Introduction 1 About This Book 1 Conventions Used in This Book 2 Foolish Assumptions 2 Icons Used in This Book 3 Where to Go from Here 3 Chapter 1: Arming Yourself with Math Basics 5 Understanding Sets of Numbers 5 The Big Four Operations 6 Adding things up 6 Take it away: Subtracting 7 Multiplying 7 Doing division lickety-split 8 Fun and Useful Properties of the Big Four Operations 9 Inverse operations 9 Commutative operations 9 Associative operations 10 Distributing to lighten the load 10 Other Operations: Exponents, Square Roots, and Absolute Values 11 Understanding exponents 11 Discovering your roots 12 Figuring out absolute value 12 Finding Factors 13 Generating factors 13 Finding the greatest common factor (GCF) 14 Finding Multiples 14 Generating multiples 14 Finding the least common multiple (LCM) 15 Chapter 2: Evaluating Arithmetic Expressions 17 The Three E''s: Equations, Expressions, and Evaluations 18 Equality for all: Equations 18 Hey, it''s just an expression 19 Evaluating the situation 19 Putting the Three E''s together 19 Following the Order of Operations 20 Order of operations and the Big Four expressions 21 Order of operations in expressions with exponents 24 Order of operations in expressions with parentheses 25 Chapter 3: Say What? Making Sense of Word Problems 29 Handling Basic Word Problems 30 Turning word problems into word equations 30 Plugging in numbers for words 33 Solving More-Challenging Word Problems 34 When numbers get serious 35 Lots of information 36 Putting it all together 37 Chapter 4: Figuring Out Fractions 41 Reducing Fractions to Lowest Terms 42 Multiplying and Dividing Fractions 42 Multiplying numerators and denominators straight across 42 Doing a flip to divide fractions 43 Adding Fractions 43 Finding the sum of fractions with the same denominator 44 Adding fractions with different denominators 45 Subtracting Fractions 47 Subtracting fractions with the same denominator 47 Subtracting fractions with different denominators 47 Working with Mixed Numbers 48 Converting between improper fractions and mixed numbers 49 Multiplying and dividing mixed numbers 50 Adding and subtracting mixed numbers 50 Chapter 5: Deciphering Decimals 57 Performing the Big Four Operations with Decimals 57 Adding decimals 58 Subtracting decimals 59 Multiplying decimals 59 Dividing decimals 61 Converting between Decimals and Fractions 63 Changing decimals to fractions 64 Changing fractions to decimals 66 Chapter 6: Puzzling Out Percents 69 Understanding Percents Greater than 100% 70 Converting to and from Percents, Decimals, and Fractions 70 Going from percents to decimals 71 Changing decimals into percents 71 Switching from percents to fractions 71 Turning fractions into percents 72 Solving Percent Problems 73 Figuring out simple percent problems 74 Deciphering more-difficult percent problems 75 Applying Percent Problems 76 Identifying the three types of percent problems 76 Introducing the percent circle 77 Chapter 7: Fraction, Decimal, and Percent Word Problems 83 Adding and Subtracting Parts of the Whole 83 Sharing a pizza: Fractions 84 Buying by the pound: Decimals 84 Splitting the vote: Percents 85 Multiplying Fractions in Everyday Situations 86 Buying less than advertised 86 Computing leftovers 87 Multiplying Decimals and Percents in Word Problems 88 Figuring out how much money is left 88 Finding out how much you started with 89 Handling Percent Increases and Decreases in Word Problems 91 Raking in the dough: Finding salary increases 91 Earning interest on top of interest 92 Getting a deal: Calculating discounts 93 Chapter 8: Using Variables in Algebraic Expressions 95 Variables: X Marks the Spot 95 Expressing Yourself with Algebraic Expressions 96 Evaluating algebraic expressions 97 Coming to algebraic terms 99 Making the commute: Rearranging your terms 99 Identifying the coefficient and variable 100 Identifying similar terms 101 Considering algebraic terms and the Big Four operations 102 Simplifying Algebraic Expressions 106 Combining similar terms 106 Removing parentheses from an algebraic expression 107 Chapter 9: X''s Secret Identity: Solving Algebraic Equations 113 Understanding Algebraic Equations 114 Using x in equations 114 Four ways to solve algebraic equations 115 Checks and Balances: Solving for X 117 Striking a balance 117 Using the balance scale to isolate x 118 Rearranging Equations to Isolate X 119 Rearranging terms on one side of an equation 120 Moving terms to the other side of the equal sign 120 Removing parentheses from equations 122 Using cross-multiplication to remove fractions 124 Chapter 10: Decoding Algebra Word Problems 127 Using a Five-Step Approach 128 Declaring a variable 128 Setting up the equation 129 Solving the equation 130 Answering the question 131 Checking your work 131 Choosing Your Variable Wisely 131 Solving More-Complex Algebra Problems 133 Chapter 11: Geometry: Perimeter, Area, Surface Area, and Volume 135 Closed Encounters: Understanding 2-D Shapes 136 Circles 136 Polygons 136 Adding Another Dimension: Solid Geometry 137 The many faces of polyhedrons 137 3-D shapes with curves 138 Measuring Shapes: Perimeter, Area, Surface Area, and Volume 139 2-D: Measuring on the flat 139 Spacing out: Measuring in three dimensions 147 Chapter 12: Picture It! Graphing Information 151 Examining Three Common Graph Styles 152 Bar graph 152 Pie chart 153 Line graph 154 Using Cartesian Coordinates 155 Plotting points on a Cartesian graph 156 Drawing lines on a Cartesian graph 157 Solving problems with a Cartesian graph 159 Chapter 13: Ten Essential Math Concepts 163 Playing with Prime Numbers 163 Zero: Much Ado about Nothing 164 Delicious Pi 164 Equal Signs and Equations 165 The Cartesian Graph 165 Relying on Functions 166 Rational Numbers 166 Irrational Numbers 167 The Real Number Line 167 Exploring the Infinite 168 Index 169.