Algebra I For Dummies

Algebra I For Dummies




von: Mary Jane Sterling

For Dummies, 2010

ISBN: 9780470636053

Sprache: Englisch

384 Seiten, Download: 2785 KB

Format:  EPUB

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Algebra I For Dummies


Let me introduce you to algebra. This introduction is somewhat like what would happen if I were to introduce you to my friend Donna. I’d say, “This is Donna. Let me tell you something about her.” After giving a few well-chosen tidbits of information about Donna, I’d let you ask more questions or fill in more details. In this book, you find some well-chosen topics and information, and I try to fill in details as I go along.

As you read this introduction, you’re probably in one of two situations:

You’ve taken the plunge and bought the book.

You’re checking things out before committing to the purchase.

In either case, you’d probably like to have some good, concrete reasons why you should go to the trouble of reading and finding out about algebra.

One of the most commonly asked questions in a mathematics classroom is, “What will I ever use this for?” Some teachers can give a good, convincing answer. Others hem and haw and stare at the floor. My favorite answer is, “Algebra gives you power.” Algebra gives you the power to move on to bigger and better things in mathematics. Algebra gives you the power of knowing that you know something that your neighbor doesn’t know. Algebra gives you the power to be able to help someone else with an algebra task or to explain to your child these logical mathematical processes.

Algebra is a system of symbols and rules that is universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end. It’s an organizational tool that is most useful when followed with the appropriate rules. What power! Some people like algebra because it can be a form of puzzle-solving. You solve a puzzle by finding the value of a variable. You may prefer Sudoku or Ken Ken or crosswords, but it wouldn’t hurt to give algebra a chance, too.

About This Book

This book isn’t like a mystery novel; you don’t have to read it from beginning to end. In fact, you can peek at how it ends and not spoil the rest of the story.

I divide the book into some general topics — from the beginning nuts and bolts to the important tool of factoring to equations and applications. So you can dip into the book wherever you want, to find the information you need.

Throughout the book, I use many examples, each a bit different from the others, and each showing a different twist to the topic. The examples have explanations to aid your understanding. (What good is knowing the answer if you don’t know how to get the right answer yourself?)

The vocabulary I use is mathematically correct and understandable. So whether you’re listening to your teacher or talking to someone else about algebra, you’ll be speaking the same language.

Along with the how, I show you the why. Sometimes remembering a process is easier if you understand why it works and don’t just try to memorize a meaningless list of steps.

Conventions Used in This Book

I don’t use many conventions in this book, but you should be aware of the following:

When I introduce a new term, I put that term in italics and define it nearby (often in parentheses).

I express numbers or numerals either with the actual symbol, such as 8, or the written-out word: eight. Operations, such as +, are either shown as this symbol or written as plus. The choice of expression all depends on the situation — and on making it perfectly clear for you.

What You’re Not to Read

The sidebars (those little gray boxes) are interesting but not essential to your understanding of the text. If you’re short on time, you can skip the sidebars. Of course, if you read them, I think you’ll be entertained.

You can also skip anything marked by a Technical Stuff icon (see “Icons Used in This Book,” for more information).

Foolish Assumptions

I don’t assume that you’re as crazy about math as I am — and you may be even more excited about it than I am! I do assume, though, that you have a mission here — to brush up on your skills, improve your mind, or just have some fun. I also assume that you have some experience with algebra — full exposure for a year or so, maybe a class you took a long time ago, or even just some preliminary concepts.

If you went to junior high school or high school in the United States, you probably took an algebra class. If you’re like me, you can distinctly remember your first (or only) algebra teacher. I can remember Miss McDonald saying, “This is an n.” My whole secure world of numbers was suddenly turned upside down. I hope your first reaction was better than mine.

You may be delving into the world of algebra again to refresh those long-ago lessons. Is your kid coming home with assignments that are beyond your memory? Are you finally going to take that calculus class that you’ve been putting off? Never fear. Help is here!

How This Book Is Organized

Where do you find what you need quickly and easily? This book is divided into parts dealing with the most frequently discussed and studied concepts of basic algebra.

Part I: Starting Off with the Basics

The “founding fathers” of algebra based their rules and conventions on the assumption that everyone would agree on some things first and adopt the process. In language, for example, we all agree that the English word for good means the same thing whenever it appears. The same goes for algebra. Everyone uses the same rules of addition, subtraction, multiplication, division, fractions, exponents, and so on. The algebra wouldn’t work if the basic rules were different for different people. We wouldn’t be able to communicate. This part reviews what all these things are that everyone has agreed on over the years.

The chapters in this part are where you find the basics of arithmetic, fractions, powers, and signed numbers. These tools are necessary to be able to deal with the algebraic material that comes later. The review of basics here puts a spin on the more frequently used algebra techniques. If you want, you can skip these chapters and just refer to them when you’re working through the material later in the book.

In these first chapters, I introduce you to the world of letters and symbols. Studying the use of the symbols and numbers is like studying a new language. There’s a vocabulary, some frequently used phrases, and some cultural applications. The language is the launching pad for further study.

Part II: Figuring Out Factoring

Part II contains factoring and simplifying. Algebra has few processes more important than factoring. Factoring is a way of rewriting expressions to help make solving the problem easier. It’s where expressions are changed from addition and subtraction to multiplication and division. The easiest way to solve many problems is to work with the wonderful multiplication property of zero, which basically says that to get a 0 you multiply by 0. Seems simple, and yet it’s really grand.

Some factorings are simple — you just have to recognize a similarity. Other factorings are more complicated — not only do you have to recognize a pattern, but you have to know the rule to use. Don’t worry — I fill you in on all the differences.

Part III: Working Equations

The chapters in this part are where you get into the nitty-gritty of finding answers. Some methods for solving equations are elegant; others are down and dirty. I show you many types of equations and many methods for solving them.

Usually, I give you one method for solving each type of equation, but I present alternatives when doing so makes sense. This way, you can see that some methods are better than others. An underlying theme in all the equation-solving is to check your answers — more on that in this part.

Part IV: Applying Algebra

The whole point of doing algebra is in this part. There are everyday formulas and not-so-everyday formulas. There are familiar situations and situations that may be totally unfamiliar. I don’t have space to show you every possible type of problem, but I give you enough practical uses, patterns, and skills to prepare you for many of the situations you encounter. I also give you some graphing basics in this part. A picture is truly worth a thousand words, or, in the case of mathematics, a graph is worth an infinite number of points.

Part V: The Part of Tens

Here I give you ten important tips: how to avoid the most common algebraic pitfalls. You also find my choice for the ten most famous equations. (You may have other favorites, but these are my...