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.
|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: