BASIC COLLEGE MATHEMATICS D. FRANKLIN WRIGHT CERRITOS COLLEGE BAM_TOC.indd3/13/2006, 3:31 PM1© Ha wk es P ublishing . A ll r igh ts reser ved . ii Editor: Cynthia Ellison Development Director: Marcel Prevuznak Production Editors: Harding Brumby, Phillip Bushkar, Mandy Glover Bethany Loftis, Nina Miller, Kim Scott Editorial Assistants: Kelly Epperson, D. Kanthi, B. Syam Prasad, Chris Yount Layout: QSI (Pvt.) Ltd.: U. Nagesh, E. Jeevan Kumar Art: Ayvin Samonte A division of Quant Systems, Inc. Copyright © 2007 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. 1023 Wappoo Rd. Suite A-6/Charleston, SC 29407 www.hawkeslearning.com No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written consent of the publisher. Library of Congress Control Number: 2006920801 Printed in the United States of America. Student Softcover Student Hardcover Student Softcover Bundle Student Hardcover Bundle 978-1-932628-19-7 978-1-932628-15-9 978-1-932628-20-3 978-1-932628-16-6 1-932628-19-3 1-932628-15-0 1-932628-20-7 1-932628-16-9 Solutions Manual 978-1-932628-17-3 1-932628-17-7 BAM_TOC.indd3/13/2006, 3:31 PM2© Ha wk es P ublishing . A ll r igh ts reser ved . iii Chapter 2 Exponents, Prime Numbers, & LCM 123 2.1 Exponents 124 2.2 Order of Operations 133 2.3 Tests for Divisibility (2, 3, 5, 6, 9, and 10) 145 2.4 Prime Numbers and Composite Numbers 157 2.5 Prime Factorizations 171 2.6 Least Common Multiple (LCM) with Applications 181 Chapter 2 Index of Key Terms and Ideas 193 Chapter 2 Review Questions 197 Chapter 2 Test 199 Cumulative Review: Chapters 1-2 201 Chapter 1 Whole Numbers 1 1.1 Reading and Writing Whole Numbers 2 1.2 Addition with Whole Numbers 13 1.3 Subtraction with Whole Numbers 25 1.4 Rounding and Estimating with Whole Numbers 39 1.5 Multiplication with Whole Numbers 49 1.6 Division with Whole Numbers 67 1.7 Problem Solving with Whole Numbers 83 1.8 Geometry: Perimeter and Area 97 Chapter 1 Index of Key Terms and Ideas 109 Chapter 1 Review Questions 113 Chapter 1 Test 119 Preface vii Contents BAM_TOC.indd3/12/2006, 9:49 PM3© Ha wk es P ublishing . A ll r igh ts reser ved . iv Chapter 4 Mixed Numbers 295 4.1 Introduction to Mixed Numbers 296 4.2 Multiplication and Division with Mixed Numbers 305 4.3 Addition with Mixed Numbers 317 4.4 Subtraction with Mixed Numbers 325 4.5 Order of Operations with Mixed Numbers 335 4.6 Denominate Numbers 343 Chapter 4 Index of Key Terms and Ideas 353 Chapter 4 Review Questions 355 Chapter 4 Test 359 Cumulative Review: Chapters 1 − 4 363 Chapter 3 Fractions 203 3.1 Basic Multiplication and Changing to Higher Terms 204 3.2 Multiplication and Reducing with Fractions 223 3.3 Division with Fractions 235 3.4 Addition with Fractions 247 3.5 Subtraction with Fractions 261 3.6 Comparisons and Order of Operations with Fractions 271 Chapter 3 Index of Key Terms and Ideas 281 Chapter 3 Review Questions 285 Chapter 3 Test 289 Cumulative Review: Chapters 1 – 3 291 Chapter 5 Decimal Numbers 367 5.1 Introduction to Decimal Numbers 368 5.2 Addition and Subtraction with Decimal Numbers 385 5.3 Multiplication with Decimal Numbers 395 5.4 Division with Decimal Numbers 411 5.5 Decimals and Fractions 429 5.6 Square Roots and the Pythagorean Theorem 443 5.7 Geometry: Circles and Volume 457 Chapter 5 Index of Key Terms and Ideas 469 Chapter 5 Review Questions 473 Chapter 5 Test 479 Cumulative Review: Chapters 1 – 5 483 BAM_TOC.indd3/12/2006, 9:49 PM4© Ha wk es P ublishing . A ll r igh ts reser ved . v Chapter 6 Ratios and Proportions 487 6.1 Ratios and Price per Unit 488 6.2 Proportions 499 6.3 Finding the Unknown Term in a Proportion 507 6.4 Problem Solving with Proportions 517 6.5 Geometry: Angles and Triangles 529 Chapter 6 Index of Key Terms and Ideas 549 Chapter 6 Review Questions 553 Chapter 6 Test 557 Cumulative Review: Chapters 1 – 6 561 Chapter 7 Percent 565 7.1 Decimals and Percents 566 7.2 Fractions and Percents 579 7.3 Solving Percent Problems Using the Proportion PA B100 = (Optional) 591 7.4 Solving Percent Problems Using the Equation R B A × = 601 7.5 Applications with Percent: Discount, Sales Tax, and Tipping 615 7.6 Applications with Percent: Commission, Profi t, and Others 625 Chapter 7 Index of Key Terms and Ideas 635 Chapter 7 Review Questions 639 Chapter 7 Test 643 Cumulative Review: Chapters 1 − 7 647 Chapter 8 Consumer Applications 651 8.1 Simple Interest 652 8.2 Compound Interest 663 8.3 Balancing a Checking Account 673 8.4 Buying and Owning a Car 683 8.5 Buying and Owning a Home 689 8.6 Reading Graphs 697 Chapter 8 Index of Key Terms and Ideas 713 Chapter 8 Review Questions 717 Chapter 8 Test 721 Cumulative Review: Chapters 1 – 8 725 BAM_TOC.indd3/12/2006, 9:49 PM5© Ha wk es P ublishing . A ll r igh ts reser ved . vi Chapter 9 Introduction to Algebra 731 9.1 Introduction to Integers 732 9.2 Addition with Integers 743 9.3 Subtraction with Integers 751 9.4 Multiplication, Division, and Order of Operations with Integers 759 9.5 Combining Like Terms and Evaluating Algebraic Expressions 769 9.6 Translating English Phrases and Solving Equations 777 9.7 Problem Solving 791 Chapter 9 Index of Key Terms and Ideas 805 Chapter 9 Review Questions 809 Chapter 9 Test 815 Cumulative Review: Chapters 1 – 9 819 Appendix I The Metric System A1 Appendix II Greatest Common Divisor (GCD) A25 Appendix III Statistics (Mean, Median, and Mode) A31 Appendix IV Base Two and Base Five A37 Appendix V Ancient Numeration Systems A53 Answer Key A67 Index A97 BAM_TOC.indd3/13/2006, 3:31 PM6 Preface vii Purpose and Style The purpose of Basic College Mathematics, Eighth Edition, is to provide students with a learning tool that will help them 1. develop basic arithmetic skills, 2. develop reasoning and problem-solving skills, and 3. achieve satisfaction in learning so that they will be encouraged to continue their education in mathematics. The writing style gives carefully worded, thorough explanations that are direct, easy to understand, and mathematically accurate. The use of color, subheadings, and shaded boxes helps students understand and reference important topics. The emphasis is on why basic operations and procedures work as they do, as well as on how to perform these operations and procedures. Point-by-point explanations are incorporated within the examples for better understanding, and directions are given in an easy-to-follow format. There are margin exercises that correspond to each example in almost every section. Practice problems (with answers) appear before the main exercises in every section to reinforce students' understanding of the concepts in that section and to provide the instructor with immediate classroom feedback. The NCTM and AMATYC curriculum standards have been taken into consideration in the devel- opment of the topics throughout the text. Enhancements to the New Edition • The appearance of the Eighth Edition has been enhanced by a new, full color design. • High quality images and drawings have been added throughout the text to illustrate math- ematical concepts and create a relaxed atmosphere inviting to the reader. • Real life application problems have been updated. • The use of calculators is encouraged starting with Chapter 5. • The new worktext edition gives students enough room to work out each problem. • The objectives are clearly pointed out using arrows throughout each section. • Completion examples and margin exercises help the student directly apply what is being taught in the section and examples. • Geometric concepts such as recognizing geometric figures, and finding perimeter and area are integrated throughout the text. Content There is sufficient material for a three- or four-semester-hour course. The topics in Chapters 1 − 7 form the core material for a three-hour course. The topics in Chapters 8 and 9 provide additional flexibility in the course depending on students' background and the goals of the course. PREFACE BAM_Preface.indd3/12/2006, 9:53 PM7viii Preface CHAPTER 1, WHOLE NUMBERS, reviews the fundamental operations of addition, subtraction, multi- plication, and division with whole numbers. Estimation is used to develop better understanding of whole number concepts, and word problems help to reinforce the need for these ideas and skills in common situations such as finding averages and making purchases. The last section of the chapter introduces the basic geometric concepts of plane geometry, polygons, length and perimeter, and area. CHAPTER 2, EXPONENTS, PRIME NUMBERS, & LCM, introduces exponents, shows how to use the rules for order of operations, and defines prime numbers. The concepts of divisibility and factors are emphasized and related to finding prime factorizations, which are used to develop skills needed for finding the least common multiple (LCM) of a set of numbers. All of these ideas form the foun- dation of the development of fractions in Chapter 3. CHAPTER 3, FRACTIONS, discusses the operations of multiplication, division, addition, and subtrac- tion with fractions. A special effort is made to demonstrate the validity of the use of improper frac- tions, and exponents and the rules for order of operations are applied to fractions. Knowledge of prime numbers (and prime factorizations) underlies all of the discussions about fractions. CHAPTER 4, MIXED NUMBERS, shows how mixed numbers are related to whole numbers and frac- tions. Topics include relating improper fractions and mixed numbers, the basic operations, the rules for order of operations, and denominate numbers. CHAPTER 5, DECIMAL NUMBERS, covers the basic operations with decimal numbers, estimating and the use of calculators. To emphasize number concepts, there is a section on operating with decimal numbers, fractions, and mixed numbers in a single expression. Square roots and the Pythagorean theorem are covered toward the end of the chapter along with the geometric concepts of circles and volume. CHAPTER 6, RATIOS AND PROPORTIONS, develops an understanding of ratios and introduces the idea of a variable. Techniques for solving equations are developed through finding the unknown term in a proportion. Angles and triangles are introduced at the end of this chapter. CHAPTER 7, PERCENT, approaches percent as hundredths and uses this idea to discuss percent of profit and to find equivalent numbers in the form of percents, decimals, and fractions. The appli- cations with percent are developed around proportions, the formula R B A × = , and the skills of solving equations. CHAPTER 8, CONSUMER APPLICATIONS, addresses the real life applications of simple interest, compound interest, balancing a checking account, buying and owning a car, buying and owning an home, and reading graphs. The use of calculators is encouraged and even necessary, such as in the case of using the formula for compound interest: A Pr n nt =+ () 1. Calculating with this formula serves to emphasize the importance of following the rules for order of operations. CHAPTER 9, INTRODUCTION TO ALGEBRA, provides a head start for those students planning to continue in their mathematics studies, either in a prealgebra course or a beginning course in alge- bra. Integers are introduced with the aid of number lines and are graphed on number lines. Topics included are absolute value, inequality symbols, order of operations, combining like terms, translat- ing phrases, solving equations, and problem solving. APPENDIX SECTIONS include five sections on various topics including the metric system, great- est common divisor, statistics, base two and base five, and ancient numeration systems. The first appendix on the metric system covers metric weight and volume and U. S. customary and metric equivalents. Greatest common divisor, statistics, and base two and base five are sections that pro- vide further discussion on topics directly related to the text. The last appendix is an interesting look at ancient forms of different number systems. BAM_Preface.indd3/12/2006, 9:53 PM8 Preface ix Practice and Review There are more than 4900 margin exercises, practice exercises, lesson exercises, and review items overall. Lesson exercises are carefully chosen and graded, proceeding from easy exercises to more difficult ones. Many sections contain a feature entitled Review Problems which generally has six to ten review exercises from previous chapters. Each chapter includes a Chapter Review, a Chapter Test, and a Cumulative Review (beginning with Chapter 2). Many sections have exercises entitled Writing and Thinking about Mathematics, Check Your Number Sense, and Collaborative Learning. These exercises are an important part of the text and provide a chance for each student to improve communication skills, develop an understanding of general concepts, and communicate his or her ideas to the instructor. Written responses can be a great help to the instructor in identifying just what students do and do not understand. Many of these questions are designed for the student to investigate ideas other than those presented in the text, with responses that are to be based on each student's own experiences and perceptions. In most cases there is no right answer. Answers to all margin exercises, many section exercises, all Chapter Review questions, all Chapter Test questions, and all Cumulative Review questions are provided in the back of the book. Answers to Practice Problems are given just below the problems themselves. BAM_Preface.indd3/12/2006, 9:53 PM9Next >