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 Unit 1: Getting Started with Basic Math & Pre-algebra 5 Chapter 1: Playing the Numbers Game 7 Inventing Numbers 8 Understanding Number Sequences 8 Evening the odds 8 Counting by threes, fours, fives, and so on 9 Getting square with square numbers 9 Composing yourself with composite numbers 10 Stepping out of the box with prime numbers 11 Multiplying quickly with exponents 12 Four Important Sets of Numbers 13 Counting on the counting numbers 13 Introducing integers 13 Staying rational 14 Getting real 14 Chapter 2: The Big Four Operations 15 The Big Four Operations 15 Adding things up: Addition 16 Take it away: Subtraction 16 A sign of the times: Multiplication 17 Doing math lickety-split: Division 18 Applying the Big Four Operations to Larger Numbers 18 Calculating stacked addition 18 Performing stacked subtraction 19 Calculating with stacked multiplication 21 Understanding long division 22 Unit 2: the Big Four Operations: Addition, Subtraction, Multiplication, and Division 25 Chapter 3: Counting on Success: Numbers and Digits 27 Knowing Your Place Value 28 Counting to ten and beyond 28 Telling placeholders from leading zeros 29 Reading long numbers 30 Close Enough for Rock ''n'' Roll: Rounding and Estimating 30 Rounding numbers 30 Estimating value to make problems easier 32 Practice Questions Answers and Explanations 34 Whaddya Know? Chapter 3 Quiz 35 Answers to Chapter 3 Quiz 36 Chapter 4: Staying Positive with Negative Numbers 37 Understanding Where Negative Numbers Come From 38 Sign-Switching: Understanding Negation and Absolute Value 39 Addition and Subtraction with Negative Numbers 41 Starting with a negative number 41 Adding a negative number 41 Subtracting a negative number 42 Knowing Signs of the Times (and Division) for Negative Numbers 44 Practice Questions Answers and Explanations 47 Whaddya Know? Chapter 4 Quiz 51 Answers to Chapter 4 Quiz 52 Chapter 5: Putting the Big Four Operations to Work 55 Switching Things Up with Inverse Operations and the Commutative Property 56 Getting with the In-Group: Parentheses and the Associative Property 59 Distribution to lighten the load 61 Understanding Inequalities 63 Doesn''t equal (≠) 63 Less than () 63 Less than or equal to (≤) and greater than or equal to (≥) 64 Approximately equals (≈) 64 Moving Beyond the Big Four: Exponents and Square Roots 65 Understanding exponents 66 Discovering your roots 67 Practice Questions Answers and Explanations 69 Whaddya Know? Chapter 5 Quiz 72 Answers to Chapter 5 Quiz 73 Unit 3: Getting a Handle on Whole Numbers 75 Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77 The Three E''s of Math: Equations, Expressions, and Evaluation 78 Seeking equality for all: Equations 78 Hey, it''s just an expression 78 Evaluating the situation 79 Putting the Three E''s together 79 Introducing Order of Operations (PEMDAS) 80 Expressions with only addition and subtraction 81 Expressions with only multiplication and division 81 Mixed-operator expressions 82 Handling Powers Responsibly 83 Prioritizing parentheses 84 Pulling apart parentheses and powers 85 Figuring out nested parentheses 86 Bringing It All Together: The Order of Operations 87 Practice Questions Answers and Explanations 89 Whaddya Know? Chapter 6 Quiz 98 Answers to Chapter 6 Quiz 99 Chapter 7: Turning Words into Numbers: Basic Math Word Problems 103 Dispelling Two Myths about Word Problems 104 Word problems aren''t always hard 104 Word problems are useful 104 Solving Basic Word Problems 105 Turning word problems into word equations 105 Plugging in numbers for words 109 Send in the clowns 109 Our house in the middle of our street 110 I hear the train a-comin'' 110 Solving More-Complex Word Problems 113 When numbers get serious 113 Too much information 115 Practice Questions Answers and Explanations 120 Whaddya Know? Chapter 7 Quiz 124 Answers to Chapter 7 Quiz 125 Chapter 8: Divisibility and Prime Numbers 127 Knowing the Divisibility Tricks 128 Counting everyone in: Numbers you can divide everything by 128 In the end: Looking at the final digits 128 Count it up: Checking divisibility by adding and subtracting digits 130 Less is more: Checking divisibility by subtracting 134 Cross-checking: Using multiple tests 135 Identifying Prime and Composite Numbers 136 Practice Questions Answers and Explanations 139 Whaddya Know? Chapter 8 Quiz 142 Answers to Chapter 8 Quiz 143 Chapter 9: Divided Attention: Factors and Multiples 145 Knowing Six Ways to Say the Same Thing 146 Understanding Factors and Multiples 146 Finding Fabulous Factors 148 Deciding when one number is a factor of another 148 Understanding factor pairs 148 Generating a Number''s Factors 149 Decomposing a Number into Its Prime Factors 150 Finding the Greatest Common Factor 151 Generating the Multiples of a Number 153 Finding the Least Common Multiple 153 Practice Questions Answers and Explanations 155 Whaddya Know? Chapter 9 Quiz 158 Answers to Chapter 9 Quiz 159 Unit 4: Fractions 161 Chapter 10: Understanding Fractions 163 Slicing a Cake into Fractions 164 Knowing the Fraction Facts of Life 165 Telling the numerator from the denominator 165 Flipping for reciprocals 166 Using ones and zeros 166 Mixing things up 167 Knowing proper from improper 167 Increasing and Reducing Terms of Fractions 169 Increasing the terms of fractions 170 Reducing fractions to lowest terms (simplifying fractions) 171 Converting between Improper Fractions and Mixed Numbers 174 Knowing the parts of a mixed number 174 Converting a mixed number to an improper fraction 175 Converting an improper fraction to a mixed number 176 Comparing Fractions with Cross-Multiplication 178 Working with Ratios and Proportions 180 Practice Questions Answers and Explanations 182 Whaddya Know? Chapter 10 Quiz 188 Answers to Chapter 10 Quiz 189 Chapter 11: Fractions and the Big Four Operations 191 Multiplying and Dividing Fractions 192 Multiplying numerators and denominators straight across 192 Doing a flip to divide fractions 194 Adding and Subtracting Fractions with the Same Denominator 196 Adding and Subtracting Fractions with Different Denominators 198 The easy case: Increasing the terms of one fraction 198 The difficult case: Increasing the terms of both fractions 200 Practice Questions Answers and Explanations 202 Whaddya Know? Chapter 11 Quiz 208 Answers to Chapter 11 Quiz 209 Chapter 12: Mixing Things Up with Mixed Numbers 213 Multiplying and Dividing Mixed Numbers 214 Adding Mixed Numbers 216 Adding mixed numbers that have the same denominator 216 Adding mixed numbers that have different denominators 217 Adding mixed numbers with carrying 217 Subtracting Mixed Numbers 220 Subtracting mixed numbers that have the same denominator 220 Subtracting mixed numbers that have different denominators 221 Subtracting mixed numbers with borrowing 222 Practice Questions Answers and Explanations 225 Whaddya Know? Chapter 12 Quiz 233 Answers to Chapter 12 Quiz 234 Unit 5: Decimals and Percents 241 Chapter 13: Getting to the Point with Decimals 243 Understanding Basic Decimal Stuff 244 Counting dollars and decimals 244 Identifying the place value of decimals 246 Knowing the decimal facts of life 247 Performing the Big Four Operations with Decimals 252 Adding decimals 253 Subtracting decimals 254 Multiplying decimals 256 Dividing decimals 257 Converting between Decimals and Fractions 262 Simple Decimal-Fraction Conversions 262 Changing decimals to fractions 264 Changing fractions to decimals 267 Practice Questions Answers and Explanations 271 Whaddya Know? Chapter 13 Quiz 279 Answers to Chapter 13 Quiz 280 Chapter 14: Playing the Percentages 285 Making Sense of Percentages 285 Dealing with Percentages Greater than 100% 286 Converting to and from Percentages, Decimals, and Fractions 287 Converting Percentages to Decimals 287 Changing Decimals to Percentages 288 Switching from Percentages to Fractions 288 Converting Fractions to Percentages 289 Solving Percentage Problems 290 Figuring out simple percent problems 291 Turning the problem around 292 Deciphering more-difficult percent problems 293 Putting All the Percent Problems Together 294 Identifying the three types of percent problems 294 Solving Percent Problems with Equatio.