## Table of Contents

**Introduction 1** About This Book 1

Foolish Assumptions 2

Icons Used in This Book 2

Beyond the Book 3

Where to Go from Here 3

**Part 1: Getting Started with Basic Math and Pre-algebra 5**

**Chapter 1: We’ve Got Your Numbers 7**

Getting in Place with Numbers and Digits 8

Rollover: Rounding Numbers Up and Down 10

Using the Number Line with the Big Four 12

The Column Lineup: Adding and Subtracting 14

Multiplying Multiple Digits 15

Cycling through Long Division 16

Solutions to We’ve Got Your Numbers 19

**Chapter 2: Smooth Operators: Working with the Big Four Operations 23**

Switching Things Up with Inverse Operations and the Commutative Property 24

Getting with the In-Group: Parentheses and the Associative Property 27

Becoming Unbalanced: Inequalities 29

Special Times: Powers and Square Roots 31

Answers to Problems in Smooth Operators 34

**Chapter 3: Getting Down with Negative Numbers 37**

Understanding Where Negative Numbers Come From 37

Sign-Switching: Understanding Negation and Absolute Value 39

Adding with Negative Numbers 40

Subtracting with Negative Numbers 42

Knowing Signs of the Times (And Division) for Negative Numbers 43

Answers to Problems in Getting Down with Negative Numbers 45

**Chapter 4: It’s Just an Expression 49**

Evaluating Expressions with Addition and Subtraction 50

Evaluating Expressions with Multiplication and Division 51

Making Sense of Mixed-Operator Expressions 52

Handling Powers Responsibly 53

Prioritizing Parentheses 55

Pulling Apart Parentheses and Powers 56

Figuring Out Nested Parentheses 58

Bringing It All Together: The Order of Operations 59

Solutions to It’s Just an Expression 61

**Chapter 5: Dividing Attention: Divisibility, Factors, and Multiples 69**

Checking for Leftovers: Divisibility Tests 70

Understanding Factors and Multiples 72

One Number, Indivisible: Identifying Prime (And Composite) Numbers 73

Generating a Number’s Factors 75

Decomposing a Number into Its Prime Factors 77

Finding the Greatest Common Factor 78

Generating the Multiples of a Number 80

Finding the Least Common Multiple 81

Solutions to Divisibility, Factors, and Multiples 83

**Part 2: Slicing Things Up: Fractions, Decimals, and Percents 89**

**Chapter 6: Fractions Are a Piece of Cake 91**

Getting Down the Basic Fraction Stuff 91

In Mixed Company: Converting between Mixed Numbers and Improper Fractions 94

Increasing and Reducing the Terms of Fractions 96

Comparing Fractions with Cross-Multiplication 99

Working with Ratios and Proportions 101

Solutions to Fractions Are a Piece of Cake 103

**Chapter 7: Fractions and the Big Four 109**

Multiplying Fractions: A Straight Shot 109

Flipping for Fraction Division 111

Reaching the Common Denominator: Adding Fractions 113

The Other Common Denominator: Subtracting Fractions 116

Multiplying and Dividing Mixed Numbers 118

Carried Away: Adding Mixed Numbers 120

Borrowing from the Whole: Subtracting Mixed Numbers 123

Solutions to Fractions and the Big Four 126

**Chapter 8: Getting to the Point with Decimals 143**

Getting in Place: Basic Decimal Stuff 143

Simple Decimal-Fraction Conversions 146

New Lineup: Adding and Subtracting Decimals 148

Counting Decimal Places: Multiplying Decimals 150

Points on the Move: Dividing Decimals 151

Decimals to Fractions 153

Fractions to Decimals 155

Solutions to Getting to the Point with Decimals 157

**Chapter 9: Playing the Percentages 165**

Converting Percents to Decimals 165

Changing Decimals to Percents 167

Switching from Percents to Fractions 168

Converting Fractions to Percents 169

Solving a Variety of Percent Problems Using Word Equations 171

Solutions to Playing the Percentages 173

**Part 3: a Giant Step Forward: Intermediate Topics 177**

**Chapter 10: Seeking a Higher Power through Scientific Notation 179**

On the Count of Zero: Understanding Powers of Ten 180

Exponential Arithmetic: Multiplying and Dividing Powers of Ten 182

Representing Numbers in Scientific Notation 183

Multiplying and Dividing with Scientific Notation 184

Answers to Problems in Seeking a Higher Power through Scientific Notation 186

**Chapter 11: Weighty Questions on Weights and Measures 189**

The Basics of the English System 190

Going International with the Metric System 192

Converting Between English and Metric Units 194

Answers to Problems in Weighty Questions on Weights and Measures 198

**Chapter 12: Shaping Up with Geometry 203**

Getting in Shape: Polygon (And Non-Polygon) Basics 204

Squaring Off with Quadrilaterals 204

Making a Triple Play with Triangles 208

Getting Around with Circle Measurements 212

Building Solid Measurement Skills 214

Answers to Problems in Shaping Up with Geometry 218

**Chapter 13: Getting Graphic: Xy-Graphs 223**

Getting the Point of the Xy-Graph 223

Drawing the Line on the Xy-Graph 227

Answers to Problems in Getting Graphic: Xy-Graphs 230

**Part 4: the X Factor: Introducing Algebra 235**

**Chapter 14: Expressing Yourself with Algebraic Expressions 237**

Plug It In: Evaluating Algebraic Expressions 238

Knowing the Terms of Separation 240

Adding and Subtracting Like Terms 242

Multiplying and Dividing Terms 243

Simplifying Expressions by Combining Like Terms 245

Simplifying Expressions with Parentheses 247

FOILing: Dealing with Two Sets of Parentheses 249

Answers to Problems in Expressing Yourself with Algebraic Expressions 251

**Chapter 15: Finding the Right Balance: Solving Algebraic Equations 259**

Solving Simple Algebraic Equations 259

Equality for All: Using the Balance Scale to Isolate X 262

Switching Sides: Rearranging Equations to Isolate X 264

Barring Fractions: Cross-Multiplying to Simplify Equations 266

Answers to Problems in Finding the Right Balance: Solving Algebraic Equations 268

**Part 5: the Part of Tens 277**

**Chapter 16: Ten Alternative Numeral and Number Systems 279**

Tally Marks 279

Bundled Tally Marks 280

Egyptian Numerals 280

Babylonian Numerals 281

Ancient Greek Numerals 281

Roman Numerals 282

Mayan Numerals 282

Base-2 (Binary) Numbers 283

Base-16 (Hexadecimal) Numbers 284

Prime-Based Numbers 285

**Chapter 17: Ten Curious Types of Numbers 287**

Square Numbers 287

Triangular Numbers 288

Cubic Numbers 289

Factorial Numbers 289

Powers of Two 290

Perfect Numbers 290

Amicable Numbers 291

Prime Numbers 291

Mersenne Primes 291

Fermat Primes 292

Index 293