Mark Zegarelli earned degrees in mathematics and English from Rutgers University. He is the founder of SimpleStep Learning, an online educational platform that teaches courses in basic concepts in ten minutes or less, keeping students engaged and learning in every moment. Mark is also author of several other successful For Dummies books.

• Introduction 1About This Book 1Foolish Assumptions 2Icons Used in This Book 2Beyond the Book 3Where to Go from Here 3Unit 1: Getting Started with Basic Math & Pre-algebra 5Chapter 1: Playing the Numbers Game 7Inventing Numbers 8Understanding Number Sequences 8Evening the odds 8Counting by threes, fours, fives, and so on 9Getting square with square numbers 9Composing yourself with composite numbers 10Stepping out of the box with prime numbers 11Multiplying quickly with exponents 12Four Important Sets of Numbers 13Counting on the counting numbers 13Introducing integers 13Staying rational 14Getting real 14Chapter 2: The Big Four Operations 15The Big Four Operations 15Adding things up: Addition 16Take it away: Subtraction 16A sign of the times: Multiplication 17Doing math lickety-split: Division 18Applying the Big Four Operations to Larger Numbers 18Calculating stacked addition 18Performing stacked subtraction 19Calculating with stacked multiplication 21Understanding long division 22Unit 2: the Big Four Operations: Addition, Subtraction, Multiplication, and Division 25Chapter 3: Counting on Success: Numbers and Digits 27Knowing Your Place Value 28Counting to ten and beyond 28Telling placeholders from leading zeros 29Reading long numbers 30Close Enough for Rock ‘n’ Roll: Rounding and Estimating 30Rounding numbers 30Estimating value to make problems easier 32Practice Questions Answers and Explanations 34Whaddya Know? Chapter 3 Quiz 35Answers to Chapter 3 Quiz 36Chapter 4: Staying Positive with Negative Numbers 37Understanding Where Negative Numbers Come From 38Sign-Switching: Understanding Negation and Absolute Value 39Addition and Subtraction with Negative Numbers 41Starting with a negative number 41Adding a negative number 41Subtracting a negative number 42Knowing Signs of the Times (and Division) for Negative Numbers 44Practice Questions Answers and Explanations 47Whaddya Know? Chapter 4 Quiz 51Answers to Chapter 4 Quiz 52Chapter 5: Putting the Big Four Operations to Work 55Switching Things Up with Inverse Operations and the Commutative Property 56Getting with the In-Group: Parentheses and the Associative Property 59Distribution to lighten the load 61Understanding Inequalities 63Doesn’t equal (≠) 63Less than (<) and greater than (>) 63Less than or equal to (≤) and greater than or equal to (≥) 64Approximately equals (≈) 64Moving Beyond the Big Four: Exponents and Square Roots 65Understanding exponents 66Discovering your roots 67Practice Questions Answers and Explanations 69Whaddya Know? Chapter 5 Quiz 72Answers to Chapter 5 Quiz 73Unit 3: Getting a Handle on Whole Numbers 75Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77The Three E’s of Math: Equations, Expressions, and Evaluation 78Seeking equality for all: Equations 78Hey, it’s just an expression 78Evaluating the situation 79Putting the Three E’s together 79Introducing Order of Operations (PEMDAS) 80Expressions with only addition and subtraction 81Expressions with only multiplication and division 81Mixed-operator expressions 82Handling Powers Responsibly 83Prioritizing parentheses 84Pulling apart parentheses and powers 85Figuring out nested parentheses 86Bringing It All Together: The Order of Operations 87Practice Questions Answers and Explanations 89Whaddya Know? Chapter 6 Quiz 98Answers to Chapter 6 Quiz 99Chapter 7: Turning Words into Numbers: Basic Math Word Problems 103Dispelling Two Myths about Word Problems 104Word problems aren’t always hard 104Word problems are useful 104Solving Basic Word Problems 105Turning word problems into word equations 105Plugging in numbers for words 109Send in the clowns 109Our house in the middle of our street 110I hear the train a-comin’ 110Solving More-Complex Word Problems 113When numbers get serious 113Too much information 115Practice Questions Answers and Explanations 120Whaddya Know? Chapter 7 Quiz 124Answers to Chapter 7 Quiz 125Chapter 8: Divisibility and Prime Numbers 127Knowing the Divisibility Tricks 128Counting everyone in: Numbers you can divide everything by 128In the end: Looking at the final digits 128Count it up: Checking divisibility by adding and subtracting digits 130Less is more: Checking divisibility by subtracting 134Cross-checking: Using multiple tests 135Identifying Prime and Composite Numbers 136Practice Questions Answers and Explanations 139Whaddya Know? Chapter 8 Quiz 142Answers to Chapter 8 Quiz 143Chapter 9: Divided Attention: Factors and Multiples 145Knowing Six Ways to Say the Same Thing 146Understanding Factors and Multiples 146Finding Fabulous Factors 148Deciding when one number is a factor of another 148Understanding factor pairs 148Generating a Number’s Factors 149Decomposing a Number into Its Prime Factors 150Finding the Greatest Common Factor 151Generating the Multiples of a Number 153Finding the Least Common Multiple 153Practice Questions Answers and Explanations 155Whaddya Know? Chapter 9 Quiz 158Answers to Chapter 9 Quiz 159Unit 4: Fractions 161Chapter 10: Understanding Fractions 163Slicing a Cake into Fractions 164Knowing the Fraction Facts of Life 165Telling the numerator from the denominator 165Flipping for reciprocals 166Using ones and zeros 166Mixing things up 167Knowing proper from improper 167Increasing and Reducing Terms of Fractions 169Increasing the terms of fractions 170Reducing fractions to lowest terms (simplifying fractions) 171Converting between Improper Fractions and Mixed Numbers 174Knowing the parts of a mixed number 174Converting a mixed number to an improper fraction 175Converting an improper fraction to a mixed number 176Comparing Fractions with Cross-Multiplication 178Working with Ratios and Proportions 180Practice Questions Answers and Explanations 182Whaddya Know? Chapter 10 Quiz 188Answers to Chapter 10 Quiz 189Chapter 11: Fractions and the Big Four Operations 191Multiplying and Dividing Fractions 192Multiplying numerators and denominators straight across 192Doing a flip to divide fractions 194Adding and Subtracting Fractions with the Same Denominator 196Adding and Subtracting Fractions with Different Denominators 198The easy case: Increasing the terms of one fraction 198The difficult case: Increasing the terms of both fractions 200Practice Questions Answers and Explanations 202Whaddya Know? Chapter 11 Quiz 208Answers to Chapter 11 Quiz 209Chapter 12: Mixing Things Up with Mixed Numbers 213Multiplying and Dividing Mixed Numbers 214Adding Mixed Numbers 216Adding mixed numbers that have the same denominator 216Adding mixed numbers that have different denominators 217Adding mixed numbers with carrying 217Subtracting Mixed Numbers 220Subtracting mixed numbers that have the same denominator 220Subtracting mixed numbers that have different denominators 221Subtracting mixed numbers with borrowing 222Practice Questions Answers and Explanations 225Whaddya Know? Chapter 12 Quiz 233Answers to Chapter 12 Quiz 234Unit 5: Decimals and Percents 241Chapter 13: Getting to the Point with Decimals 243Understanding Basic Decimal Stuff 244Counting dollars and decimals 244Identifying the place value of decimals 246Knowing the decimal facts of life 247Performing the Big Four Operations with Decimals 252Adding decimals 253Subtracting decimals 254Multiplying decimals 256Dividing decimals 257Converting between Decimals and Fractions 262Simple Decimal-Fraction Conversions 262Changing decimals to fractions 264Changing fractions to decimals 267Practice Questions Answers and Explanations 271Whaddya Know? Chapter 13 Quiz 279Answers to Chapter 13 Quiz 280Chapter 14: Playing the Percentages 285Making Sense of Percentages 285Dealing with Percentages Greater than 100% 286Converting to and from Percentages, Decimals, and Fractions 287Converting Percentages to Decimals 287Changing Decimals to Percentages 288Switching from Percentages to Fractions 288Converting Fractions to Percentages 289Solving Percentage Problems 290Figuring out simple percent problems 291Turning the problem around 292Deciphering more-difficult percent problems 293Putting All the Percent Problems Together 294Identifying the three types of percent problems 294Solving Percent Problems with Equations 295Practice Questions Answers and Explanations 299Whaddya Know? Chapter 14 Quiz 303Answers to Chapter 14 Quiz 304Chapter 15: Word Problems with Fractions, Decimals, and Percentages 307Adding and Subtracting Parts of the Whole in Word Problems 308Sharing a pizza: Fractions 308Buying by the pound: Decimals 309Splitting the vote: Percentages 309Problems about Multiplying Fractions 310Renegade grocery shopping: Buying less than they tell you to 310Easy as pie: Working out what’s left on your plate 311Multiplying Decimals and Percentages in Word Problems 313To the end: Figuring out how much money is left 313Finding out how much you started with 314Handling Percent Increases and Decreases in Word Problems 316Raking in the dough: Finding salary increases 316Earning interest on top of interest 316Getting a deal: Calculating discounts 317Practice Questions Answers and Explanations 319Whaddya Know? Chapter 15 Quiz 322Answers to Chapter 15 Quiz 324Unit 6: Reaching the Summit: Advanced Pre-algebra Topics 327Chapter 16: Powers and Roots 329Memorizing Powers and Roots 329Remembering square numbers and square roots 330Keeping track of cubic numbers and cube roots 330Knowing a few powers of 2 and their related roots 331Changing the Base 332Negating a number raised to an exponent 332Finding powers of negative numbers 332Finding powers of fractions 333Mixing negative numbers and fractions with exponents 333Exponents of 0 and Negative Numbers 334Exponents of 0 334Negative exponents 335Fractional Exponents 337Exponents of 1 2 337Exponents of 1 3 338Exponents of 1 4 , 1 5 , 1 , and so forth 6 339Other fractional exponents 339Practice Questions Answers and Explanations 341Whaddya Know? Chapter 16 Quiz 343Answers to Chapter 16 Quiz 344Chapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation 347First Things First: Using Powers of Ten as Exponents 348Counting zeros and writing exponents 348Exponential Arithmetic: Multiplying and Dividing Powers of Ten 350Working with Scientific Notation 352Writing in scientific notation 352Understanding order of magnitude 354Multiplying with scientific notation 355Dividing with Scientific Notation 356Practice Questions Answers and Explanations 357Whaddya Know? Chapter 17 Quiz 360Answers to Chapter 17 Quiz 361Chapter 18: How Much Have You Got? Weights and Measures 363Understanding Units 364Adding and subtracting units 364Multiplying and dividing units 364Examining Differences between the English and Metric Systems 365Looking at the English system 365Looking at the metric system 369Estimating and Converting between the English and Metric Systems 372Estimating in the metric system 373Converting units of measurement 375Converting between English and Metric Units 377Practice Questions Answers and Explanations 381Whaddya Know? Chapter 18 Quiz 388Answers to Chapter 18 Quiz 389Chapter 19: Getting the Picture with Geometry 393Getting on the Plane: Points, Lines, Angles, and Shapes 394Making some points 394Knowing your lines 394Figuring the angles 395Shaping things up 396Getting in Shape: Polygon (and Non-Polygon) Basics 396Closed Encounters: Shaping Up Your Understanding of 2-D Shapes 397Polygons 397Circles 399Squaring Off with Quadrilaterals 400Making a Triple Play with Triangles 403Getting Around with Circle Measurements 405Taking a Trip to Another Dimension: Solid Geometry 406The many faces of polyhedrons 4073-D shapes with curves 408Building Solid Measurement Skills 409Solving Geometry Word Problems 413Working from words and images 413Breaking out those sketching skills 415Practice Questions Answers and Explanations 418Whaddya Know? Chapter 19 Quiz 425Answers to Chapter 19 Quiz 427Chapter 20: Figuring Your Chances: Statistics and Probability 431Gathering Data Mathematically: Basic Statistics 432Understanding differences between qualitative and quantitative data 432Working with qualitative data 433Working with quantitative data 436Looking at Likelihoods: Basic Probability 439Figuring the probability 440Oh, the possibilities! Counting outcomes with multiple coins 441Practice Questions Answers and Explanations 444Whaddya Know? Chapter 20 Quiz 447Answers to Chapter 20 Quiz 449Chapter 21: Setting Things Up with Basic Set Theory 451Understanding Sets 451Elementary, my dear: Considering what’s inside sets 452Sets of numbers 454Performing Operations on Sets 455Union: Combined elements 455Intersection: Elements in common 456Relative complement: Subtraction (sorta) 457Complement: Feeling left out 457Practice Questions Answers and Explanations 459Whaddya Know? Chapter 21 Quiz 461Answers to Chapter 21 Quiz 462Unit 7: the X-files: Introduction to Algebra 463Chapter 22: Working with Algebraic Expressions 465Seeing How X Marks the Spot 466Expressing Yourself with Algebraic Expressions 466Evaluating Algebraic Expressions 467Knowing the Terms 470Making the commute: Rearranging your terms 471Identifying the coefficient and variable 472Adding and Subtracting Like Terms 473Identifying like terms 473Adding and subtracting terms 474Multiplying and Dividing Terms 475Simplifying Expressions by Combining Like Terms 479Removing Parentheses from an Algebraic Expression 481Drop everything: Parentheses with a plus sign 481Sign turnabout: Parentheses with a negative sign 481Distribution: Parentheses with no sign 482FOILing: Dealing with Two Sets of Parentheses 484Practice Questions Answers and Explanations 487Whaddya Know? Chapter 22 Quiz 495Answers to Chapter 22 Quiz 496Chapter 23: Solving Algebraic Equations 499Understanding Algebraic Equations 500Using X in Equations 500Choosing among four ways to solve algebraic equations 501The Balancing Act: Solving for x 503Striking a balance 504Using the Balance Scale to Isolate X 504Rearranging Equations and Isolating x 506Rearranging terms on one side of an equation 506Moving terms to the other side of the equals sign 507Removing parentheses from equations 509Cross-multiplying 512Practice Questions Answers and Explanations 515Whaddya Know? Chapter 23 Quiz 525Answers to Chapter 23 Quiz 526Chapter 24: Tackling Algebra Word Problems 531Solving Algebra Word Problems in Five Steps 531Declaring a variable 532Setting up the equation 533Solving the equation 533Answering the question 534Checking your work 534Choosing Your Variable Wisely 536Solving More-Complex Algebraic Problems 539Charting four people 539Crossing the finish line with five people 540Practice Questions Answers and Explanations 545Whaddya Know? Chapter 24 Quiz 549Answers to Chapter 24 Quiz 550Chapter 25: Graphing Algebraic Equations 553Graphing on the xy-Plane 554Understanding the axes, the origin, and the quadrants 554Plotting coordinates on the xy-plane 554Graphing equations on the xy-plane 555Understanding Linear Equations 559Knowing the most basic linear equation 559Changing the slope (m) 560Changing the y-intercept (b) 561Understanding slope-intercept form 562Measuring the Slope of a Line 564Estimating slope 564Eyeballing slope on the xy-plane 566Using the two-point slope formula 569Graphing Linear Equations Using the Slope and y-intercept 572Practice Questions Answers and Explanations 574Whaddya Know? Chapter 25 Quiz 577Answers to Chapter 25 Quiz 581Index 583

Mark Zegarelli earned degrees in mathematics and English from Rutgers University. He is the founder of SimpleStep Learning, an online educational platform that teaches courses in basic concepts in ten minutes or less, keeping students engaged and learning in every moment. Mark is also author of several other successful For Dummies books.

• Introduction 1About This Book 1Foolish Assumptions 2Icons Used in This Book 2Beyond the Book 3Where to Go from Here 3Unit 1: Getting Started with Basic Math & Pre-algebra 5Chapter 1: Playing the Numbers Game 7Inventing Numbers 8Understanding Number Sequences 8Evening the odds 8Counting by threes, fours, fives, and so on 9Getting square with square numbers 9Composing yourself with composite numbers 10Stepping out of the box with prime numbers 11Multiplying quickly with exponents 12Four Important Sets of Numbers 13Counting on the counting numbers 13Introducing integers 13Staying rational 14Getting real 14Chapter 2: The Big Four Operations 15The Big Four Operations 15Adding things up: Addition 16Take it away: Subtraction 16A sign of the times: Multiplication 17Doing math lickety-split: Division 18Applying the Big Four Operations to Larger Numbers 18Calculating stacked addition 18Performing stacked subtraction 19Calculating with stacked multiplication 21Understanding long division 22Unit 2: the Big Four Operations: Addition, Subtraction, Multiplication, and Division 25Chapter 3: Counting on Success: Numbers and Digits 27Knowing Your Place Value 28Counting to ten and beyond 28Telling placeholders from leading zeros 29Reading long numbers 30Close Enough for Rock ‘n’ Roll: Rounding and Estimating 30Rounding numbers 30Estimating value to make problems easier 32Practice Questions Answers and Explanations 34Whaddya Know? Chapter 3 Quiz 35Answers to Chapter 3 Quiz 36Chapter 4: Staying Positive with Negative Numbers 37Understanding Where Negative Numbers Come From 38Sign-Switching: Understanding Negation and Absolute Value 39Addition and Subtraction with Negative Numbers 41Starting with a negative number 41Adding a negative number 41Subtracting a negative number 42Knowing Signs of the Times (and Division) for Negative Numbers 44Practice Questions Answers and Explanations 47Whaddya Know? Chapter 4 Quiz 51Answers to Chapter 4 Quiz 52Chapter 5: Putting the Big Four Operations to Work 55Switching Things Up with Inverse Operations and the Commutative Property 56Getting with the In-Group: Parentheses and the Associative Property 59Distribution to lighten the load 61Understanding Inequalities 63Doesn’t equal (≠) 63Less than (<) and greater than (>) 63Less than or equal to (≤) and greater than or equal to (≥) 64Approximately equals (≈) 64Moving Beyond the Big Four: Exponents and Square Roots 65Understanding exponents 66Discovering your roots 67Practice Questions Answers and Explanations 69Whaddya Know? Chapter 5 Quiz 72Answers to Chapter 5 Quiz 73Unit 3: Getting a Handle on Whole Numbers 75Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77The Three E’s of Math: Equations, Expressions, and Evaluation 78Seeking equality for all: Equations 78Hey, it’s just an expression 78Evaluating the situation 79Putting the Three E’s together 79Introducing Order of Operations (PEMDAS) 80Expressions with only addition and subtraction 81Expressions with only multiplication and division 81Mixed-operator expressions 82Handling Powers Responsibly 83Prioritizing parentheses 84Pulling apart parentheses and powers 85Figuring out nested parentheses 86Bringing It All Together: The Order of Operations 87Practice Questions Answers and Explanations 89Whaddya Know? Chapter 6 Quiz 98Answers to Chapter 6 Quiz 99Chapter 7: Turning Words into Numbers: Basic Math Word Problems 103Dispelling Two Myths about Word Problems 104Word problems aren’t always hard 104Word problems are useful 104Solving Basic Word Problems 105Turning word problems into word equations 105Plugging in numbers for words 109Send in the clowns 109Our house in the middle of our street 110I hear the train a-comin’ 110Solving More-Complex Word Problems 113When numbers get serious 113Too much information 115Practice Questions Answers and Explanations 120Whaddya Know? Chapter 7 Quiz 124Answers to Chapter 7 Quiz 125Chapter 8: Divisibility and Prime Numbers 127Knowing the Divisibility Tricks 128Counting everyone in: Numbers you can divide everything by 128In the end: Looking at the final digits 128Count it up: Checking divisibility by adding and subtracting digits 130Less is more: Checking divisibility by subtracting 134Cross-checking: Using multiple tests 135Identifying Prime and Composite Numbers 136Practice Questions Answers and Explanations 139Whaddya Know? Chapter 8 Quiz 142Answers to Chapter 8 Quiz 143Chapter 9: Divided Attention: Factors and Multiples 145Knowing Six Ways to Say the Same Thing 146Understanding Factors and Multiples 146Finding Fabulous Factors 148Deciding when one number is a factor of another 148Understanding factor pairs 148Generating a Number’s Factors 149Decomposing a Number into Its Prime Factors 150Finding the Greatest Common Factor 151Generating the Multiples of a Number 153Finding the Least Common Multiple 153Practice Questions Answers and Explanations 155Whaddya Know? Chapter 9 Quiz 158Answers to Chapter 9 Quiz 159Unit 4: Fractions 161Chapter 10: Understanding Fractions 163Slicing a Cake into Fractions 164Knowing the Fraction Facts of Life 165Telling the numerator from the denominator 165Flipping for reciprocals 166Using ones and zeros 166Mixing things up 167Knowing proper from improper 167Increasing and Reducing Terms of Fractions 169Increasing the terms of fractions 170Reducing fractions to lowest terms (simplifying fractions) 171Converting between Improper Fractions and Mixed Numbers 174Knowing the parts of a mixed number 174Converting a mixed number to an improper fraction 175Converting an improper fraction to a mixed number 176Comparing Fractions with Cross-Multiplication 178Working with Ratios and Proportions 180Practice Questions Answers and Explanations 182Whaddya Know? Chapter 10 Quiz 188Answers to Chapter 10 Quiz 189Chapter 11: Fractions and the Big Four Operations 191Multiplying and Dividing Fractions 192Multiplying numerators and denominators straight across 192Doing a flip to divide fractions 194Adding and Subtracting Fractions with the Same Denominator 196Adding and Subtracting Fractions with Different Denominators 198The easy case: Increasing the terms of one fraction 198The difficult case: Increasing the terms of both fractions 200Practice Questions Answers and Explanations 202Whaddya Know? Chapter 11 Quiz 208Answers to Chapter 11 Quiz 209Chapter 12: Mixing Things Up with Mixed Numbers 213Multiplying and Dividing Mixed Numbers 214Adding Mixed Numbers 216Adding mixed numbers that have the same denominator 216Adding mixed numbers that have different denominators 217Adding mixed numbers with carrying 217Subtracting Mixed Numbers 220Subtracting mixed numbers that have the same denominator 220Subtracting mixed numbers that have different denominators 221Subtracting mixed numbers with borrowing 222Practice Questions Answers and Explanations 225Whaddya Know? Chapter 12 Quiz 233Answers to Chapter 12 Quiz 234Unit 5: Decimals and Percents 241Chapter 13: Getting to the Point with Decimals 243Understanding Basic Decimal Stuff 244Counting dollars and decimals 244Identifying the place value of decimals 246Knowing the decimal facts of life 247Performing the Big Four Operations with Decimals 252Adding decimals 253Subtracting decimals 254Multiplying decimals 256Dividing decimals 257Converting between Decimals and Fractions 262Simple Decimal-Fraction Conversions 262Changing decimals to fractions 264Changing fractions to decimals 267Practice Questions Answers and Explanations 271Whaddya Know? Chapter 13 Quiz 279Answers to Chapter 13 Quiz 280Chapter 14: Playing the Percentages 285Making Sense of Percentages 285Dealing with Percentages Greater than 100% 286Converting to and from Percentages, Decimals, and Fractions 287Converting Percentages to Decimals 287Changing Decimals to Percentages 288Switching from Percentages to Fractions 288Converting Fractions to Percentages 289Solving Percentage Problems 290Figuring out simple percent problems 291Turning the problem around 292Deciphering more-difficult percent problems 293Putting All the Percent Problems Together 294Identifying the three types of percent problems 294Solving Percent Problems with Equations 295Practice Questions Answers and Explanations 299Whaddya Know? Chapter 14 Quiz 303Answers to Chapter 14 Quiz 304Chapter 15: Word Problems with Fractions, Decimals, and Percentages 307Adding and Subtracting Parts of the Whole in Word Problems 308Sharing a pizza: Fractions 308Buying by the pound: Decimals 309Splitting the vote: Percentages 309Problems about Multiplying Fractions 310Renegade grocery shopping: Buying less than they tell you to 310Easy as pie: Working out what’s left on your plate 311Multiplying Decimals and Percentages in Word Problems 313To the end: Figuring out how much money is left 313Finding out how much you started with 314Handling Percent Increases and Decreases in Word Problems 316Raking in the dough: Finding salary increases 316Earning interest on top of interest 316Getting a deal: Calculating discounts 317Practice Questions Answers and Explanations 319Whaddya Know? Chapter 15 Quiz 322Answers to Chapter 15 Quiz 324Unit 6: Reaching the Summit: Advanced Pre-algebra Topics 327Chapter 16: Powers and Roots 329Memorizing Powers and Roots 329Remembering square numbers and square roots 330Keeping track of cubic numbers and cube roots 330Knowing a few powers of 2 and their related roots 331Changing the Base 332Negating a number raised to an exponent 332Finding powers of negative numbers 332Finding powers of fractions 333Mixing negative numbers and fractions with exponents 333Exponents of 0 and Negative Numbers 334Exponents of 0 334Negative exponents 335Fractional Exponents 337Exponents of 1 2 337Exponents of 1 3 338Exponents of 1 4 , 1 5 , 1 , and so forth 6 339Other fractional exponents 339Practice Questions Answers and Explanations 341Whaddya Know? Chapter 16 Quiz 343Answers to Chapter 16 Quiz 344Chapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation 347First Things First: Using Powers of Ten as Exponents 348Counting zeros and writing exponents 348Exponential Arithmetic: Multiplying and Dividing Powers of Ten 350Working with Scientific Notation 352Writing in scientific notation 352Understanding order of magnitude 354Multiplying with scientific notation 355Dividing with Scientific Notation 356Practice Questions Answers and Explanations 357Whaddya Know? Chapter 17 Quiz 360Answers to Chapter 17 Quiz 361Chapter 18: How Much Have You Got? Weights and Measures 363Understanding Units 364Adding and subtracting units 364Multiplying and dividing units 364Examining Differences between the English and Metric Systems 365Looking at the English system 365Looking at the metric system 369Estimating and Converting between the English and Metric Systems 372Estimating in the metric system 373Converting units of measurement 375Converting between English and Metric Units 377Practice Questions Answers and Explanations 381Whaddya Know? Chapter 18 Quiz 388Answers to Chapter 18 Quiz 389Chapter 19: Getting the Picture with Geometry 393Getting on the Plane: Points, Lines, Angles, and Shapes 394Making some points 394Knowing your lines 394Figuring the angles 395Shaping things up 396Getting in Shape: Polygon (and Non-Polygon) Basics 396Closed Encounters: Shaping Up Your Understanding of 2-D Shapes 397Polygons 397Circles 399Squaring Off with Quadrilaterals 400Making a Triple Play with Triangles 403Getting Around with Circle Measurements 405Taking a Trip to Another Dimension: Solid Geometry 406The many faces of polyhedrons 4073-D shapes with curves 408Building Solid Measurement Skills 409Solving Geometry Word Problems 413Working from words and images 413Breaking out those sketching skills 415Practice Questions Answers and Explanations 418Whaddya Know? Chapter 19 Quiz 425Answers to Chapter 19 Quiz 427Chapter 20: Figuring Your Chances: Statistics and Probability 431Gathering Data Mathematically: Basic Statistics 432Understanding differences between qualitative and quantitative data 432Working with qualitative data 433Working with quantitative data 436Looking at Likelihoods: Basic Probability 439Figuring the probability 440Oh, the possibilities! Counting outcomes with multiple coins 441Practice Questions Answers and Explanations 444Whaddya Know? Chapter 20 Quiz 447Answers to Chapter 20 Quiz 449Chapter 21: Setting Things Up with Basic Set Theory 451Understanding Sets 451Elementary, my dear: Considering what’s inside sets 452Sets of numbers 454Performing Operations on Sets 455Union: Combined elements 455Intersection: Elements in common 456Relative complement: Subtraction (sorta) 457Complement: Feeling left out 457Practice Questions Answers and Explanations 459Whaddya Know? Chapter 21 Quiz 461Answers to Chapter 21 Quiz 462Unit 7: the X-files: Introduction to Algebra 463Chapter 22: Working with Algebraic Expressions 465Seeing How X Marks the Spot 466Expressing Yourself with Algebraic Expressions 466Evaluating Algebraic Expressions 467Knowing the Terms 470Making the commute: Rearranging your terms 471Identifying the coefficient and variable 472Adding and Subtracting Like Terms 473Identifying like terms 473Adding and subtracting terms 474Multiplying and Dividing Terms 475Simplifying Expressions by Combining Like Terms 479Removing Parentheses from an Algebraic Expression 481Drop everything: Parentheses with a plus sign 481Sign turnabout: Parentheses with a negative sign 481Distribution: Parentheses with no sign 482FOILing: Dealing with Two Sets of Parentheses 484Practice Questions Answers and Explanations 487Whaddya Know? Chapter 22 Quiz 495Answers to Chapter 22 Quiz 496Chapter 23: Solving Algebraic Equations 499Understanding Algebraic Equations 500Using X in Equations 500Choosing among four ways to solve algebraic equations 501The Balancing Act: Solving for x 503Striking a balance 504Using the Balance Scale to Isolate X 504Rearranging Equations and Isolating x 506Rearranging terms on one side of an equation 506Moving terms to the other side of the equals sign 507Removing parentheses from equations 509Cross-multiplying 512Practice Questions Answers and Explanations 515Whaddya Know? Chapter 23 Quiz 525Answers to Chapter 23 Quiz 526Chapter 24: Tackling Algebra Word Problems 531Solving Algebra Word Problems in Five Steps 531Declaring a variable 532Setting up the equation 533Solving the equation 533Answering the question 534Checking your work 534Choosing Your Variable Wisely 536Solving More-Complex Algebraic Problems 539Charting four people 539Crossing the finish line with five people 540Practice Questions Answers and Explanations 545Whaddya Know? Chapter 24 Quiz 549Answers to Chapter 24 Quiz 550Chapter 25: Graphing Algebraic Equations 553Graphing on the xy-Plane 554Understanding the axes, the origin, and the quadrants 554Plotting coordinates on the xy-plane 554Graphing equations on the xy-plane 555Understanding Linear Equations 559Knowing the most basic linear equation 559Changing the slope (m) 560Changing the y-intercept (b) 561Understanding slope-intercept form 562Measuring the Slope of a Line 564Estimating slope 564Eyeballing slope on the xy-plane 566Using the two-point slope formula 569Graphing Linear Equations Using the Slope and y-intercept 572Practice Questions Answers and Explanations 574Whaddya Know? Chapter 25 Quiz 577Answers to Chapter 25 Quiz 581Index 583

Mark Zegarelli earned degrees in mathematics and English from Rutgers University. He is the founder of SimpleStep Learning, an online educational platform that teaches courses in basic concepts in ten minutes or less, keeping students engaged and learning in every moment. Mark is also author of several other successful For Dummies books.

• Introduction 1About This Book 1Foolish Assumptions 2Icons Used in This Book 2Beyond the Book 3Where to Go from Here 3Unit 1: Getting Started with Basic Math & Pre-algebra 5Chapter 1: Playing the Numbers Game 7Inventing Numbers 8Understanding Number Sequences 8Evening the odds 8Counting by threes, fours, fives, and so on 9Getting square with square numbers 9Composing yourself with composite numbers 10Stepping out of the box with prime numbers 11Multiplying quickly with exponents 12Four Important Sets of Numbers 13Counting on the counting numbers 13Introducing integers 13Staying rational 14Getting real 14Chapter 2: The Big Four Operations 15The Big Four Operations 15Adding things up: Addition 16Take it away: Subtraction 16A sign of the times: Multiplication 17Doing math lickety-split: Division 18Applying the Big Four Operations to Larger Numbers 18Calculating stacked addition 18Performing stacked subtraction 19Calculating with stacked multiplication 21Understanding long division 22Unit 2: the Big Four Operations: Addition, Subtraction, Multiplication, and Division 25Chapter 3: Counting on Success: Numbers and Digits 27Knowing Your Place Value 28Counting to ten and beyond 28Telling placeholders from leading zeros 29Reading long numbers 30Close Enough for Rock ‘n’ Roll: Rounding and Estimating 30Rounding numbers 30Estimating value to make problems easier 32Practice Questions Answers and Explanations 34Whaddya Know? Chapter 3 Quiz 35Answers to Chapter 3 Quiz 36Chapter 4: Staying Positive with Negative Numbers 37Understanding Where Negative Numbers Come From 38Sign-Switching: Understanding Negation and Absolute Value 39Addition and Subtraction with Negative Numbers 41Starting with a negative number 41Adding a negative number 41Subtracting a negative number 42Knowing Signs of the Times (and Division) for Negative Numbers 44Practice Questions Answers and Explanations 47Whaddya Know? Chapter 4 Quiz 51Answers to Chapter 4 Quiz 52Chapter 5: Putting the Big Four Operations to Work 55Switching Things Up with Inverse Operations and the Commutative Property 56Getting with the In-Group: Parentheses and the Associative Property 59Distribution to lighten the load 61Understanding Inequalities 63Doesn’t equal (≠) 63Less than (<) and greater than (>) 63Less than or equal to (≤) and greater than or equal to (≥) 64Approximately equals (≈) 64Moving Beyond the Big Four: Exponents and Square Roots 65Understanding exponents 66Discovering your roots 67Practice Questions Answers and Explanations 69Whaddya Know? Chapter 5 Quiz 72Answers to Chapter 5 Quiz 73Unit 3: Getting a Handle on Whole Numbers 75Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77The Three E’s of Math: Equations, Expressions, and Evaluation 78Seeking equality for all: Equations 78Hey, it’s just an expression 78Evaluating the situation 79Putting the Three E’s together 79Introducing Order of Operations (PEMDAS) 80Expressions with only addition and subtraction 81Expressions with only multiplication and division 81Mixed-operator expressions 82Handling Powers Responsibly 83Prioritizing parentheses 84Pulling apart parentheses and powers 85Figuring out nested parentheses 86Bringing It All Together: The Order of Operations 87Practice Questions Answers and Explanations 89Whaddya Know? Chapter 6 Quiz 98Answers to Chapter 6 Quiz 99Chapter 7: Turning Words into Numbers: Basic Math Word Problems 103Dispelling Two Myths about Word Problems 104Word problems aren’t always hard 104Word problems are useful 104Solving Basic Word Problems 105Turning word problems into word equations 105Plugging in numbers for words 109Send in the clowns 109Our house in the middle of our street 110I hear the train a-comin’ 110Solving More-Complex Word Problems 113When numbers get serious 113Too much information 115Practice Questions Answers and Explanations 120Whaddya Know? Chapter 7 Quiz 124Answers to Chapter 7 Quiz 125Chapter 8: Divisibility and Prime Numbers 127Knowing the Divisibility Tricks 128Counting everyone in: Numbers you can divide everything by 128In the end: Looking at the final digits 128Count it up: Checking divisibility by adding and subtracting digits 130Less is more: Checking divisibility by subtracting 134Cross-checking: Using multiple tests 135Identifying Prime and Composite Numbers 136Practice Questions Answers and Explanations 139Whaddya Know? Chapter 8 Quiz 142Answers to Chapter 8 Quiz 143Chapter 9: Divided Attention: Factors and Multiples 145Knowing Six Ways to Say the Same Thing 146Understanding Factors and Multiples 146Finding Fabulous Factors 148Deciding when one number is a factor of another 148Understanding factor pairs 148Generating a Number’s Factors 149Decomposing a Number into Its Prime Factors 150Finding the Greatest Common Factor 151Generating the Multiples of a Number 153Finding the Least Common Multiple 153Practice Questions Answers and Explanations 155Whaddya Know? Chapter 9 Quiz 158Answers to Chapter 9 Quiz 159Unit 4: Fractions 161Chapter 10: Understanding Fractions 163Slicing a Cake into Fractions 164Knowing the Fraction Facts of Life 165Telling the numerator from the denominator 165Flipping for reciprocals 166Using ones and zeros 166Mixing things up 167Knowing proper from improper 167Increasing and Reducing Terms of Fractions 169Increasing the terms of fractions 170Reducing fractions to lowest terms (simplifying fractions) 171Converting between Improper Fractions and Mixed Numbers 174Knowing the parts of a mixed number 174Converting a mixed number to an improper fraction 175Converting an improper fraction to a mixed number 176Comparing Fractions with Cross-Multiplication 178Working with Ratios and Proportions 180Practice Questions Answers and Explanations 182Whaddya Know? Chapter 10 Quiz 188Answers to Chapter 10 Quiz 189Chapter 11: Fractions and the Big Four Operations 191Multiplying and Dividing Fractions 192Multiplying numerators and denominators straight across 192Doing a flip to divide fractions 194Adding and Subtracting Fractions with the Same Denominator 196Adding and Subtracting Fractions with Different Denominators 198The easy case: Increasing the terms of one fraction 198The difficult case: Increasing the terms of both fractions 200Practice Questions Answers and Explanations 202Whaddya Know? Chapter 11 Quiz 208Answers to Chapter 11 Quiz 209Chapter 12: Mixing Things Up with Mixed Numbers 213Multiplying and Dividing Mixed Numbers 214Adding Mixed Numbers 216Adding mixed numbers that have the same denominator 216Adding mixed numbers that have different denominators 217Adding mixed numbers with carrying 217Subtracting Mixed Numbers 220Subtracting mixed numbers that have the same denominator 220Subtracting mixed numbers that have different denominators 221Subtracting mixed numbers with borrowing 222Practice Questions Answers and Explanations 225Whaddya Know? Chapter 12 Quiz 233Answers to Chapter 12 Quiz 234Unit 5: Decimals and Percents 241Chapter 13: Getting to the Point with Decimals 243Understanding Basic Decimal Stuff 244Counting dollars and decimals 244Identifying the place value of decimals 246Knowing the decimal facts of life 247Performing the Big Four Operations with Decimals 252Adding decimals 253Subtracting decimals 254Multiplying decimals 256Dividing decimals 257Converting between Decimals and Fractions 262Simple Decimal-Fraction Conversions 262Changing decimals to fractions 264Changing fractions to decimals 267Practice Questions Answers and Explanations 271Whaddya Know? Chapter 13 Quiz 279Answers to Chapter 13 Quiz 280Chapter 14: Playing the Percentages 285Making Sense of Percentages 285Dealing with Percentages Greater than 100% 286Converting to and from Percentages, Decimals, and Fractions 287Converting Percentages to Decimals 287Changing Decimals to Percentages 288Switching from Percentages to Fractions 288Converting Fractions to Percentages 289Solving Percentage Problems 290Figuring out simple percent problems 291Turning the problem around 292Deciphering more-difficult percent problems 293Putting All the Percent Problems Together 294Identifying the three types of percent problems 294Solving Percent Problems with Equations 295Practice Questions Answers and Explanations 299Whaddya Know? Chapter 14 Quiz 303Answers to Chapter 14 Quiz 304Chapter 15: Word Problems with Fractions, Decimals, and Percentages 307Adding and Subtracting Parts of the Whole in Word Problems 308Sharing a pizza: Fractions 308Buying by the pound: Decimals 309Splitting the vote: Percentages 309Problems about Multiplying Fractions 310Renegade grocery shopping: Buying less than they tell you to 310Easy as pie: Working out what’s left on your plate 311Multiplying Decimals and Percentages in Word Problems 313To the end: Figuring out how much money is left 313Finding out how much you started with 314Handling Percent Increases and Decreases in Word Problems 316Raking in the dough: Finding salary increases 316Earning interest on top of interest 316Getting a deal: Calculating discounts 317Practice Questions Answers and Explanations 319Whaddya Know? Chapter 15 Quiz 322Answers to Chapter 15 Quiz 324Unit 6: Reaching the Summit: Advanced Pre-algebra Topics 327Chapter 16: Powers and Roots 329Memorizing Powers and Roots 329Remembering square numbers and square roots 330Keeping track of cubic numbers and cube roots 330Knowing a few powers of 2 and their related roots 331Changing the Base 332Negating a number raised to an exponent 332Finding powers of negative numbers 332Finding powers of fractions 333Mixing negative numbers and fractions with exponents 333Exponents of 0 and Negative Numbers 334Exponents of 0 334Negative exponents 335Fractional Exponents 337Exponents of 1 2 337Exponents of 1 3 338Exponents of 1 4 , 1 5 , 1 , and so forth 6 339Other fractional exponents 339Practice Questions Answers and Explanations 341Whaddya Know? Chapter 16 Quiz 343Answers to Chapter 16 Quiz 344Chapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation 347First Things First: Using Powers of Ten as Exponents 348Counting zeros and writing exponents 348Exponential Arithmetic: Multiplying and Dividing Powers of Ten 350Working with Scientific Notation 352Writing in scientific notation 352Understanding order of magnitude 354Multiplying with scientific notation 355Dividing with Scientific Notation 356Practice Questions Answers and Explanations 357Whaddya Know? Chapter 17 Quiz 360Answers to Chapter 17 Quiz 361Chapter 18: How Much Have You Got? Weights and Measures 363Understanding Units 364Adding and subtracting units 364Multiplying and dividing units 364Examining Differences between the English and Metric Systems 365Looking at the English system 365Looking at the metric system 369Estimating and Converting between the English and Metric Systems 372Estimating in the metric system 373Converting units of measurement 375Converting between English and Metric Units 377Practice Questions Answers and Explanations 381Whaddya Know? Chapter 18 Quiz 388Answers to Chapter 18 Quiz 389Chapter 19: Getting the Picture with Geometry 393Getting on the Plane: Points, Lines, Angles, and Shapes 394Making some points 394Knowing your lines 394Figuring the angles 395Shaping things up 396Getting in Shape: Polygon (and Non-Polygon) Basics 396Closed Encounters: Shaping Up Your Understanding of 2-D Shapes 397Polygons 397Circles 399Squaring Off with Quadrilaterals 400Making a Triple Play with Triangles 403Getting Around with Circle Measurements 405Taking a Trip to Another Dimension: Solid Geometry 406The many faces of polyhedrons 4073-D shapes with curves 408Building Solid Measurement Skills 409Solving Geometry Word Problems 413Working from words and images 413Breaking out those sketching skills 415Practice Questions Answers and Explanations 418Whaddya Know? Chapter 19 Quiz 425Answers to Chapter 19 Quiz 427Chapter 20: Figuring Your Chances: Statistics and Probability 431Gathering Data Mathematically: Basic Statistics 432Understanding differences between qualitative and quantitative data 432Working with qualitative data 433Working with quantitative data 436Looking at Likelihoods: Basic Probability 439Figuring the probability 440Oh, the possibilities! Counting outcomes with multiple coins 441Practice Questions Answers and Explanations 444Whaddya Know? Chapter 20 Quiz 447Answers to Chapter 20 Quiz 449Chapter 21: Setting Things Up with Basic Set Theory 451Understanding Sets 451Elementary, my dear: Considering what’s inside sets 452Sets of numbers 454Performing Operations on Sets 455Union: Combined elements 455Intersection: Elements in common 456Relative complement: Subtraction (sorta) 457Complement: Feeling left out 457Practice Questions Answers and Explanations 459Whaddya Know? Chapter 21 Quiz 461Answers to Chapter 21 Quiz 462Unit 7: the X-files: Introduction to Algebra 463Chapter 22: Working with Algebraic Expressions 465Seeing How X Marks the Spot 466Expressing Yourself with Algebraic Expressions 466Evaluating Algebraic Expressions 467Knowing the Terms 470Making the commute: Rearranging your terms 471Identifying the coefficient and variable 472Adding and Subtracting Like Terms 473Identifying like terms 473Adding and subtracting terms 474Multiplying and Dividing Terms 475Simplifying Expressions by Combining Like Terms 479Removing Parentheses from an Algebraic Expression 481Drop everything: Parentheses with a plus sign 481Sign turnabout: Parentheses with a negative sign 481Distribution: Parentheses with no sign 482FOILing: Dealing with Two Sets of Parentheses 484Practice Questions Answers and Explanations 487Whaddya Know? Chapter 22 Quiz 495Answers to Chapter 22 Quiz 496Chapter 23: Solving Algebraic Equations 499Understanding Algebraic Equations 500Using X in Equations 500Choosing among four ways to solve algebraic equations 501The Balancing Act: Solving for x 503Striking a balance 504Using the Balance Scale to Isolate X 504Rearranging Equations and Isolating x 506Rearranging terms on one side of an equation 506Moving terms to the other side of the equals sign 507Removing parentheses from equations 509Cross-multiplying 512Practice Questions Answers and Explanations 515Whaddya Know? Chapter 23 Quiz 525Answers to Chapter 23 Quiz 526Chapter 24: Tackling Algebra Word Problems 531Solving Algebra Word Problems in Five Steps 531Declaring a variable 532Setting up the equation 533Solving the equation 533Answering the question 534Checking your work 534Choosing Your Variable Wisely 536Solving More-Complex Algebraic Problems 539Charting four people 539Crossing the finish line with five people 540Practice Questions Answers and Explanations 545Whaddya Know? Chapter 24 Quiz 549Answers to Chapter 24 Quiz 550Chapter 25: Graphing Algebraic Equations 553Graphing on the xy-Plane 554Understanding the axes, the origin, and the quadrants 554Plotting coordinates on the xy-plane 554Graphing equations on the xy-plane 555Understanding Linear Equations 559Knowing the most basic linear equation 559Changing the slope (m) 560Changing the y-intercept (b) 561Understanding slope-intercept form 562Measuring the Slope of a Line 564Estimating slope 564Eyeballing slope on the xy-plane 566Using the two-point slope formula 569Graphing Linear Equations Using the Slope and y-intercept 572Practice Questions Answers and Explanations 574Whaddya Know? Chapter 25 Quiz 577Answers to Chapter 25 Quiz 581Index 583