. The point corresponding to 0 on the 14. x, for x 5 23 number line is called the origin.

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

 

 

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,On some third line, partythe content may suppressed from the eBook and/or eChapter(s). Editorial review has Unless otherwise noted, all content on this page is © Cengage Learning. a number numbers get be larger as we move from left to right. The numbers get deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at Therefore, any time if subsequent rights restrictions require it. smaller as we move from right to left. a number line can be used to visualize the order relation between two integers.

7/25/12 11:23 AM

An Objective-Based Review This “objective-based” approach continues through the end-of-chapter review and addresses a broad range of study styles by offering a wide variety of review tools.     114

−6 −5 −4 −3 −2 −1

2. On the number line, which number is 5 units to the left of 2?

3. Place the correct symbol, , or ., between the two numbers. 212 216

4. Write the given numbers in order from smallest to largest. 28, 7, 219, 4

5. F ind the opposite of the number. a. 211 b. 13 c. 2m

6. Write the expression in words. 25 2 (27)

137

CHAPTER 2    Summary

CHAPTER

2

7. Simplify. a. 2(242) b. 2(t)

8. Find the absolute value of a. 218 and b. 37.

Summary

9. Evaluate a. 0 251 0 and b. 2 0 67 0 .

10. Evaluate 2 0 x 0 for x 5 22.

Key Words

Examples

11. P lace the correct symbol, < or >, between 12. Write the given numbers in order from smallest to the two numbers.greater than zero are called positive numbers largest. . Numbers 9, 87, and 603 are positive numbers. Numbers

86] , 0 3 0 , 2 0 28 0 , 2 0 12 0 than 0 0 7 0 zero are 0 25 0 , p. called negative numbers . [2.1A, 2 1262 0 219 less 25, 241, and 2729 are negative numbers.



139 2729, 241, 25, 9, 87, and 603 are integers. 0 is an integer, but it is neither a positive nor a negative integer.

CHAPTER 2    Review exeRcises

are . . . , 24, 23, 22, 21, 0, 14. 1, 2,Add: 3, 4, 20 . . .1. The The1integers 13. Add: 28 (212) (23) 1 (27) integers can be defined as the whole numbers and their opposites. Positive integers are to the right of zero on the number line. CHAPTER Negative integers are to the left of zero on the number line. 15. Subtract: 5 2 40 16. Subtract: 232 2 (216) [2.1A, p. 86]

2

Review Exercises

Opposite numbers are What the same distance 8 is the opposite, or additive inverse, of 28. 17. Simplify: 4 2 (215) 2 3 1 7are two numbers that18. is 211 minus 16? from zero on the number line but on opposite sides of zero. The 22 is the opposite, or additive inverse, of 2. opposite of a number is called its additive inverse. [2.1B, p. 88;   1. Write the expression 8 2 1212  in words.  2. Evaluate 2 0 236 0 . 2.2A, p. 100] 19. Find the sum of 26, 29, and 14. 20. Evaluate 2x 1 y for x 5 26 and y 5 22.

The absolute value of a number is the distance from zero to the 090 5 9 number on the a number is aofposi21. Evaluate a 2 (2b) fornumber a 5 25 line. and bThe 5 7.absolute value 22. of Is 27 a solution the equation 23 5 y 2 4?   3.  Find the product of 240 and 25. 4. Evaluate 2a0 249 0b for a 5 9 5 227 and b 5 23. tive number or zero. The symbol for absolute value is “ 0 0 ”. HAPTER 2    TEST 2 0 9 0 5C 29 [2.1C, p. 89] 23. T emperature Which is the colder temperature, 216°F or 24°F?

CHAPTER

  5.  Add: 228 1 14





2

TEST

141

6. Simplify: 2 12132

24. T emperature Find theRules temperature afterProcedures a rise of 8°C from 23°C. Essential and

Examples

Order Relations a . b if a is line. 26 . 212   7.  Graph 22 on the number line. to the right of b on the number 8. Solve: 224 5 26y 25. M athematics The distance andof point number line to thealeft b onb on thethe number line. a ,d between b if a is point 28 , 4 0 a1 22bp.03.87] is given by the formula d 5[2.1A, Find d 6when a 5 9 and b 5 25. −6 −5 −4 −3 −2 −1 0 4 5 1. Write the expression 23 1 1252 in words. 2. Evaluate 2 0 234 0 .

To add integers with the same sign, add the absolute values of 6 1 4 5 10 otherwise noted, all content on this page is © Cengage Learning. the numbers. Then attach sign p. Unless 99] 1242 5 2611b for a 210 4 1232 the 1 of the addends. [2.2A,10. Find the quotient of 840 and 24.   9.  Divide: 251 5 211 and b 5 29. 3. What is 3 minus 215? 4. Evaluate a

65457_Ch02_085-144.indd 114

To add integers with different signs, find the absolute values 26 1 4 5 22 Cumulative Review exeRCises 143 of theEvaluate numbers. Subtract the lesser absolute 12y2 for x 12x2 6 1 1242 5 2 5 24 and y 5value 26. from the greater 6. Identify the property that justifies the statement. 5. 12122 2 1272 2 15the 2 sign 12. Evaluate 2ab for a 5 22 and b 5 29.7/25/12 11:23 AM 11.  Subtract: 26 absolute value. Then attach of the addend with the greater 223 1 4 5 4 1 12232 absolute value. [2.2A, p. 99]

Cumulative Review Exercises

To subtract two integers, add the opposite of the second integer 6 21424 5 6 1 1242 5 2 13.  Find the sum of 18, 213, and 26. 14. Estimate the product of 439 and 28. Multiply: 218 Find the difference between 227 and 232. 7. 8. Find the sum of 23, 26, and 11. 1. 2. to theWhat is 2360 divided by 230? first integer. [2.2B, p. 103] 6 2 1242 5 6 1 4 5 10 26 2 4 5 26 1 1242 5 210 26 2 1242 5 26 1 4 5 22 9. Place the correct symbol between the two numbers. 10. Subtract: 7 2 1232 2 12 2 2 2 # 15.  Simplify:  1222 2 1232 4 11 2 42 2 2 6 16. Evaluate 2x 2 y for x 5 21 and y 5 3. 4. Simplify: 16 4 13 1 52 # 9 2 24 3. Divide: 19,254 16 219 4 6

1.  Evaluate 5xy for x Estimate the sum of5672, 843, 509, and 417.   7. 80 and y 5 6. 15. Is 29 a solution of the equation 17 2 x 5 8? 12172 9. Subtract: 228 2 12132 2 on this 10 Learning. 17   3.  28 UnlessSimplify: otherwise noted, all content page is ©2 Cengage

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Le

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FINAL EXAM

12. Simplify: 2 12492 FINAL EXAM 647 4 6. Write three hundred nine thousand four hundred eighty in standard form. 0 14. Write the given numbers in order from smallest −4 to largest. −8   8. 2.  Simplify: 18 1 316 2 42 2 4 2 What is 2294 divided by 214? 2 0 5 0 , 2 12112 , 0 29 0 , 2 132 −12 − 6

11. Evaluate a 2 b 2 c for a 5 6, b 5 22, and 17. Golf The scores of four golfers after the final  c 5 11. 0 282 0 . 5. Evaluate 2 round of the 2011 Boeing Classic are shown in the  right.  What  is  the  difference  between  figure  at  the  Tom  Lehman’s  score  and  Mark  Calcavecchia’s  13. score?  Find the product of 50 and 25.

65457_Ch02_085-144.indd 137

k

A FINAL EXAM is provided following the last chapter of the text. The Final Exam is designed to simulate a comprehensive exam covering all the concepts presented in the text. The ANSWERS to the Final Exam questions are provided in the appendix at the back of the text and include references to the section objectives on which the questions are based.



0 1 2 3 4 5 6

Ca lc

CUMULATIVE REVIEW EXERCISES, which appear at the end of each chapter (beginning with Chapter 2), help you maintain previously learned skills. The ANSWERS include references to the section objectives on which the exercises are based.

1. Graph 23 on the number line.

B ec

Each CHAPTER TEST is designed to simulate a typical test of the concepts covered in the chapter. Each ANSWER includes an objective reference as well as a reference to a numbered Example, You Try It, or HOW TO in the text that is similar to the given test question.

CheCk Your Progress: ChaPter 2

− 9

By completing the CHAPTER REVIEW EXERCISES, you can practice working on problems in an order that is different from the order in which they were presented in the chapter. The ANSWER to each Chapter Review exercise includes a reference to the objective on which the exercise is based. This reference will help you quickly identify where to go if you need further practice with a particular concept.

Integers

−16

− 14

At the end of each chapter, you will find a CHAPTER SUMMARY containing KEY WORDS and ESSENTIAL RULES AND PROCEDURES presented in the chapter. Each entry includes an objective reference and a page reference that show where in the chapter the concept was introduced. An example demonstrating the concept is also included.

CHAPTER 2

Score

CHECK YOUR PROGRESS exercises appear approximately mid-chapter and test your understanding of the concepts presented up to that point in the chapter.

16. On the number line, which number is 2 units to Golfers’ Scores in 2011 Boeing Classic 10. Find the sum of 224, 16, and 232. the right of 25? 0 a 2 b 0 2 3bc3 for a 5 22, b 5 4,   4.  Evaluate and c 5 21.

PREFACE 

  xix

g

en

Ya ng

−4

9

Score

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on

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Pr

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Golf The scores of four golfers af4 2 y for x 5 2 and y 5 11. 11. 17. Find all the factors of 44. 12. Evaluate x 4 ter the final round of the 2011 Wegmans 0 LPGA Championship are shown in the Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has −4 7 5 figure the right. What is difference   5.  What is 5 38 at minus 2 11    at the   6. restrictions Find the quotient deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional any time if subsequent rights require it.of 9 and 6 . 16 ? content −8 between Taylor Leon’s score and Yani 65457_Ch02_085-144.indd 139

7/25/12 11:24 AM

SECTION 2.3    Multiplication and division of integers

Understanding the Concepts

115

s e c t i o n

2.3

Multiplication and Division of Integers

Each of the following features is designed to give you a fuller understanding of the key concepts.  

CHAPTER 7    MeasureMent and ProPortion

When 5 is multiplied by a sequence of decreasing integers, each product decreases by 5.

5132 5122 5112 5102

7.4  EXERCISES

5 15 5 10 55 50

The pattern can be continued so that 5 is multiplied by a sequence Concept Check

51212 5 25 51222 5 210 of negative numbers.a To cmaintain the pattern of decreasing by 5,   1.  A   n  equation  of  the products form  b 5 which  states  that  two  ratios  or  rates  are  equal,  d ,  be the resulting must negative. 51232 is  5 215 called a  . The extremes are the terms   and  , and the  51242 5 220 means are the terms   and  . In a true proportion, the product of the  . number and means and the product of the extremes are  This example illustrates that the product of a positive a negative number is negative. CHAPTER 2    Integers

x 5   2.   The  first  step  the  write  the  equation  that 5 215 25132 17   is  to  integers, When 25in  is solving  multiplied byproportion  a sequence85 of5 decreasing each states product that  the  product  increases byof  5. the  means  equals  the  product  of  the  extremes:  25122 5  210 25112 5 25  ? 17. 85 #   5 Apply the concept 25102 5 0 Bromine Mercury Figure 2.5 shows the melting points of 0 251212 5 5 The pattern can be continued so point that 25 is multiplied by a sePoint of Interest bromine and mercury. The melting To maintain of increasing 251222 5 10 Operations with negative of quence helium ofisnegative 7 timesnumbers. the melting point the pattern −10 For Exercises 3 and 4, use the information that Jane ran 4 mi in 50 min. Let n be the  5, the resulting products must be positive. 251232 5 15 numbers were not accepted of by mercury. Find the melting point of number of miles Jane can run in 30 min at the same rate. until the late thirteenth 251242 5 20 −20 helium. century. One of the first determine  how  illustrates many  miles  Jane  can  run ofin  30 negative min,  solve  the  proportion  This example that the product two numbers attempts to prove that  3.  the  To To find the melting point of helium, multi−30 4 miis positive. mi product of two negative ply the 5 melting. point of mercury (239°C) numbers is positive was 50 min  min −40 made in the book Ars Magna,by 7. The pattern for multiplication shown above is summarized in the following rule for mulby Girolamo Cardan, in 1545. 239(7) 5 2273 tiplying integers. Figure 2.5  Melting Points of Chemi  4.   To determine how many miles Jane can run in 30 min, one student used the procal Elements (in degrees Celsius) The melting point of helium is 2273°C. 4 n Multiplying Two Integers 30 50 portion  Rule 5 for and a second student used the proportion  5 . Can either of  n 50 30 4 The properties of multiplication presented in Chapter 1 hold true for integers as well as To multiply two integers with the same sign, multiply the absolute values of the facthese proportions be used to solve this problem? whole numbers. These properties are restated below. tors. The product is positive.     Integrating To multiply two integers with different signs, multiply the absolute values of the factechnology The Multiplication tors. The product Property is negative. To multiply (26)(215) with yourof Zero a # 0 5 0   or  0 # a 5 0 − 7

− 39

 

calculator, enter the following: 6

1/2 3



15

EXAMPLES Property   OBJECTIVE A To solve proportions 5 The Multiplication 1/2 1. 241122 5 248 •  The signs are different. The product is negative. a # 1 5 a   or  1 # a 5 a of One 1262 12152 2. 5 90 •  The signs are the same. The product is positive. Determine whether the proportion is true or not true. The Commutative Property a#b5b#a of Multiplication

⎫ ⎪ ⎬ ⎪ ⎭

⎫ ⎪ ⎬ ⎪ ⎭

 

26

 

215

27 9 3 4 45 3 5 How  Associative   6.  the product 5   of 211 and 25.   7.  5   The Property to 1 Find 8 18 19 135 9 4 1a # b2 # c 5 a # 1b # c2 of Multiplication A product is the answer to a multiplication problem. EXAMPLES Multiply 211 and 25. The signs are the same. The product is positive. 1.  28(0) 5 0  2.  24(1) 5 24 6 min 30 min5 55 7 tiles 42 tiles 300 ft 450 ft 3.  (25)(3) 5 3(25)  4.  (26  2)  (21) 5 26  [2  (21)] 211(25)   9.  5   10.  5   11.  5   5 cents 25 cents 4 ft 20 ft 4 rolls 7 rolls

  5. 

 

how to 2

take note

Multiply: 21232 1252 1272

For HOW TO 2 at the right,  Multiply the first two numbers. the product is the same if the  Solve. Round to the nearest hundredth. numbers are multiplied in a  Then multiply the product by the third number. different order. For instance, 65457_Ch02_085-144.indd 115 2 Continue n 7 havenbeen multiplied. 2(23)(25)(27) until all the numbers 5   14.  5   13.  5 2(23)(35) 3 15 15 15 5 2(2105) 5 2210 By the Multiplication Property of One, 1 # 6 5 6 and 1

  8. 

3 54 5 4 72

12. 

$65 $26 5 5 days 2 days

21232 1252 1272 5 261252 1272

15. 

5 301272 n 512 5 2210   5 25

n 7 5 8 8

7/25/12 11:25 AM

16. 

# x 5 x. Applying the rules for multiplication, we can extend this to 21 # 6 5 26 and 21 # x 5 2x. how to 3

take note

Evaluate 2ab for a 5 22 and b 5 29.

Replace a with 22 When variables are placed  next to each other, it is  Simplify 2 1222 . understood that the operation  65457_Ch07_431-480.indd 460 is multiplication. 2ab means  Multiply. “the opposite of a times b.”

and b with 29.

2ab 2 1222 1292

5 21292

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5 218

119

SECTION 2.3    Multiplication and division of integers

how to 4

Is 24 a solution of the equation 5x 5 220?

5x 5 220

Replace x by 24 and then simplify. 51242 220 The division properties of zero and one, which were presented in Chapter 1, hold true for The results 220 5 220 integers as wellare as equal. whole numbers. These properties are restated here. Yes, 24 is a solution of the equation. Unless otherwise noted, all content on this page is © Cengage Learning. Division Properties of Zero and One If a 2 0,

POINT OF INTEREST boxes, which relate to the topic under discussion, may be historical in nature or of general interest.

0 5 0. a

a 5 1. a a is undefined. 0

If a 2 0,

a 5a 1

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EXAMPLES 1.

0 50 27

How to 5

Point of Interest Historical manuscripts indicate that mathematics is at least 4000 years old. Yet it was only 400 years ago that mathematicians started using variables to stand for numbers. Before that time, mathematics was written in words.

2.

23 51 23

3.

29 5 29 1

4.

218 is undefined. 0

Evaluate a 4 12b2 for a 5 228 and b 5 24.

Replace a with 228 and b with 24. Simplify 2 1242 . How to 6

a 4 12b2 228 4 12 1242 2 5 228 4 142

Divide.

5 27

Is 24 a solution of the equation 220 x 5 5?

Replace x by 24 and then simplify. The results are equal.

xx    PREFACE

Phase4Photography/Shutterstock.com

116

Definition/key concept boxes contain examples to illustrate how each definition or key concept is applied in practice.

TAKE NOTE boxes alert you to concepts that require special attention.

To multiply integers

460

Degrees Celsius

concept check exercises promote conceptual understanding. Completing these exercises will deepen your understanding of the concepts you are learning and provide the foundation you need to successfully complete the remaining exercises in the exercise set.

OBJECTIVE A

220 55 x 220 5 24 555 Yes, 24 is a solution of the equation.

EXAMPLE 5

yOu Try IT 5

Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has FindCengage the quotient of 223 and 223. What is 0time divided by 217? rights restrictions require it. deemed that any suppressed content does not materially affect the overall learning experience. Learning reserves the right to remove additional content at any if subsequent

1

2

ExAmPlE 4

3 n 17. 5 8 12 Write 0.35% as a decimal.

18.

5 40 you TRy iT 4 3 7 5 19. 5 n n 8 40 Write 0.8% as a decimal.

Solution your solution 0.35% 5 0.3510.012 5 0.0035 •   Move the decimal point two  16 25 15 72 120 144 21. places to the left. 5 22. 5 23. 5 n n n 45 25 40

20.

7 25 5 n 12

24.

65 14 5 n 20

Solutions on p. S23

Application of the Concepts OBJECTIVE B 25.

 

0.7 6.4 0.5 To write fractions and decimals as percents n 1.2 n 5 26. 5 27. 5 n 1.2 2.3 20 2.8 32

28.

2.5 165 5 n 0.6

To write a fraction as a percent, multiply the fraction by 100%. Because 100% 5 100 100 5 1,

The section exercises offer many opportunities to put the multiplying concepts you learning practice. a number by 100% isare the same as multiplying theinto number by 1. 29.

x 16 5 6.25 87

x 132 5 2.54 640 7 Write 8 as a percent. 30.

How to 3

31.

1.2 y 5 0.44 14.2

32.

12.5 102 5 y 55

7 7 5 1100%2 463 8 S8E C T I O N 7 . 4     P r o P o r t i o n s 4 n2 3 n7 35. 5 7 36. 5 # 3 6 8 5 5 a 100b% 8 62. Automobile Recall An automobile recall was based on engineering tests that 700 showed 22 defects in 1000 cars. At this rate, how many defects would be found in % 5 87.5% 5 8 125,000 cars? 2 7 5 7 7 31n 3 51n 37. 5 38. 5 39. 5 40. 5 n13 n11 3 10 4 12 2 2 63. Exercise Walking 5 mi in 2 h will burn 650 calories. Walking at the same rate, Apply tHe concept how many miles would a person need to walk to lose 1 lb? (The burning of 3500 In a recent year, 14 of college students who were credit card holders used a credit card calories is equivalent to the loss of 1 lb.) Round to the nearest hundredth. to pay for tuition. (Source: American Council on Education) What percent of college x4 3 x1 5 6 x2 7 x4 41. 5students 42. 43. 44. 5 who were credit card5holders used a credit card5 to pay for tuition? 3 An 4account executive bought 8 a new 3 8 2 car and drove 22,000 1 mi 5in the first 64. Travel 1 1 4 months. Write At the 1 same rate, how many miles 1 will the account executive drive in 5 25% 5 1100%2 4 as a percent by multiplying 4 by 100%. 4 4 3 years?

APPLY THE CONCEPT boxes illustrate how an arithmetic operation is applied to a realworld situation so that you understand how the operation is used in everyday life. © Najlah Feanny/Corbis

Multiply 78 by 100%. n12 1 51n 3 5 34. 5 33. 5 2 8 4

25% of students who were credit card holders used a credit card to pay for tuition. 5 2 5 1 3 5 8 5 45. 5 46. 5 47. 5 48. 5 Elections 65. 8 2 x4 x  3A pre-election survey showed that 2 out of every 3 eligible voters would x6 3 x6 4 cast ballots in the county election. There are 240,000 eligible voters in the county. How many people are expected to vote in the election? 49. a. Write a true proportion using the numbers 9, 4, 2, and 18. b. Write a true proportion using only the numbers 8, 2, and 4. How Much7/25/12 Food11:28 DoAM 66. Food Waste Using the rate given in the news clipping at the right, find the cost You Waste? of food wasted by a. the average family of three and b. the average family of five.

In the NEWS!

THINK ABOUT IT exercises promote deeper conceptual understanding. Completing these exercises will expand your understanding of the concepts being addressed.

65457_Ch08_481-532.indd 484

In the United States, the estimated cost of food

50.

a. Write a proportion in which the product of the means and the product of the wasted each year by the 1 extremes is 60. average family of four is The scale on a map is 2 in. equals 8 mi. What is the actual distance 67. Cartography b. Using different numbers 1 than you used in part (a), write another proportion in $590. in. apart on the map? between two points that are 1 Source: University of Arizona 4 which the product of the means and the product of the extremes is 60.

68. Candles A slow-burning candle will burn 1.5 in. in 40 min. How many inches will the candle burn in 4 h?

CRITICAL THINKING exercises may involve further exploration or analysis of the topic at hand. They may also integrate concepts introduced earlier in the text.

SECTION 7.4    ProPortions

463

Critical Thinking 69. 62. Automobile Recall An automobile recall was based on engineering tests that Elections A survey of voters in a city claimed that 2 people of every 5 who voted cast a ballot in favor of city amendment A, and 3 people of every 4 who voted showed 22 defects in 1000 cars. At this rate, how many defects would be found in cast a ballot against amendment A. Is this possible? Explain your answer. 125,000 cars?

65457_Ch07_431-480.indd 461

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SECTION 7.4    ProPortions

64. Travel An account executive bought a new car and drove 22,000 mi in the first 4 months. Three people put their money together to buy lottery tickets. The first At the same rate, how many miles will the account executive drive in 71. Lotteries 62. Automobile Recall An automobile recall was based on engineering tests that 3 years? person put in $25, the second person put in $30, and the third person put in $35. One showed 22 defects in 1000 cars. At this rate, how many defects would be found in of the tickets was a winning ticket. If the winning ticket paid $4.5 million, what was 125,000 cars? the first person’s share of the winnings? 65. Elections A pre-election survey showed that 2 out of every 3 eligible voters would cast ballots in the county election. There are 240,000 eligible voters in the county. 63. Exercise Walking 5 mi in 2 h will burn 650 calories. Walking at the same rate, 72. How many people are expected to vote in the election? Nutrition A pancake 4 in. in diameter contains 5 g of fat. How many grams how many miles would a person need to walk to lose 1 lb? (The burning of 3500 of fat are contained in a pancake 6 in. in diameter? Explain how you arrived at your calories is equivalent to the loss of 1 lb.) Round to the nearest hundredth. answer. 66. Food Waste Using the rate given in the news clipping at the right, find the cost of food wasted by a. the average family of three and b. the average family of five. 64. Travel An account executive bought a new car and drove 22,000 mi in the first 4 months. At the same rate, how many miles will the account executive drive in

Working through the application exercises will prepare you that contain real data to answer questions and solve problems that you encounter outside of class, using facts and information that you gather on your own.

IN THE NEWS exercises help you understand the importance of mathematics in our everyday world. These application exercises are based on information taken from popular media sources such as newspapers, magazines, and the Internet.

3 years? 1 67. Cartography The scale on a map is 2 in. equals 8 mi. What is the actual distance

65457_Ch07_431-480.indd 463

1 between two points that are 1 in. apart on the map?

4 65. Elections A pre-election survey showed that 2 out of every 3 eligible voters would cast ballots in the county election. There are 240,000 eligible voters in the county. How many people are expected to vote in the election? 68. Candles A slow-burning candle will burn 1.5 in. in 40 min. How many inches will

463

In the NEWS!

Marie C Fields/Shutterstock.com

70. 63. Determine whether the statement is true or false. Exercise Walking 5 mi in 2 h will burn 650 calories. Walking at the same rate, how many miles would a person need to walk to lose 1 lb? (The burning of 3500 a c b d b. If b 5 d , then a 5 c . a. A quotient 1a 4 b2 is a ratio. calories is equivalent to the loss of 1 lb.) Round to the nearest hundredth. a c a c c. If ab 5 dc , then ac 5 db . d. If b 5 d , then d 5 b .

How Much Food Do You Waste?

In the United States, the estimated cost of food wasted each year by the average family of four is $590. 7/25/12

11:27 AM

Source: University of Arizona

In the NEWS!

the candle burn in 4 h? 66.

How Much Food Do You Waste?

Food Waste Using the rate given in the news clipping at the right, find the cost of food wasted by a. the average family of three and b. the average family of five.

Critical Thinking

In the United States, the estimated cost of food

69.

wasted each year by the Elections A survey of voters in a city claimed that 2 people of every 5 who average family of four is voted cast a ballot in favor of city amendment A, and 3 people of every 4 who voted The scale on a map is 12 in. equals 8 mi. What is the actual distance 67. Cartography $590. 1 cast a ballot against amendment A. Is this possible? Explain your answer. in. apart on the map? between two points that are 1 Source: University of Arizona 4

70. Determine whether the statement is true or false. 68. Candles A slow-burning candle will burn 1.5 in. in 40 min. How many inches will a c b d the candle burn in 4 h? 1a

a. A quotient



c. If ab 5 dc , then ac 5 db .

4 b2 is a ratio.

Critical Thinking 69.



b. If b 5 d , then a 5 c . a c a c d. If b 5 d , then d 5 b .

Elections A survey of voters in a city claimed that 2 people of every 5 who 71. Lotteries Three people put their money together to buy lottery tickets. The first voted cast a ballot in favor of city amendment A, and 3 people of every 4 who voted person put in $25, the second person put in $30, and the third person put in $35. One cast a ballot against amendment A. Is this possible? Explain your answer.

of the tickets was a winning ticket. If the winning ticket paid $4.5 million, what was the first person’s share of the winnings?

Marie C Fields/Shutterstock.com

By completing the writing exercises, you will improve your communication skills while increasing your understanding of mathematical concepts.



70. Determine whether the statement is true or false.

b. If ab 5 dc , then ba 5 dc . a. A quotient 1a 4 b2 is a ratio. A pancake 4 in. in diameter contains 5 g of fat. How many grams 72. cNutrition a b c. If ab 5 d. If ab 5 dc , then da 5 bc . of fat are contained in a pancake 6 in. in diameter? Explain how you arrived at your d , then c 5 d .

65457_Ch07_431-480.indd 463

PREFACE 

Marie C Fields/Shutterstock.com

answer.

71. Lotteries Three people put their money together to buy lottery tickets. The first person put in $25, the second person put in $30, and the third person put in $35. One of the tickets was a winning ticket. If the winning ticket paid $4.5 million, what was the first person’s share of the winnings?

  xxi

72. Nutrition A pancake 4 in. in diameter contains 5 g of fat. How many grams of fat are contained in a pancake 6 in. in diameter? Explain how you arrived at your answer. Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

7/25/12 11:27 AM

Focus on Study Skills An emphasis on setting a foundation of good study habits is woven into the text.

Updated! AIM for Success Chapter A, AIM for Success, outlines study skills that are used by students who have been successful in this course. By making Chapter A the first chapter of the text, the stage is set for a successful beginning to the course.

OBJECTIVES

A

Focus on Success

SECTIOn A.1

• Get Ready • Motivate Yourself • Develop a “Can Do” Attitude Toward Math • Strategies for Success • Time Management • Habits of Successful Students

This important chapter describes study skills that are used by students who have been successful in this course. Chapter A covers a wide range of topics that focus on what you need to do to succeed in this class. It includes a complete guide to the textbook and how to use its features to become a successful student.

SECTIOn A.2

• • • •

Get the Big Picture Understand the Organization Use the Interactive Method Use a Strategy to Solve Word Problems • Ace the Test • Ready, Set, Succeed!

Prep Test

hxdbzxy/Shutterstock.com

Are you ready to succeed in this course?

1.   Read this chapter. Answer all of the questions. Write down your answers on paper. 2.  Write down your instructor’s name. 3.  Write down the classroom number.

Integers

4.  Write down the days and times the class meets. 5.  Bring your textbook, a notebook, and a pen or pencil to every class. 6.  Be an active participant, not a passive observer.

Focus on success appears at the start of each Chapter Opener. These tips are designed to help you make the most of the text and your time as you progress through the course and prepare for tests and exams.

OBJECTIVES

2

Focus on Success

SECTIOn 2.1

A To identify the order relation between two integers B To find the opposite of a number C To evaluate expressions that contain the absolute value symbol D To solve application problems

Have you formed or are you part of a study group? Remember that a study group can be a great way to stay focused on succeeding in this course. You can support each other, get help and offer help on homework, and prepare for tests together. (See Homework Time, page AIM-5.)

SECTIOn 2.2

A To add integers B To subtract integers C To solve application problems and use formulas

AIM-1

SECTIOn 2.3

65457_fm-aim_1-12.indd 1

Prep Test

A To multiply integers B To divide integers C To solve application problems

© iStockphoto.com/CEFutcher

Are you ready to succeed in this chapter? Take the Prep Test below to find out if you are ready to learn the new material.

SECTIOn 2.4

A To solve equations B To solve application problems and use formulas

8/10/12 8:00 AM

1. Place the correct symbol, , or ., between the two numbers. 54

SECTIOn 2.5

45

2. What is the distance from 4 to 8 on the number line?

A To use the Order of Operations Agreement to simplify expressions

For Exercises 3 to 6, add, subtract, multiply, or divide. 3. 7654 1 8193 4. 6097 2 2318 5. 472 3 56

86

tips for success boxes outline good study habits and function as reminders throughout the text.

 

6. 144 4 24 CHAPTER 2    Integers 7. Solve: 22 5 y 1 9

s e c t i o n

8. Solve: 12b 5 60

2.1

9. W hat is the price of a scooter that cost a business $129 and has a markup of $43? Use the formula P 5 C 1 M, where P is the price of a product to a consumer, C is the cost paid by the store for the product, and M is the markup.

OBJECTIVE A

Tips for Success Before you begin a new chapter, you should take some time to review previously learned skills. One way to do this is to complete the Prep Test. See page 85. This test focuses on the particular skills that will be required for the new chapter.

65457_Ch02_085-144.indd 85

Point of Interest Chinese manuscripts dating from about 250 b.c. contain the first recorded use of negative numbers. However, it was not until late in the fourteenth century that mathematicians generally accepted these numbers.

Introduction to Integers 10. Simplify: 18 2 62 2 1 12 4 4 # 32

To identify the order relation between two integers

Numbers greater than zero are called positive numbers. Numbers less than zero are called negative numbers.

A positive number can be indicated by placing a plus sign (1) in front of the number. For example, we can write 14 instead of 4. Both 14 and 4 represent “positive 4.” Usually, however, the plus sign is omitted and it is understood that the number is a positive number. A negative number is indicated by placing a negative sign (2) in front of the number. The number 21 is read “negative one,” 22 is read “negative two,” and so on. The number line can be extended to the left of zero to show negative numbers.

−7

xxii    PREFACE

85

In Chapter 1, only zero and numbers greater than zero were discussed. In this chapter, numbers less than zero are introduced. Phrases such as “7 degrees below zero,” “$50 in debt,” and “20 feet below sea level” refer to numbers less than zero. 7/25/12 11:23 AM

−6

−5

−4

−3

−2

−1

0

1

2

3

4

5

6

7

The integers are . . . , 24, 23, 22, 21, 0, 1, 2, 3, 4, . . . . The integers to the right of zero are the positive integers. The integers to the left of zero are the negative integers. Zero is an integer, but it is neither positive nor negative. The point corresponding to 0 on the number line is called the origin.

On a number line, the numbers get larger as we move from left to right. The numbers get smallersome as wethird move from right to left.beTherefore, a number can and/or be usedeChapter(s). to visualizeEditorial review has Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, party content may suppressed from theline eBook the right ordertorelation twocontent integers.at any time if subsequent rights restrictions require it. deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the removebetween additional

493

SECTION 8.2    The Basic PercenT equaTion

Focus on Skills and Problem Solving

In most cases, the percent is written as a decimal before the basic percent equation is solved. However, some percents are more easily written as a fraction than as a decimal. For example, 1

1

2

2

2

1

1

5

33 % 5 66 % 5 16 % 5 83 % 5 3 3 3 3 3 6 3 6 The following features exemplify the emphasis on skills and the problem-solving process. In HOW TO 2, the percent is written as a fraction rather than as a decimal. What is 33 13 % of 90?

How to 2

Use the basic percent equation.

HOW TO examples provide solutions with detailed explanations for selected topics in each section.

1

Percent # base 5 amount 1# 90 5 n 3

1

Percent 5 333% 5 3, base 5 90, amount 5 n

30 5 n

1

33 3 % of 90 is 30. The three elements of the basic percent equation are the percent, the base, and the amount. If any two elements of the basic percent equation are given, the third element can be found.

88

 

INTEGRATING TECHNOLOGY margin notes offer optional instruction in the use of a scientific calculator.

CHAPTER 2    Integers

OBJECTIVE B

Integrating Technology The  1/2  key on your  calculator is used to find the  opposite of a number. The  2  key is used to perform  the operation of subtraction.

In HOW TO 1 and HOW TO 2, the unknown was the amount. In HOW TO 3 below, the unknown is the percent. In HOW TO 4, the unknown is the base. To find the opposite of a number TheHow distance onwhat the number is 3 units. tofrom 3 0 to203 is percentline of 32? The distance from 0 to 23 on the number line is 3 the 23 basic equation. units.Use 3 and arepercent the same distance from 0 on the number line, but 3 is to the right of 0 and 23 is to the 5 n, base 5 32, amount 5 20 left ofPercent 0.

3

3

S−3 o l−2 ut i o n S # t o2 “ 5 Y3oamount u trY it” Percent −1 0 1base

Solve for n by dividing each side of

S23

n # 32 5 20 32n

5

20

Two numbers that are the same distance from zero on the3number opposite 32 3 line but on 32 300 equation by 32.opposites. You Try It 7 sidesthe of zero are called 5 1100%2 5 % 5 60% 5 5 5n 5 0.625 To find the resistance: 60% of consumers have a rewards credit card. 23 isthe the decimal oppositeas of a3percent. and 3 is the opposite of 23. c Write the basic inverse variation equation, Write n 5 62.5% replace the variables by the given values, and 20 is 62.5%n,ofthe 32.opposite of n is 2n and the opposite of 2n is n. For any number 5e r 0.0381100%2 8 e B a 0.038 solve for k. S E C T I O NYou 8 . 2Try     ItT h sic P cenT equaTion 495 5 3.8% c Write the inverse variation equation, replac We can now define the integers as the whole numbers and their opposites. ing k by its value. Substitute 0.02 for the Apply tHe concept SecTIon 8.2 diameter and solve for the resistance. A negative sign cananswered be read as96 “the of.” You correctly of opposite the 120 questions on an exam. What percent of the quesTryTry It 1 IT 3 ExamplE 3 yOu tions did you answer correctly?You k Solution R 5 2 132 5 23 The opposite of positive 3 is negative 3. 2 To find the amount, use the basic percent # Use the basic percent equation.Strategy 60 is 2.5% of what? d 16 23 % of what is 15? Percent base 5 2amount 2 53 of negative 3. 2 1232 5 k Percent n, baseThe 55opposite 120, amount n # 120 5 96% 5 , 5 96 3 is positive equation. Percent 5 66         •     R 5 0.5 when  d 0.01. 0.5 5 3 3 Solution 10.012 2 Therefore, 2 1a2 5 2a and 2 12a2 5 a. Your solution 120n5 n 96 base 5 45, amount of Solve for n by dividing each side 5 k Use the basic percent equation. 120 120 •   Solve for k.         0.5 5 # base equation by 120. Solution Percentthe 5 amount that with the introduction of negative integers and opposites, symbols 1 and 2 0.0001 Notethe Percent 5 2.5% 5 0.025, base n, in different ways. can 5 be read 2 n 5 0.8 0.00005 5 k 1452 5 n amount 5 60 3 Write the decimal as a percent. n 5 80% 0.00005 6 12 “six plus two” 1 is read “plus” # base 5 R amount 5 30 5 n Percent 2 d You answered 80% of the questions correctly. 1 is read “positive” 12 “positive two” 0.025 # n 5 60 0.00005 2 % of 45. 2 is 30 is 66 read “minus” 0.025n R 56010.022 2         •6  d252 0.02“six minus two” 3 5 “negative two” 2 is read “negative” 0.025 0.025 0.00005         •22   Solve for R. You Try It 2 R 5 n 5 24000.0004 2 1262 “the opposite of negative six” 2 is read first as “the opposite of” Strategy and then To find the percent, use the basic peras “negative” C H A P T E R R5 8  0.125   Percent 49860 40, cent equation. Percent 5 n, base 7/25/125 11:29 AM 65457_Ch08_481-532.indd is 2.5%493of 2400. When the symbols 1 and 2 indicate the operations of addition and subtraction, spaces Solution on p. S23 The resistance is 0.125 ohm. amount 5 25

You Try It 4 Strategy

The EXAMPLE/YOU TRY IT matched pairs are designed to actively involve you in the learning process. The You Try Its are based on the Examples. These problems are paired so that you can easily refer to the steps in the Example as you work through the accompanying You Try It.

are inserted before and after the symbol. When the symbols 1 and 2 indicate the sign # base of a number (positive or negative), there is no space between the symbol and5the number. Solution Percent amount

Complete, WORKED-OUT SOLUTIONS to the You Try Its are included in an appendix at the back of the text. Compare your solution to the solution given in the appendix to obtain immediate feedback and reinforcement of the concept you are studying.

The PROBLEM-SOLVING APPROACH used throughout the text emphasizes the importance of problem-solving strategies. Model strategies are presented as guides for you to follow as you attempt the You Try Its that accompany the numbered Examples.

you TRy n # 40 5 25 ExAmPlE 8 iT 8 40n 25   OBJECTIVE B To solve percent problems using proportions ExAmPlE 5 you iT 5 TRy 5 A taxpayer pays a tax rate of 35% for state and According to Board-Trac, 19% 40 approximately 40 federal taxes. The taxpayer has an income the country’s 2.4equation million nsurfers are5 Problems that of can basic percent can also bewomen. solved using ofthe 5 0.625 62.5% Find opposite number. Find the opposite number. Solutions to the Chapter 8 “You Try It”be solved using $47,500. a.  Find state number female surfers in this b.  15 ofproportions. c.  aand federal a.  Estimate 24 b. the 213 c.  of2b 28the amount 25 is 62.5% of 40. taxes8.1 paid by the taxpayer. country. Write the number in standard form. SecTIon Solution Your solution You Try Ittwo 3 ratios . One ratio is the percent ratio, writThe proportion method is based on writing 8 b.  215 c.  2a You Try It 1 a. 33% means 33 out of 100. amount Strategy Your strategy Strategy To find the base, use the basic percent Solution on p. S5 ten as percent 33 out of every 100 Americans carry balances 100 . The second ratio is the amount-to-base ratio, written as base . These two 2 1 Unless otherwise noted, all content on this page is © Cengage Learning. To find theup to $10,000 on their credit cards. amount, use the basic ratios percent form the proportion equation. Percent 5 16 % 5 , base 5 n, equation. 3 6 percent amount Percent 5 35% 5 0.35, base amount 5 15 1 5 1 5 47,500, 110 1 You Try It 2 5 n 110% 5 110a b5a b5 100 base Solution # amount P ercent base 5 amount 100 100 10 65457_Ch02_085-144.indd 88 7/25/12 11:25 AM 1# The5proportion method can be illustrated by a diagram. The rectangle n 5 15 at the left is divided 5 11010.012 1.10 Percent 110% 6 represented by 100 and the Amount into two parts. On the left-hand side, the whole rectangle is 1 Solution Your solution the percent. On the right-hand side, the whole rectangle by the base 100 Base 1 1part by 100 1 1 15 # 6 6 # nis5represented % amount 5 33 a and You Try It 3 # base 33 5 b5 b amount. The ratio of the percent to 1006 is equal to the ratio of the the parta by the Percent 3 3 100 3 100 n 5 90 amount to the base. 0.35 # 47,500 5 n 100 1 2 16,625 5 n5 5 16 % of 90 is 15. 300 When 3 solving a percent problem using the basic percent 3 equation, we first have to identify The amount of taxes paid is the $16,625. percent, the base, and the amount. The same is true when solving a percent problem You Trythat It 4 the base Percent 5 25, base n, amount You Try It 4 0.8% 5 0.810.012using 5 0.008 the proportion method. Remember usually follows5the word of.5 8 25 8 5 5 5 500 3 100 n You Try It 5 5 1100%2 5 How % to 5 71 5 % What is 32% of 85? you TRy iT 9 25 # n 5 100 # 8 7 7 ExAmPlE 79 7 percent amount 25n 5 800 CHAPTER 8    Percent 524 5 Use the proportion method. A department5 store sale for An electrician’s wage year is $30.13 14has a14blue blazer on 1400 25nthis800 100 per hour, base 1100%2 price. You Try It 6 5 of5the original 5 What %