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[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.
1525-35; < Medieval Latin commūtātīvus, equivalent to Latin commūtāt(us) (past participle of commūtāre; see commute, -ate1) + -īvus -ive
Related forms
commutatively, adverb
commutativity, noun
noncommutative, adjective
uncommutative, adjective
uncommutatively, adverb
uncommutativeness, noun Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the web for commutative
  • In arithmetic, operations are interchangeable if they are commutative.
  • All anybody needs to know about mathematics is that the commutative property of addition exists only in the human imagination.
  • Students are able to recognize and use the commutative property of addition and multiplication.
  • Identifies symbolic representations of the commutative property.
  • Addition and multiplication are commutative, while subtraction is not.
  • Products are sorted into a canonical order using the commutative law.
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 property: the commutative law of addition
Derived Forms
commutatively, 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
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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
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commutative in Science
  (kə-my'tə-tĭv, kŏm'yə-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 - b ` a - b unless both a and b are zero. See also associative, distributive.

The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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