PREALGEBRA FOURTH EDITION A Worktext D. Franklin Wright Instructor’s Annotated Edition © All Rights Reser ved.Editor: Cynthia Christine Ellison Development Director: Marcel Prevuznak Production Editors: Harding Brumby, Phillip Bushkar, Mandy Glover, Bethany Loftis, Nina Miller, Kimberly Scott Editorial Assistants: K. V. S. Anil, Kelly Epperson, D. Kanthi, B. Syam Prasad, Tristan Vogler, Ashley Wood, Chris Yount Layout: QSI (Pvt.) Ltd.: U. Nagesh, E. Jeevan Kumar Art: Ayvin Samonte Photo Credits: p. iv, p. 421, and p. 422 ©Associated Press A division of Quant Systems, Inc. Copyright © 2008 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: 2006933713 Printed in the United States of America. Student ISBN: 978-1-932628-25-8 Student Bundle ISBN: 978-1-932628-30-2 PRE_TOC.indd9/24/2006, 9:06 PM2 © All Rights Reser ved.© Ha wk es L ear ning S yst ems . A ll r igh ts reser ved . iii Chapter 2 Integers 113 2.1 Introduction to Integers 114 2.2 Addition with integers 129 2.3 Subtraction with Integers 141 2.4 Multiplication, Division, and Order of Operations with Integers 155 2.5 Applications: Change in Value and Average 167 2.6 Introduction to Like Terms and Polynomials 177 2.7 Solving Equations with Integers (x + b = c and ax = c) 189 Chapter 2 Index of Key Terms and Ideas 197 Chapter 2 Test 201 Cumulative Review: Chapters 1 – 2 205 Chapter 1 Whole Numbers 1 1.1 Whole Numbers and Rounding 2 1.2 Addition and Subtaction with Whole Numbers (Calculators Included) 11 1.3 Multiplication and Division with Whole Numbers (Calculators Included) 29 1.4 Applications: Number Problems, Consumer Items, Checking, Geometry, and Reading Graphs 53 1.5 Solving Equations with Whole Numbers (x + b = c and ax = c) 69 1.6 Exponents and Order of Operations 79 1.7 Introduction to Polynomials 95 Chapter 1 Index of Key Terms and Ideas 105 Chapter 1 Test 109 Preface vii Contents PRE_TOC.indd9/25/2006, 12:17 PM3 © All Rights Reser ved.© Ha wk es L ear ning S yst ems . A ll r igh ts reser ved . iv Chapter 4 Mixed Numbers, Ratios, and Proportions 319 4.1 Introduction to Mixed Numbers 320 4.2 Multiplication and Division with Mixed Numbers 331 4.3 Addition and Subtraction with Mixed Numbers 349 4.4 Complex Fractions and Order of Operations 363 4.5 Solving Equations with Fractions (ax + b = c) 371 4.6 Solving Equations: Ratios and Proportions 383 Chapter 4 Index of Key Terms and Ideas 407 Chapter 4 Test 411 Cumulative Review: Chapters 1 − 4 415 Chapter 3 Prime Numbers and Fractions 211 3.1 Tests for Divisibility 212 3.2 Prime Numbers 225 3.3 Prime Factorization 234 3.4 Least Common Multiple (LCM) 247 3.5 Reducing and Multiplication with Fractions 261 3.6 Division with Fractions 279 3.7 Addition and Subtraction with Fractions 291 Chapter 3 Index of Key Terms and Ideas 309 Chapter 3 Test 313 Cumulative Review: Chapters 1 – 3 315 Chapter 5 Decimal Numbers and Square Roots 421 5.1 Reading, Writing, and Rounding Decimal Numbers 422 5.2 Addition and Subtraction with Decimal Numbers 437 5.3 Multiplication and Division with Decimal Numbers 449 5.4 Applications in Statistics (Mean, Median, Mode, and Range) 469 5.5 Decimals, Fractions, and Scientific Notation 485 5.6 Solving Equations with Decimal Numbers and Circumference and Area of Circles 501 5.7 Square Roots and the Pythagorean Theorem 513 5.8 Simplifying Square Roots 529 Chapter 5 Index of Key Terms and Ideas 537 Chapter 5 Test 541 Cumulative Review: Chapters 1 – 5 545 PRE_TOC.indd9/25/2006, 12:17 PM4 © All Rights Reser ved.© Ha wk es L ear ning S yst ems . A ll r igh ts reser ved . v Chapter 6 Percent 551 6.1 Understanding Percent 552 6.2 Solving Percent Problems 571 6.3 Estimating with Percent 587 6.4 Applications: Discount, Sales Tax, Commission, Profit, and Tipping 599 6.5 Applications: Buying a Car and Buying a Home 617 6.6 Simple Interest and Compound Interest 625 Chapter 6 Index of Key Terms and Ideas 645 Chapter 6 Test 649 Cumulative Review: Chapters 1 – 6 653 Chapter 7 Algebraic Topics I 661 7.1 Translating English Phrases 662 7.2 Solving Equations I 673 7.3 Solving Equations II 679 7.4 Applications: Numbers and Consecutive Integers 685 7.5 Working with Formulas 699 7.6 Linear Inequalities (ax + b < c) 709 Chapter 7 Index of Key Terms and Ideas 725 Chapter 7 Test 729 Cumulative Review: Chapters 1 − 7 733 Chapter 8 Algebraic Topics II 739 8.1 Integer Exponents 740 8.2 Addition and Subtraction with Polynomials 753 8.3 Multiplication with Polynomials I 761 8.4 Multiplication with Polynomials II 771 8.5 Factoring Polynomials I 781 8.6 Factoring Polynomials II 791 Chapter 8 Index of Key Terms and Ideas 797 Chapter 8 Test 799 Cumulative Review: Chapters 1 – 8 803 PRE_TOC.indd9/24/2006, 9:07 PM5 © All Rights Reser ved.© Ha wk es L ear ning S yst ems . A ll r igh ts reser ved . vi Chapter 9 Graphing in Two Dimensions 809 9.1 Graphing Ordered Pairs of Real Numbers 810 9.2 Graphing Linear Equations I: Ax + By = C 827 9.3 Graphing Linear Equations II: Horizontal and Vertical Lines, Calculators 845 9.4 Constructing Graphs from Databases 857 Chapter 9 Index of Key Terms and Ideas 869 Chapter 9 Test 873 Cumulative Review: Chapters 1 – 9 877 Appendix I Practice with Basic Addition Facts A1 Appendix II Practice with Basic Multiplication Facts A3 Appendix III Ancient Numeration Systems A5 Appendix IV Greatest Common Divisor (GCD) A17 Appendix V Division with Polynomials A23 Tables A33 Answer Key A39 Index A71 Chapter 10 Geometry and Measurement 883 10.1 Angles and Triangles 884 10.2 Length and Perimeter 903 10.3 Area 917 10.4 Volume 935 Chapter 10 Index of Key Terms and Ideas 947 Chapter 10 Test 953 Cumulative Review: Chapters 1 – 10 957 PRE_TOC.indd9/25/2006, 12:18 PM6 © All Rights Reser ved. Preface vii Purpose and Style The purpose of Prealgebra: A Worktext, Fourth Edition, is to provide students with both an introduction to algebra and a learning tool that will help them 1. review basic arithmetic skills, 2. develop reasoning and problem-solving skills, 3. become familiar with algebraic notation, 4. understand the connections between arithmetic and algebra, 5. develop basic algebraic skills, and 6. achieve satisfaction in learning so 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 the connection between arithmetic and algebraic operations and 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 and easy-to-follow format. There are margin exercises that correspond to each example in almost every section with answers provided in the back of the text. Also, most sections contain completion examples with worked-out answers provided at the end of the section. These exercises and examples provide the student with immediate reinforcement and the instructor with immediate feedback as to how well the students understand the material. Solving equations, one of the most important topics in mathematics, is developed throughout the text. Featured in increasingly difficult levels (a spiral approach), solving equations is discussed in Sections 1.5, 2.7, 4.5, 4.6, 5.6, 7.2, 7.3, and 7.5. Topics from geometry are integrated within the discussions and problems in many sections. For example, perimeter is discussed as early as Section 1.2 and area in Sections 1.3 and 1.4. Volume is introduced in Section 4.2 and similar triangles in Section 4.6. Students are encouraged to use calculators when appropriate and explicit directions and diagrams are provided as they relate to a TI-84 Plus calculator. Also, new problems related to reading graphs and statistical concepts are included in many sections. In particular, Section 5.4 develops the statistical concepts of mean, median, mode, and range. The NCTM and AMATYC curriculum standards have been taken into consideration in the development of the topics throughout the text. PREFACE PRE_Preface.indd9/25/2006, 11:53 PM7 © All Rights Reser ved.viii Preface Updates to this Edition • Red objective arrows point out each objective in each section for easy reference. • Each example has its own corresponding margin exercise so that students can directly apply what they just learned. • Use of the TI-84 Plus graphing calculator is encouraged in the Fourth Edition. • The Index of Key Terms and Ideas is now more comprehensive, giving definitions and key topics as they appear in the section. Each index is divided up by section and page numbers are given for easy reference. • Addition and subtraction with fractions is now included in Chapter 3 while solving equations with fractions is now a part of Chapter 4. Solving equations with fractions in Chapter 4 serves as a segway to solving equations with ratios and proportions, which comes in the following section. • Applications in statistics, including mean, median, mode, and range are now included in Chapter 5 instead of Chapter 9 to fit better with the text, since the topic of Chapter 9 is graphing in two dimensions. • The section on multiplication with polynomials in Chapter 8 has been split into 2 sections. Factoring polynomials has also been split into 2 sections to break down the more difficult concepts and help students become more comfortable working with polynomials. • The sections on graphing in Chapter 8 have been moved to Chapter 9. The title of Chapter 9 is now "Graphing in Two Dimensions." Chapter 9 now covers graphing ordered pairs and linear equations, as well as constructing graphs from databases. Important Topics and Ideas A central consideration throughout this text is the development of an understanding of the interrelationship between arithmetic and algebra. With this in mind, special efforts have been made to help students gain skill and understanding of mathematics in the following ways: • Exponents and order of operations are introduced in Chapter 1 to help in evaluating polynomials. • Discussion of polynomials also begins in Chapter 1 as an early introduction to algebraic expressions and use of order of operations. • Techniques for understanding equations and solving equations are developed in a spiral approach of increasing difficulty throughout the text. • Emphasis has been placed on the development of reading and writing skills as they relate to mathematics. • Combining like terms is introduced in Section 2.6 so these ideas can be used in solving equations. • A special effort has been made to make the exercises motivating and interesting. Applications are varied and practical and contain many facts of interest. • The use of calculators is encouraged from the beginning. However, students are cautioned that “calculators do not think.” A section on scientific notation helps students understand this type of display on their calculators. • Estimating is an integral part of many discussions. • Geometric concepts such as finding perimeter and area and recognizing geometric figures are integrated throughout the text, with a formal introduction in Chapter 10. Chapter 10 also includes an introduction to measurement in both the U.S. customary system and the metric system. PRE_Preface.indd9/25/2006, 11:53 PM8 © All Rights Reser ved. Preface ix Special Features In each chapter: • Mathematics at Work! presents a brief discussion related to an upcoming concept from the chapter ahead and an example of mathematics used in daily life situations. Sometimes these sections are challenging and may be better understood after the student completes a portion of the chapter. • What to Expect in This Chapter opens each chapter and offers an overview of the topics that will be covered. • Learning Objectives are listed at the beginning of each section and red arrows point out each objective throughout the section. • Cumulative Review exercises appear in each chapter beyond Chapter 1 to provide continuous, cumulative review. In the exercise sets: • Writing and Thinking About Mathematics exercises encourage students to express their ideas, interpretations, and understanding in writing. • Collaborative Learning Exercises are designed to be done in interactive groups. • Review Problems are skills refreshers that provide maintenance exercises on important topics from previous sections or chapters. Pedagogical Features In each section, the presentation and development are based on the following format for learning and teaching: 1. Each section begins with a list of learning objectives for that section. 2. Subsection topics are introduced by boldface subheadings for easy reference. 3. Thorough and mathematically accurate discussions feature several detailed examples completely worked out with step-by-step explanations. 4. Completion examples help students to reinforce thinking patterns developed in previous examples. The answers are at the end of each section. 5. Students are prompted to complete margin exercises as they read the lessons, which provide them with immediate reinforcement of the basic ideas presented. The answers are in the back of the text. 6. Graded exercises offer variety in style and level of difficulty including drill, multiple choice, matching, applications, written responses, estimating, and group discussion exercises. 7. Real-life applications appear in most sections, with several sections devoted solely to applications. 8. A full-color design provides visual support to the text’s pedagogy. 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