commutative

adjective

com·​mu·​ta·​tive kə-ˈmyü-tə-tiv  ˈkäm-yə-ˌtā-tiv 

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

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

The elements of class groups must obey the associative and commutative properties of addition, and must include a zero element, such that zero plus any other element leaves the element unchanged. —Kevin Hartnett, Quanta Magazine, 2 Mar. 2017

Word History

First Known Use

1612, in the meaning defined at sense 1

Rhymes for commutative

• allocative
• appellative
• connotative
• copulative
• degradative
• dissipative
• educative
• exudative
• facultative
• imitative
• infiltrative
• innovative

Kids Definition

commutative

adjective

com·​mu·​ta·​tive ˈkäm-yə-ˌtāt-iv  kə-ˈmyüt-ət-iv 

: 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