[ kuh-myoo-tuh-tiv, kom-yuh-tey-tiv ]
/ kəˈmyu tə tɪv, ˈkɒm yəˌteɪ tɪv /


of or relating to commutation, exchange, substitution, or interchange.
  1. (of a binary operation) having the property that one term operating on a second is equal to the second operating on the first, as a × b = b × a.
  2. having reference to this property: commutative law for multiplication.

Nearby words

  1. communize,
  2. commutable,
  3. commutate,
  4. commutation,
  5. commutation ticket,
  6. commutative group,
  7. commutative law,
  8. commutator,
  9. commutator group,
  10. commute

Origin of commutative

1525–35; < Medieval Latin commūtātīvus, equivalent to Latin commūtāt(us) (past participle of commūtāre; see commute, -ate1) + -īvus -ive

Related forms Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

Examples from the Web for commutative

British Dictionary definitions for commutative


/ (kəˈmjuːtətɪv, ˈkɒmjʊˌteɪtɪv) /


relating to or involving substitution
maths logic
  1. (of an operator) giving the same result irrespective of the order of the arguments; thus disjunction and addition are commutative but implication and subtraction are not
  2. relating to this propertythe commutative law of addition
Derived Formscommutatively, adverb

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for commutative



1530s, from Medieval Latin commutativus, from Latin commutat-, past participle stem of commutare (see commute (v.)).

Online Etymology Dictionary, © 2010 Douglas Harper

Science definitions for commutative


[ kə-myōōtə-tĭv, kŏmyə-tā′tĭv ]

Of or relating to binary operations for which changing the order of the inputs does not change the result of the operation. For example, addition is commutative, since a + b = b + a for any two numbers a and b, while subtraction is not commutative, since a - ba - b unless both a and b are zero. See also associative distributive.
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.