associative property


Definition of Associative Property


Associative Property of Addition

The problem (3 + 6) + 8 = 3 + (6 + 8) demonstrates the associative property of addition.

Observe that the addends are the same on either side of the equal sign: 3 plus 6 plus 8

The associative property of addition says that when we add more than two numbers the grouping of the addends does not change the sum.

In the example above, we can easily observe that:

(3 + 6) + 8                  =          3 + (6 + 8)

9 + 8                           =          3 + 14

17                                =          17

 
Notice that the SUM is the same no matter what way you group the addends.

In general, the associative property of addition can be written as:

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

 

Associative Property of Multiplication

The problem (2 × 4) × 3 = 2 × (4 × 3) demonstrates the associative property of multiplication.

Observe that the factors are the same on either side of the equal sign: 2 times 4 times 3

The associative property of multiplication says that when we multiply more than two numbers the grouping of the factors does not change the product.

In the example above, we can easily observe that:

(2 × 4) × 3                  =          2 × (4 × 3)

8 × 3                           =          2 × 12

24                                =          24

 
Notice that the PRODUCT is the same no matter what way you group the factors.
 
In general, the associative property of multiplication can be written as:

(a × b) × c = a × (b × c)

 
More about Associative Property
 
Associative property holds good for both addition and multiplication, but not for subtraction and division.