# Associative property

The associative property states that changing the grouping of the numbers used in the operations of addition or multiplication does not affect the result. The associative property does not apply to the operations of division or subtraction.

## Associative property of addition

The associative property of addition states that when adding three or more numbers, the way the numbers are grouped will not change the result. The sum will remain the same.

(a + b) + c = a + (b + c)

Example

Show that (6 + 3) + 7 = 6 + (3 + 7).

(6 + 3) + 7 = 6 + (3 + 7)

(9) + 7 = 6 + (10)

16 = 16

One way to visualize the associative property of addition is through use of groupings of different colored objects.

No matter how the colored stars are grouped in an addition problem, the total number of stars remain the same.

## Associative property of multiplication

The associative property of multiplication states that when multiplying three or more numbers, the way the numbers are grouped will not change the result. The product will remain the same.

a × (b × c) = (a × b) × c

Example

Show that 4 × (2 × 5) = (4 × 2) × 5.

4 × (2 × 5) = (4 × 2) × 5

4 × (10) = (8) × 5

40 = 40