✓ Online practice and study aids: The online practice that comes free with this book offers 1,001 questions and answers that allow you to gain more practice with Algebra I concepts. The beauty of the online questions is that you can customize your online practice to focus on the topic areas that give you the most trouble. So, if you need help with factoring or story problems, just select those question types online and start practicing. Or if you’re short on time but want to get a mixed bag of a limited number of questions, you can specify the number of questions you want to practice. Whether you practice a few hundred questions in one sitting or a couple dozen, and whether you focus on a few types of questions or practice every type, the online program keeps track of the questions you get right and wrong so you can monitor your progress and spend time studying exactly what you need.
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Ready to start? All psyched and ready to go? Then it’s time to take this excursion in algebra. Yes, this book is a grand adventure just waiting for you to take the first step. If you want to refresh your basic skills or boost your confidence, start with Part I. If you’re ready for some factoring practice and need to pinpoint which method to use with what, go to Part II. Part III is for you if you’re ready to solve equations; you can find just about any type you’re ready to attack. Part IV is where the good stuff is – applications – things to do with all those good solutions. The lists in Part V are usually what you’d look at after visiting one of the other parts, but why not start there? It’s a fun place!
Studying algebra can give you some logical exercises. As you get older, the more you exercise your brain cells, the more alert and “with it” you remain. “Use it or lose it” means a lot in terms of the brain. What a good place to use it, right here!
The best why for studying algebra is just that it’s beautiful. Yes, you read that right. Algebra is poetry, deep meaning, and artistic expression. Just look, and you’ll find it. Also, don’t forget that it gives you power.
Welcome to algebra! Enjoy the adventure!
Part I
In this part …
Chapter 1
Assembling Your Tools
In This Chapter
You’ve probably heard the word algebra on many occasions, and you knew that it had something to do with mathematics. Perhaps you remember that algebra has enough information to require taking two separate high school algebra classes – Algebra I and Algebra II. But what exactly is algebra? What is it really used for?
This book answers these questions and more, providing the straight scoop on some of the contributions to algebra’s development, what it’s good for, how algebra is used, and what tools you need to make it happen. In this chapter, you find some of the basics necessary to more easily find your way through the different topics in this book. I also point you toward these topics.
In a nutshell, algebra is a way of generalizing arithmetic. Through the use of variables (letters representing numbers) and formulas or equations involving those variables, you solve problems. The problems may be in terms of practical applications, or they may be puzzles for the pure pleasure of the solving. Algebra uses positive and negative numbers, integers, fractions, operations, and symbols to analyze the relationships between values. It’s a systematic study of numbers and their relationships, and it uses specific rules.
Where would mathematics and algebra be without numbers? A part of everyday life, numbers are the basic building blocks of algebra. Numbers give you a value to work with. Where would civilization be today if not for numbers? Without numbers to figure the distances, slants, heights, and directions, the pyramids would never have been built. Without numbers to figure out navigational points, the Vikings would never have left Scandinavia. Without numbers to examine distance in space, humankind could not have landed on the moon.
Even the simple tasks and the most common of circumstances require a knowledge of numbers. Suppose that you wanted to figure the amount of gasoline it takes to get from home to work and back each day. You need a number for the total miles between your home and business and another number for the total miles your car can run on a gallon of gasoline.
The different sets of numbers are important because what they look like and how they behave can set the scene for particular situations or help to solve particular problems. It’s sometimes really convenient to declare, “I’m only going to look at whole-number answers,” because whole numbers don’t include fractions or negatives. You could easily end up with a fraction if you’re working through a problem that involves a number of cars or people. Who wants half