Fractions For Dummies

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 Decrease Word Problems 242

Finding the starting value 242

Finding the percentage value 244

Part 5: the Part of Tens 249

Chapter 15: Ten Important Points for Working with Fractions 251

Simplifying Fractions 251

Increasing the Terms of Fractions 252

Changing Mixed Numbers to Improper Fractions 253

Knowing When to Find a Common Denominator 254

Knowing When You Don't Need a Common Denominator 255

Canceling Factors Before Multiplying Fractions 255

Using Keep-Change-Flip Only When Dividing Fractions 256

Using Keep-Change-Flip Before Canceling Factors 257

When to Change Mixed Numbers to Improper Fractions 257

When Not to Change Mixed Numbers to Improper Fractions 258

Chapter 16: Ten Real-World Uses for Fractions 261

Cooking and Baking 261

Construction and Building 262

Money and Finance 263

Sports 264

Telling Time 264

Music and Visual Art 265

Gambling 265

Nursing and Medicine 266

Health and Fitness 266

Travel and Fuel Efficiency 267

Index 269