Pronunciation: /kəˈmjuːtteɪ.tɪv/ Explain
A binary operation
'*' is commutative if
a * b = b * a.
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.
- McAdams, David E.. All Math Words Dictionary, commutative. 2nd Classroom edition 20150108-4799968. pg 37. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Jones, Burton. Elementary Concepts of Mathematics. pp 31-34. 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.. 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 6/25/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n14/mode/1up/search/commutative. Buy the book
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 28-29. Thomson, Brooks/Cole. 2005. Last Accessed 6/25/2018. Buy the book
- McAdams, David E.. Commutative Property of Addition. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. https://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. https://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. https://www.allmathwords.org/en/c/commutative.html.
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.)