Associative property

The associative property means that changing the grouping of the numbers used in an operation does not change the result of that operation. The associative property applies in both addition and multiplication, but not to division or subtraction.


associative property of addition


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

Examples

Ex 1
 6 + 3 + 7  =
 (6 + 3) + 7  =
 9 + 7  =  16
Ex 2
 6 + 3 + 7  =
 6 + (3 + 7)  =
 6 + 10  =  16

The associative property of addition is often written as:

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


associative property of multiplication


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

Examples

Ex 1
 4 × 2 × 5  =
 (4 × 2) × 5  =
 8 × 5  =  40
Ex 2
 4 × 2 × 5  =
 4 × (2 × 5)  =
 4 × 10  =  40

The associative property of multiplication is written as:

(a × b) × c = a × (b × c)