What is a definition for the associative property of multiplication and how you would use it to compute 4 times 25 times 27 mentally?

Answer 1

The addition or multiplication of a set of numbers is the same regardless of how the numbers are grouped. The associative property will involve 3 or more numbers. The parenthesis indicates the terms that are considered one unit.The groupings (Associative Property) are within the parenthesis. Hence, the numbers are 'associated' together. In multiplication, the product is always the same regardless of their grouping. The Associative Property is pretty basic to computational strategies. Remember, the groupings in the brackets are always done first, this is part of the order of operations.

When we change the groupings of addends, the sum does not change:

(2 + 5) + 4 = 11 or 2 + (5 + 4) = 11

(9 + 3) + 4 = 16 or 9 + (3 + 4) = 16

Just remember that when the grouping of addends changes, the sum remains the same.

Multiplication Example

When we change the groupings of factors, the product does not change:

(3 x 2) x 4 = 24 or 3 x (2 x 4) = 24.

Just remember that when the grouping of factors changes, the product remains the same.

Think Grouping! Changing the grouping of addends does not change the sum, changing the groupings of factors, does not change the product.

*** 4x(25x27) = (4x25)x27***