LESSON: Variables and Expressions

READ: Evaluating Variable Expressions

Evaluating Variable Expressions

What is a variable? A variable is a letter that is used to represent an unknown quantity. Often we use $x$ or $y$ to represent the unknown quantity, but any letter can be used as a variable.

Here are some examples of variables.

$a$

$b$

$c$

Notice that the variables here are all lowercase letters. This is often the case with variables.

A variable can be used in any variable expression. A variable expression is an expression with one or more operations that has variables but no equals sign. We can evaluate different variable expressions when we have a given value for the variable.

Example 1

Evaluate $5+a$ , when $a = 18$ .

Here we are going to substitute our given value for the variable. In this case, we substitute 18 in for $a$ and then add.

$& 5 + 18\ & 23$

Our answer is 23.

We can evaluate any variable expression as long as we have been given a value for the variable.

Example 2

Evaluate $b-22$ when $b$ is 40.

Next, we complete the subtraction by substituting our given value 40 into the expression for $b$ .

$& 40 - 22 \ & 18$

Our answer is 18.

Example 3

Evaluate $7x$ when $x$ is 12.

This is a multiplication problem. We substitute our given value in for $x$ and then multiply.

$& 7(12)\ & 84$

Example 4

Evaluate $\frac{14}{x}$ when $x$ is 2.

Here we have a fraction bar which tells us that this is a division problem. We substitute the given value in for $x$ and divide.

$\frac{14}{2} = 7$

Example 5

Evaluate $6a+b$ when $a$ is 4 and $b$ is 5.

First, of all, you can see that there are two variables in this expression. There are also two operations here. The first one is multiplication $6a$ lets us know that we are going to multiply 6 times the value of $a$ . The second one is addition show by the $+ \ b$ letting us know that we are going to add the value of $b$ . We have also been given the values of $a$ and $b$ , we substitute the given values for each variable into the expression and evaluate it.

$& 6(4)+5\ & 24+5\ & 29$

Our answer is 29. Notice that we used the order of operations when working through this problem.Whenever we are evaluating expressions with more than one operation in it, always refer back and use the order of operations.