Algebra I Workbook For Dummies Read online

  Algebra I Workbook For Dummies®, 2nd Edition

  Visit www.dummies.com/cheatsheet/algebra1wb to view this book's cheat sheet.

  Table of Contents

  Introduction

  About This Book

  Conventions Used in This Book

  Foolish Assumptions

  How This Book Is Organized

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

  Part II: Changing the Format of Expressions

  Part III: Seek and Ye Shall Find. . .Solutions

  Part IV: Solving Story Problems and Sketching Graphs

  Part V: The Part of Tens

  Icons Used in This Book

  Where to Go from Here

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

  Chapter 1: Deciphering Signs in Numbers

  Assigning Numbers Their Place

  Reading and Writing Absolute Value

  Adding Signed Numbers

  Making a Difference with Signed Numbers

  Multiplying Signed Numbers

  Dividing Signed Numbers

  Answers to Problems on Signed Numbers

  Chapter 2: Incorporating Algebraic Properties

  Getting a Grip on Grouping Symbols

  Distributing the Wealth

  Making Associations Work

  Computing by Commuting

  Answers to Problems on Algebraic Properties

  Chapter 3: Making Fractions and Decimals Behave

  Converting Improper and Mixed Fractions

  Finding Fraction Equivalences

  Making Proportional Statements

  Finding Common Denominators

  Adding and Subtracting Fractions

  Multiplying and Dividing Fractions

  Simplifying Complex Fractions

  Changing Fractions to Decimals and Vice Versa

  Performing Operations with Decimals

  Answers to Problems on Fractions

  Chapter 4: Exploring Exponents

  Multiplying and Dividing Exponentials

  Raising Powers to Powers

  Using Negative Exponents

  Writing Numbers with Scientific Notation

  Answers to Problems on Discovering Exponents

  Chapter 5: Taming Rampaging Radicals

  Simplifying Radical Expressions

  Rationalizing Fractions

  Arranging Radicals as Exponential Terms

  Using Fractional Exponents

  Simplifying Expressions with Exponents

  Estimating Answers

  Answers to Problems on Radicals

  Chapter 6: Simplifying Algebraic Expressions

  Adding and Subtracting Like Terms

  Multiplying and Dividing Algebraically

  Incorporating Order of Operations

  Evaluating Expressions

  Answers to Problems on Algebraic Expressions

  Part II: Changing the Format of Expressions

  Chapter 7: Specializing in Multiplication Matters

  Distributing One Factor over Many

  Curses, FOILed Again — Or Not

  Squaring Binomials

  Multiplying the Sum and Difference of the Same Two Terms

  Cubing Binomials

  Creating the Sum and Difference of Cubes

  Raising Binomials to Higher Powers

  Answers to Problems on Multiplying Expressions

  Chapter 8: Dividing the Long Way to Simplify Algebraic Expressions

  Dividing by a Monomial

  Dividing by a Binomial

  Dividing by Polynomials with More Terms

  Simplifying Division Synthetically

  Answers to Problems on Division

  Chapter 9: Figuring on Factoring

  Pouring Over Prime Factorizations

  Factoring Out the Greatest Common Factor

  Reducing Algebraic Fractions

  Answers to Problems on Factoring Expressions

  Chapter 10: Taking the Bite Out of Binomial Factoring

  Factoring the Difference of Squares

  Factoring Differences and Sums of Cubes

  Making Factoring a Multiple Mission

  Answers to Problems on Factoring

  Chapter 11: Factoring Trinomials and Special Polynomials

  Focusing First on the Greatest Common Factor (GCF)

  “Un”wrapping the FOIL

  Factoring Quadratic-Like Trinomials

  Factoring Trinomials Using More Than One Method

  Factoring by Grouping

  Putting All the Factoring Together

  Answers to Problems on Factoring Trinomials and Other Expressions

  Part III: Seek and Ye Shall Find. . .Solutions

  Chapter 12: Lining Up Linear Equations

  Using the Addition/Subtraction Property

  Using the Multiplication/Division Property

  Putting Several Operations Together

  Solving Linear Equations with Grouping Symbols

  Working It Out with Fractions

  Solving Proportions

  Answers to Problems on Solving Linear Equations

  Chapter 13: Muscling Up to Quadratic Equations

  Using the Square Root Rule

  Solving by Factoring

  Using the Quadratic Formula

  Completing the Square

  Dealing with Impossible Answers

  Answers to Problems on Solving Quadratic Equations

  Chapter 14: Yielding to Higher Powers

  Determining How Many Possible Roots

  Applying the Rational Root Theorem

  Using the Factor/Root Theorem

  Solving By Factoring

  Solving Powers That Are Quadratic-Like

  Answers to Problems on Solving Higher Power Equations

  Chapter 15: Reeling in Radical and Absolute Value Equations

  Squaring Both Sides to Solve Radical Equations

  Doubling the Fun with Radical Equations

  Solving Absolute Value Equations

  Answers to Problems on Radical and Absolute Value Equations

  Chapter 16: Getting Even with Inequalities

  Using the Rules to Work on Inequality Statements

  Rewriting Inequalities by Using Interval Notation

  Solving Linear Inequalities

  Solving Quadratic Inequalities

  Dealing with Polynomial and Rational Inequalities

  Solving Absolute Value Inequalities

  Solving Complex Inequalities

  Answers to Problems on Working with Inequalities

  Part IV: Solving Story Problems and Sketching Graphs

  Chapter 17: Facing Up to Formulas

  Working with Formulas

  Deciphering Perimeter, Area, and Volume

  Using perimeter formulas to get around

  Squaring off with area formulas

  Working with volume formulas

  Getting Interested in Using Percent

  Answers to Problems on Using Formulas

  Chapter 18: Making Formulas Work in Basic Story Problems

  Applying the Pythagorean Theorem

  Using Geometry to Solve Story Problems

  Putting Distance, Rate, and Time in a Formula

  Examining the distance-rate-time formula

  Going the distance with story problems

  Answers to Making Formulas Work in Basic Story Problems

  Chapter 19: Relating Values in Story Problems

  Tackling Age Problems

  Tackling Consecutive Integer Problems

  Working Together on Work Problems

  Answers to Relating Values in Story Problems

  Chapter 20: Measuring Up with Quality and Quantity Story Problem
s

  Achieving the Right Blend with Mixtures Problems

  Concocting the Correct Solution One Hundred Percent of the Time

  Dealing with Money Problems

  Answers to Problems on Measuring Up with Quality and Quantity

  Chapter 21: Getting a Handle on Graphing

  Thickening the Plot with Points

  Sectioning Off by Quadrants

  Using Points to Lay Out Lines

  Graphing Lines with Intercepts

  Computing Slopes of Lines

  Graphing with the Slope-Intercept Form

  Changing to the Slope-Intercept Form

  Writing Equations of Lines

  Picking on Parallel and Perpendicular Lines

  Finding Distances between Points

  Finding the Intersections of Lines

  Graphing Parabolas and Circles

  Graphing with Transformations

  Answers to Problems on Graphing

  Part V: The Part of Tens

  Chapter 22: Ten Common Errors That Get Noticed

  Squaring a Negative or Negative of a Square

  Squaring a Binomial

  Operating on Radicals

  Distributing a Negative Throughout

  Fracturing Fractions

  Raising a Power to a Power

  Making Negative Exponents Flip

  Making Sense of Reversing the Sense

  Using the Slope Formula Correctly

  Writing Several Fractions as One

  Chapter 23: Ten Quick Tips to Make Algebra a Breeze

  Flipping Proportions

  Multiplying Through to Get Rid of Fractions

  Zeroing In on Fractions

  Finding a Common Denominator

  Dividing by 3 or 9

  Dividing by 2, 4, or 8

  Commuting Back and Forth

  Factoring Quadratics

  Making Radicals Less Rad, Baby

  Applying Acronyms

  Cheat Sheet

  Algebra I Workbook For Dummies®, 2nd Edition

  by Mary Jane Sterling

  Algebra I Workbook For Dummies®, 2nd Edition

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  Copyright © 2011 by Wiley Publishing, Inc., Indianapolis, Indiana

  Published simultaneously in Canada

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  ISBN 978-1-118-04922-8 (cloth); ISBN 978-1-118-10204-6 (ebk); ISBN 978-1-118-10205-3 (ebk); ISBN 978-1-118-10206-0 (ebk)

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  About the Author

  Mary Jane Sterling is the author of Algebra I For Dummies, 2nd Edition, Trigonometry For Dummies, Algebra II For Dummies, Math Word Problems For Dummies, Business Math For Dummies, and Linear Algebra For Dummies. She taught junior high and high school math for many years before beginning her current 30-years-and-counting tenure at Bradley University in Peoria, Illinois. Mary Jane especially enjoys working with future teachers and trying out new technology.

  Dedication

  This book is dedicated to my parents. My father, Tom Mackie, always encouraged me to pursue my interests in mathematics and science — at a time when girls were encouraged to study home economics. My mother, Jane Mackie, was a woman before her time — stepping out into the world when it wasn’t all that fashionable for women to do so. And at 84-years old, she proudly announced that she had read Algebra For Dummies from beginning to end and understood it!

  Author’s Acknowledgments

  I’d like to thank Tracy Barr for being a great editor — taking care of all those nitty-gritty details, as well as the big issues. A big thanks also goes to the technical editors, Mike McAsey and Shira Fass, who didn’t let me get away with any slips or missteps. Also, thanks to Lindsay LeFevere for providing another project — lest I sit around, twiddling my thumbs.

  Publisher’s Acknowledgments

  We’re proud of this book; please send us your comments through our online registration form located at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.

  Some of the people who helped bring this book to market include the following:

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  Project Editor: Tracy Barr

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  Introduction

  Some of my earliest grade-school memories include receiving brand-new workbooks at the beginning of the school year. The pages of these workbooks were crisp, pristine, beautiful — and intimidating at the same time. But it didn’t take long for those workbooks to become well used and worn. My goal with Algebra I Workbook For Dummies, 2nd Edition, is to give you that same workbook experience — without the intimidation, of course. This book is filled with algebra problems you can study, solve, and learn from. But you’re not going to be doing these problems alone. As you proceed through Algebra I Workbook For Dummies, 2nd Edition, you’ll see plenty of road signs that clearly mark the way. You’ll find plenty of explanations, examples, and other bits of info to make this journey as smooth an experience as possible. You also get to do your own grading with the solutions I provide at the end of each chapter. You can even go back and change your answers to the correct ones, if you made an error. No, you’re not cheating. You’re figuring out how to correctly work algebra problems. (Actually, changing answers to the correct ones is a great way to learn from your mistakes.)