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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.
Grouping: We evaluate what's inside grouping symbols first, before anything else. For example, 2×(3+1)=2×4=8.
Two common types of grouping symbols are parentheses and the fraction bar.
Exponents: We evaluate exponents before multiplying, dividing, adding, or subtracting. For example, 2×32=2×9=18.
Multiplication and Division: We multiply and divide before we add or subtract. For example, 1+4÷2=1+2=3.
Addition and Subtraction: Lastly, we add and subtract.
Many people memorize the order of operations as GE(MD)(AS) (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 42+3 or 4÷23 (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.
=6×4+2×3Multiply 6 and 4.
=24+2×3Multiply 2 and 3.
=24+6Add 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 622(5+1+3).
=622(5+1+3)Add 5+1+3 inside the parentheses first.
=622(9)Find 62, which is 66=36.
=362(9)Multiply 2 and 9.
=3618Subtract 18 from 36.
=18... and we're done!

Example 3

Evaluate 72+3.
One correct way to do this is to work from left to right.
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.
Want to learn more about order of operations? Check out this video.


Problem 1
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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

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