Commutative
Pronunciation: /kəˈmjuːtteɪ.tɪv/ Explain
A binary operation
'*' is commutative if
a * b = b * a.^{[2]}
In this example, '*' can represent any binary operation.
Some binary operations that are commutative are:
Some binary operations that are not commutative are:
Figure 1  Commutative Property of a Binary Operator 

One way to remember 'commutative' is to use the root word, 'commute'. Commute
means to travel from one place to another, such as commuting to work. So in a binary
operation that is commutative, the variable 'a' commutes to where the
'b' was, and the variable 'b' commutes to where the 'a' was.

References
 McAdams, David E.. All Math Words Dictionary, commutative. 2nd Classroom edition 201501084799968. pg 37. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Jones, Burton. Elementary Concepts of Mathematics. pp 3134. www.archive.org. MacMillan and Company. 1947. Last Accessed 6/25/2018. http://www.archive.org/stream/elementaryconcep029487mbp#page/n52/mode/1up/search/commutative. Buy the book
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 2. www.archive.org. International Textbook Company. January 1963. Last Accessed 6/25/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
 Fine, Henry B., Ph. D.. NumberSystem of Algebra Treated Theoretically and Historically. 2nd edition. pg 5. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 6/25/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920pdf#page/n14/mode/1up/search/commutative. Buy the book
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 2829. Thomson, Brooks/Cole. 2005. Last Accessed 6/25/2018. Buy the book
More Information
 McAdams, David E.. Commutative Property of Addition. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/c/commuteadd.html.
 David E. McAdams. Commutative Property of Multiplication. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/c/commutemult.html.
Cite this article as:
McAdams, David E. Commutative. 4/14/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/commutative.html.
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Revision History
4/14/2019: Updated equations and expressions to new format. (
McAdams, David E.)
3/6/2019: Added vocabulary links. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (
McAdams, David E.)
1/15/2010: Added "References". (
McAdams, David E.)
7/7/2008: Added example. (
McAdams, David E.)
4/22/2008: Initial version. (
McAdams, David E.)