Prealgebra Second Edition Jamie Blair Orange Coast College, Costa Mesa, California John Tobey North Shore Community College, Danvers, Massachusetts Jeffrey Slater North Shore Community College, Danvers, Massachusetts Prentice Hall Upper Saddle River, NJ 07458
Contents Preface xi Acknowledgments xviii To the Student xxv Chapter 1 Whole Numbers and Introduction to Algebra 1 Pretest Chapter 1 2 1.1 Understanding Whole Numbers 4 1.2 Addition of Whole Number Expressions 12 1.3 Subtraction of Whole Number Expressions 25 1.4 Multiplication of Whole Number Expressions: Part I 34 1.5 Multiplication of Whole Number Expressions: Part II 43 1.6 Division of Whole Number Expressions 49 1.7 Exponents and Order of Operations 59 1.8 Introduction to Equations 66 1.9 Applied Problems Involving Several Operations 76 Putting Your Skills to Work 86 Chapter 1 Organizer 88 Chapter 1 Review Problems 92 Chapter 1 Test 98 Chapter 2 Integers 101 Pretest Chapter 2 102 2.1 Understanding Integers 103 2.2 Addition of Integers 112 2.3 Subtraction of Integers 122 2.4 Multiplication and Division of Integers 130 2.5 Order of Operations and Applications Involving Integers 2.6 Simplifying and Evaluating Algebraic Expressions 144 Putting Your Skills to Work 151 Chapter 2 Organizer 153 Chapter 2 Review Problems 155 Chapter 2 Test 158 Cumulative Test for Chapters 1-2 160 139 vii
VIII Contents Chapter 3 Introduction to Equations and Algebraic Expressions 161 Pretest Chapter 3 162 3.1 Solving Equations of the Form x + a = c and x - a = c 164 3.2 Solving Equations of the Form ax = c 172 3.3 Equations and Geometric Formulas 180 3.4 Performing Operations with Exponents 192 Putting Your Skills to Work 200 Chapter 3 Organizer 201 Chapter 3 Review Problems 203 Chapter 3 Test 207 Cumulative Test for Chapters 1-3 209 Chapter 4 Fractions, Ratio, and Proportion 211 Pretest Chapter 4 212 4.1 Factoring Whole Numbers 213 4.2 Understanding Fractions 220 4.3 Simplifying Fractional Expressions 228 4.4 Simplifying Fractional Expressions with Exponents 236 4.5 Ratios and Rates 243 4.6 Proportions 252 4.7 Applied Problems Involving Proportions 260 Putting Your Skills to Work 266 Chapter 4 Organizer 268 Chapter 4 Review Problems 270 Chapter 4 Test 275 Cumulative Test for Chapters 1-4 277 Chapter 5 Operations on Fractional Expressions 279 Pretest Chapter 5 280 5.1 Multiplication and Division of Fractional Expressions 282 5.2 Multiples and Least Common Multiples of Expressions 292 5.3 Addition and Subtraction of Fractional Expressions 298 5.4 Operations with Mixed Numbers 308 Putting Your Skills to Work 314 5.5 Order of Operations and Complex Fractions 319 5.6 Applied Problems Involving Fractions 324 5.7 Solving Equations of the Form x/a = c 331 Chapter 5 Organizer 337 Chapter 5 Review Problems 339 Chapter 5 Test 342 Cumulative Test for Chapters 1-5 344
Contents ix Chapter 6 Polynomials 347 Pretest Chapter 6 348 6.1 Addition and Subtraction of Polynomials 349 6.2 Multiplication of Polynomials 354 6.3 Translating English to Algebra 360 Putting Your Skills to Work 366 6.4 Factoring: The Greatest Common Factor 368 Chapter 6 Organizer 373 Chapter 6 Review Problems 374 Chapter 6 Test 377 Cumulative Test for Chapters 1-6 378 Chapter 7 Equations 379 Pretest Chapter 7 380 7.1 Solving Equations Using One Principle of Equality 7.2 Solving Equations Using More than One Principle of Equality 388 7.3 Solving Equations with Parentheses 394 7.4 Solving Equations with Fractions 398 7.5 Using Equations to Solve Applied Problems 402 Putting Your Skills to Work 410 Chapter 7 Organizer 412 Chapter 7 Review Problems 415 Chapter 7 Test 417 Cumulative Test for Chapters 1-7 418 381 Chapter 8 Decimals and Percents 421 Pretest Chapter 8 422 8.1 Understanding Decimal Fractions 424 8.2 Addition and Subtraction of Decimal Expressions 432 Putting Your Skills to Work 435 8.3 Multiplication and Division of Decimals 439 8.4 Solving Equations and Applied Problems Involving Decimals 8.5 Percents 456 8.6 Solving Percent Problems Using Equations 464 8.7 Solving Percent Problems Using Proportions (Optional) 472 8.8 Estimating with Percents 479 Putting Your Skills to Work 484 8.9 Applied Problems Involving Percents 486 Chapter 8 Organizer 493 Chapter 8 Review Problems 496 Chapter 8 Test 501 Cumulative Test for Chapters 1-8 503 448
X Contents Chapter Graphing and Statistics 505 Pretest Chapter 9 506 9.1 Interpreting and Constructing Graphs Putting Your Skills to Work 513 507 9.2 Mean, Median, and Mode 520 9.3 The Rectangular Coordinate System 527 9.4 Linear Equations with Two Variables Putting Your Skills to Work 545 Chapter 9 Organizer 551 Chapter 9 Review Problems 554 Chapter 9 Test 559 537 Cumulative Test for Chapters 1-9 562 Chapter 10 Measurement and Geometric Figures 565 Pretest Chapter 10 566 10.1 Converting between U. S. Units; Converting between Metric Units 568 10.2 Converting between the U. S. and Metric Systems (Optional) 577 Putting Your Skills to Work 582 10.3 Angles 583 10.4 Square Roots and the Pythagorean Theorem 593 10.5 The Circle and Applied Problems 603 Putting Your Skills to Work 609 10.6 Volume 611 10.7 Similar Geometric Figures 617 Chapter 10 Organizer 623 Chapter 10 Review Problems 627 Chapter 10 Test 631 Cumulative Test for Chapters 1-10 633 Practice Final Examination 635 Appendix A: Introduction to U.S. and Metric Units of Measurement A-l Appendix B: Scientific Calculators A-7 Appendix C: Congruent Triangles A-13 Appendix D: Additional Arithmetic Practice A-19 Appendix E: Math in the Media A-21 Solutions to Practice Problems SP-1 Selected Answers SA-1 Applications Index 1-1 Subject Index 1-5 Photo Credits P-l