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6

Algebraic Expressions

This chapter presents a discussion of algebraic expressions. It begins with

the basic terminology that is critical to your understanding of the concept of

an algebraic expression.

Algebraic Terminology

A variable holds a place open for a number (or numbers, in some cases)

whose value may vary. You usually express a variable as an upper or lower-

case letter (e.g., x, y, z, A, B, or C); for simplicity, the letter is the “name”

of the variable. In problem situations,

you use variables to represent unknown

quantities. Although a variable may rep-

resent any number, in many problems the

variables represent specific numbers, but

the values are unknown.

A constant is a quantity that has a fi xed, defi nite value that does not

change in a problem situation. For example, all the real numbers are con-

stants, including πe real numbers whose units are units of measure such as

5 feet, 60 degrees, 100 pounds, and so forth.

Problem Name the variable(s) and constant(s) in the given expression.

a.

5

9

() 32 , where F is the number of degrees Fahrenheit

b. πd, where d is the measure of the diameter of a circle

You can think of variables as numbers in

disguise. Not recognizing that variables

represent numbers is a common mistake for

beginning students of algebra.