Please Excuse My Dear Aunt Sally
This sentence, also known as PEMDAS, is probably one of the most well-known mnemonic devices in math. PEMDAS refers to the order in which you perform mathematical operations. Perform the operations out of order and you will most surely get an incorrect answer that will sneakily be one of your answer choices on the exam. Don’t fall for it!
Always perform the operations in the following order:
- P stands for parenthesis. Anytime you have a parenthesis in a problem, knock that bad boy out first. Example: 6 + (3 * 8). Work inside the parenthesis first to get 6 + 24 = 30. If you just go left to right, then you will get an incorrect answer.
- E stands for exponents. Get that exponent solved before doing any operations outside of the parenthesis. The exception to the rule is, of course, if your exponent is inside your parenthesis. Then, you would have to work the exponent first to be able to work the parenthesis. Example (3⁴ + 10) – 15. First solve the exponent 3⁴, which equals 81, then work the parenthesis so (81 + 10) -15 = 76.
- M and D stand for multiplication and division. These two are grouped together because you work these in order of left to right after the first two steps. Sometimes you will have division come first and other times multiplication. Let’s look at two examples. For 1 + 10 ÷ 2 * 5, do the division first so 10 divided by 2 is 5, then 5 times 5 is 25. Last, add the 1 for an answer of 26.
- A and S stand for addition and subtraction. Same rules applies as step 3. Work addition and subtraction in order from left to right. For example, 5 – 2 * 6 + 3 would give us -4 as the answer, while 5 + 2 * 6 – 3 would yield 14 as the answer.
Order of Operations Examples
Work each step on a new line to avoid skipping a step. Your work will look like an upside down triangle when you reach your final answer.
The last example problem might lead some to believe that the answer was going to be zero. Watch out for tricky problems like that. As long as you work in the correct order though, you won’t have any trouble.
You give it a try!
What is (6 + 7) -11 * -3?