Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online) - Mark Zegarelli

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own. The answers and detailed solutions are available so you can feel confident about your progress.

      In addition to the book you’re reading right now, be sure to check out the free Cheat Sheet on Dummies.com. This handy Cheat Sheet covers some common “math demons” that students often stumble over. To access it, simply go to Dummies.com and type Basic Math & Pre-Algebra All in One Cheat Sheet in the Search box.

      You’ll also have access to online quizzes related to each chapter, starting with Chapter 3. These quizzes provide a whole new set of problems for practice and confidence-building. To access the quizzes, follow these simple steps:

      1 Register your book or ebook at Dummies.com to get your PIN. Go to www.dummies.com/go/getaccess.

      2 Select your product from the drop-down list on that page.

      3 Follow the prompts to validate your product, and then check your email for a confirmation message that includes your PIN and instructions for logging in.

      If you do not receive this email within two hours, please check your spam folder before contacting us through our Technical Support website at http://support.wiley.com or by phone at 877-762-2974.

      Now you’re ready to go! You can come back to the practice material as often as you want — simply log on with the username and password you created during your initial login. No need to enter the access code a second time.

      Your registration is good for one year from the day you activate your PIN.

      You can use this book in a variety of ways. If you’re reading without immediate time pressure from a test or homework assignment, start at the beginning and keep going, chapter by chapter, to the end. If you do this, you’ll be surprised by how much of the math you may have been dreading will be almost easy. Additionally, setting up some solid groundwork is a great way to prepare for what follows later in the book.

      If your time is limited — especially if you’re taking a math course and you’re looking for help with your homework or an upcoming test — skip directly to the topic you’re studying. Wherever you open the book, you can find a clear explanation of the topic at hand, as well as a variety of hints and tricks. Read through the examples and try to do them yourself, or use them as templates to help you with assigned problems.

      Getting Started with Basic Math & Pre-Algebra

      1  Chapter 1: Playing the Numbers Game Inventing Numbers Understanding Number Sequences Four Important Sets of Numbers

      2  Chapter 2: The Big Four Operations The Big Four Operations Applying the Big Four Operations to Larger Numbers

      Playing the Numbers Game

      IN THIS CHAPTER

       Bullet Finding out how numbers were invented

       Bullet Looking at a few familiar number sequences

       Bullet Examining the number line

       Bullet Understanding four important sets of numbers

      One useful characteristic of numbers is that they’re conceptual, which means that, in an important sense, they’re all in your head. (This fact probably won’t get you out of having to know about them, though — nice try!)

      For example, you can picture three of anything: three cats, three baseballs, three tigers, three planets. But just try to picture the concept of three all by itself, and you find it’s impossible. Oh, sure, you can picture the numeral 3, but threeness itself — much like love or beauty or honor — is beyond direct understanding. But when you understand the concept of three (or four, or a million), you have access to an incredibly powerful system for understanding the world: mathematics.

      In this chapter, I give you a brief history of how numbers likely came into being. I discuss a few common number sequences and show you how these connect with simple math operations like addition, subtraction, multiplication, and division.

      After that, I describe how some of these ideas come together with a simple yet powerful tool: the number line. I discuss how numbers are arranged on the number line, and I also show you how to use the number line as a calculator for simple arithmetic. Finally, I describe how the counting numbers (1, 2, 3, …) sparked the invention of more unusual types of numbers, such as negative numbers, fractions, and irrational numbers. I also show you how these sets of numbers are nested — that is, how one set of numbers fits inside another, which fits inside another.

      Historians believe that the first written number systems came into being at the same time as agriculture and commerce. Before that, people in prehistoric, hunter-gatherer societies were pretty much content to identify bunches of things as “a lot” or “a little.” They may have had concepts of small numbers, probably less than five or ten, but lacked a coherent way to think about, for example, the number 42.

      Throughout the ages, the Babylonians, Egyptians, Greeks, Hindus, Romans, Mayans, Arabs, and Chinese (to name just a few) all developed their own systems of writing numbers.

      Although Roman numerals gained wide currency as the Roman Empire expanded throughout Europe and parts of Asia and Africa, the more advanced system that was invented in India and adapted by the Arabs turned out to be more useful. Our own number system, the Hindu-Arabic numbers (also called decimal numbers), is mainly derived from these earlier number systems.

      Although humans invented numbers for counting commodities, as I explain in the preceding section, they soon put them to use in a wide range of applications. Numbers were useful for measuring distances, counting money, amassing armies, levying taxes, building pyramids, and lots more.

      But beyond their many uses for understanding the external world, numbers have an internal order all their own. So numbers are not only an invention, but equally a

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