commutative

adjective

com·​mu·​ta·​tive kə-ˈmyü-tə-tiv How to pronounce commutative (audio) ˈkäm-yə-ˌtā-tiv How to pronounce commutative (audio)
1
: of, relating to, or showing commutation
2
: of, relating to, having, or being the property that a given mathematical operation and set have when the result obtained using any two elements of the set with the operation does not differ with the order in which the elements are used
a commutative group
addition of the positive integers is commutative

Examples of commutative in a Sentence

Recent Examples on the Web
Examples are automatically compiled from online sources to show current usage. Read More Opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback.
Those of justice, the habit of treating others fairly and with respect, include honesty, gratitude, and what is called commutative justice, which is the habit of fairness in exchange. Andrew Abela, Forbes.com, 3 May 2025 What if, through the commutative property, the man is basically the child at seven? Joshua Rothman, The New Yorker, 3 Dec. 2024 These subgroups retain some of the most useful properties of commutativity, without forcing the entire group to be commutative. Leila Sloman, WIRED, 6 Oct. 2024 In a commutative group, all subgroups are normal, but this isn’t always true more generally. Leila Sloman, WIRED, 6 Oct. 2024 The effects are commutative: the benefits of exercise compound when done on a daily basis. Marie Bladt, Vogue, 10 Sep. 2024 Rearranging the roots in this way preserves the algebraic relationship between them: The equation is still true because multiplication and addition are commutative, meaning that swapping the order of things — like shuffling the roots around — doesn’t change the answer. Quanta Magazine, 3 Aug. 2021 Addition of ordinary numbers is commutative, as is multiplication, and this is very helpful for simplifying computations. Eugenia Cheng, WSJ, 30 June 2022 Like the quaternions, octonion multiplication is not commutative. Quanta Magazine, 25 Oct. 2018

Word History

First Known Use

1612, in the meaning defined at sense 1

Time Traveler
The first known use of commutative was in 1612

Cite this Entry

“Commutative.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/commutative. Accessed 20 May. 2025.

Kids Definition

commutative

adjective
com·​mu·​ta·​tive ˈkäm-yə-ˌtāt-iv How to pronounce commutative (audio) kə-ˈmyüt-ət-iv How to pronounce commutative (audio)
: of, relating to, having, or being the property of giving the same mathematical result no matter in which order two numbers are used with an operation
addition is commutative because a + b = b + a
commutativity
kə-ˌmyüt-ə-ˈtiv-ət-ē
ˌkäm-yə-tə-
noun
Last Updated: - Updated example sentences
Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!