com·​mu·​ta·​tive | \ kə-ˈmyü-tə-tiv How to pronounce commutative (audio) , ˈkäm-yə-ˌtā-tiv How to pronounce commutative (audio) \

Definition of commutative

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 Like the quaternions, octonion multiplication is not commutative. Quanta Magazine, "The (Imaginary) Numbers at the Edge of Reality," 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, "New Number Systems Seek Their Lost Primes," 2 Mar. 2017 Notice this means that, unlike with the real and complex numbers, multiplication of quaternions is not commutative. Quanta Magazine, "The (Imaginary) Numbers at the Edge of Reality," 25 Oct. 2018

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'commutative.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

See More

First Known Use of commutative

1612, in the meaning defined at sense 1

Keep scrolling for more

Learn More about commutative

Time Traveler for commutative

Time Traveler

The first known use of commutative was in 1612

See more words from the same year

Statistics for commutative

Cite this Entry

“Commutative.” Dictionary, Merriam-Webster, Accessed 9 Jul. 2020.

Keep scrolling for more

More Definitions for commutative


com·​mu·​ta·​tive | \ ˈkä-myə-ˌtā-tiv How to pronounce commutative (audio) \

Kids Definition of commutative

: being a property of a mathematical operation (as addition or multiplication) in which the result does not depend on the order of the elements The commutative property of addition states that 1 + 2 and 2 + 1 will both have a sum of 3.

More from Merriam-Webster on commutative

Rhyming Dictionary: Words that rhyme with commutative

Britannica English: Translation of commutative for Arabic Speakers

Comments on commutative

What made you want to look up commutative? Please tell us where you read or heard it (including the quote, if possible).


See Definitions and Examples »

Get Word of the Day daily email!

Test Your Vocabulary

Words for Summer: A Quiz

  • a closeup of a sunflower
  • Which of the following words means “of or relating to summer”?
Spell It

Can you spell these 10 commonly misspelled words?

Bee Cubed

Test Your Knowledge - and learn some interesting things along the way.

Love words? Need even more definitions?

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