Associative Property

In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. Addition and multiplication of real numbers are associative operations.

For any real numbers a, b, and c:

\begin{align} (a+b)+c &= a+(b+c) \\ \\ (a\times b) \times c &= a\times (b\times c) \\ \end{align}

If a binary operation is associative, repeated application of the operation produces the same result regardless of how valid pairs of parentheses are inserted in the expression. This is called the generalized associative law.

Associativity is not the same as commutativity, which addresses whether the order of two operands affects the result.

See also: