211 771 406 III T H I R D E D I T I O N Integrated Arithmetic and Basic Algebra Bill E. Jordan Seminole Community College William P. Palow Miami-Dade College Boston San Francisco New York London Toronto Sydney Tokyo Singapore Madrid Mexico City Munich Paris Cape Town Hong Kong Montreal \Z*< f
Contents Preface XI?* T»i in 0.1 0.2 0.3 0.4 0.5 0.6 0.7 U W Basic Ideas Reading and Writing Numerals Addition and Subtraction of Whole Numbers Multiplication of Whole Numbers Division of Whole Numbers A Brief Introduction to Fractions Addition and Subtraction of Decimal Numerals Multiplication and Division of Decimal Numerals 2 8 20 26 34 46 57 66 68 71 Adding and Subtracting Integers and Polynomials 1.1 Variables, Exponents, and Order of Operations 74 1.2 Unit Conversions and Perimeters of Geometric Figures 85 1.3 Areas of Geometric Figures 99 1.4 Volumes and Surface Areas of Geometric Figures 109 1.5 Introduction to Integers 118 1.6 Addition of Integers 126 1.7 Subtraction of Integers and Combining Like Terms 137 1.8 Polynomial Definitions and Combining Polynomials 149 161 164 167
vi Contents 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 1S9 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Qy^Kip Laws of Exponents, Products and Quotients of Integers and Polynomials Multiplication of Integers Multiplication Laws of Exponents Products of Polynomials Special Products Division of Integers and Order of Operations with Integers Quotient Rule and Integer Exponents Power Rule for Quotients and Using Combined Laws of Exponents Division of Polynomials by Monomials An Application of Exponents: Scientific Notation HaJlSP Linear Equations and Inequalities Addition Property of Equality Multiplication Property of Equality Combining Properties in Solving Linear Equations Using and Solving Formulas Solving Linear Inequalities General, Consecutive Integer, and Distance Application Problems Money, Investment, and Mixture Application Problems Geometric Application Problems Graphing Linear Equations and Inequalities 170 181 189 197 205 216 226 234 240 248 249 252 256 266 276 286 291 305 319 332 340 342 345 4.1 Reading Graphs and the Cartesian Coordinate System 348 4.2 Graphing Linear Equations with Two Variables 368 4.3 Graphing Linear Equations Using Intercepts 381 4.4 Slope of a Line 389 4.5 Slope-Intercept Form of a Line 403 4.6 Point-Slope Form of a Line 414 4.7 Graphing Linear Inequalities with Two Variables 426 4.8 Relations and Functions 436
Contents vii 445 448 456 Systems of Linear Equations 5.1 Defining Linear Systems and Solving by Graphing 460 5.2 Solving Systems of Linear Equations Using Elimination by Addition 474 5.3 Solving Systems of Linear Equations Using Substitution 485 5.4 Solving Application Problems Using Systems of Equations 493 5.5 Systems of Linear Inequalities 504 510 512 514 Factors, Divisors, and Factoring 6.1 Prime Factorization and Greatest Common Factor 518 6.2 Factoring Polynomials with Common Factors and by Grouping 528 6.3 Factoring General Trinomials with Leading Coefficients of One 537 6.4 Factoring General Trinomials with Leading Coefficients Other Than One 547 6.5 Factoring Binomials 554 6.6 Factoring Perfect Square Trinomials 561 6.7 Mixed Factoring 566 6.8 Solving Quadratic Equations by Factoring 569 579 581 583 Multiplication and Division of Rational Numbers and Expressions 7.1 Fractions and Rational Numbers 586 7.2 Reducing Rational Numbers and Rational Expressions 597 7.3 Further Reduction of Rational Expressions 602 7.4 Multiplication of Rational Numbers and Expressions 610 7.5 Further Multiplication of Rational Expressions 619
viii Contents 7.6 7.7 Division of Rational Numbers and Expressions Division of Polynomials (Long Division) 624 630 636 638 641 Addition and Subtraction of Rational Numbers and Expressions 8.1 Addition and Subtraction of Rational Numbers and Expressions with Like Denominators 644 8.2 Least Common Multiple and Equivalent Rational Expressions 655 8.3 The Least Common Denominator of Fractions and Rational Expressions 667 8.4 Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators 674 8.5 Complex Fractions 682 8.6 Solving Equations Containing Rational Numbers and Expressions 689 8.7 Applications with Rational Expressions 696 706 707 710 Ratios, Percents, and Applications 9.1 Ratios and Rates 712 9.2 Proportions 720 9.3 Percent 728 9.4 Applications of Percent 737 9.5 Further Applications of Percent 745 758 761 763 P Roots and Radicals 10.1 Defining and Finding Roots 766 10.2 Simplifying Radicals 774 10.3 Products and Quotients of Radicals 782
Contents ix 10.4 10.5 10.6 10.7 Addition, Subtraction, and Mixed Operations with Radicals Rationalizing the Denominator Solving Equations with Radicals Pythagorean Theorem 790 800 809 817 826 828 830 Solving Quadratic Equations 11.1 Solving Incomplete Quadratic Equations 832 11.2 Solving Quadratic Equations by Completing the Square 839 11.3 Solving Quadratic Equations by the Quadratic Formula 848 11.4 Quadratic Equations with Complex Solutions 854 11.5 Solving Mixed Equations 863 11.6 Applications Involving Quadratic Equations 871 879 881 883 Table 1: Powers and Roots Answers to Odd-Numbered Exercises T-l AN-1 Index 1-1