How to Apply the Order of Operations

Lengthy expressions really aren't that hard if you just do things one at a time and in the right order. The reason this exists is so mathematicians have a universal order. Otherwise you could have two different answers to a simple math problem like 2 x 3 + 4.

Steps

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    Perform any calculations inside the innermost parenthesis (or any other types of grouping symbols) first. Then progress outward.

    12 - 8 ÷ 4 + [(6 + 2) - 3]2•3

    12 - 8 ÷ 4 + [(8) - 3]2•3

    12 - 8 ÷ 4 + [5]2•3
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    Perform any exponents (roots count too).

    12 - 8 ÷ 4 + [5]2•3 12 - 8 ÷ 4 + 25•3
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    Perform any multiplications or divisions, going from left to right. 12 - 8 ÷ 4 + 25•3 12 - 2 + 75
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    Perform any additions or subtractions, going from left to right. 12 - 2 + 75 10 + 75 85

Tips

  • Remember PEMDAS: P stands for Parentheses, E stands for exponents, M stands for multiplication, D stands for division, A stands for addition, and S stands for subtraction. Also, remember that when you have simplified the expression and there are either only multiplication and division left or subtraction and addition left, be sure to then do the equation from left to right. Write "PEMDAS" at the top of the page you're simplifying the problems on to help you remember the order.
  • You can also remember this sentence: "Please Excuse My Dear Aunt Sally."
  • If you are just learning Order of Operations, there are a few things to know. Dots are considered multiplication, as well as a number by parenthesis 4(7+8). The same goes for division. It might look like a fraction with an equation on top and another on the bottom. This means to divide.

Article Info

Categories: Mathematics