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The associative property

Like the communicative property discussed previously, the associative property is a property applicable to both addition and multiplication. As the name of the property suggests, the concept involves "associating" terms with specific other terms by means of a proper application of parentheses. In the case of addition, we can illustrate the associative property by writing x + (y + z) = (x + y) + z. In other words, regardless of how we group the terms with the parentheses, the sum will always be the same. For example 1 + (2 + 3) = (1 + 2) + 3. In both cases, regardless of how we group the integers, the sum is 6.

The associative property is also operative in the case of multiplication. We write this by writing x(yx) = (xy)z. Both methods of grouping the terms in the equation give us the same product.