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### Course: MAP Recommended Practice>Unit 44

Lesson 14: Order of operations

# Order of operations review

The order of operations are a set of rules for how to evaluate expressions. They make sure everyone gets to the same answer. Many people memorize the order of operations as PEMDAS (parentheses, exponents, multiplication/division, and addition/subtraction).
The order of operations are one set of agreements for how to evaluate expressions. They make sure everyone gets to the same value.
$\text{G}$rouping: We evaluate what's inside grouping symbols first, before anything else. For example, $2×\left(3+1\right)=2×4=8$.
Two common types of grouping symbols are parentheses and the fraction bar.
$\text{E}$xponents: We evaluate exponents before multiplying, dividing, adding, or subtracting. For example, $2×{3}^{2}=2×9=18$.
$\text{M}$ultiplication and $\text{D}$ivision: We multiply and divide before we add or subtract. For example, $1+4÷2=1+2=3$.
$\text{A}$ddition and $\text{S}$ubtraction: Lastly, we add and subtract.
Many people memorize the order of operations as $\text{G}\text{E}\left(\text{MD}\right)\left(\text{AS}\right)$ (pronounced as it's spelled), where the "G" is for grouping, the "E" is for exponents, and so on.
Important note: When we have more than one of the same type of operation, we work from left to right. This can matter when subtraction or division are on the left side of your expression, like $4-2+3$ or $4÷2\ast 3$ (see example 3 below to understand why this matters).

## Example 1

Evaluate $6×4+2×3$.
There are no parentheses or exponents, so we jump straight to multiplication and division.
$\phantom{=}6×4+2×3$
$=6×4+2×3$Multiply $6$ and $4$.
$=24+2×3$Multiply $2$ and $3$.
$=24+6$Add $24$ and $6$.
$=30$... and we're done!
Notice: We took care of all multiplication before doing the addition. If we had done $24+2$ before multiplying $2×3$, we would have gotten the wrong answer.

## Example 2

Evaluate ${6}^{2}-2\left(5+1+3\right)$.
$\phantom{=}{6}^{2}-2\left(5+1+3\right)$
$={6}^{2}-2\left(5+1+3\right)$Add $5+1+3$ inside the parentheses first.
$={6}^{2}-2\left(9\right)$Find ${6}^{2}$, which is $6\cdot 6=36$.
$=36-2\left(9\right)$Multiply $2$ and $9$.
$=36-18$Subtract $18$ from $36$.
$=18$... and we're done!

## Example 3

Evaluate $7-2+3$.
One correct way to do this is to work from left to right.
CorrectIncorrect
$\begin{array}{rl}& 7-2+3\\ \\ =& 5+3\\ \\ =& 8\end{array}$$\begin{array}{rl}& 7-2+3\\ \\ =& 7-5\\ \\ =& 2\end{array}$
Remember: Even though "A" comes before "S" in GE(MD)(AS), that doesn't mean we need to add before we subtract. Addition and subtraction are at the same "level" in the order of operations. The same is true of multiplication and division.

## Practice

Problem 1
$2+12÷2×3=$

Want to practice more problems like these? Check out this introductory exercise and these more challenging exercises: exercise one and exercise two.

## Want to join the conversation?

• the last question is absolutely wrong, the answer should be 12 because
-10 + 8 = -2
-2^2 = -4
8 - -4 = 12
• In the second step, there should be a parenthesis around the -2 (as it is the sum of -10 and +8 from the previous step). Because the negative sign is also included, -2 rather than +2 is squared. This results in +4. Here are the steps:
8 − (−10 + 8)^2
=8 - (-2)^2
=8 - 4
=4
Edit: fixed typos and added explanation.
• Is there another way to say PEMDAS?( it could be another word) I really don't like the sound of it...
• It's normally "Please excuse my dear Aunt Sally", even though I don't know what the aunt did. :D Hope this helped!
• A way to remember PEMDAS is "Please Excuse My Dear Aunt Sally"
Go Aunt Sally and all her arithmatic glory!
• ACTUALLY ITS SPEMDAS. slice pizzas except my dads awesome slice. the s is for substitution in algibra
(1 vote)
• what if its 25^10x12(50+12)
• I think you have to use a calculator.
First calculate (50+12). And calculate 25^10 with your calculator. Then we only have multiplication symbols. So, just calculate from left to right with your calculator.
• I don't understand when there is division then straight up multiplacation
• look like 20/5=? but we know our multiplication so we could say 4x5=20 so the missing number is 4 and 20/5=4
• What is the best way to solve a quotation with a exponent when the exponent is 3 or above? For example if the exponent of the number 2 is 3, should I do 2 times 2 which is 4 and then do 4 times 2 which equals 8 again? How am I suppose to do that with bigger exponents?
• Remember exponents are just a simpler way of multiplication where instead of saying 2*2*2, we can say 2^3, or in word form, two to the third power, so to answer question yes you could multiply 2*2=4, and then multiply 4*2=8.
(1 vote)
• apparently it's now PEDMAS my teacher told me that, I'm not quite sure though. I'm just a little confused weather its PEDMAS or PEMDAS but I guess it wouldn't really matter
• No its Please excuse my dear aunt sally
• : Deal with what's in the parentheses first. While working inside the parentheses, follow PEMDAS as well. So -(2^2+6)... first, I'm going to assume the "+6" is not part of the exponent. It's hard to tell with the way it is typed.
There are no more parentheses so inside the one set, we'll move to "E". 2^2 becomes 4. Now our expression looks like:
-(4+6)
There are no multiplication or division inside the parentheses so we'll move on the AS: 4+6 = 10 so now the expression looks like:
-(10…