# commutative

com·​mu·​ta·​tive
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 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 Notice this means that, unlike with the real and complex numbers, multiplication of quaternions is not commutative. Quanta Magazine, 25 Oct. 2018

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'commutative.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

First Known Use

1612, in the meaning defined at sense 1

Time Traveler
The first known use of commutative was in 1612

commutative

## Cite this Entry

“Commutative.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/commutative. Accessed 25 May. 2024.

## Kids Definition

commutative

com·​mu·​ta·​tive
: 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

## More from Merriam-Webster on commutative

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