# Associative

Pronunciation: /əˈsoʊ.siˌeɪ.tɪv/ Explain

A binary operation '*' is associative if, for all values of a, b, and c; a * (b * c) = (a * b) * c.[2]

Some binary operations that are associative are:

• Addition: a + (b + c) = (a + b) + c.
• Multiplication: <a(bc) = (ab)c.

A binary operation that is not associative is:

• Subtraction: a - (b - c) ≠ (a - b) - c.

### References

1. McAdams, David E.. All Math Words Dictionary, associative. 2nd Classroom edition 20150108-4799968. pg 21. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically. 2nd edition. pg 5. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 6/12/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n14/mode/1up/search/associative. Buy the book
3. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 28-29. Thomson, Brooks/Cole. 2005. Last Accessed 6/12/2018. Buy the book

### More Information

• McAdams, David E.. Associative Property of Addition. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. http://www.allmathwords.org/en/a/associativeaddition.html.
• McAdams, David E.. Associative Property of Multiplication. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. http://www.allmathwords.org/en/a/associativemultiplication.html.

### Cite this article as:

McAdams, David E. Associative. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/associative.html.

### Revision History

4/12/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/15/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
1/7/2010: Added "References". (McAdams, David E.)
4/24/2008: Added 'Associative Property of Multiplication' to More Information. (McAdams, David E.)
4/22/2008: Initial version. (McAdams, David E.)

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