Pre-Algebra Essentials For Dummies

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