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Table of Contents
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
