Algebra I Workbook for Dummies, 2nd Edition (For Dummies (Math & Science))

Algebra I Workbook For Dummies, 2nd Edition......Page 1
Author’s Acknowledgments......Page 5
Contents at a Glance......Page 7
Table of Contents......Page 9
About This Book......Page 15
Foolish Assumptions......Page 16
How This Book Is Organized......Page 17
Icons Used in This Book......Page 18
Where to Go from Here......Page 19
Part I: Getting Down to the Nitty-Gritty on Basic Operations......Page 21
Assigning Numbers Their Place......Page 23
Reading and Writing Absolute Value......Page 24
Adding Signed Numbers......Page 25
Making a Difference with Signed Numbers......Page 26
Multiplying Signed Numbers......Page 27
Dividing Signed Numbers......Page 28
Answers to Problems on Signed Numbers......Page 30
Getting a Grip on Grouping Symbols......Page 33
Distributing the Wealth......Page 35
Making Associations Work......Page 36
Computing by Commuting......Page 37
Answers to Problems on Algebraic Properties......Page 39
Converting Improper and Mixed Fractions......Page 41
Finding Fraction Equivalences......Page 43
Making Proportional Statements......Page 44
Finding Common Denominators......Page 46
Adding and Subtracting Fractions......Page 47
Multiplying and Dividing Fractions......Page 48
Simplifying Complex Fractions......Page 51
Changing Fractions to Decimals and Vice Versa......Page 52
Performing Operations with Decimals......Page 54
Answers to Problems on Fractions......Page 55
Multiplying and Dividing Exponentials......Page 61
Raising Powers to Powers......Page 63
Using Negative Exponents......Page 65
Writing Numbers with Scientific Notation......Page 66
Answers to Problems on Discovering Exponents......Page 68
Simplifying Radical Expressions......Page 71
Rationalizing Fractions......Page 73
Arranging Radicals as Exponential Terms......Page 74
Using Fractional Exponents......Page 76
Simplifying Expressions with Exponents......Page 77
Estimating Answers......Page 79
Answers to Problems on Radicals......Page 80
Adding and Subtracting Like Terms......Page 83
Multiplying and Dividing Algebraically......Page 85
Incorporating Order of Operations......Page 86
Evaluating Expressions......Page 87
Answers to Problems on Algebraic Expressions......Page 90
Part II: Changing the Format of Expressions......Page 93
Distributing One Factor over Many......Page 95
Curses, FOILed Again — Or Not......Page 96
Squaring Binomials......Page 98
Multiplying the Sum and Difference of the Same Two Terms......Page 99
Cubing Binomials......Page 100
Creating the Sum and Difference of Cubes......Page 101
Raising Binomials to Higher Powers......Page 102
Answers to Problems on Multiplying Expressions......Page 104
Dividing by a Monomial......Page 107
Dividing by a Binomial......Page 109
Dividing by Polynomials with More Terms......Page 112
Simplifying Division Synthetically......Page 113
Answers to Problems on Division......Page 115
Pouring Over Prime Factorizations......Page 119
Factoring Out the Greatest Common Factor......Page 121
Reducing Algebraic Fractions......Page 122
Answers to Problems on Factoring Expressions......Page 124
Factoring the Difference of Squares......Page 127
Factoring Differences and Sums of Cubes......Page 128
Making Factoring a Multiple Mission......Page 129
Answers to Problems on Factoring......Page 131
Focusing First on the Greatest Common Factor (GCF)......Page 133
“Un” wrapping the FOIL......Page 135
Factoring Quadratic-Like Trinomials......Page 137
Factoring Trinomials Using More Than One Method......Page 138
Factoring by Grouping......Page 140
Putting All the Factoring Together......Page 142
Answers to Problems on Factoring Trinomials and Other Expressions......Page 144
Part III: Seek and Ye Shall Find. . . Solutions......Page 149
Using the Addition/Subtraction Property......Page 151
Using the Multiplication/Division Property......Page 153
Putting Several Operations Together......Page 154
Solving Linear Equations with Grouping Symbols......Page 156
Working It Out with Fractions......Page 158
Solving Proportions......Page 160
Answers to Problems on Solving Linear Equations......Page 162
Using the Square Root Rule......Page 169
Solving by Factoring......Page 170
Using the Quadratic Formula......Page 172
Completing the Square......Page 175
Dealing with Impossible Answers......Page 176
Answers to Problems on Solving Quadratic Equations......Page 178
Determining How Many Possible Roots......Page 183
Applying the Rational Root Theorem......Page 185
Using the Factor/Root Theorem......Page 186
Solving By Factoring......Page 188
Solving Powers That Are Quadratic-Like......Page 190
Answers to Problems on Solving Higher Power Equations......Page 192
Squaring Both Sides to Solve Radical Equations......Page 195
Doubling the Fun with Radical Equations......Page 198
Solving Absolute Value Equations......Page 199
Answers to Problems on Radical and Absolute Value Equations......Page 201
Using the Rules to Work on Inequality Statements......Page 205
Rewriting Inequalities by Using Interval Notation......Page 206
Solving Linear Inequalities......Page 207
Solving Quadratic Inequalities......Page 209
Dealing with Polynomial and Rational Inequalities......Page 210
Solving Absolute Value Inequalities......Page 212
Solving Complex Inequalities......Page 214
Answers to Problems on Working with Inequalities......Page 215
Part IV: Solving Story Problems and Sketching Graphs......Page 219
Working with Formulas......Page 221
Deciphering Perimeter, Area, and Volume......Page 223
Getting Interested in Using Percent......Page 229
Answers to Problems on Using Formulas......Page 231
Applying the Pythagorean Theorem......Page 235
Using Geometry to Solve Story Problems......Page 237
Putting Distance, Rate, and Time in a Formula......Page 240
Answers to Making Formulas Work in Basic Story Problems......Page 244
Tackling Age Problems......Page 249
Tackling Consecutive Integer Problems......Page 251
Working Together on Work Problems......Page 254
Answers to Relating Values in Story Problems......Page 256
Achieving the Right Blend with Mixtures Problems......Page 259
Concocting the Correct Solution One Hundred Percent of the Time......Page 262
Dealing with Money Problems......Page 264
Answers to Problems on Measuring Up with Quality and Quantity......Page 266
Thickening the Plot with Points......Page 271
Sectioning Off by Quadrants......Page 273
Using Points to Lay Out Lines......Page 274
Graphing Lines with Intercepts......Page 276
Computing Slopes of Lines......Page 277
Graphing with the Slope-Intercept Form......Page 279
Changing to the Slope-Intercept Form......Page 281
Writing Equations of Lines......Page 282
Picking on Parallel and Perpendicular Lines......Page 283
Finding Distances between Points......Page 284
Finding the Intersections of Lines......Page 285
Graphing Parabolas and Circles......Page 286
Graphing with Transformations......Page 288
Answers to Problems on Graphing......Page 291
Part V: The Part of Tens......Page 299
Squaring a Binomial......Page 301
Fracturing Fractions......Page 302
Making Sense of Reversing the Sense......Page 303
Writing Several Fractions as One......Page 304
Multiplying Through to Get Rid of Fractions......Page 305
Dividing by 3 or 9......Page 306
Commuting Back and Forth......Page 307
Applying Acronyms......Page 308
Index......Page 309