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Order of Operations: Comprehensive Examples

This page is a review of everything you've learned about order of operations. The following two examples are longer than the examples on the previous pages.

Here's what you've learned about order of operations:

* Go from left to right and do any equations that are inside parentheses.

* Start again from the left and go from left to right and do any multiplication and division equations.

* Start again from the left and go from left to right and do any addition and subtraction equations.


Here's an example:

(5 - 3) + 9 × (11 - 10)

Going from left to right, we see 5 - 3 inside parentheses. 5 - 3 = 2. So, our equation becomes:

2 + 9 × (11 - 10)

Again, starting from left to right, we see 11 - 10 inside parentheses. 11 - 10 = 1. So, our equation becomes:

2 + 9 × 1

Again, we start from the left and go from left to right. The + sign is not multiplication or division. The 9 is not multiplication or division. The × sign is multiplication. So, 9 × 1 = 9 and our equations becomes:

2 + 9

which equals 11.


Here's another example:

10 ÷ (12 ÷ 6) + 6 - 3

Going from left to right, we see 12 ÷ 6 inside parentheses. 12 ÷ 6 = 2. So, our equation becomes:

10 ÷ 2 + 6 - 3

Again, we start from the left and go from left to right. The / sign is division. 10 ÷ 2 = 5. So, our equation becomes:

5 + 6 - 3.

Again, we start from the left and go from left to right. The + sign and the - sign are neither multiplication nor division. 5 + 6 = 11. So, our equation becomes:

11 - 3

which equals 8.

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