Prealgebra: Variables

Variables

A variable is a symbol that represents a number. A variable can represent any number. In the algebraic expression 27 + b , b is a variable. Likewise, variables can appear in equations. In the algebraic equation 11×s = 22 , s is a variable. If we replace s with the number 2, the equation will be true, since 11×2 = 22 .

We use variables in algebraic expressions when the quantity of something is unknown. For example, if I want to talk about "Peter's monthly salary plus $200," but I do not know his monthly salary, I might write s + 200 , where s represents Peter's monthly salary in dollars. Or, if I want to say, "My book weighs three times as much as yours, plus 5 lbs. more," but I do not know how much your book weighs, I might write that my book weighs 3w + 5 , where w represents the weight of your book in pounds.

We also use variables to represent unknowns in algebraic equations. Consider the statement, "If Greg grows 2 inches, he will be 60 inches tall." This statement says that Greg's current height plus 2 inches is equal to 60 inches. We write h + 2 = 60 , where h represents Greg's current height.

Algebraic expressions and algebraic equations can contain more than one variable. For example, 2×(h + w) is an algebraic expression that contains two variables, h and w .