# 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

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!