Associative Property (mathematics).

Associative Property (mathematics). Associative Property (mathematics), trait of mathematical operations that are independent of grouping applied to the numbers involved. Grouping symbols such as parentheses () appear in expressions and equations to indicate that the operation within the parentheses should be performed first. The operation of addition, for example, is associative because the value of 7 + (1 + 5) is the same as that of (7 + 1) + 5 or (7 + 1 + 5). Stated more generally as the associative law of addition, x + (y + z) = (x + y) + z for all numbers x, y, and z. The same property applies to multiplication: x(yz) = (xy)z for all numbers x, y, and z. Thus 2(3 × 4) and (2 × 3)4 both equal 24. If the associative property applies to an operation, it applies to an unlimited number of instances of that operation. No matter what grouping symbols are applied to the expression w + x + y + z, the answer will be the same. Not all operations are associative. Subtraction is not: 9 - (6 - 4) ? (does not equal) (9 - 6) - 4. The first expression equals 7, while the second equals -1. Division is also not associative: 24/(2/3) = 36 while (24/2)/3 = 4. Arithmetic; Commutative Property; Distributive Property. Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.