Commutative property

property of binary operations, for which changing the order of the operands does not change the result

The commutative property says that the order of the numbers when adding or multiplying can be changed without changing the answer. For example, both and are equal to 10, and both and are equal to 35. This can be done with any numbers, or with more than two numbers.



The definition of commutative property of addition is  . a and b are variables and can be any number.

Some operations like dividing are not commutative. For instance,   is 2, but   is  . Subtraction is not commutative either:   is 4, but   is negative 4.

Higher mathematics


In higher mathematics like calculus, there are other commutative operations besides adding and multiplying. Commutative property must hold for each two elements of an Abelian group.