Algebra I Workbook For Dummies

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.)

Remember, mathematics is a subject that has to be handled. You can read English literature and understand it without having to actually write it. You can read about biological phenomena and understand them, too, without taking part in an experiment. Mathematics is different. You really do have to do it, practice it, play with it, and use it. Only then does the mathematics become a part of your knowledge and skills. And what better way to get your fingers wet than by jumping into this workbook? Remember only practice, practice, and some more practice can help you master algebra! Have at it!

About This Book

I’ve organized Algebra I Workbook For Dummies, 2nd Edition, very much like the way I organized Algebra I For Dummies (Wiley), which you may already have: I introduce basic concepts and properties first and then move on to the more complex ones. That way, if you’re pretty unsteady on your feet, algebra-wise, you can begin at the beginning and build your skills and your confidence as you progress through the different chapters.

But maybe you don’t need practice problems from beginning to end. Maybe you just need a bit of extra practice with specific types of algebra problems. One nice thing about this workbook is that you can start wherever you want. If your nemesis is graphing, for example, you can go straight to the chapters that focus on graphing. Formulas your problem area? Then go to the chapters that deal with formulas.

Bottom line: You do need the basic algebra concepts to start anywhere in this workbook, but after you have those down, you can pick and choose where you want to work. You can jump in wherever you want and work from there.

Conventions Used in This Book

I use the following conventions in this book to make things consistent and easy to understand, regardless which practice problems you’re tackling:

New terms appear in italic and are closely followed by a clear definition.

I bold the answers to the examples and the practice questions for easy identification. However, I don’t bold the punctuation that follows the answer because I want to prevent any confusion with periods and decimal points that could be considered part of the answer.

Algebra uses a lot of letters to represent numbers. In general, I use letters at the beginning of the alphabet ( a, b, c, k) to represent constants — numbers that don’t change all the time but may be special to a particular situation. The letters at the end of the alphabet usually represent variables — what you’re solving for. I use the most commonly used letters (x , y and z) for variables. And all constants and variables are italicized. And if, for any reason, I don’t follow this convention, I let you know so that you aren’t left guessing. (You may see breaks from the convention in some old, traditional formulas, for example, or when you want a particular letter to stand for someone’s age, which just may happen to start with the letter A.)

I use the corresponding symbols to represent the math operations of addition, subtraction, multiplication, and division: +, –, ×, and ÷. But keep the following special rules in mind when using them in algebra and in this book:

• Subtraction (–) is an operation, but that symbol also represents opposite of, minus, and negative. When you get to the different situations, you can figure out how to interpret the wording, based on the context.

• Multiplication (×) is usually indicated with a dot (·) or parentheses ( ) in algebra. In this book, I use parentheses most often, but you may occasionally see a × symbol. Don’t confuse the × symbol with the italicized variable, x.

• Division (÷) is sometimes indicated with a slash (/) or fraction line. I use these interchangeably in the problems throughout this book.

Foolish Assumptions

When writing this book, I made the following assumptions about you, my dear reader:

You already have reasonable experience with basic algebra concepts and want an opportunity to practice those skills.

Note: Workbooks in general — and this workbook in particular — are designed to provide additional practice opportunities for concepts and processes that have been introduced elsewhere. For that reason, I don’t go into great depth when explaining the theories and rules behind each problem I’ve included in this book because I assume you have some other book, like my Algebra I For Dummies (Wiley), for more in-depth reference, if necessary.

You took or currently are taking Algebra I, but you need to brush up on certain areas.

Your son, daughter, grandson, granddaughter, niece, nephew, or special someone is taking Algebra I. You haven’t looked at an equation for years, and you want to help him or her.

You love math, and your idea of a good time is solving equations on a rainy afternoon while listening to your iPod.

How This Book Is Organized

Like all books in the For Dummies series, this book is divided into a variety of chapters, each tackling a particular topic. The chapters are then organized into parts. Each part covers a general area of study or type of concept. This organization allows you to pinpoint where you want to start or where you need to revisit. To help you access important concepts in algebra, I’ve divided the chapters in Algebra I Workbook For Dummies, 2nd Edition, into the following five parts.

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

This first part starts with essential algebra topics, but it doesn’t start at the beginning of arithmetic or cover much pre-algebra. Here, you can find out how to work with signed numbers and their operations. You also see those ever-loving fractions and get to add or multiply them. This part also focuses on exponents, numbers, and variables and how they combine — or don’t combine. I follow exponents with radicals — not the hippies from the 1960s, but those operations that can be represented with fractional exponents. And, lastly, the basics include combining terms that are alike enough to go together.

Part II: Changing the Format of Expressions

Algebra is a stepping-stone to higher mathematics. In fact, you really can’t do much advanced mathematics without algebra. After you acquaint yourself with the symbols and operations of algebra, you can move on to other algebraic processes such as solving equations and graphing. This part describes and refines the basic operations and then coordinates the operations in terms of having unknown or variable terms and factors. The operations act the same as when you perform them on numbers; they just look different and have different types of results.

The factoring part is big. True, factoring is really just undoing something that got multiplied out. You can think of factoring as being the first step in solving an equation or a puzzle or challenge. Get good at factoring, and the answer comes much more easily.

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

Discovering a solution to an equation is usually everyone’s favorite part of algebra. It provides a motivation for performing all those algebraic operations and processes. You finally have an answer! Sometimes you can just look at an equation, and the solution pops right out at...