Table of Contents
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
Arriving on the dot 7
Speaking parenthetically 8
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 11
Other Operations: Exponents, Square Roots, and Absolute Values 11
Understanding exponents 11
Discovering your roots 12
Figuring out absolute value 13
Finding Factors 13
Generating factors 13
Finding the greatest common factor (GCF) 14
Finding Multiples 15
Generating multiples 15
Finding the least common multiple (LCM) 16
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 20
Following the Order of Operations 20
Order of operations and the Big Four expressions 21
Expressions with only addition and subtraction 22
Expressions with only multiplication and division 23
Mixed-operator expressions 24
Order of operations in expressions with exponents 25
Order of operations in expressions with parentheses 25
Big Four expressions with parentheses 26
Expressions with exponents and parentheses 26
Expressions with parentheses raised to an exponent 27
Expressions with nested parentheses 28
Chapter 3 Say What? Making Sense of Word Problems 31
Handling Basic Word Problems 32
Turning word problems into word equations 32
Jotting down information as word equations 32
Turning more-complex statements into word equations 33
Figuring out what the problem's asking 34
Plugging in numbers for words 35
Example: Send in the clowns 35
Example: Our house in the middle of our street 36
Solving More-Challenging Word Problems 36
When numbers get serious 37
Lots of information 38
Putting it all together 40
Chapter 4 Figuring Out Fractions 43
Reducing Fractions to Lowest Terms 44
Multiplying and Dividing Fractions 44
Multiplying numerators and denominators straight across 45
Doing a flip to divide fractions 45
Adding Fractions 46
Finding the sum of fractions with the same denominator 46
Adding fractions with different denominators 47
Subtracting Fractions 49
Subtracting fractions with the same denominator 49
Subtracting fractions with different denominators 50
Working with Mixed Numbers 51
Converting between improper fractions and mixed numbers 51
Switching to an improper fraction 51
Switching to a mixed number 52
Multiplying and dividing mixed numbers 52
Adding and subtracting mixed numbers 53
Adding two mixed numbers 53
Subtracting mixed numbers 55
Chapter 5 Deciphering Decimals 59
Performing the Big Four Operations with Decimals 59
Adding decimals 60
Subtracting decimals 61
Multiplying decimals 62
Dividing decimals 63
Dealing with more zeros in the dividend 64
Completing decimal division 64
Converting between Decimals and Fractions 65
Changing decimals to fractions 66
Doing a basic decimal-to-fraction conversion 66
Mixing numbers and reducing fractions 67
Changing fractions to decimals 68
The last stop: Terminating decimals 68
The endless ride: Repeating decimals 69
Chapter 6 Puzzling Out Percents 71
Understanding Percents Greater than 100% 72
Converting to and from Percents, Decimals, and Fractions 72
Going from percents to decimals 73
Changing decimals into percents 73
Switching from percents to fractions 73
Turning fractions into percents 74
Solving Percent Problems 75
Figuring out simple percent problems 76
Deciphering more-difficult percent problems 77
Applying Percent Problems 78
Identifying the three types of percent problems 79
Introducing the percent circle 80
Finding the ending number 81
Discovering the percentage 81
Tracking down the starting number 82
Chapter 7 Fraction, Decimal, and Percent Word Problems 85
Adding and Subtracting Parts of the Whole 85
Sharing a pizza: Fractions 86
Buying by the pound: Decimals 86
Splitting the vote: Percents 87
Multiplying Fractions in Everyday Situations 88
Buying less than advertised 88
Computing leftovers 89
Multiplying Decimals and Percents in Word Problems 90
Figuring out how much money is left 90
Finding out how much you started with 91
Handling Percent Increases and Decreases in Word Problems 93
Raking in the dough: Finding salary increases 94
Earning interest on top of interest 94
Getting a deal: Calculating discounts 96
Chapter 8 Using Variables in Algebraic Expressions 97
Variables: X Marks the Spot 97
Expressing Yourself with Algebraic Expressions 98
Evaluating algebraic expressions 99
Coming to algebraic terms 101
Making the commute: Rearranging your terms 102
Identifying the coefficient and variable 103
Identifying similar terms 104
Considering algebraic terms and the Big Four operations 104
Adding terms 104
Subtracting terms 105
Multiplying terms 106
Dividing terms 107
Simplifying Algebraic Expressions 108
Combining similar terms 109
Removing parentheses from an algebraic expression 110
Drop everything: Parentheses with a plus sign 110
Switch signs: Parentheses with a minus sign 110
Distribute: Parentheses with no sign 111
Foil: Two terms in each set of parentheses 112
Chapter 9 X's Secret Identity: Solving Algebraic Equations 115
Understanding Algebraic Equations 116
Using x in equations 116
Four ways to solve algebraic equations 117
Eyeballing easy equations 117
Rearranging slightly harder equations 117
Guessing and checking equations 118
Applying algebra to more-difficult equations 119
Checks and Balances: Solving for X 119
Striking a balance 119
Using the balance scale to isolate x 120
Rearranging Equations to Isolate X 122
Rearranging terms on one side of an equation 122
Moving terms to the other side of the equal sign 123
Removing parentheses from equations 124
Using cross-multiplication to remove fractions 127
Chapter 10 Decoding Algebra Word Problems 129
Using a Five-Step Approach 130
Declaring a variable 130
Setting up the equation 131
Solving the equation 132
Answering the question 133
Checking your work 133
Choosing Your Variable Wisely 134
Solving More Complex Algebra Problems 135
Chapter 11 Geometry: Perimeter, Area, Surface Area, and Volume 139
Closed Encounters: Understanding 2-D Shapes 139
Circles 140
Polygons 140
Adding Another Dimension: Solid Geometry 141
The many faces of polyhedrons 141
3-D shapes with curves 142
Measuring Shapes: Perimeter, Area, Surface Area, and Volume 143
2-D: Measuring on the flat 143
Going 'round in circles 144
Measuring triangles 146
Measuring squares 147
Working with rectangles 148
Calculating with rhombuses 148
Measuring parallelograms 149
Measuring trapezoids 150
Spacing out: Measuring in three dimensions 151
Spheres 152
Cubes 153
Boxes (Rectangular solids) 153
Prisms 154
Cylinders 154
Pyramids and cones 155
Chapter 12 Picture It! Graphing Information 157
Examining Three Common Graph Styles 158
Bar graph 158
Pie chart 159
Line graph 160
Using Cartesian Coordinates 162
Plotting points on a Cartesian graph 162
Drawing lines on a Cartesian graph 164
Solving problems with a Cartesian graph 167
Chapter 13 Ten Essential Math Concepts 169
Playing with Prime Numbers 169
Zero: Much Ado about Nothing 170
Delicious Pi 170
Equal Signs and Equations 171
The Cartesian Graph 171
Relying on Functions 172
Rational Numbers 172
Irrational Numbers 173
The Real Number Line 173
Exploring the Infinite 174
Index 175
