Commutative Property (mathematics).

Commutative Property (mathematics). Commutative Property (mathematics), trait of mathematical operations that are independent of the order of the numbers or symbols involved. Addition, for example, is an operation that is commutative: The result of adding 4 + 2 is the same as that of adding 2 + 4. The commutative law of addition states that x + y = y + x for any choice of numbers x and y. Multiplication is also commutative. The commutative law for multiplication states that x × y = y × x for any two numbers x and y. This law implies that 576 × 873 is the same as 873 × 576 without the need of calculating the answer at all. The commutative property also applies to multiple instances of an operation. No matter how many numbers are successively added, the order does not matter. So for three numbers x, y, and z, the commutative law of addition holds that x + y + z, x + z + y, y + x + z, y + z + x, z + x + y, and z + y + x are all the same. Multiplication functions similarly, so x × y × z = x × z × y = y × x × z = y × z × x = z × x × y = z × y × x. Not all operations are commutative. Subtraction, for example, is not: 12 - 8 = 4, but 8 - 12 = -4. Division is also not commutative: 18/6 = 3, while 6/18 = ? . Arithmetic; Associative Property; Distributive Property. Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.