# 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.

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

### References

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

McAdams, David E. Order of Operations. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://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.)