Introduction 1

About This Book 1

Conventions Used in This Book 2

What You're Not to Read 2

Foolish Assumptions 3

How This Book Is Organized 3

Part 1: Starting Off with the Basics 3

Part 2: Figuring Out Factoring 4

Part 3: Working Equations 4

Part 4: Applying Algebra 4

Part 5: The Part of Tens 5

Icons Used in This Book 5

Where to Go from Here 6

Part 1: Starting off with the Basics 7

Chapter 1: Assembling Your Tools 9

Beginning with the Basics: Numbers 10

Really real numbers 10

Counting on natural numbers 10

Wholly whole numbers 11

Integrating integers 12

Being reasonable: Rational numbers 12

Restraining irrational numbers 12

Picking out primes and composites 13

Speaking in Algebra 13

Taking Aim at Algebra Operations 14

Deciphering the symbols 14

Grouping 15

Defining relationships 16

Taking on algebraic tasks 16

Chapter 2: Assigning Signs: Positive and Negative Numbers 19

Showing Some Signs 20

Picking out positive numbers 20

Making the most of negative numbers 20

Comparing positives and negatives 21

Zeroing in on zero 22

Going In for Operations 22

Breaking into binary operations 22

Introducing non-binary operations 23

Operating with Signed Numbers 25

Adding like to like: Same-signed numbers 25

Adding different signs 26

Subtracting signed numbers 27

Multiplying and dividing signed numbers 29

Working with Nothing: Zero and Signed Numbers 31

Associating and Commuting with Expressions 31

Reordering operations: The commutative property 32

Associating expressions: The associative property 33

Chapter 3: Figuring Out Fractions and Dealing with Decimals 35

Pulling Numbers Apart and Piecing Them Back Together 36

Making your bow to proper fractions 36

Getting to know improper fractions 37

Mixing it up with mixed numbers 37

Following the Sterling Low-Fraction Diet 38

Inviting the loneliest number one 39

Figuring out equivalent fractions 40

Realizing why smaller or fewer is better 41

Preparing Fractions for Interactions 43

Finding common denominators 43

Working with improper fractions 45

Taking Fractions to Task 46

Adding and subtracting fractions 46

Multiplying fractions 47

Dividing fractions 50

Dealing with Decimals 51

Changing fractions to decimals 52

Changing decimals to fractions 53

Chapter 4: Exploring Exponents and Raising Radicals 55

Multiplying the Same Thing Over and Over and Over 55

Powering up exponential notation 56

Comparing with exponents 57

Taking notes on scientific notation 58

Exploring Exponential Expressions 60

Multiplying Exponents 65

Dividing and Conquering 66

Testing the Power of Zero 66

Working with Negative Exponents 67

Powers of Powers 68

Squaring Up to Square Roots 69

Chapter 5: Doing Operations in Order and Checking Your Answers 73

Ordering Operations 74

Gathering Terms with Grouping Symbols 76

Checking Your Answers 78

Making sense or cents or scents 79

Plugging in to get a charge of your answer 79

Curbing a Variable's Versatility 80

Representing numbers with letters 81

Attaching factors and coefficients 82

Interpreting the operations 82

Doing the Math 83

Adding and subtracting variables 84

Adding and subtracting with powers 85

Multiplying and Dividing Variables 86

Multiplying variables 86

Dividing variables 87

Doing it all 88

Part 2: Figuring Out Factoring 91

Chapter 6: Working with Numbers in Their Prime 93

Beginning with the Basics 94

Composing Composite Numbers 95

Writing Prime Factorizations 96

Dividing while standing on your head 96

Getting to the root of primes with a tree 98

Wrapping your head around the rules of divisibility 99

Getting Down to the Prime Factor 100

Taking primes into account 100

Pulling out factors and leaving the rest 103

Chapter 7: Sharing the Fun: Distribution 107

Giving One to Each 108

Distributing first 109

Adding first 109

Distributing Signs 110

Distributing positives 110

Distributing negatives 111

Reversing the roles in distributing 112

Mixing It Up with Numbers and Variables 113

Negative exponents yielding fractional answers 115

Working with fractional powers 115

Distributing More Than One Term 117

Distributing binomials 117

Distributing trinomials 118

Multiplying a polynomial times another polynomial 119

Making Special Distributions 120

Recognizing the perfectly squared binomial 120

Spotting the sum and difference of the same two terms 121

Working out the difference and sum of two cubes 123

Chapter 8: Getting to First Base with Factoring 127

Factoring 127

Factoring out numbers 128

Factoring out variables 130

Unlocking combinations of numbers and variables 131

Changing factoring into a division problem 133

Grouping Terms 134

Chapter 9: Getting the Second Degree 139

The Standard Quadratic Expression 140

Reining in Big and Tiny Numbers 141

FOILing 142

FOILing basics 142

FOILed again, and again 143

Applying FOIL to a special product 146

UnFOILing 147

Unwrapping the FOILing package 148

Coming to the end of the FOIL roll 151

Making Factoring Choices 152

Combining unFOIL and the greatest common factor 153

Grouping and unFOILing in the same package 154

Chapter 10: Factoring Special Cases 157

Befitting Binomials 157

Factoring the difference of two perfect squares 158

Factoring the difference of perfect cubes 159

Factoring the sum of perfect cubes 162

Tinkering with Multiple Factoring Methods 163

Starting with binomials 163

Ending with binomials 164

Knowing When to Quit 165

Incorporating the Remainder Theorem 166

Synthesizing with synthetic division 166

Choosing numbers for synthetic division 167

Part 3: Working Equations 169

Chapter 11: Establishing Ground Rules for Solving Equations 171

Creating the Correct Setup for Solving Equations 172

Keeping Equations Balanced 172

Balancing with binary operations 173

Squaring both sides and suffering the consequences 174

Taking a root of both sides 175

Undoing an operation with its opposite 176

Solving with Reciprocals 176

Making a List and Checking It Twice 179

Doing a reality check 179

Thinking like a car mechanic when checking your work 180

Finding a Purpose 181

Chapter 12: Solving Linear Equations 183

Playing by the Rules 184

Solving Equations with Two Terms 184

Devising a method using division 185

Making the most of multiplication 186

Reciprocating the invitation 188

Extending the Number of Terms to Three 189

Eliminating the extra constant term 189

Vanquishing the extra variable term 190

Simplifying to Keep It Simple 191

Nesting isn't for the birds 192

Distributing first 192

Multiplying or dividing before distributing 194

Featuring Fractions 196

Promoting practical proportions 196

Transforming fractional equations into proportions 198

Solving for Variables in Formulas 199

Chapter 13: Taking a Crack at Quadratic Equations 203

Squaring Up to Quadratics 204

Rooting Out Results from Quadratic Equations 206

Factoring for a Solution 208

Zeroing in on the multiplication property of zero 209

Assigning the greatest common factor and multiplication property of zero to solving quadratics 210

Solving Quadratics with Three Terms 211

Applying Quadratic Solutions 217

Figuring Out the Quadratic Formula 219

Imagining the Worst with Imaginary Numbers 221

Chapter 14: Distinguishing Equations with Distinctive Powers 223

Queuing Up to Cubic Equations 224

Solving perfectly cubed equations 224

Working with the not-so-perfectly cubed 225

Going for the greatest common factor 226

Grouping cubes 228

Solving cubics with integers 228

Working Quadratic-Like Equations 230

Rooting Out Radicals 234

Powering up both sides 235

Squaring both sides twice 237

Solving Synthetically 239

Chapter 15: Rectifying Inequalities 243

Translating between Inequality and Interval Notation 244

Intervening with interval notation 244

Grappling with graphing inequalities 246

Operating on Inequalities 247

Adding and subtracting inequalities 247

Multiplying and dividing inequalities 248

Solving Linear Inequalities 249

Working with More Than Two Expressions 250

Solving Quadratic and Rational Inequalities 252

Working without zeros 255

Dealing with more than two factors 255

Figuring out fractional inequalities 256

Working with Absolute-Value Inequalities 258

Working absolute-value equations 258

Working absolute-value inequalities 260

Part 4: Applying Algebra 263

Chapter 16: Taking Measure with Formulas 265

Measuring Up 265

Finding out how long: Units of length...