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.

The Three Types of Big Four Expressions
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:

  1. Evaluate the multiplication and division from left to right.

  2. Evaluate the addition and subtraction from left to right.

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

image0.jpg

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:

image1.jpg

Now evaluate what you underlined from left to right:

image2.jpg

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

image3.jpg

Thus,

image4.jpg
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