Variables and Expressions

After completing this lesson, you will be able to:

• Write mathematical expressions using verbal expressions
• Define variable and algebraic expression

In algebra, letters are often used to represent numbers. These are called variables. An algebraic expression is a mathematical statement which at least one number and at least one variable along with at least one arithmetic operation.

Example 1

Write an algebraic expression for the difference of x and 7.

The word difference means subtract, so the algebraic expression would be x - 7

This is an algebraic expression because it contains at least one number (7), at least one variable (x), and at least one arithmetic operation (subtraction).

Example 2

Write an algebraic expression for the number y added to 4 times the number x.

This would be written as y + 4x

The 4x means 4 times the number x

Example 3

Write an algebraic expression for the sum of twelve and the product of five and x.

The word sum means to add.

The word product means to multiply. Therefore, our algebraic expression would be 12 + 5x

Example 4

Write a verbal expression for z + 10.

This time, we are taking an algebraic expression and translating it to a verbal expression.

The term for + is sum. Therefore, we would write the sum of z and ten

Example 5

Write a verbal expression for 10xy. Since the only operation here is multiplication, we could write ten times x times y or we Could write times the product of x and y. Either expression is correct.

In the expression , 10 is called the base and 3 is called the exponent . The meaning of this expression is 10 · 10 · 10 . If you were asked to find the answer you would multiply 10 · 10 · 10 and get 1000. This is called evaluating the expression. The algebraic expression 4 · x · x · x · y · y could be written using exponents. The new expression would be . The algebraic expression 4 · 4 · x · y · y · y could be written using exponents. The new expression would be or it could also be written because is the same as 16.

Example 6

Evaluate the expression Evaluate simply means that we want to find an answer. Remember that means 2 · 2 · 2 · 2 · 2 . (It does not mean 2 times 5). Since 2 · 2 · 2 · 2 · 2 is 32, that is the answer.