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