Pre-Algebra Essentials For Dummies

Mark Zegarelli is a math tutor and author of several books, including Basic Math & Pre-Algebra For Dummies.

• Introduction 1About This Book 1Conventions Used in This Book 2Foolish Assumptions 2Icons Used in This Book 3Where to Go from Here 3Chapter 1: Arming Yourself with Math Basics 5Understanding Sets of Numbers 5The Big Four Operations 6Adding things up 6Take it away: Subtracting 7Multiplying 7Doing division lickety-split 8Fun and Useful Properties of the Big Four Operations 9Inverse operations 9Commutative operations 9Associative operations 10Distributing to lighten the load 10Other Operations: Exponents, Square Roots, and Absolute Values 11Understanding exponents 11Discovering your roots 12Figuring out absolute value 12Finding Factors 13Generating factors 13Finding the greatest common factor (GCF) 14Finding Multiples 14Generating multiples 14Finding the least common multiple (LCM) 15Chapter 2: Evaluating Arithmetic Expressions 17The Three E’s: Equations, Expressions, and Evaluations 18Equality for all: Equations 18Hey, it’s just an expression 19Evaluating the situation 19Putting the Three E’s together 19Following the Order of Operations 20Order of operations and the Big Four expressions 21Order of operations in expressions with exponents 24Order of operations in expressions with parentheses 25Chapter 3: Say What? Making Sense of Word Problems 29Handling Basic Word Problems 30Turning word problems into word equations 30Plugging in numbers for words 33Solving More-Challenging Word Problems 34When numbers get serious 35Lots of information 36Putting it all together 37Chapter 4: Figuring Out Fractions 41Reducing Fractions to Lowest Terms 42Multiplying and Dividing Fractions 42Multiplying numerators and denominators straight across 42Doing a flip to divide fractions 43Adding Fractions 43Finding the sum of fractions with the same denominator 44Adding fractions with different denominators 45Subtracting Fractions 47Subtracting fractions with the same denominator 47Subtracting fractions with different denominators 47Working with Mixed Numbers 48Converting between improper fractions and mixed numbers 49Multiplying and dividing mixed numbers 50Adding and subtracting mixed numbers 50Chapter 5: Deciphering Decimals 57Performing the Big Four Operations with Decimals 57Adding decimals 58Subtracting decimals 59Multiplying decimals 59Dividing decimals 61Converting between Decimals and Fractions 63Changing decimals to fractions 64Changing fractions to decimals 66Chapter 6: Puzzling Out Percents 69Understanding Percents Greater than 100% 70Converting to and from Percents, Decimals, and Fractions 70Going from percents to decimals 71Changing decimals into percents 71Switching from percents to fractions 71Turning fractions into percents 72Solving Percent Problems 73Figuring out simple percent problems 74Deciphering more-difficult percent problems 75Applying Percent Problems 76Identifying the three types of percent problems 76Introducing the percent circle 77Chapter 7: Fraction, Decimal, and Percent Word Problems 83Adding and Subtracting Parts of the Whole 83Sharing a pizza: Fractions 84Buying by the pound: Decimals 84Splitting the vote: Percents 85Multiplying Fractions in Everyday Situations 86Buying less than advertised 86Computing leftovers 87Multiplying Decimals and Percents in Word Problems 88Figuring out how much money is left 88Finding out how much you started with 89Handling Percent Increases and Decreases in Word Problems 91Raking in the dough: Finding salary increases 91Earning interest on top of interest 92Getting a deal: Calculating discounts 93Chapter 8: Using Variables in Algebraic Expressions 95Variables: X Marks the Spot 95Expressing Yourself with Algebraic Expressions 96Evaluating algebraic expressions 97Coming to algebraic terms 99Making the commute: Rearranging your terms 99Identifying the coefficient and variable 100Identifying similar terms 101Considering algebraic terms and the Big Four operations 102Simplifying Algebraic Expressions 106Combining similar terms 106Removing parentheses from an algebraic expression 107Chapter 9: X’s Secret Identity: Solving Algebraic Equations 113Understanding Algebraic Equations 114Using x in equations 114Four ways to solve algebraic equations 115Checks and Balances: Solving for X 117Striking a balance 117Using the balance scale to isolate x 118Rearranging Equations to Isolate X 119Rearranging terms on one side of an equation 120Moving terms to the other side of the equal sign 120Removing parentheses from equations 122Using cross-multiplication to remove fractions 124Chapter 10: Decoding Algebra Word Problems 127Using a Five-Step Approach 128Declaring a variable 128Setting up the equation 129Solving the equation 130Answering the question 131Checking your work 131Choosing Your Variable Wisely 131Solving More-Complex Algebra Problems 133Chapter 11: Geometry: Perimeter, Area, Surface Area, and Volume 135Closed Encounters: Understanding 2-D Shapes 136Circles 136Polygons 136Adding Another Dimension: Solid Geometry 137The many faces of polyhedrons 1373-D shapes with curves 138Measuring Shapes: Perimeter, Area, Surface Area, and Volume 1392-D: Measuring on the flat 139Spacing out: Measuring in three dimensions 147Chapter 12: Picture It! Graphing Information 151Examining Three Common Graph Styles 152Bar graph 152Pie chart 153Line graph 154Using Cartesian Coordinates 155Plotting points on a Cartesian graph 156Drawing lines on a Cartesian graph 157Solving problems with a Cartesian graph 159Chapter 13: Ten Essential Math Concepts 163Playing with Prime Numbers 163Zero: Much Ado about Nothing 164Delicious Pi 164Equal Signs and Equations 165The Cartesian Graph 165Relying on Functions 166Rational Numbers 166Irrational Numbers 167The Real Number Line 167Exploring the Infinite 168Index 169