Table of Contents
Preface 11
Chapter 1 Numbers 15
Lesson 1-1 Symbols Used 16
Lesson 1-2 Addition 17
Lesson 1-3 Subtraction 19
Lesson 1-4 Multiplication 22
Lesson 1-5 Properties of 0 and 1 25
Lesson 1-6 Division 26
Lesson 1-7 Prime Numbers and Factoring 28
Lesson 1-8 Order of Operations 34
Lesson 1-9 Variables and the Distributive Property 35
Chapter 2 Integers 41
Lesson 2-1 The Number Line and Absolute Value 42
Lesson 2-2 Adding Integers 43
Lesson 2-3 Subtracting Integers 47
Lesson 2-4 Multiplying Integers 48
Lesson 2-5 Dividing Integers 50
Lesson 2-6 Integers and the Distributive Property 52
Chapter 3 Operations With Fractions 55
Lesson 3-1 Multiplying Fractions 57
Lesson 3-2 Simplifying Fractions 58
Lesson 3-3 Dividing Fractions 63
Lesson 3-4 Adding Fractions 65
Lesson 3-5 Subtracting Fractions 67
Lesson 3-6 Fractions and the Distributive Property 69
Chapter 4 Exponents 73
Lesson 4-1 Positive Integer Powers 73
Lesson 4-2 Rules for Exponents 77
Lesson 4-3 Negative Integer Powers 81
Lesson 4-4 When the Power Is Zero 82
Lesson 4-5 Powers of Quotients and Products 83
Lesson 4-6 Square Roots and Irrational Numbers 85
Chapter 5 Decimals 91
Lesson 5-1 The Decimal System 92
Lesson 5-2 Adding and Subtracting Decimal Numbers 96
Lesson 5-3 Multiplying Decimal Numbers 100
Lesson 5-4 Dividing Decimal Numbers 102
Lesson 5-5 Rounding and Estimating 104
Lesson 5-6 Comparing Decimals and Fractions 108
Chapter 6 Expressions and Equations 115
Lesson 6-1 Evaluating Expressions 116
Lesson 6-2 Equations 118
Lesson 6-3 Equality 119
Lesson 6-4 Algebraic Properties of Equality 120
Lesson 6-5 Solving Linear Equations in 1 Step 121
Lesson 6-6 Solving Linear Equations in 2 Steps 126
Chapter 7 Ratios, Proportions, and Percents 131
Lesson 7-1 Ratios and Unit Rates 131
Lesson 7-2 Proportions 134
Lesson 7-3 Proportions and Percents 138
Lesson 7-4 Percents and Equations 141
Lesson 7-5 Percent Change 143
Lesson 7-6 Mark-up and Discount 146
Chapter 8 Inequalities and Graphs 153
Lesson 8-1 Inequalities 153
Lesson 8-2 Properties of Inequalities 155
Lesson 8-3 Solving Inequalities in 1 Step 156
Lesson 8-4 Solving Inequalities in 2 Steps 160
Lesson 8-5 Graphing Inequalities Using the Number Line 162
Chapter 9 Linear Functions and Graphs 169
Lesson 9-1 Relations and Functions 170
Lesson 9-2 Linear Functions and Equations 172
Lesson 9-3 The Cartesian Coordinate System 174
Lesson 9-4 Slope and Intercepts 177
Lesson 9-5 Graphing Linear Equations 183
Chapter 10 Algebra and Geometry 191
Lesson 10-1 Polygons 191
Lesson 10-2 Midpoint 194
Lesson 10-3 Perimeter 196
Lesson 10-4 Right Triangles and the Pythagorean Theorem 199
Lesson 10-5 Special Right Triangles 202
Lesson 10-6 The Distance Formula 205
Lesson 10-7 Area 211
Lesson 10-8 Circles 214
Chapter 11 Monomials and Polynomials 219
Lesson 11-1 Adding and Subtracting Monomials 220
Lesson 11-2 Multiplying and Dividing Monomials 221
Lesson 11-3 Adding and Subtracting Polynomials 224
Lesson 11-4 Multiplying Polynomials 231
Chapter 12 Applications 231
Lesson 12-1 How to Approach Word Problems 231
Lesson 12-2 Finding Integers 233
Lesson 12-3 Rate Problems 235
Lesson 12-4 Money Problems 237
Lesson 12-5 Spatial Problems 239
Final Exam 243
Index 251
About the Author 255
