Remembering the Order of Operations

By Emma Davis

Edited by Ella Fasciano


Imagine a problem on your math test that asks you to simplify 5(3+4²/2). Overwhelming, right? It doesn’t have to be. Take a breath— it’s time to get reacquainted with the order of operations.


An easy way to remember the order of operations is through the acronym PEMDAS, often taught in school. It’s often remembered as “Please Excuse My Dear Aunt Sally,” but it stands for:

P - PARENTHESES

E - EXPONENTS

M - MULTIPLICATION

D - DIVISION

A - ADDITION

S - SUBTRACTION


This is the correct order to follow! Always focus on parentheses first, then exponents, then multiplication, then division, then addition, and finally, subtraction. What does this mean? Let’s see it in action.


5(3 + 4²/2)


Here we see the problem again. Time to break it down. First, we want to focus on the P- parentheses. This means that you always want to complete simplification WITHIN the parentheses first. So, you would be focusing on 3 + 4²/2 to begin. Don’t forget about the multiplying 5 though— we’ll come back to it later!

3 + 4²/2


Now that you’re focused on the expression within the parentheses, what do you do? We need to look at the E: exponents. You must evaluate numbers with exponents next— in this case, 4². 4² is 16, so the expression would become

3 + 16/2


Next in the acronym is multiplication, but within the parentheses, there was no multiplying. Thus, we move on to division. In this problem, you’ll be dividing 16 by 2, which is 8. The expression becomes


3 + 8


Now, we focus on addition. This is simple, just 3 + 8 = 11! There is no need to focus on subtraction, as there is no subtracting in the problem. However, we’re not done quite yet! Remember the multiplying 5 we pushed away in the beginning? Let’s bring that back.


5(11)


This 5 never actually disappeared, but we disregarded it to focus on what was within the parentheses, as this always comes first. Now that the expression within is simplified, we can multiply! In a different problem, if there were more operations outside the parentheses, make sure to follow the proper order (PEMDAS).


55


And you’re done! See how simple that was? I hope this served as a good refresher on the proper order of operations. Remember, PEMDAS!

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