Algebra I Workbook For Dummies

Introduction 1

About This Book 1

Foolish Assumptions 2

Icons Used in This Book 3

Beyond the Book 3

Where to Go from Here 4

Part 1: Getting Down to the Nitty-Gritty on Basic Operations 5

Chapter 1: Deciphering Signs in Numbers 7

Assigning Numbers Their Place 7

Reading and Writing Absolute Value 9

Adding Signed Numbers 10

Making a Difference with Signed Numbers 11

Multiplying Signed Numbers 12

Dividing Signed Numbers 14

Answers to Problems on Signed Numbers 15

Chapter 2: Incorporating Algebraic Properties 17

Getting a Grip on Grouping Symbols 17

Distributing the Wealth 19

Making Associations Work 20

Computing by Commuting 21

Answers to Problems on Algebraic Properties 23

Chapter 3: Making Fractions and Decimals Behave 25

Converting Improper and Mixed Fractions 25

Finding Fraction Equivalences 27

Making Proportional Statements 28

Finding Common Denominators 30

Adding and Subtracting Fractions 31

Multiplying and Dividing Fractions 32

Simplifying Complex Fractions 35

Changing Fractions to Decimals and Vice Versa 36

Performing Operations with Decimals 38

Answers to Problems on Fractions 39

Chapter 4: Exploring Exponents 45

Multiplying and Dividing Exponentials 45

Raising Powers to Powers 47

Using Negative Exponents 49

Writing Numbers with Scientific Notation 50

Answers to Problems on Discovering Exponents 52

Chapter 5: Taming Rampaging Radicals 55

Simplifying Radical Expressions 55

Rationalizing Fractions 57

Arranging Radicals as Exponential Terms 58

Using Fractional Exponents 60

Simplifying Expressions with Exponents 61

Estimating Answers 63

Answers to Problems on Radicals 64

Chapter 6: Simplifying Algebraic Expressions 67

Adding and Subtracting Like Terms 68

Multiplying and Dividing Algebraically 69

Incorporating Order of Operations 70

Evaluating Expressions 71

Answers to Problems on Algebraic Expressions 74

Part 2: Changing the Format of Expressions 77

Chapter 7: Specializing in Multiplication Matters 79

Distributing One Factor over Many 79

Curses, FOILed again - or not 80

Squaring binomials 82

Multiplying the sum and difference

of the same two terms 83

Cubing binomials 84

Creating the Sum and Difference of Cubes 85

Raising binomials to higher powers 86

Answers to Problems on Multiplying Expressions 88

Chapter 8: Dividing the Long Way to Simplify Algebraic Expressions 91

Dividing by a Monomial 91

Dividing by a Binomial 93

Dividing by Polynomials with More Terms 96

Simplifying Division Synthetically 97

Answers to Problems on Division 99

Chapter 9: Figuring on Factoring 103

Pouring Over Prime Factorizations 103

Factoring Out the Greatest Common Factor 105

Reducing Algebraic Fractions 106

Answers to Problems on Factoring Expressions 108

Chapter 10: Taking the Bite Out of Binomial Factoring 111

Factoring the Difference of Squares 112

Factoring Differences and Sums of Cubes 113

Making Factoring a Multiple Mission 114

Answers to Problems on Factoring 115

Chapter 11: Factoring Trinomials and Special Polynomials 117

Focusing First on the Greatest Common Factor (GCF) 118

"Un"wrapping the FOIL 119

Factoring Quadratic-Like Trinomials 121

Factoring Trinomials Using More than One Method 122

Factoring by Grouping .124

Putting All the Factoring Together 126

Answers to Problems on Factoring Trinomials and Other Expressions 128

Part 3: Seek and Ye Shall Find Solutions 131

Chapter 12: Lining Up Linear Equations 133

Using the Addition/Subtraction Property 133

Using the Multiplication/Division Property 135

Putting Several Operations Together 136

Solving Linear Equations with Grouping Symbols 138

Working It Out with Fractions 140

Solving Proportions 142

Answers to Problems on Solving Linear Equations 144

Chapter 13: Muscling Up to Quadratic Equations 151

Using the Square Root Rule 152

Solving by Factoring 153

Using the Quadratic Formula 155

Completing the Square 158

Dealing with Impossible Answers 159

Answers to Problems on Solving Quadratic Equations 161

Chapter 14: Yielding to Higher Powers 167

Determining How Many Possible Roots 168

Applying the Rational Root Theorem 169

Using the Factor/Root Theorem 170

Solving by Factoring 172

Solving Powers That Are Quadratic-Like 174

Answers to Problems on Solving Higher Power Equations 176

Chapter 15: Reeling in Radical and Absolute Value Equations 179

Squaring Both Sides to Solve Radical Equations 180

Doubling the Fun with Radical Equations .182

Solving Absolute Value Equations 183

Answers to Problems on Radical and Absolute Value Equations 185

Chapter 16: Getting Even with Inequalities 189

Using the Rules to Work on Inequality Statements 190

Rewriting Inequalities by Using Interval Notation 191

Solving Linear Inequalities 192

Solving Quadratic Inequalities 193

Dealing with Polynomial and Rational Inequalities 195

Solving Absolute Value Inequalities 196

Solving Complex Inequalities 198

Answers to Problems on Working with Inequalities 199

Part 4: Solving Story Problems and Sketching Graphs 203

Chapter 17: Facing Up to Formulas 205

Working with Formulas 206

Deciphering Perimeter, Area, and Volume 207

Using perimeter formulas to get around 207

Squaring off with area formulas 209

Working with volume formulas 211

Getting Interested in Using Percent 213

Answers to Problems on Using Formulas 215

Chapter 18: Making Formulas Work in Basic Story Problems 219

Applying the Pythagorean Theorem 220

Using Geometry to Solve Story Problems 221

Putting Distance, Rate, and Time in a Formula 224

Examining the distance-rate-time formula 224

Going the distance with story problems 226

Answers to Making Formulas Work in Basic Story Problems 228

Chapter 19: Relating Values in Story Problems 233

Tackling Age Problems 234

Tackling Consecutive Integer Problems 235

Working Together on Work Problems 238

Answers to Relating Values in Story Problems 240

Chapter 20: Measuring Up with Quality and Quantity Story Problems 243

Achieving the Right Blend with Mixtures Problems 244

Concocting the Correct Solution One Hundred Percent of the Time 246

Dealing with Money Problems 248

Answers to Problems on Measuring Up with Quality and Quantity 250

Chapter 21: Getting a Handle on Graphing 255

Thickening the Plot with Points 255

Sectioning Off by Quadrants 257

Using Points to Lay Out Lines 258

Graphing Lines with Intercepts 260

Computing Slopes of Lines 261

Graphing with the Slope-Intercept Form 263

Changing to the Slope-Intercept Form 265

Writing Equations of Lines 266

Picking on Parallel and Perpendicular Lines 267

Finding Distances between Points 268

Finding the Intersections of Lines 269

Graphing Parabolas and Circles 270

Graphing with Transformations 272

Answers to Problems on Graphing 275

Part 5: The Part of Tens 283

Chapter 22: Ten Common Errors That Get Noticed 285

Squaring a Negative or Negative of a Square 285

Squaring a Binomial 286

Operating on Radicals 286

Distributing a Negative Throughout 287

Fracturing Fractions 287

Raising a Power to a Power 288

Making Negative Exponents Flip 288

Making Sense of Reversing the Sense 288

Using the Slope Formula Correctly 289

Writing Several Fractions as One 289

Chapter 23: Ten Quick Tips to Make Algebra a Breeze 291

Flipping Proportions 291

Multiplying Through to Get Rid of Fractions 292

Zeroing In on Fractions 292

Finding a Common Denominator 292

Dividing by 3 or 9 293

Dividing by 2, 4, or 8 293

Commuting Back and Forth 293

Factoring Quadratics 294

Making Radicals Less Rad, Baby 294

Applying Acronyms 294

Index 295