Test Prep Thursday: Order of Operations

Please Excuse My Dear Aunt Sally

This is a common mnemonic device for remembering PEMDAS, the acronym for order of operations (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). According to PEMDAS, solving equations should follow the following steps in order:

1. Simplify all expressions contained within parentheses.
2. Simplify all expressions involving exponents.
3. Perform all multiplication and division as it arises from left to right.
4. Perform all addition and subtraction as it arises from left to right.

If there are multiple groupings in a problem, apply the same steps within each grouping. For example, when faced with the following problem, what is the first step?

(30 - 2 x 10) + 4(2³ – 15 ÷ 3) = ___

There are two parenthetical expressions we need to resolve before we tackle the rest problem. Remember: we need to abide by PEMDAS within each parenthesis. So, for the first, we multiply 2 x 10 before subtracting, which gives us 30 – 20 = 10. For the second parentheses, we evaluate the exponent first, which means we get 2³ = 2 x 2 x 2 = 8. Then, we divide 15 by 3, before finally subtracting the two numbers (8 – 15 ÷ 3 = 8 – 5 = 3). Now that we’ve evaluated the parentheses, we can move on the rest of the problem. All we’re left with is 10 + 4(3) = 10 + 12 = 22!

Feeling confident now? Let’s give PEMDAS a try. See if you can solve the problems below:

1. -2(3-1) + 4 x 3 – 2 = ___
2. 12² _­+ 4 x 7 = ___
3. (40 – 18 x 2)³ ÷ 2 – 5 = ___
4. 20 + 3[8² + 5(200 x 4 - 2⁵) – 11] = ___

Make sure to check back next Thursday when we reveal the answers and explain how to solve these tricky equations!