Order of Operations Explained

Apr 17, 2023 | Oquirrh

Imagine this: You’re scrolling through Facebook, and a friend has shared one of those simple “Are you as smart as a 5th grader?” challenges.

4 + 3 x 2

It may look easy, but the answers in the comments are far from unanimous, being equally split between two answers: 14 or 10.

Some people are performing the operations as 4 + 3 = 7, then 7 x 2 = 14

Others are performing the operations as 3 x 2 = 6, then 4 + 6 = 10

Which is the right answer?

Mathematical problems with multiple operations follow an order. This order makes the math easy and reliable so that everyone will evaluate it the exact same way. Known as the order of operations, it allows us to tackle many different operations that may show up together in a single mathematical problem. An easy way to remember this rule is with PEMDAS.

P = Parentheses (this could also be Brackets) E = Exponents M = Multiplication D = Division A = Addition S = Subtraction

The PEMDAS rule reminds us to always start by solving the part of the equation in parentheses, working from the innermost parenthesis outward. Next tackle the exponents. After that, solve the multiplication and division operations, working left to right. Finally, solve the addition and subtraction operations, working left to right. One way to remember the PEMDAS rule, including solving left to right, is with “Please Excuse My Dear Aunt Sally and Let her Rest.”

Let’s practice together with an example:

2 + 3(8 - 6)

  1. Begin with the innermost parentheses: 8 - 6 = 2 We now have 2 + 3(2)
  2. Having solved what was in the parentheses, and having no exponents, our next step is to multiply 3(2), or 3 x 2 = 6, giving us: 2 + 6
  3. Our final step is the addition of 2 + 6, giving us our answer!

Answer: 8

Once you know the PEMDAS rule, you can use it to evaluate any expression with multiple operations! By the way, the correct answer to your friend’s Facebook math problem in the example at the top of this post is 10. Did you get it right?

Practice evaluating expressions using the order of operations PEMDAS rule with some sample problems on our free downloadable practice page and answer key below. Practicing this concept (and others) is the very best way to become comfortable and proficient in math. Once you’ve mastered one concept, the new material you encounter in middle school and high school will feel like a natural extension of what you’ve already learned, making new concepts that much easier.

Click here to download the PEMDAS Order of Operations practice sheet.

Click here to download the PEMDAS Order of Operations answer key.

We invite parents and adults to do these practice exercises with their children. As with reading, children who see adult role models doing math on a regular basis are more likely to be comfortable doing math themselves. (Adults may want to check their mastery as well. You would be surprised at how easy it is to lose the knowledge learned in school when you’re no longer practicing it every day!)

Check back here regularly for more math mastery tips to help elementary school, middle school, and high school students gain math understanding. With understanding comes passion, and with passion comes growth — a treasure is unlocked!