Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online)

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 1

About This Book 1

Foolish Assumptions 2

Icons Used in This Book 2

Beyond the Book 3

Where to Go from Here 3

Unit 1: Getting Started with Basic Math & Pre-algebra 5

Chapter 1: Playing the Numbers Game 7

Inventing Numbers 8

Understanding Number Sequences 8

Evening the odds 8

Counting by threes, fours, fives, and so on 9

Getting square with square numbers 9

Composing yourself with composite numbers 10

Stepping out of the box with prime numbers 11

Multiplying quickly with exponents 12

Four Important Sets of Numbers 13

Counting on the counting numbers 13

Introducing integers 13

Staying rational 14

Getting real 14

Chapter 2: The Big Four Operations 15

The Big Four Operations 15

Adding things up: Addition 16

Take it away: Subtraction 16

A sign of the times: Multiplication 17

Doing math lickety-split: Division 18

Applying the Big Four Operations to Larger Numbers 18

Calculating stacked addition 18

Performing stacked subtraction 19

Calculating with stacked multiplication 21

Understanding long division 22

Unit 2: the Big Four Operations: Addition, Subtraction, Multiplication, and Division 25

Chapter 3: Counting on Success: Numbers and Digits 27

Knowing Your Place Value 28

Counting to ten and beyond 28

Telling placeholders from leading zeros 29

Reading long numbers 30

Close Enough for Rock ‘n’ Roll: Rounding and Estimating 30

Rounding numbers 30

Estimating value to make problems easier 32

Practice Questions Answers and Explanations 34

Whaddya Know? Chapter 3 Quiz 35

Answers to Chapter 3 Quiz 36

Chapter 4: Staying Positive with Negative Numbers 37

Understanding Where Negative Numbers Come From 38

Sign-Switching: Understanding Negation and Absolute Value 39

Addition and Subtraction with Negative Numbers 41

Starting with a negative number 41

Adding a negative number 41

Subtracting a negative number 42

Knowing Signs of the Times (and Division) for Negative Numbers 44

Practice Questions Answers and Explanations 47

Whaddya Know? Chapter 4 Quiz 51

Answers to Chapter 4 Quiz 52

Chapter 5: Putting the Big Four Operations to Work 55

Switching Things Up with Inverse Operations and the Commutative Property 56

Getting with the In-Group: Parentheses and the Associative Property 59

Distribution to lighten the load 61

Understanding Inequalities 63

Doesn’t equal (≠) 63

Less than (<) and greater than (>) 63

Less than or equal to (≤) and greater than or equal to (≥) 64

Approximately equals (≈) 64

Moving Beyond the Big Four: Exponents and Square Roots 65

Understanding exponents 66

Discovering your roots 67

Practice Questions Answers and Explanations 69

Whaddya Know? Chapter 5 Quiz 72

Answers to Chapter 5 Quiz 73

Unit 3: Getting a Handle on Whole Numbers 75

Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77

The Three E’s of Math: Equations, Expressions, and Evaluation 78

Seeking equality for all: Equations 78

Hey, it’s just an expression 78

Evaluating the situation 79

Putting the Three E’s together 79

Introducing Order of Operations (PEMDAS) 80

Expressions with only addition and subtraction 81

Expressions with only multiplication and division 81

Mixed-operator expressions 82

Handling Powers Responsibly 83

Prioritizing parentheses 84

Pulling apart parentheses and powers 85

Figuring out nested parentheses 86

Bringing It All Together: The Order of Operations 87

Practice Questions Answers and Explanations 89

Whaddya Know? Chapter 6 Quiz 98

Answers to Chapter 6 Quiz 99

Chapter 7: Turning Words into Numbers: Basic Math Word Problems 103

Dispelling Two Myths about Word Problems 104

Word problems aren’t always hard 104

Word problems are useful 104

Solving Basic Word Problems 105

Turning word problems into word equations 105

Plugging in numbers for words 109

Send in the clowns 109

Our house in the middle of our street 110

I hear the train a-comin’ 110

Solving More-Complex Word Problems 113

When numbers get serious 113

Too much information 115

Practice Questions Answers and Explanations 120

Whaddya Know? Chapter 7 Quiz 124

Answers to Chapter 7 Quiz 125

Chapter 8: Divisibility and Prime Numbers 127

Knowing the Divisibility Tricks 128

Counting everyone in: Numbers you can divide everything by 128

In the end: Looking at the final digits 128

Count it up: Checking divisibility by adding and subtracting digits 130

Less is more: Checking divisibility by subtracting 134

Cross-checking: Using multiple tests 135

Identifying Prime and Composite Numbers 136

Practice Questions Answers and Explanations 139

Whaddya Know? Chapter 8 Quiz 142

Answers to Chapter 8 Quiz 143

Chapter 9: Divided Attention: Factors and Multiples 145

Knowing Six Ways to Say the Same Thing 146

Understanding Factors and Multiples 146

Finding Fabulous Factors 148

Deciding when one number is a factor of another 148

Understanding factor pairs 148

Generating a Number’s Factors 149

Decomposing a Number into Its Prime Factors 150

Finding the Greatest Common Factor 151

Generating the Multiples of a Number 153

Finding the Least Common Multiple 153

Practice Questions Answers and Explanations 155

Whaddya Know? Chapter 9 Quiz 158

Answers to Chapter 9 Quiz 159

Unit 4: Fractions 161

Chapter 10: Understanding Fractions 163

Slicing a Cake into Fractions 164

Knowing the Fraction Facts of Life 165

Telling the numerator from the denominator 165

Flipping for reciprocals 166

Using ones and zeros 166

Mixing things up 167

Knowing proper from improper 167

Increasing and Reducing Terms of Fractions 169

Increasing the terms of fractions 170

Reducing fractions to lowest terms (simplifying fractions) 171

Converting between Improper Fractions and Mixed Numbers 174

Knowing the parts of a mixed number 174

Converting a mixed number to an improper fraction 175

Converting an improper fraction to a mixed number 176

Comparing Fractions with Cross-Multiplication 178

Working with Ratios and Proportions 180

Practice Questions Answers and Explanations 182

Whaddya Know? Chapter 10 Quiz 188

Answers to Chapter 10 Quiz 189

Chapter 11: Fractions and the Big Four Operations 191

Multiplying and Dividing Fractions 192

Multiplying numerators and denominators straight across 192

Doing a flip to divide fractions 194

Adding and Subtracting Fractions with the Same Denominator 196

Adding and Subtracting Fractions with Different Denominators 198

The easy case: Increasing the terms of one fraction 198

The difficult case: Increasing the terms of both fractions 200

Practice Questions Answers and Explanations 202

Whaddya Know? Chapter 11 Quiz 208

Answers to Chapter 11 Quiz 209

Chapter 12: Mixing Things Up with Mixed Numbers 213

Multiplying and Dividing Mixed Numbers 214

Adding Mixed Numbers 216

Adding mixed numbers that have the same denominator 216

Adding mixed numbers that have different denominators 217

Adding mixed numbers with carrying 217

Subtracting Mixed Numbers 220

Subtracting mixed numbers that have the same denominator 220

Subtracting mixed numbers that have different denominators 221

Subtracting mixed numbers with borrowing 222

Practice Questions Answers and Explanations 225

Whaddya Know? Chapter 12 Quiz 233

Answers to Chapter 12 Quiz 234

Unit 5: Decimals and Percents 241

Chapter 13: Getting to the Point with Decimals 243

Understanding Basic Decimal Stuff 244

Counting dollars and decimals 244

Identifying the place value of decimals 246

Knowing the decimal facts of life 247

Performing the Big Four Operations with Decimals 252

Adding decimals 253

Subtracting decimals 254

Multiplying decimals 256

Dividing decimals 257

Converting between Decimals and Fractions 262

Simple Decimal-Fraction Conversions 262

Changing decimals to fractions 264

Changing fractions to decimals 267

Practice Questions Answers and Explanations 271

Whaddya Know? Chapter 13 Quiz 279

Answers to Chapter 13 Quiz 280

Chapter 14: Playing the Percentages 285

Making Sense of Percentages 285

Dealing with Percentages Greater than 100% 286

Converting to and from Percentages, Decimals, and Fractions 287

Converting Percentages to Decimals 287

Changing Decimals to Percentages 288

Switching from Percentages to Fractions 288

Converting Fractions to Percentages 289

Solving Percentage Problems 290

Figuring out simple percent problems 291

Turning the problem around 292

Deciphering more-difficult percent problems 293

Putting All the Percent Problems Together 294

Identifying the three types of percent problems 294

Solving Percent Problems with Equations 295

Practice Questions Answers and Explanations 299

Whaddya Know? Chapter 14 Quiz 303

Answers to Chapter 14 Quiz 304

Chapter 15: Word Problems with Fractions, Decimals, and Percentages 307

Adding and Subtracting Parts of the Whole in Word Problems 308

Sharing a pizza: Fractions 308

Buying by the pound: Decimals 309

Splitting the vote: Percentages 309

Problems about Multiplying Fractions 310

Renegade grocery shopping: Buying less than they tell you to 310

Easy as pie: Working out what’s left on your plate 311

Multiplying Decimals and Percentages in Word Problems 313

To the end: Figuring out how much money is left 313

Finding out how much you started with 314

Handling Percent Increases and Decreases in Word Problems 316

Raking in the dough: Finding salary increases 316

Earning interest on top of interest 316

Getting a deal: Calculating discounts 317

Practice Questions Answers and Explanations 319

Whaddya Know? Chapter 15 Quiz 322

Answers to Chapter 15 Quiz 324

Unit 6: Reaching the Summit: Advanced Pre-algebra Topics 327

Chapter 16: Powers and Roots 329

Memorizing Powers and Roots 329

Remembering square numbers and square roots 330

Keeping track of cubic numbers and cube roots 330

Knowing a few powers of 2 and their related roots 331

Changing the Base 332

Negating a number raised to an exponent 332

Finding powers of negative numbers 332

Finding powers of fractions 333

Mixing negative numbers and fractions with exponents 333

Exponents of 0 and Negative Numbers 334

Exponents of 0 334

Negative exponents 335

Fractional Exponents 337

Exponents of 1 2 337

Exponents of 1 3 338

Exponents of 1 4 , 1 5 , 1 , and so forth 6 339

Other fractional exponents 339

Practice Questions Answers and Explanations 341

Whaddya Know? Chapter 16 Quiz 343

Answers to Chapter 16 Quiz 344

Chapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation 347

First Things First: Using Powers of Ten as Exponents 348

Counting zeros and writing exponents 348

Exponential Arithmetic: Multiplying and Dividing Powers of Ten 350

Working with Scientific Notation 352

Writing in scientific notation 352

Understanding order of magnitude 354

Multiplying with scientific notation 355

Dividing with Scientific Notation 356

Practice Questions Answers and Explanations 357

Whaddya Know? Chapter 17 Quiz 360

Answers to Chapter 17 Quiz 361

Chapter 18: How Much Have You Got? Weights and Measures 363

Understanding Units 364

Adding and subtracting units 364

Multiplying and dividing units 364

Examining Differences between the English and Metric Systems 365

Looking at the English system 365

Looking at the metric system 369

Estimating and Converting between the English and Metric Systems 372

Estimating in the metric system 373

Converting units of measurement 375

Converting between English and Metric Units 377

Practice Questions Answers and Explanations 381

Whaddya Know? Chapter 18 Quiz 388

Answers to Chapter 18 Quiz 389

Chapter 19: Getting the Picture with Geometry 393

Getting on the Plane: Points, Lines, Angles, and Shapes 394

Making some points 394

Knowing your lines 394

Figuring the angles 395

Shaping things up 396

Getting in Shape: Polygon (and Non-Polygon) Basics 396

Closed Encounters: Shaping Up Your Understanding of 2-D Shapes 397

Polygons 397

Circles 399

Squaring Off with Quadrilaterals 400

Making a Triple Play with Triangles 403

Getting Around with Circle Measurements 405

Taking a Trip to Another Dimension: Solid Geometry 406

The many faces of polyhedrons 407

3-D shapes with curves 408

Building Solid Measurement Skills 409

Solving Geometry Word Problems 413

Working from words and images 413

Breaking out those sketching skills 415

Practice Questions Answers and Explanations 418

Whaddya Know? Chapter 19 Quiz 425

Answers to Chapter 19 Quiz 427

Chapter 20: Figuring Your Chances: Statistics and Probability 431

Gathering Data Mathematically: Basic Statistics 432

Understanding differences between qualitative and quantitative data 432

Working with qualitative data 433

Working with quantitative data 436

Looking at Likelihoods: Basic Probability 439

Figuring the probability 440

Oh, the possibilities! Counting outcomes with multiple coins 441

Practice Questions Answers and Explanations 444

Whaddya Know? Chapter 20 Quiz 447

Answers to Chapter 20 Quiz 449

Chapter 21: Setting Things Up with Basic Set Theory 451

Understanding Sets 451

Elementary, my dear: Considering what’s inside sets 452

Sets of numbers 454

Performing Operations on Sets 455

Union: Combined elements 455

Intersection: Elements in common 456

Relative complement: Subtraction (sorta) 457

Complement: Feeling left out 457

Practice Questions Answers and Explanations 459

Whaddya Know? Chapter 21 Quiz 461

Answers to Chapter 21 Quiz 462

Unit 7: the X-files: Introduction to Algebra 463

Chapter 22: Working with Algebraic Expressions 465

Seeing How X Marks the Spot 466

Expressing Yourself with Algebraic Expressions 466

Evaluating Algebraic Expressions 467

Knowing the Terms 470

Making the commute: Rearranging your terms 471

Identifying the coefficient and variable 472

Adding and Subtracting Like Terms 473

Identifying like terms 473

Adding and subtracting terms 474

Multiplying and Dividing Terms 475

Simplifying Expressions by Combining Like Terms 479

Removing Parentheses from an Algebraic Expression 481

Drop everything: Parentheses with a plus sign 481

Sign turnabout: Parentheses with a negative sign 481

Distribution: Parentheses with no sign 482

FOILing: Dealing with Two Sets of Parentheses 484

Practice Questions Answers and Explanations 487

Whaddya Know? Chapter 22 Quiz 495

Answers to Chapter 22 Quiz 496

Chapter 23: Solving Algebraic Equations 499

Understanding Algebraic Equations 500

Using X in Equations 500

Choosing among four ways to solve algebraic equations 501

The Balancing Act: Solving for x 503

Striking a balance 504

Using the Balance Scale to Isolate X 504

Rearranging Equations and Isolating x 506

Rearranging terms on one side of an equation 506

Moving terms to the other side of the equals sign 507

Removing parentheses from equations 509

Cross-multiplying 512

Practice Questions Answers and Explanations 515

Whaddya Know? Chapter 23 Quiz 525

Answers to Chapter 23 Quiz 526

Chapter 24: Tackling Algebra Word Problems 531

Solving Algebra Word Problems in Five Steps 531

Declaring a variable 532

Setting up the equation 533

Solving the equation 533

Answering the question 534

Checking your work 534

Choosing Your Variable Wisely 536

Solving More-Complex Algebraic Problems 539

Charting four people 539

Crossing the finish line with five people 540

Practice Questions Answers and Explanations 545

Whaddya Know? Chapter 24 Quiz 549

Answers to Chapter 24 Quiz 550

Chapter 25: Graphing Algebraic Equations 553

Graphing on the xy-Plane 554

Understanding the axes, the origin, and the quadrants 554

Plotting coordinates on the xy-plane 554

Graphing equations on the xy-plane 555

Understanding Linear Equations 559

Knowing the most basic linear equation 559

Changing the slope (m) 560

Changing the y-intercept (b) 561

Understanding slope-intercept form 562

Measuring the Slope of a Line 564

Estimating slope 564

Eyeballing slope on the xy-plane 566

Using the two-point slope formula 569

Graphing Linear Equations Using the Slope and y-intercept 572

Practice Questions Answers and Explanations 574

Whaddya Know? Chapter 25 Quiz 577

Answers to Chapter 25 Quiz 581

Index 583