Basic Math & Pre-Algebra For Dummies

Mark Zegarelli

• Publisher: For Dummies
• Year: 2016
• ISBN:
  9781119298885
• Edition: 2
• Topic: Mathematik
• Subtopic: Algebra

Basic Math & Pre-Algebra For Dummies, 2nd Edition (9781119293637) was previously published as Basic Math & Pre-Algebra For Dummies, 2nd Edition (9781118791981). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Tips for simplifying tricky basic math and pre-algebra operations

Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.

• Explanations and practical examples that mirror today's teaching methods
• Relevant cultural vernacular and references
• Standard For Dummies materials that match the current standard and design

Basic Math & Pre-Algebra For Dummies takes the intimidation out of tricky operations and helps you get ready for algebra!

Part 1

Getting Started with Basic Math and Pre-Algebra

IN THIS PART …

See how the number system was invented and how it works.

Identify four important sets of numbers: counting numbers, integers, rational numbers, and real numbers.

Use place value to write numbers of any size.

Round numbers to make calculating quicker.

Work with the Big Four operations: adding, subtracting, multiplying, and dividing.

Chapter 1

Playing the Numbers Game

IN THIS CHAPTER

Finding out how numbers were invented

Looking at a few familiar number sequences

Examining the number line

Understanding four important sets of numbers

One useful characteristic about 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 cannibals, 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 the 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 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.

Inventing Numbers

Historians believe that the first 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.”

But as farming developed and trade between communities began, more precision was needed. So people began using stones, clay tokens, and similar objects to keep track of their goats, sheep, oil, grain, or whatever commodity they had. They exchanged these tokens for the objects they represented in a one-to-one exchange.

Eventually, traders realized that they could draw pictures instead of using tokens. Those pictures evolved into tally marks and, in time, ...