Algebra I Workbook For Dummies

1 - Title Page [Seite 3]
2 - Copyright Page [Seite 4]
3 - Table of Contents [Seite 7]
4 - Introduction [Seite 13]
4.1 - About This Book [Seite 13]
4.2 - Foolish Assumptions [Seite 14]
4.3 - Icons Used in This Book [Seite 15]
4.4 - Beyond the Book [Seite 15]
4.5 - Where to Go from Here [Seite 16]
5 - Part 1 Getting Down to the Nitty-Gritty on Basic Operations [Seite 17]
5.1 - Chapter 1 Deciphering Signs in Numbers [Seite 19]
5.1.1 - Assigning Numbers Their Place [Seite 19]
5.1.2 - Reading and Writing Absolute Value [Seite 21]
5.1.3 - Adding Signed Numbers [Seite 22]
5.1.4 - Making a Difference with Signed Numbers [Seite 23]
5.1.5 - Multiplying Signed Numbers [Seite 24]
5.1.6 - Dividing Signed Numbers [Seite 26]
5.1.7 - Answers to Problems on Signed Numbers [Seite 27]
5.2 - Chapter 2 Incorporating Algebraic Properties [Seite 29]
5.2.1 - Getting a Grip on Grouping Symbols [Seite 29]
5.2.2 - Distributing the Wealth [Seite 31]
5.2.3 - Making Associations Work [Seite 32]
5.2.4 - Computing by Commuting [Seite 33]
5.2.5 - Answers to Problems on Algebraic Properties [Seite 35]
5.3 - Chapter 3 Making Fractions and Decimals Behave [Seite 37]
5.3.1 - Converting Improper and Mixed Fractions [Seite 37]
5.3.2 - Finding Fraction Equivalences [Seite 39]
5.3.3 - Making Proportional Statements [Seite 40]
5.3.4 - Finding Common Denominators [Seite 42]
5.3.5 - Adding and Subtracting Fractions [Seite 43]
5.3.6 - Multiplying and Dividing Fractions [Seite 44]
5.3.7 - Simplifying Complex Fractions [Seite 47]
5.3.8 - Changing Fractions to Decimals and Vice Versa [Seite 48]
5.3.9 - Performing Operations with Decimals [Seite 50]
5.3.10 - Answers to Problems on Fractions [Seite 51]
5.4 - Chapter 4 Exploring Exponents [Seite 57]
5.4.1 - Multiplying and Dividing Exponentials [Seite 57]
5.4.2 - Raising Powers to Powers [Seite 59]
5.4.3 - Using Negative Exponents [Seite 61]
5.4.4 - Writing Numbers with Scientific Notation [Seite 62]
5.4.5 - Answers to Problems on Discovering Exponents [Seite 64]
5.5 - Chapter 5 Taming Rampaging Radicals [Seite 67]
5.5.1 - Simplifying Radical Expressions [Seite 67]
5.5.2 - Rationalizing Fractions [Seite 69]
5.5.3 - Arranging Radicals as Exponential Terms [Seite 70]
5.5.4 - Using Fractional Exponents [Seite 72]
5.5.5 - Simplifying Expressions with Exponents [Seite 73]
5.5.6 - Estimating Answers [Seite 75]
5.5.7 - Answers to Problems on Radicals [Seite 76]
5.6 - Chapter 6 Simplifying Algebraic Expressions [Seite 79]
5.6.1 - Adding and Subtracting Like Terms [Seite 80]
5.6.2 - Multiplying and Dividing Algebraically [Seite 81]
5.6.3 - Incorporating Order of Operations [Seite 82]
5.6.4 - Evaluating Expressions [Seite 83]
5.6.5 - Answers to Problems on Algebraic Expressions [Seite 86]
6 - Part 2 Changing the Format of Expressions [Seite 89]
6.1 - Chapter 7 Specializing in Multiplication Matters [Seite 91]
6.1.1 - Distributing One Factor over Many [Seite 91]
6.1.1.1 - Curses, FOILed again - or not [Seite 92]
6.1.1.2 - Squaring binomials [Seite 94]
6.1.1.3 - Multiplying the sum and difference of the same two terms [Seite 95]
6.1.1.4 - Cubing binomials [Seite 96]
6.1.2 - Creating the Sum and Difference of Cubes [Seite 97]
6.1.2.1 - Raising binomials to higher powers [Seite 98]
6.1.3 - Answers to Problems on Multiplying Expressions [Seite 100]
6.2 - Chapter 8 Dividing the Long Way to Simplify Algebraic Expressions [Seite 103]
6.2.1 - Dividing by a Monomial [Seite 103]
6.2.2 - Dividing by a Binomial [Seite 105]
6.2.3 - Dividing by Polynomials with More Terms [Seite 108]
6.2.4 - Simplifying Division Synthetically [Seite 109]
6.2.5 - Answers to Problems on Division [Seite 111]
6.3 - Chapter 9 Figuring on Factoring [Seite 115]
6.3.1 - Pouring Over Prime Factorizations [Seite 115]
6.3.2 - Factoring Out the Greatest Common Factor [Seite 117]
6.3.3 - Reducing Algebraic Fractions [Seite 118]
6.3.4 - Answers to Problems on Factoring Expressions [Seite 120]
6.4 - Chapter 10 Taking the Bite Out of Binomial Factoring [Seite 123]
6.4.1 - Factoring the Difference of Squares [Seite 124]
6.4.2 - Factoring Differences and Sums of Cubes [Seite 125]
6.4.3 - Making Factoring a Multiple Mission [Seite 126]
6.4.4 - Answers to Problems on Factoring [Seite 127]
6.5 - Chapter 11 Factoring Trinomials and Special Polynomials [Seite 129]
6.5.1 - Focusing First on the Greatest Common Factor (GCF) [Seite 130]
6.5.2 - "Un"wrapping the FOIL [Seite 131]
6.5.3 - Factoring Quadratic-Like Trinomials [Seite 133]
6.5.4 - Factoring Trinomials Using More than One Method [Seite 134]
6.5.5 - Factoring by Grouping [Seite 136]
6.5.6 - Putting All the Factoring Together [Seite 138]
6.5.7 - Answers to Problems on Factoring Trinomials and Other Expressions [Seite 140]
7 - Part 3 Seek and Ye Shall Find . . . Solutions [Seite 143]
7.1 - Chapter 12 Lining Up Linear Equations [Seite 145]
7.1.1 - Using the Addition/Subtraction Property [Seite 145]
7.1.2 - Using the Multiplication/Division Property [Seite 147]
7.1.3 - Putting Several Operations Together [Seite 148]
7.1.4 - Solving Linear Equations with Grouping Symbols [Seite 150]
7.1.5 - Working It Out with Fractions [Seite 152]
7.1.6 - Solving Proportions [Seite 154]
7.1.7 - Answers to Problems on Solving Linear Equations [Seite 156]
7.2 - Chapter 13 Muscling Up to Quadratic Equations [Seite 163]
7.2.1 - Using the Square Root Rule [Seite 164]
7.2.2 - Solving by Factoring [Seite 165]
7.2.3 - Using the Quadratic Formula [Seite 167]
7.2.4 - Completing the Square [Seite 170]
7.2.5 - Dealing with Impossible Answers [Seite 171]
7.2.6 - Answers to Problems on Solving Quadratic Equations [Seite 173]
7.3 - Chapter 14 Yielding to Higher Powers [Seite 179]
7.3.1 - Determining How Many Possible Roots [Seite 180]
7.3.2 - Applying the Rational Root Theorem [Seite 181]
7.3.3 - Using the Factor/Root Theorem [Seite 182]
7.3.4 - Solving by Factoring [Seite 184]
7.3.5 - Solving Powers That Are Quadratic-Like [Seite 186]
7.3.6 - Answers to Problems on Solving Higher Power Equations [Seite 188]
7.4 - Chapter 15 Reeling in Radical and Absolute Value Equations [Seite 191]
7.4.1 - Squaring Both Sides to Solve Radical Equations [Seite 192]
7.4.2 - Doubling the Fun with Radical Equations [Seite 194]
7.4.3 - Solving Absolute Value Equations [Seite 195]
7.4.4 - Answers to Problems on Radical and Absolute Value Equations [Seite 197]
7.5 - Chapter 16 Getting Even with Inequalities [Seite 201]
7.5.1 - Using the Rules to Work on Inequality Statements [Seite 202]
7.5.2 - Rewriting Inequalities by Using Interval Notation [Seite 203]
7.5.3 - Solving Linear Inequalities [Seite 204]
7.5.4 - Solving Quadratic Inequalities [Seite 205]
7.5.5 - Dealing with Polynomial and Rational Inequalities [Seite 207]
7.5.6 - Solving Absolute Value Inequalities [Seite 208]
7.5.7 - Solving Complex Inequalities [Seite 210]
7.5.8 - Answers to Problems on Working with Inequalities [Seite 211]
8 - Part 4 Solving Story Problems and Sketching Graphs [Seite 215]
8.1 - Chapter 17 Facing Up to Formulas [Seite 217]
8.1.1 - Working with Formulas [Seite 218]
8.1.2 - Deciphering Perimeter, Area, and Volume [Seite 219]
8.1.2.1 - Using perimeter formulas to get around [Seite 219]
8.1.2.2 - Squaring off with area formulas [Seite 221]
8.1.2.3 - Working with volume formulas [Seite 223]
8.1.3 - Getting Interested in Using Percent [Seite 225]
8.1.4 - Answers to Problems on Using Formulas [Seite 227]
8.2 - Chapter 18 Making Formulas Work in Basic Story Problems [Seite 231]
8.2.1 - Applying the Pythagorean Theorem [Seite 232]
8.2.2 - Using Geometry to Solve Story Problems [Seite 233]
8.2.3 - Putting Distance, Rate, and Time in a Formula [Seite 236]
8.2.3.1 - Examining the distance-rate-time formula [Seite 236]
8.2.3.2 - Going the distance with story problems [Seite 238]
8.2.4 - Answers to Making Formulas Work in Basic Story Problems [Seite 240]
8.3 - Chapter 19 Relating Values in Story Problems [Seite 245]
8.3.1 - Tackling Age Problems [Seite 246]
8.3.2 - Tackling Consecutive Integer Problems [Seite 247]
8.3.3 - Working Together on Work Problems [Seite 250]
8.3.4 - Answers to Relating Values in Story Problems [Seite 252]
8.4 - Chapter 20 Measuring Up with Quality and Quantity Story Problems [Seite 255]
8.4.1 - Achieving the Right Blend with Mixtures Problems [Seite 256]
8.4.2 - Concocting the Correct Solution One Hundred Percent of the Time [Seite 258]
8.4.3 - Dealing with Money Problems [Seite 260]
8.4.4 - Answers to Problems on Measuring Up with Quality and Quantity [Seite 262]
8.5 - Chapter 21 Getting a Handle on Graphing [Seite 267]
8.5.1 - Thickening the Plot with Points [Seite 267]
8.5.2 - Sectioning Off by Quadrants [Seite 269]
8.5.3 - Using Points to Lay Out Lines [Seite 270]
8.5.4 - Graphing Lines with Intercepts [Seite 272]
8.5.5 - Computing Slopes of Lines [Seite 273]
8.5.6 - Graphing with the Slope-Intercept Form [Seite 275]
8.5.7 - Changing to the Slope-Intercept Form [Seite 277]
8.5.8 - Writing Equations of Lines [Seite 278]
8.5.9 - Picking on Parallel and Perpendicular Lines [Seite 279]
8.5.10 - Finding Distances between Points [Seite 280]
8.5.11 - Finding the Intersections of Lines [Seite 281]
8.5.12 - Graphing Parabolas and Circles [Seite 282]
8.5.13 - Graphing with Transformations [Seite 284]
8.5.14 - Answers to Problems on Graphing [Seite 287]
9 - Part 5 The Part of Tens [Seite 295]
9.1 - Chapter 22 Ten Common Errors That Get Noticed [Seite 297]
9.1.1 - Squaring a Negative or Negative of a Square [Seite 297]
9.1.2 - Squaring a Binomial [Seite 298]
9.1.3 - Operating on Radicals [Seite 298]
9.1.4 - Distributing a Negative Throughout [Seite 299]
9.1.5 - Fracturing Fractions [Seite 299]
9.1.6 - Raising a Power to a Power [Seite 300]
9.1.7 - Making Negative Exponents Flip [Seite 300]
9.1.8 - Making Sense of Reversing the Sense [Seite 300]
9.1.9 - Using the Slope Formula Correctly [Seite 301]
9.1.10 - Writing Several Fractions as One [Seite 301]
9.2 - Chapter 23 Ten Quick Tips to Make Algebra a Breeze [Seite 303]
9.2.1 - Flipping Proportions [Seite 303]
9.2.2 - Multiplying Through to Get Rid of Fractions [Seite 304]
9.2.3 - Zeroing In on Fractions [Seite 304]
9.2.4 - Finding a Common Denominator [Seite 304]
9.2.5 - Dividing by 3 or 9 [Seite 305]
9.2.6 - Dividing by 2, 4, or 8 [Seite 305]
9.2.7 - Commuting Back and Forth [Seite 305]
9.2.8 - Factoring Quadratics [Seite 306]
9.2.9 - Making Radicals Less Rad, Baby [Seite 306]
9.2.10 - Applying Acronyms [Seite 306]
10 - Index [Seite 307]
11 - EULA [Seite 315]