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
