Fractions For Dummies

Mark Zegarelli is a math teacher and tutor. He holds degrees in Mathematics and English from Rutgers University and is the author of several math and puzzle books, including Basic Math & Pre-Algebra For Dummies, Basic Math & Pre-Algebra Workbook For Dummies, and Logic For Dummies.

• Introduction 1About This Book 1Foolish Assumptions 2Icons Used in This Book 3Beyond the Book 3Where to Go from Here 4Part 1: An Overview of Fractions, Decimals, and Percents 5Chapter 1: What Are Fractions, Decimals, and Percents? 7Taking a First Look at Fractions 8Understanding how fractions work 8Making sense of equivalent fractions 9Understanding improper fractions 10Seeing how improper fractions and mixed numbers relate 10Seeing Why Decimals Are So User-Friendly 11Understanding decimals that have one decimal place 12Understanding decimals that have two decimal places 13Understanding fraction-decimal equivalence 14Putting Percents into Perspective 15Making sense of percents 16Converting percents to decimals and fractions 17Chapter 2: Boosting Basic Skills 19Knowing Basic Math Words 20Knowing a number from a numeral 20Getting your digits sorted 20Finding values in numbers 21Counting on integers 21Examining mathematical operations 22Talking the talk for the basic four operations 23Knowing the Basics of Number Sets 24Describing sets of numbers 24Integers 25Rational numbers 25Irrational numbers 26Real numbers 26Reviewing Place Value in Whole Numbers 27Putting values in their place 28Looking at leading and placeholding zeros 28Making Sense of Integer Division 29Getting a remainder with division 30Following the cycle of remainders 30Chapter 3: Understanding Factors and Multiples 33Understanding Divisibility 34Making sense of divisibility 34Knowing some divisibility tricks 35Finding Factors and Multiples 40Identifying factors 40Making sense of multiples 47Relating factors and multiples 47Going Big with the Greatest Common Factor 48Finding common factors 48Identifying the GCF 49Tricks to help you find the GCF 50Playing Small with the Least Common Multiple 51Finding the LCM 51Tricks for calculating the LCM 51Part 2: Fractions 55Chapter 4: Figuring Fractions 57Visualizing Fractions 58Using divided circles to represent parts of the whole 58Working with fractions on the number line 60Understanding Basic Fraction Terminology 62Numerators and denominators 62Proper and improper fractions 62Representing whole numbers as fractions 63Understanding why a zero denominator is undefined 63Fractions and their reciprocals 64Understanding Equivalent Fractions 65Using models to understand equivalent fractions 65Changing a fraction to an equivalent form 68Working with Improper Fractions and Mixed Numbers 73Figuring out improper fractions 73Mixing it up with mixed numbers 75Changing mixed numbers to improper fractions by using Popcorn 78Changing improper fractions to mixed numbers 79Comparing Fractions’ Values 82Comparing fractions that have the same denominator 82Comparing fractions by finding a common denominator 83Chapter 5: Adding and Subtracting Fractions 89Adding and Subtracting Fractions that Have a Common Denominator 90Adding fractions that have a common denominator 90Subtracting fractions that have a common denominator 94Adding and subtracting three or more fractions 96Adding and Subtracting Fractions that Have Different Denominators 97Adding and subtracting two fractions by increasing terms 98Adding and subtracting two fractions by cross-multiplying 101Solving Bigger Problems That Have Different Denominators 104Breaking a big problem into steps 104Finding a common denominator for more than two fractions 105Chapter 6: Multiplying and Dividing Fractions 107Multiplying Fractions 107Multiplying a pair of fractions 108Multiplying more than two fractions 108Canceling factors to make multiplication easier 109Dividing Fractions 112Using Keep-Change-Flip to turn division into multiplication 112Canceling factors after Keep-Change-Flip 113Converting results of division from improper fractions to mixed numbers 114Chapter 7: Working with Mixed Numbers 117Adding Mixed Numbers 118Adding mixed numbers that have a common denominator 118Adding a pair of mixed numbers that have different denominators 120Adding a pair of mixed numbers when carrying is required 123Subtracting Mixed Numbers 126Subtracting mixed numbers that have a common denominator 126Subtracting a pair of mixed numbers that have different denominators 128Subtracting mixed numbers when borrowing is required 130Multiplying Mixed Numbers 134Multiplying a pair of mixed numbers 135Canceling factors to make multiplying mixed numbers easier 135Dividing Mixed Numbers 136Dividing a pair of mixed numbers 137Canceling factors to make dividing mixed numbers easier 138Chapter 8: Word Problems with Fractions 141Solving Word Problems by Adding and Subtracting Fractions 142Putting the pieces together: Adding fractions 142Finding the difference: Subtracting fractions 144Figuring out what’s left over 146Multiplying Fractions to Solve Word Problems 147Multiplying a fraction by a whole number 147Multiplying a pair of fractions 148Using multiplication to translate the word of 149Handling problems that have multiple steps, including multiplication 150Solving Word Problems by Dividing Fractions 151Dividing a fraction by a whole number 151Dividing a fraction by a fraction 152Solving Word Problems by Using Ratios 153Ratios that have two values 154Ratios that have more than two values 155Ratios that include the total value 156Using Proportional Equations to Solve Word Problems 157Building proportional equations 157Using the total value in a proportional equation 158Part 3: Decimals 165Chapter 9: Deciphering Decimals 167Making Cents of Decimals by Using Money 168Understanding Decimals by Using Visual Aids 169Seeing decimals as divided circles 169Working with decimals on the number line 170Seeing the Value in Decimal Place Value 170Multiplying and Dividing by Moving the Decimal Point 172Multiplying decimals by 10, 100, 1,000, and beyond 173Dividing decimals by 10, 100, 1,000, and more 173Converting Between Decimals and Fractions 174Working with common decimal-fraction conversions 174Changing decimals less than 1 to fractions 175Changing decimals greater than 1 to fractions 177Changing a fraction to a terminating decimal 178Changing a fraction to a repeating decimal 179Chapter 10: Applying the Basic Four Operations to Decimals 183Adding Decimals 183Subtracting Decimals 185Multiplying Decimals 188Dividing Decimals 190Adding trailing zeros when needed 191Dealing with repeating decimal quotients 193Chapter 11: Word Problems with Decimals 197Solving Word Problems by Adding and Subtracting Decimals 198Adding things up with decimals 198Using decimals to find the difference 198Calculating what’s left over with decimals 199Combining addition and subtraction to solve decimal word problems 199Multiplying Decimals to Solve Word Problems 201Multiplying by 10 and powers of 10 201Multiplying by other numbers 202Multiplying decimals to find area 202Solving multi-step word problems that involve decimal multiplication 203Solving Word Problems that Involve Decimal Division 204Dividing by 10 and powers of 10 205Dividing by other numbers 205Dividing decimals by other decimals 206Dividing decimals to solve area problems 206Solving multi-step word problems that involve decimal division 207Part 4: Percents 211Chapter 12: Probing Percents 213Understanding Percentages 214Calculating Common Percents in Your Head 216Calculating 100%, 200%, and 50% 216Calculating 10%, 20%, and 5% 216Calculating 25% and 75% 217Switching Around Numbers to Calculate Percents 218Changing Percents to Decimals, and Vice Versa 219Converting decimals to percents 219Converting percents to decimals 220Converting Between Percents and Fractions 221Changing fractions to percents 221Changing percents to fractions 222Chapter 13: Solving Percentage Problems 227Calculating Percents 228Meeting Three Types of Percentage Problems 228Solving Percentage Problems by Building Equations 230Using an equation to find the starting number 230Using an equation to find the percentage value 232Chapter 14: Word Problems with Percents 235Solving Straightforward Percentage Word Problems 236Solving More Difficult Percentage Word Problems 237Finding the starting value 237Calculating the percentage value 238Working Simple Problems That Involve Percent Increase and Decrease 239Calculating percent increase 240Calculating percent decrease 240Solving Tricky Percent Increase and Decrease Word Problems 242Finding the starting value 242Finding the percentage value 244Part 5: the Part of Tens 249Chapter 15: Ten Important Points for Working with Fractions 251Simplifying Fractions 251Increasing the Terms of Fractions 252Changing Mixed Numbers to Improper Fractions 253Knowing When to Find a Common Denominator 254Knowing When You Don’t Need a Common Denominator 255Canceling Factors Before Multiplying Fractions 255Using Keep-Change-Flip Only When Dividing Fractions 256Using Keep-Change-Flip Before Canceling Factors 257When to Change Mixed Numbers to Improper Fractions 257When Not to Change Mixed Numbers to Improper Fractions 258Chapter 16: Ten Real-World Uses for Fractions 261Cooking and Baking 261Construction and Building 262Money and Finance 263Sports 264Telling Time 264Music and Visual Art 265Gambling 265Nursing and Medicine 266Health and Fitness 266Travel and Fuel Efficiency 267Index 269