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: An Overview of Fractions, Decimals, and Percents 5 Chapter 1: What Are Fractions, Decimals, and Percents? 7 Taking a First Look at Fractions 8 Understanding how fractions work 8 Making sense of equivalent fractions 9 Understanding improper fractions 10 Seeing how improper fractions and mixed numbers relate 10 Seeing Why Decimals Are So User-Friendly 11 Understanding decimals that have one decimal place 12 Understanding decimals that have two decimal places 13 Understanding fraction-decimal equivalence 14 Putting Percents into Perspective 15 Making sense of percents 16 Converting percents to decimals and fractions 17 Chapter 2: Boosting Basic Skills 19 Knowing Basic Math Words 20 Knowing a number from a numeral 20 Getting your digits sorted 20 Finding values in numbers 21 Counting on integers 21 Examining mathematical operations 22 Talking the talk for the basic four operations 23 Knowing the Basics of Number Sets 24 Describing sets of numbers 24 Integers 25 Rational numbers 25 Irrational numbers 26 Real numbers 26 Reviewing Place Value in Whole Numbers 27 Putting values in their place 28 Looking at leading and placeholding zeros 28 Making Sense of Integer Division 29 Getting a remainder with division 30 Following the cycle of remainders 30 Chapter 3: Understanding Factors and Multiples 33 Understanding Divisibility 34 Making sense of divisibility 34 Knowing some divisibility tricks 35 Finding Factors and Multiples 40 Identifying factors 40 Making sense of multiples 47 Relating factors and multiples 47 Going Big with the Greatest Common Factor 48 Finding common factors 48 Identifying the GCF 49 Tricks to help you find the GCF 50 Playing Small with the Least Common Multiple 51 Finding the LCM 51 Tricks for calculating the LCM 51 Part 2: Fractions 55 Chapter 4: Figuring Fractions 57 Visualizing Fractions 58 Using divided circles to represent parts of the whole 58 Working with fractions on the number line 60 Understanding Basic Fraction Terminology 62 Numerators and denominators 62 Proper and improper fractions 62 Representing whole numbers as fractions 63 Understanding why a zero denominator is undefined 63 Fractions and their reciprocals 64 Understanding Equivalent Fractions 65 Using models to understand equivalent fractions 65 Changing a fraction to an equivalent form 68 Working with Improper Fractions and Mixed Numbers 73 Figuring out improper fractions 73 Mixing it up with mixed numbers 75 Changing mixed numbers to improper fractions by using Popcorn 78 Changing improper fractions to mixed numbers 79 Comparing Fractions'' Values 82 Comparing fractions that have the same denominator 82 Comparing fractions by finding a common denominator 83 Chapter 5: Adding and Subtracting Fractions 89 Adding and Subtracting Fractions that Have a Common Denominator 90 Adding fractions that have a common denominator 90 Subtracting fractions that have a common denominator 94 Adding and subtracting three or more fractions 96 Adding and Subtracting Fractions that Have Different Denominators 97 Adding and subtracting two fractions by increasing terms 98 Adding and subtracting two fractions by cross-multiplying 101 Solving Bigger Problems That Have Different Denominators 104 Breaking a big problem into steps 104 Finding a common denominator for more than two fractions 105 Chapter 6: Multiplying and Dividing Fractions 107 Multiplying Fractions 107 Multiplying a pair of fractions 108 Multiplying more than two fractions 108 Canceling factors to make multiplication easier 109 Dividing Fractions 112 Using Keep-Change-Flip to turn division into multiplication 112 Canceling factors after Keep-Change-Flip 113 Converting results of division from improper fractions to mixed numbers 114 Chapter 7: Working with Mixed Numbers 117 Adding Mixed Numbers 118 Adding mixed numbers that have a common denominator 118 Adding a pair of mixed numbers that have different denominators 120 Adding a pair of mixed numbers when carrying is required 123 Subtracting Mixed Numbers 126 Subtracting mixed numbers that have a common denominator 126 Subtracting a pair of mixed numbers that have different denominators 128 Subtracting mixed numbers when borrowing is required 130 Multiplying Mixed Numbers 134 Multiplying a pair of mixed numbers 135 Canceling factors to make multiplying mixed numbers easier 135 Dividing Mixed Numbers 136 Dividing a pair of mixed numbers 137 Canceling factors to make dividing mixed numbers easier 138 Chapter 8: Word Problems with Fractions 141 Solving Word Problems by Adding and Subtracting Fractions 142 Putting the pieces together: Adding fractions 142 Finding the difference: Subtracting fractions 144 Figuring out what''s left over 146 Multiplying Fractions to Solve Word Problems 147 Multiplying a fraction by a whole number 147 Multiplying a pair of fractions 148 Using multiplication to translate the word of 149 Handling problems that have multiple steps, including multiplication 150 Solving Word Problems by Dividing Fractions 151 Dividing a fraction by a whole number 151 Dividing a fraction by a fraction 152 Solving Word Problems by Using Ratios 153 Ratios that have two values 154 Ratios that have more than two values 155 Ratios that include the total value 156 Using Proportional Equations to Solve Word Problems 157 Building proportional equations 157 Using the total value in a proportional equation 158 Part 3: Decimals 165 Chapter 9: Deciphering Decimals 167 Making Cents of Decimals by Using Money 168 Understanding Decimals by Using Visual Aids 169 Seeing decimals as divided circles 169 Working with decimals on the number line 170 Seeing the Value in Decimal Place Value 170 Multiplying and Dividing by Moving the Decimal Point 172 Multiplying decimals by 10, 100, 1,000, and beyond 173 Dividing decimals by 10, 100, 1,000, and more 173 Converting Between Decimals and Fractions 174 Working with common decimal-fraction conversions 174 Changing decimals less than 1 to fractions 175 Changing decimals greater than 1 to fractions 177 Changing a fraction to a terminating decimal 178 Changing a fraction to a repeating decimal 179 Chapter 10: Applying the Basic Four Operations to Decimals 183 Adding Decimals 183 Subtracting Decimals 185 Multiplying Decimals 188 Dividing Decimals 190 Adding trailing zeros when needed 191 Dealing with repeating decimal quotients 193 Chapter 11: Word Problems with Decimals 197 Solving Word Problems by Adding and Subtracting Decimals 198 Adding things up with decimals 198 Using decimals to find the difference 198 Calculating what''s left over with decimals 199 Combining addition and subtraction to solve decimal word problems 199 Multiplying Decimals to Solve Word Problems 201 Multiplying by 10 and powers of 10 201 Multiplying by other numbers 202 Multiplying decimals to find area 202 Solving multi-step word problems that involve decimal multiplication 203 Solving Word Problems that Involve Decimal Division 204 Dividing by 10 and powers of 10 205 Dividing by other numbers 205 Dividing decimals by other decimals 206 Dividing decimals to solve area problems 206 Solving multi-step word problems that involve decimal division 207 Part 4: Percents 211 Chapter 12: Probing Percents 213 Understanding Percentages 214 Calculating Common Percents in Your Head 216 Calculating 100%, 200%, and 50% 216 Calculating 10%, 20%, and 5% 216 Calculating 25% and 75% 217 Switching Around Numbers to Calculate Percents 218 Changing Percents to Decimals, and Vice Versa 219 Converting decimals to percents 219 Converting percents to decimals 220 Converting Between Percents and Fractions 221 Changing fractions to percents 221 Changing percents to fractions 222 Chapter 13: Solving Percentage Problems 227 Calculating Percents 228 Meeting Three Types of Percentage Problems 228 Solving Percentage Problems by Building Equations 230 Using an equation to find the starting number 230 Using an equation to find the percentage value 232 Chapter 14: Word Problems with Percents 235 Solving Straightforward Percentage Word Problems 236 Solving More Difficult Percentage Word Problems 237 Finding the starting value 237 Calculating the percentage value 238 Working Simple Problems That Involve Percent Increase and Decrease 239 Calculating percent increase 240 Calculating percent decrease 240 Solving Tricky Percent Increase and Decreas.