How to Apply the Order of Operations

Last Updated: February 17, 2023

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.

Steps

1
Perform any calculations inside the innermost parenthesis (or any other types of grouping symbols) first. Then progress outward.^{[1]
X
Research source}

12 - 8 ÷ 4 + [(6 + 2) - 3]²•3

12 - 8 ÷ 4 + [(8) - 3]²•3

12 - 8 ÷ 4 + [5]²•3
2
Perform any exponents (roots count too).^{[2]
X
Research source}

12 - 8 ÷ 4 + [5]²•312 - 8 ÷ 4 + 25•3

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3
Perform any multiplications or divisions, going from left to right.^{[3]
X
Research source}12 - 8 ÷ 4 + 25•312 - 2 + 75
4
Perform any additions or subtractions, going from left to right.^{[4]
X
Research source}12 - 2 + 7510 + 7585

Community Q&A

Question

What does the term BODMAS mean?

Technist

Community Answer

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).
Question

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

Donagan

Top Answerer

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

How did you arrive at 25?

Community Answer

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