Order of Operations

Pronunciation: /ˈɔr dər ʌv ˌɒ pəˈreɪ ʃənz/ ?

The order of operations is the order in which arithmetic operations are performed. If the order of operations was not set by convention the value of 3 + 2·5 could be evaluated as (3 + 2)·5 = 25 or 3 + (2·5) = 13.

The order of operations established by mathematicians is:

  1. Evaluate all expressions inside parenthesis. This includes functions.
  2. Simplify terms with exponents.
  3. Multiply and divide from left to right.
  4. Add and subtract from left to right.

Mnemonic What is a mnemonic?

Please excuse my dear Aunt Sally.

Please stands for parenthesis.
excuse stands for exponents.
my dear stands for multiplication and division.
Aunt Sally stands for addition and subtraction.


  1. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pg 20. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.

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Cite this article as:

Order of Operations. 2007-08-08. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/o/orderofoperations.html.


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2007-08-08: Initial version (McAdams, David.)

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