Basic Math & Pre-Algebra For Dummies von Mark Zegarelli

<i><b>Basic Math& Pre-Algebra For Dummies, 2nd Edition (9781119293637) was previously published as Basic Math& Pre-Algebra For Dummies, 2nd Edition (9781118791981). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.</b></i><p><b><br />Tips for simplifying tricky basic math and pre-algebra operations</b></p><p>Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.</p><ul><li>Explanations and practical examples that mirror today's teaching methods</li><li>Relevant cultural vernacular and references</li><li><i>Standard For Dummies</i>materials that match the current standard and design</li></ul><p><i>Basic Math& Pre-Algebra For Dummies</i> takes the intimidation out of tricky operations and helps you get ready for algebra!</p>

Mark Zegarelli is the author of many successfulFor Dummies titles on math, logic, and test prep topics. He holds degrees in both English and math from Rutgers University and is the founder of SimpleStep Learning, an educational website (https://simplestep.co).

Introduction 1About This Book 1Foolish Assumptions 2Icons Used in This Book 3Beyond the Book 3Where to Go from Here 4Part 1: Getting Started with Basic Math and Pre-algebra 5Chapter 1: Playing the Numbers Game 7Inventing Numbers 8Understanding Number Sequences 8Evening the odds 9Counting by threes, fours, fives, and so on 9Getting square with square numbers 10Composing yourself with composite numbers 11Stepping out of the box with prime numbers 12Multiplying quickly with exponents 13Looking at the Number Line 14Adding and subtracting on the number line 14Getting a handle on nothing, or zero 15Taking a negative turn: Negative numbers 16Multiplying the possibilities 17Dividing things up 17Discovering the space in between: Fractions 19Four Important Sets of Numbers 19Counting on the counting numbers 20Introducing integers 20Staying rational 21Getting real 21Chapter 2: Its All in the Fingers: Numbers and Digits 23Knowing Your Place Value 23Counting to ten and beyond 24Telling placeholders from leading zeros 25Reading long numbers 26Close Enough for Rock n Roll: Rounding and Estimating 26Rounding numbers 26Estimating value to make problems easier 28Table of ContentsChapter 3: The Big Four: Addition, Subtraction, Multiplication, and Division 29Adding Things Up 30In line: Adding larger numbers in columns 30Carry on: Dealing with two-digit answers 31Take It Away: Subtracting 31Columns and stacks: Subtracting larger numbers 32Can you spare a ten? Borrowing to subtract 33Multiplying 35Signs of the times 36Memorizing the multiplication table 37Double digits: Multiplying larger numbers 40Doing Division Lickety-Split 42Making short work of long division 42Getting leftovers: Division with a remainder 45Part 2: Getting a Handle on Whole Numbers 47Chapter 4: Putting the Big Four Operations to Work 49Knowing Properties of the Big Four Operations 50Inverse operations 50Commutative operations 51Associative operations 52Distribution to lighten the load 53Doing Big Four Operations with Negative Numbers 53Addition and subtraction with negative numbers 54Multiplication and division with negative numbers 56Understanding Units 57Adding and subtracting units 57Multiplying and dividing units 57Understanding Inequalities 58Doesnt equal () 58Less than () 59Less than or equal to () and greater than or equal to () 59Approximately equals () 60Moving Beyond the Big Four: Exponents, Square Roots, and Absolute Value 60Understanding exponents 60Discovering your roots 61Figuring out absolute value 62Chapter 5: A Question of Values: Evaluating Arithmetic Expressions 63Seeking Equality for All: Equations 64Basic Math& Pre-Algebra For Dummies, 2nd EditionHey, its just an expression 64Evaluating the situation 65Putting the Three Es together 66Introducing Order of Operations 66Applying order of operations to Big Four expressions 67Using order of operations in expressions with exponents 70Understanding order of precedence in expressionswith parentheses 71Chapter 6: Say What? Turning Words into Numbers 75Dispelling Two Myths about Word Problems 76Word problems arent always hard 76Word problems are useful 76Solving Basic Word Problems 77Turning word problems into word equations 77Plugging in numbers for words 80Solving More-Complex Word Problems 82When numbers get serious 82Too much information 83Putting it all together 85Chapter 7: Divisibility 87Knowing the Divisibility Tricks 87Counting everyone in: Numbers you can divide everything by 88In the end: Looking at the final digits 88Add it up: Checking divisibility by adding up digits 90Ups and downs: Divisibility by 11 91Identifying Prime and Composite Numbers 92Chapter 8: Fabulous Factors and Marvelous Multiples 95Knowing Six Ways to Say the Same Thing 96Connecting Factors and Multiples 97Finding Fabulous Factors 97Deciding when one number is a factor of another 97Understanding factor pairs 98Generating a numbers factors 98Identifying prime factors 100Finding the greatest common factor (GCF) 105Making Marvelous Multiples 105Generating multiples 105Finding the least common multiple (LCM) 106Table of ContentsPart 3: Parts of the Whole: Fractions, Decimals, and Percents 109Chapter 9: Fooling with Fractions 111Slicing a Cake into Fractions 112Knowing the Fraction Facts of Life 114Telling the numerator from the denominator 114Flipping for reciprocals 114Using ones and zeros 115Mixing things up 115Knowing proper from improper 115Increasing and Reducing Terms of Fractions 116Increasing the terms of fractions 117Reducing fractions to lowest terms 118Converting between Improper Fractions and Mixed Numbers 120Knowing the parts of a mixed number 121Converting a mixed number to an improper fraction 121Converting an improper fraction to a mixed number 122Understanding Cross-multiplication 122Making Sense of Ratios and Proportions 123Chapter 10: Parting Ways: Fractions and the Big Four Operations 125Multiplying and Dividing Fractions 126Multiplying numerators and denominators straight across 126Doing a flip to divide fractions 127All Together Now: Adding Fractions 129Finding the sum of fractions with the same denominator 129Adding fractions with different denominators 130Taking It Away: Subtracting Fractions 137Subtracting fractions with the same denominator 137Subtracting fractions with different denominators 138Working Properly with Mixed Numbers 140Multiplying and dividing mixed numbers 141Adding and subtracting mixed numbers 142Chapter 11: Dallying with Decimals 149Understanding Basic Decimal Stuff 150Counting dollars and decimals 150Identifying the place value of decimals 152Knowing the decimal facts of life 153Basic Math& Pre-Algebra For Dummies, 2nd EditionPerforming the Big Four with Decimals 157Adding decimals 158Subtracting decimals 159Multiplying decimals 160Dividing decimals 161Converting between Decimals and Fractions 165Making simple conversions 165Changing decimals to fractions 165Changing fractions to decimals 167Chapter 12: Playing with Percents 171Making Sense of Percents 171Dealing with Percents Greater than 100% 172Converting to and from Percents, Decimals, and Fractions 173Going from percents to decimals 173Changing decimals into percents 174Switching from percents to fractions 174Turning fractions into percents 175Solving Percent Problems 175Figuring out simple percent problems 176Turning the problem around 177Deciphering more-difficult percent problems 178Putting All the Percent Problems Together 178Identifying the three types of percent problems 179Solving percent problems with equations 180Chapter 13: Word Problems with Fractions, Decimals, and Percents 183Adding and Subtracting Parts of the Whole in Word Problems 184Sharing a pizza: Fractions 184Buying by the pound: Decimals 185Splitting the vote: Percents 185Problems about Multiplying Fractions 186Renegade grocery shopping: Buying less than they tell you to 186Easy as pie: Working out whats left on your plate 187Multiplying Decimals and Percents in Word Problems 188To the end: Figuring out how much money is left 188Finding out how much you started with 189Handling Percent Increases and Decreases in Word Problems 191Raking in the dough: Finding salary increases 191Earning interest on top of interest 192Getting a deal: Calculating discounts 193Table of ContentsPart 4: Picturing and Measuring Graphs, Measures, Stats, and Sets 195Chapter 14: A Perfect Ten: Condensing Numbers with Scientific Notation 197First Things First: Using Powers of Ten as Exponents 198Counting zeros and writing exponents 198Adding exponents to multiply 200Working with Scientific Notation 200Writing in scientific notation 201Seeing why scientific notation works 202Understanding order of magnitude 203Multiplying with scientific notation 203Chapter 15: How Much Have You Got? Weights andMeasures 205Examining Differences between the English and Metric Systems 206Looking at the English system 206Looking at the metric system 208Estimating and Converting between the English and Metric Systems 210Estimating in the metric system 211Converting units of measurement 213Chapter 16: Picture This: Basic Geometry 217Getting on the Plane: Points, Lines, Angles, and Shapes 218Making some points 218Knowing your lines 218Figuring the angles 219Shaping things up 221Closed Encounters: Shaping Up Your Understandingof 2-D Shapes 221Polygons 222Circles 224Taking a Trip to Another Dimension: Solid Geometry 225The many faces of polyhedrons 2253-D shapes with curves 226Measuring Shapes: Perimeter, Area, Surface Area, and Volume 2272-D: Measuring on the flat 228Spacing out: Measuring in three dimensions 235Basic Math& Pre-Algebra For Dummies, 2nd EditionChapter 17: Seeing Is Believing: Graphing as a Visual Tool 239Looking at Three Important Graph Styles 240Bar graph 240Pie chart 241Line graph 242Using the xy-Graph 243Plotting points on an xy-graph 244Drawing lines on an xy-graph 245Chapter 18: Solving Geometry and Measurement Word Problems 247The Chain Gang: Solving Measurement Problems with Conversion Chains 248Setting up a short chain 248Working with more links 249Pulling equations out of the text 250Rounding off: Going for the short answer 251Solving Geometry Word Problems 253Working from words and images 253Breaking out those sketching skills 255Chapter 19: Figuring Your Chances: Statistics and Probability 259Gathering Data Mathematically: Basic Statistics 260Understanding differences between qualitative and quantitative data 260Working with qualitative data 261Working with quantitative data 264Looking at Likelihoods: Basic Probability 266Figuring the probability 267Oh, the possibilities! Counting outcomes with multiple coins 268Chapter 20: Setting Things Up with Basic Set Theory 271Understanding Sets 272Elementary, my dear: Considering whats inside sets 273Sets of numbers 275Performing Operations on Sets 275Union: Combined elements 276Intersection: Elements in common 276Relative complement: Subtraction (sorta) 277Complement: Feeling left out 277Table of ContentsPart 5: the X-files: Introduction to Algebra 279Chapter 21: Enter Mr X: Algebra and AlgebraicExpressions 281Seeing How X Marks the Spot 282Expressing Yourself with Algebraic Expressions 282Evaluating algebraic expressions 283Coming to algebraic terms 285Making the commute: Rearranging your terms 286Identifying the coefficient and variable 287Identifying like terms 288Considering algebraic terms and the Big Four 289Simplifying Algebraic Expressions 292Combining like terms 292Removing parentheses from an algebraic expression 293Chapter 22: Unmasking Mr X: Algebraic Equations 299Understanding Algebraic Equations 300Using X in Equations 300Choosing among four ways to solve algebraic equations 301The Balancing Act: Solving for x 302Striking a balance 303Using the Balance Scale to Isolate X 304Rearranging Equations and Isolating x 305Rearranging terms on one side of an equation 305Moving terms to the other side of the equals sign 306Removing parentheses from equations 307Cross-multiplying 309Chapter 23: Putting Mr X to Work: Algebra Word Problems 311Solving Algebra Word Problems in Five Steps 312Declaring a variable 312Setting up the equation 313Solving the equation 314Answering the question 314Checking your work 315Choosing Your Variable Wisely 315Solving More-Complex Algebraic Problems 316Charting four people 316Crossing the finish line with five people 318Basic Math& Pre-Algebra For Dummies, 2nd EditionPart 6: the Part of Tens 321Chapter 24: Ten Little Math Demons That Trip People Up 323Knowing the Multiplication Table 324Adding and Subtracting Negative Numbers 324Multiplying and Dividing Negative Numbers 325Knowing the Difference between Factors and Multiples 325Reducing Fractions to Lowest Terms 326Adding and Subtracting Fractions 326Multiplying and Dividing Fractions 327Identifying Algebras Main Goal: Find X 327Knowing Algebras Main Rule: Keep the Equation in Balance 328Seeing Algebras Main Strategy: Isolate x 328Chapter 25: Ten Important Number Sets to Know 329Counting on Counting (or Natural) Numbers 330Identifying Integers 330Knowing the Rationale behind Rational Numbers 331Making Sense of Irrational Numbers 331Absorbing Algebraic Numbers 332Moving through Transcendental Numbers 333Getting Grounded in Real Numbers 333Trying to Imagine Imaginary Numbers 333Grasping the Complexity of Complex Numbers 334Going beyond the Infinite with Transfinite Numbers 335Index 337

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