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Introduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 3 Beyond the Book 3 Where to Go from Here 4
Part 1: Getting Started with Basic Math and Pre-algebra 5
Chapter 1: Playing the Numbers Game 7 Inventing Numbers 8 Understanding Number Sequences 8 Evening the odds 9 Counting by threes, fours, fives, and so on 9 Getting square with square numbers 10 Composing yourself with composite numbers 11 Stepping out of the box with prime numbers 12 Multiplying quickly with exponents 13 Looking at the Number Line 14 Adding and subtracting on the number line 14 Getting a handle on nothing, or zero 15 Taking a negative turn: Negative numbers 16 Multiplying the possibilities 17 Dividing things up 17 Discovering the space in between: Fractions 19 Four Important Sets of Numbers 19 Counting on the counting numbers 20 Introducing integers 20 Staying rational 21 Getting real 21
Chapter 2: It''s All in the Fingers: Numbers and Digits 23 Knowing Your Place Value 23 Counting to ten and beyond 24 Telling placeholders from leading zeros 25 Reading long numbers 26 Close Enough for Rock ''n'' Roll: Rounding and Estimating 26 Rounding numbers 26 Estimating value to make problems easier 28 Table of Contents
Chapter 3: The Big Four: Addition, Subtraction, Multiplication, and Division 29 Adding Things Up 30 In line: Adding larger numbers in columns 30 Carry on: Dealing with two-digit answers 31 Take It Away: Subtracting 31 Columns and stacks: Subtracting larger numbers 32 Can you spare a ten? Borrowing to subtract 33 Multiplying 35 Signs of the times 36 Memorizing the multiplication table 37 Double digits: Multiplying larger numbers 40 Doing Division Lickety-Split 42 Making short work of long division 42 Getting leftovers: Division with a remainder 45
Part 2: Getting a Handle on Whole Numbers 47
Chapter 4: Putting the Big Four Operations to Work 49 Knowing Properties of the Big Four Operations 50 Inverse operations 50 Commutative operations 51 Associative operations 52 Distribution to lighten the load 53 Doing Big Four Operations with Negative Numbers 53 Addition and subtraction with negative numbers 54 Multiplication and division with negative numbers 56 Understanding Units 57 Adding and subtracting units 57 Multiplying and dividing units 57 Understanding Inequalities 58 Doesn''t equal (â? ) 58 Less than () 59 Less than or equal to (â?¤) and greater than or equal to (â?¥) 59 Approximately equals (â??) 60 Moving Beyond the Big Four: Exponents, Square Roots, and Absolute Value 60 Understanding exponents 60 Discovering your roots 61 Figuring out absolute value 62
Chapter 5: A Question of Values: Evaluating Arithmetic Expressions 63 Seeking Equality for All: Equations 64 Basic Math & Pre-Algebra For Dummies, 2nd Edition Hey, it''s just an expression 64 Evaluating the situation 65 Putting the Three E''s together 66 Introducing Order of Operations 66 Applying order of operations to Big Four expressions 67 Using order of operations in expressions with exponents 70 Understanding order of precedence in expressions with parentheses 71
Chapter 6: Say What? Turning Words into Numbers 75 Dispelling Two Myths about Word Problems 76 Word problems aren''t always hard 76 Word problems are useful 76 Solving Basic Word Problems 77 Turning word problems into word equations 77 Plugging in numbers for words 80 Solving More-Complex Word Problems 82 When numbers get serious 82 Too much information 83 Putting it all together 85
Chapter 7: Divisibility 87 Knowing the Divisibility Tricks 87 Counting everyone in: Numbers you can divide everything by 88 In the end: Looking at the final digits 88 Add it up: Checking divisibility by adding up digits 90 Ups and downs: Divisibility by 11 91 Identifying Prime and Composite Numbers 92
Chapter 8: Fabulous Factors and Marvelous Multiples 95 Knowing Six Ways to Say the Same Thing 96 Connecting Factors and Multiples 97 Finding Fabulous Factors 97 Deciding when one number is a factor of another 97 Understanding factor pairs 98 Generating a number''s factors 98 Identifying prime factors 100 Finding the greatest common factor (GCF) 105 Making Marvelous Multiples 105 Generating multiples 105 Finding the least common multiple (LCM) 106 Table of Contents
Part 3: Parts of the Whole: Fractions, Decimals, and Percents 109
Chapter 9: Fooling with Fractions 111 Slicing a Cake into Fractions 112 Knowing the Fraction Facts of Life 114 Telling the numerator from the denominator 114 Flipping for reciprocals 114 Using ones and zeros 115 Mixing things up 115 Knowing proper from improper 115 Increasing and Reducing Terms of Fractions 116 Increasing the terms of fractions 117 Reducing fractions to lowest terms 118 Converting between Improper Fractions and Mixed Numbers 120 Knowing the parts of a mixed number 121 Converting a mixed number to an improper fraction 121 Converting an improper fraction to a mixed number 122 Understanding Cross-multiplication 122 Making Sense of Ratios and Proportions 123
Chapter 10: Parting Ways: Fractions and the Big Four Operations 125 Multiplying and Dividing Fractions 126 Multiplying numerators and denominators straight across 126 Doing a flip to divide fractions 127 All Together Now: Adding Fractions 129 Finding the sum of fractions with the same denominator 129 Adding fractions with different denominators 130 Taking It Away: Subtracting Fractions 137 Subtracting fractions with the same denominator 137 Subtracting fractions with different denominators 138 Working Properly with Mixed Numbers 140 Multiplying and dividing mixed numbers 141 Adding and subtracting mixed numbers 142
Chapter 11: Dallying with Decimals 149 Understanding Basic Decimal Stuff 150 Counting dollars and decimals 150 Identifying the place value of decimals 152 Knowing the decimal facts of life 153 Basic Math & Pre-Algebra For Dummies, 2nd Edition Performing the Big Four with Decimals 157 Adding decimals 158 Subtracting decimals 159 Multiplying decimals 160 Dividing decimals 161 Converting between Decimals and Fractions 165 Making simple conversions 165 Changing decimals to fractions 165 Changing fractions to decimals 167
Chapter 12: Playing with Percents 171 Making Sense of Percents 171 Dealing with Percents Greater than 100% 172 Converting to and from Percents, Decimals, and Fractions 173 Going from percents to decimals 173 Changing decimals into percents 174 Switching from percents to fractions 174 Turning fractions into percents 175 Solving Percent Problems 175 Figuring out simple percent problems 176 Turning the problem around 177 Deciphering more-difficult percent problems 178 Putting All the Percent Problems Together 178 Identifying the three types of percent problems 179 Solving percent problems with equations 180
Chapter 13: Word Problems with Fractions, Decimals, and Percents 183 Adding and Subtracting Parts of the Whole in Word Problems 184 Sharing a pizza: Fractions 184 Buying by the pound: Decimals 185 Splitting the vote: Percents 185 Problems about Multiplying Fractions 186 Renegade grocery shopping: Buying less than they tell you to 186 Easy as pie: Working out what''s left on your plate 187 Multiplying Decimals and Percents in Word Problems 188 To the end: Figuring out how much money is left 188 Finding out how much you started with 189 Handling Percent Increases and Decreases in Word Problems 191 Raking in the dough: Finding salary increases 191 Earning interest on top of interest 192 Getting a deal: Calculating discounts 193 Table of Contents
Part 4: Picturing and Measuring -- Graphs, Measures, Stats, and Sets 195
Chapter 14: A Perfect Ten: Condensing Numbers with Scientific Notation 197 First Things First: Using Powers of Ten as Exponents 198 Counting zeros and writing exponents 198 Adding exponents to multiply 200 Working with Scientific Notation 200 Writing in scientific notation 201 Seeing why scientific notation works 202 Understanding order of magnitude 203 Multiplying with scientific notation 203
Chapter 15: How Much Have You Got? Weights and Measures 205 Examining Differences between the English and Metric Systems 206 Looking at the English system 206 Looking at the metric system 208 Estimating and Converting between the English and Metric Systems 210 Estimating in the metric system 211 Converting units of measurement 213
Chapter 16: Picture This: Basic Geometry 217 Getting on t