Basic Arithmetic & Algebra - XYZ Custom Plus

Brief ContentsChapter 1 Whole Numbers 1Chapter 2 Fractions and Mixed Numbers 87Chapter 3 Decimals 183Chapter 4 Ratio and Proportions 249Chapter 5 Descriptive Statistics 301Chapter 6 Introduction to Algebra 349Chapter 7 Solving Equations 409Chapter 8 Linear Equations and Inequalities 485Chapter 9 Linear Equations and Inequalities in Two Variables 587Chapter 10 Systems of Linear Equations 667Chapter 11 Exponents and Polynomials 715Chapter 12 Factoring 797Chapter 13 Rational Expressions 863Chapter 14 Roots and Radicals 947Solutions to Selected Practice Problems S-1Answers to Odd-Numbered Problems A-1iii

Contents1Whole Numbers 1Introduction 11.1 Place Value and Names for Numbers 31.2 Addition with Whole Numbers, and Perimeter 131.3 Rounding and Estimating 251.4 Subtraction with Whole Numbers 331.5 Multiplication with Whole Numbers, and Area 411.6 Division with Whole Numbers 551.7 Exponents and Order of Operations 67Summary 75Review 77Test 79Projects 81A Glimpse of Algebra 832Fractions and Mixed Numbers 87Introduction 872.1 The Meaning and Properties of Fractions 892.2 Prime Numbers, Factors, and Reducing to Lowest Terms 1012.3 Multiplication with Fractions, and the Area of a Triangle 1092.4 Division with Fractions 1212.5 Addition and Subtraction with Fractions 1292.6 Mixed-Number Notation 1412.7 Multiplication and Division with Mixed Numbers 1472.8 Addition and Subtraction with Mixed Numbers 1532.9 Combinations of Operations and Complex Fractions 161Summary 169Review 173Cumulative Review 175Test 176Projects 177A Glimpse of Algebra 179v

viContents3Decimals 183Introduction 1833.1 Decimal Notation and Place Value 1853.2 Addition and Subtraction with Decimals 1933.3 Multiplication with Decimals; Circumference and Area of a Circle 2013.4 Division with Decimals 2133.5 Fractions and Decimals, and the Volume of a Sphere 225Summary 237Review 239Cumulative Review 241Test 242Projects 243A Glimpse of Algebra 2454Ratio and Proportion 249Introduction 2494.1 Ratios 2514.2 Rates and Unit Pricing 2594.3 Solving Equations by Division 2654.4 Proportions 2694.5 Applications of Proportions 2754.6 Similar Figures 281Summary 289Review 291Cumulative Review 293Test 294Projects 295A Glimpse of Algebra 297

Contentsvii5Descriptive Statistics 301Introduction 3015.1 Mean, Median, and Mode 3035.2 Displaying Information 3115.3 Pie Charts 3215.4 Introduction to Probability 329Summary 339Review 343Cumulative Review 345Test 346Projects 3476Introduction to Algebra 349Introduction 3496.1 Positive and Negative Numbers 3516.2 Addition with Negative Numbers 3616.3 Subtraction with Negative Numbers 3716.4 Multiplication with Negative Numbers 3816.5 Division with Negative Numbers 3896.6 Simplifying Algebraic Expressions 395Summary 401Review 403Cumulative Review 405Test 406Projects 407

viiiContents7Solving Equations 409Introduction 4097.1 The Distributive Property and Algebraic Expressions 4117.2 The Addition Property of Equality 4237.3 The Multiplication Property of Equality 4317.4 Linear Equations in One Variable 4397.5 Applications 4477.6 Evaluating Formulas 4597.7 Paired Data and the Rectangular Coordinate System 469Summary 477Review 479Cumulative Review 481Test 482Projects 4838Linear Equations and Inequalities 485Introduction 4858.1 Simplifying Expressions 4878.2 Addition Property of Equality 4978.3 Multiplication Property of Equality 5078.4 Solving Linear Equations 5178.5 Formulas 5258.6 Applications 5378.7 More Applications 5498.8 Linear Inequalities 5598.9 Compound Inequalities 571Summary 577Review 581Cumulative Review 583Test 584Projects 585

Contentsix9Linear Equations andInequalities in Two Variables 587Introduction 5879.1 Paired Data and Graphing Ordered Pairs 5899.2 Solutions to Linear Equations in Two Variables 5979.3 Graphing Linear Equations in Two Variables 6059.4 More on Graphing: Intercepts 6179.5 The Slope of a Line 6279.6 Finding the Equation of a Line 6399.7 Linear Inequalities in Two Variables 651Summary 659Review 661Cumulative Review 663Test 664Projects 66510Systems of Linear Equations 667Introduction 66710.1 Solving Linear Systems by Graphing 66910.2 The Elimination Method 67910.3 The Substitution Method 68910.4 Applications 697Summary 707Review 709Cumulative Review 711Test 712Projects 713

11Exponents and Polynomials 715Introduction 71511.1 Multiplication with Exponents 71711.2 Division with Exponents 72911.3 Operations with Monomials 74111.4 Addition and Subtraction of Polynomials 74911.5 Multiplication with Polynomials 75511.6 Binomial Squares and Other Special Products 76511.7 Dividing a Polynomial by a Monomial 77311.8 Dividing a Polynomial by a Polynomial 779Summary 787Review 791Cumulative Review 793Test 794Projects 79512Factoring 797Introduction 79712.1 The Greatest Common Factor and Factoring by Grouping 79912.2 Factoring Trinomials 80712.3 More Trinomials to Factor 81312.4 The Difference of Two Squares 82112.5 The Sum and Difference of Two Cubes 82712.6 Factoring: A General Review 83112.7 Solving Equations by Factoring 83512.8 Applications 843Summary 855Review 857Cumulative Review 859Test 860Projects 861

Contentsxi13Rational Expressions 863Introduction 86313.1 Reducing Rational Expressions to Lowest Terms 86513.2 Multiplication and Division of Rational Expressions 87713.3 Addition and Subtraction of Rational Expressions 88913.4 Equations Involving Rational Expressions 89713.5 Applications 90513.6 Complex Fractions 91513.7 Proportions 92313.8 Variation 931Summary 939Review 941Cumulative Review 943Test 944Projects 94514Roots and Radicals 947Introduction 94714.1 Definitions and Common Roots 94914.2 Properties of Radicals 95914.3 Simplified Form for Radicals 96714.4 Addition and Subtraction of Radical Expressions 97514.5 Multiplication and Division of Radicals 98114.6 Equations Involving Radicals 989Summary 999Review 1001Cumulative Review 1003Test 1004Projects 1005Solutions to Selected Practice Problems S-1Answers to Odd-Numbered Problems A-1