Chapter 1-1. Introduction to Algebra : "VARIABLES"

VARIABLES

Objective : To simplify numerical expressions and evaluate algebraic expressions.

When you go to an ocean beach, you may find small shops that rent recreational equipment, such as scuba gear, surfboards, and snorkeling gear. Suppose the rental charge for snorkeling gear is $4.50 per hour. The amount you'll pay for using the gear depends on the amount of time you have it.

The rental charge follows this pattern :

Rental charge = $4.50 x number of hours

                         = $4.50 x h

The letter h stands for the hours shown in the table : 1, 2, 3, or 4. Also, h can stand for other hours not in the table. We call h a variable.

A variable is a symbol used to represent one or more numbers. The numbers are called values of the variable. An expression that contains a variable, such as the expression 4.50 x h , is called a variable expression. An expression, such as 4.50 x 4, that names a particular number is called a numerical expression, or numeral.

Another way to indicate multiplication is to use a raised dot, for example, 4.5 . 4.

In Algebra, products that contain a variable are usually written without multiplication sign because it looks to much like the letter x, which is often used as a variable.

The number named by a numerical expression is called the value of the expression. Since the expression 4 + 2 and 6 name the same number, they have the same value. To show that these expression have the same value, you use the equals sign, =.

You write               4 + 2 = 6

and say "Four plus two equals (or is equals to or is) six." The simplest, or most common, name for the number six is 6.

to show that the expression 4 + 2 and 5 do not have the same value.