# Applying Order of Operations to Mixed-Operator Expressions

Often an expression contains at least one addition or subtraction operator and at least one multiplication or division operator. These expressions are *mixed-operator expressions.* To evaluate them, you need some stronger medicine.

Expression | Example | Rule |
---|---|---|

Contains only addition and subtraction | 12 + 7 – 6 – 3 + 8 | Evaluate left to right. |

Contains only multiplication and division | 18 ÷ 3 x 7 ÷ 14 | Evaluate left to right. |

Mixed-operator expression: contains a combination of addition/subtraction and multiplication/division | 9 + 6 ÷ 3 | 1. Evaluate multiplication and division left to right. 2. Evaluate addition and subtraction left to right. |

Evaluate mixed-operator expressions as follows:

Evaluate the multiplication and division from left to right.

Evaluate the addition and subtraction from left to right.

For example, suppose you want to evaluate the following expression:

As you can see, this expression contains addition, multiplication, and division, so it’s a mixed-operator expression. To evaluate it, start by underlining the multiplication and division in the expression:

Now evaluate what you underlined from left to right:

At this point, you’re left with an expression that contains only addition, so you can evaluate it from left to right:

Thus,