Title: LESSON: Variables and Expressions
Course: Mathematics Essentials Q1 > Section: Week 2

Variables and Expressions

INTRODUCTION

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 or to represent the unknown quantity, but any letter can be used as a variable.

Here are some examples of variables.

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 , when .

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

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 when is 40.

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

Our answer is 18.

Example 3

Evaluate when is 12.

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

Example 4

Evaluate when is 2.

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

Example 5

Evaluate when is 4 and 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 lets us know that we are going to multiply 6 times the value of . The second one is addition show by the letting us know that we are going to add the value of . We have also been given the values of and , we substitute the given values for each variable into the expression and evaluate it.

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.

Order of Operations

P - parentheses

E - exponents

MD - multiplication and division in order from left to right

AS - addition and subtraction in order from left to right

Example 6

Evaluate when is 7 and is 11.

First, we substitute the given values in for the variables.

Our answer is 38.

Example 7

Evaluate when is 4, is 3, is 10 and is 6.

We work on this one in the same way as the other examples. Begin by substituting the given values in for the variables.

We have two multiplication problems here and one addition. Next, we follow the order of operations to evaluate the expression.

Our answer is 72

WATCH: Evaluating Algebraic Expressions

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

EXAMPLE 4

CHECK Yourself! Evaluating Expressions