How to Apply the Order of Operations

Co-authored by David Jia

Last Updated: September 8, 2024 Fact Checked

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.The order of operations gives us instructions on how to simplify expressions that contain more than one operation.

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Then progress outward.^{[1]
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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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12 - 8 ÷ 4 + [5]²•312 - 8 ÷ 4 + 25•3

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What does the term BODMAS mean?

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BODMAS stands for Brackets, Order, Division, Multiplication, Addition, and Subtraction. Like PEMDAS, it is an abbreviation for the order of operations. In this case, Brackets stand for Parentheses; Order stands for Exponents (as in Order of Powers).

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Why did you subtract first in 12 - 2 + 75?

Donagan

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When adding and subtracting (or multiplying and dividing) it's customary -- but not mandatory -- to work from left to right.

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How did you arrive at 25?

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Twenty-five came from 5 squared, or 5x5. The 5 came from 8-3, and the 8 came from 6+2.

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You can also remember this sentence: "Please Excuse My Dear Aunt Sally."^{[5]
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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.

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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.

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