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
