Basic Math and Pre-Algebra For Dummies (20 page)

You probably won't use square roots much until you get to algebra, but at that point, they become handy.

The
absolute value
of a number is the positive value of that number. It tells you how far away from 0 a number is on the number line. The symbol for absolute value is a set of vertical bars.

Taking the absolute value of a positive number doesn't change that number's value. For example,

•  |3| = 3
  

   |12| = 12
  

  |145| = 145
  

However, taking the absolute value of a negative number changes it to a positive number: 

•        |−5| = 5
  

      |−10| = 10
  

  |−212| = 212
  

Finally, the absolute value of 0 is simply 0:  

• |0| = 0
  

Chapter 5

In This Chapter

Understanding the Three E's of math — equations, expressions, and evaluation

Using order of precedence to evaluate expressions containing the Big Four operations

Working with expressions that contain exponents

Evaluating expressions with parentheses

In this chapter, I introduce you to what I call the Three E's of math: equations, expressions, and evaluation. You'll likely find the Three E's of math familiar because, whether you realize it or not, you've been using them for a long time. Whenever you add up the cost of several items at the store, balance your checkbook, or figure out the area of your room, you're evaluating expressions and setting up equations. In this section, I shed light on this stuff and give you a new way to look at it.

You probably already know that an
equation
is a mathematical statement that has an equals sign (=) — for example, 1 + 1 = 2. An
expression
is a string of mathematical symbols that can be placed on one side of an equation — for example, 1 + 1. And
evaluation
is finding out the
value
of an expression as a number — for example, finding out that the expression 1 + 1 is equal to the number 2.

Throughout the rest of the chapter, I show you how to turn expressions into numbers using a set of rules called the
order of operations
(or
order of precedence
). These rules look complicated, but I break them down so you can see for yourself what to do next in any situation.

An
equation
is a mathematical statement that tells you that two things have the same value — in other words, it's a statement with an equals sign. The
equation is one of the most important concepts in mathematics because it allows you to boil down a bunch of complicated information into a single number.

Mathematical equations come in a lot of varieties: arithmetic equations, algebraic equations, differential equations, partial differential equations, Diophantine equations, and many more. In this book, I look at only two types: arithmetic equations and algebraic equations.

In this chapter, I discuss only
arithmetic equations,
which are equations involving numbers, the Big Four operations, and the other basic operations I introduce in Chapter
4
(absolute values, exponents, and roots). In Part
V
, I introduce you to algebraic equations. Here are a few examples of simple arithmetic equations:

And here are a few examples of more-complicated arithmetic equations:

An
expression
is any string of mathematical symbols that can be placed on one side of an equation. Mathematical expressions, just like equations, come in a lot of varieties. In this chapter, I focus only on
arithmetic expressions,
which are expressions that contain numbers, the Big Four operations, and a few other basic operations (see Chapter
4
). In Part
V
, I introduce you to algebraic expressions. Here are a few examples of simple expressions:

And here are a few examples of more-complicated expressions:

At the root of the word
evaluation
is the word
value.
In other words, when you evaluate something, you find its value. Evaluating an expression is also referred to as
simplifying, solving,
or
finding the value of an expression.
The words may change, but the idea is the same — boiling down a string of numbers and math symbols to a single number.