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
