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
Published by
Wiley Publishing, Inc.
111 River St.
Hoboken, NJ 07030-5774
www.wiley.com
Copyright © 2011 by Wiley Publishing, Inc., Indianapolis, Indiana
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.
Trademarks: Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries, and may not be used without written permission. All other trademarks are the property of their respective owners. Wiley Publishing, Inc., is not associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: The publisher and the author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation warranties of fitness for a particular purpose. No warranty may be created or extended by sales or promotional materials. The advice and strategies contained herein may not be suitable for every situation. This work is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional services. If professional assistance is required, the services of a competent professional person should be sought. Neither the publisher nor the author shall be liable for damages arising herefrom. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read.
For general information on our other products and services, 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.
For technical support, please visit www.wiley.com/techsupport.
Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats. For more information about Wiley products, visit us at www.wiley.com.
Library of Congress Control Number: 2011930305
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)
Manufactured in the United States of America
10 9 8 7 6 5 4 3 2 1
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:
Acquisitions, Editorial, and Media Development
Project Editor: Tracy Barr
(Previous Edition: Alissa Schwipps)
Executive Editor: Lindsay Sandman Lafevere
Assistant Editor: David Lutton
Editorial Program Coordinator: Joe Niesen
Technical Editors: Michael McAsey, Shira Fass
Senior Editorial Manager: Jennifer Ehrlich
Editorial Supervisor and Reprint Editor: Carmen Krikorian
Editorial Assistants: Rachelle S. Amick
Cover Photos: © iStockphoto.com / porcorex
Cartoons: Rich Tennant (www.the5thwave.com)
Composition Services
Project Coordinator: Patrick Redmond
Layout and Graphics: Carrie A. Cesav
ice, Nikki Gately, Mark Pinto, Christin Swinford
Proofreaders: Melissa D. Buddendeck, Lauren Mandelbaum
Indexer: Potomac Indexing, LLC
Publishing and Editorial for Consumer Dummies
Diane Graves Steele, Vice President and Publisher, Consumer Dummies
Kristin Ferguson-Wagstaffe, Product Development Director, Consumer Dummies
Ensley Eikenburg, Associate Publisher, Travel
Kelly Regan, Editorial Director, Travel
Publishing for Technology Dummies
Andy Cummings, Vice President and Publisher, Dummies Technology/General User
Composition Services
Debbie Stailey, Director of Composition Services
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.)
Algebra I Workbook For Dummies Page 1