Meaning & use
commutative
Last updated
Meaning
adjectivenot comparabletechnicalmathematics
Of a mathematical operation: giving the same result when the order of the two elements is changed.
Grammar: Not used in comparative forms; you say an operation is commutative or not commutative.
Patterns
- commutative operation
- commutative property
- commutative law
Addition of real numbers is commutative: 2 + 3 = 3 + 2.
Subtraction is not commutative, because 5 − 3 is not the same as 3 − 5.
The commutative property does not hold for matrix multiplication.
Common combinations
- commutative property
- The commutative property lets you swap the numbers in addition.
- commutative operation
- Is multiplication a commutative operation?
- commutative law
- The commutative law applies to addition but not subtraction.
- not commutative
- Division is not commutative.
Synonyms and how they differ
- abelian
- Abelian is used mainly for groups and means the same as commutative, but it is more advanced and specific to group theory.
Opposites
Word family
- commute verb
- In mathematics, to change the order of elements in an operation.
- commutativity noun
- The property of being commutative.
Commonly confused: commutative or associative? commutative or commutable?
commutative vs associative
Associative concerns grouping: (a + b) + c = a + (b + c). Commutative concerns order: a + b = b + a.
commutative vs commutable
Commutable means able to be exchanged or reduced (e.g. a commutable sentence), not a mathematical property.
Practice
Which of these operations is commutative?
Choose one answer.
Addition is commutative because a + b = b + a for all real numbers. Subtraction and division are not commutative, and matrix multiplication is a well-known noncommutative operation.
Make it your own
Write a sentence using “commutative”, then check it and compare it with the examples above.