Order of Operations

Pronunciation: /ˈɔr.dər ʌv ˌɒpərˈeɪ.ʃənz/ Explain

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. McAdams, David E.. All Math Words Dictionary, order of operations. 2nd Classroom edition 20150108-4799968. pg 131. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 20. www.archive.org. International Textbook Company. January 1963. Last Accessed 9/5/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book

More Information

Cite this article as:

McAdams, David E. Order of Operations. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/o/orderofoperations.html.

Revision History

4/27/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/5/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
8/8/2007: Initial version. (McAdams, David E.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License