Integrated Arithmetic and Basic Algebra

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1 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

2 Contents Preface XI?* T»i in 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 Adding and Subtracting Integers and Polynomials 1.1 Variables, Exponents, and Order of Operations Unit Conversions and Perimeters of Geometric Figures Areas of Geometric Figures Volumes and Surface Areas of Geometric Figures Introduction to Integers Addition of Integers Subtraction of Integers and Combining Like Terms Polynomial Definitions and Combining Polynomials

3 vi Contents S 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 Reading Graphs and the Cartesian Coordinate System Graphing Linear Equations with Two Variables Graphing Linear Equations Using Intercepts Slope of a Line Slope-Intercept Form of a Line Point-Slope Form of a Line Graphing Linear Inequalities with Two Variables Relations and Functions 436

4 Contents vii Systems of Linear Equations 5.1 Defining Linear Systems and Solving by Graphing Solving Systems of Linear Equations Using Elimination by Addition Solving Systems of Linear Equations Using Substitution Solving Application Problems Using Systems of Equations Systems of Linear Inequalities Factors, Divisors, and Factoring 6.1 Prime Factorization and Greatest Common Factor Factoring Polynomials with Common Factors and by Grouping Factoring General Trinomials with Leading Coefficients of One Factoring General Trinomials with Leading Coefficients Other Than One Factoring Binomials Factoring Perfect Square Trinomials Mixed Factoring Solving Quadratic Equations by Factoring Multiplication and Division of Rational Numbers and Expressions 7.1 Fractions and Rational Numbers Reducing Rational Numbers and Rational Expressions Further Reduction of Rational Expressions Multiplication of Rational Numbers and Expressions Further Multiplication of Rational Expressions 619

5 viii Contents Division of Rational Numbers and Expressions Division of Polynomials (Long Division) Addition and Subtraction of Rational Numbers and Expressions 8.1 Addition and Subtraction of Rational Numbers and Expressions with Like Denominators Least Common Multiple and Equivalent Rational Expressions The Least Common Denominator of Fractions and Rational Expressions Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators Complex Fractions Solving Equations Containing Rational Numbers and Expressions Applications with Rational Expressions Ratios, Percents, and Applications 9.1 Ratios and Rates Proportions Percent Applications of Percent Further Applications of Percent P Roots and Radicals 10.1 Defining and Finding Roots Simplifying Radicals Products and Quotients of Radicals 782

6 Contents ix Addition, Subtraction, and Mixed Operations with Radicals Rationalizing the Denominator Solving Equations with Radicals Pythagorean Theorem Solving Quadratic Equations 11.1 Solving Incomplete Quadratic Equations Solving Quadratic Equations by Completing the Square Solving Quadratic Equations by the Quadratic Formula Quadratic Equations with Complex Solutions Solving Mixed Equations Applications Involving Quadratic Equations Table 1: Powers and Roots Answers to Odd-Numbered Exercises T-l AN-1 Index 1-1

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