# Associative Property – Definition with Examples

» Associative Property – Definition with Examples

## What is Associative Property?

This property states that when three or more numbers are added (or multiplied), the sum (or the product) is the same regardless of the grouping of the addends (or the multiplicands).

• Grouping means the use of parentheses or brackets to group numbers.
• Associative property involves 3 or more numbers.
• The numbers that are grouped within a parenthesis or bracket become one unit.
• Associative property can only be used with addition and multiplication and not with subtraction or division.

## Examples of Associative Property for Multiplication

The above examples indicate that changing the grouping doesn’t change the answer in any way.

The associative property is helpful while adding or multiplying multiple numbers. By grouping, we can create smaller components to solve. It makes the addition or multiplication of multiple numbers easier and faster.

## Why Associative Property Doesn’t Work for Subtraction & Division

17 + 5 + 3 = (17 + 3) + 5

= 20 + 5

= 25

Here, adding 17 and 3 gives 20. Then, adding 5 to 20 gives 25. The grouping helped us get to the answer quickly and easily.

Example Multiplication:

3 × 4 × 25 = (25 × 4) × 3

= 100 × 3

= 300

Here, multiplying 25 by 4 gives 100. Then, 3 can be easily multiplied by 100 to get 300. However, we cannot apply the associative property to subtraction or division. When we change the grouping of numbers in subtraction or division, it changes the answer, and hence, this property is not applicable.

Example Subtraction:

10 – (5 – 2) = 10 – 3 = 7

(10 – 5) – 2 = 5 – 2 = 3

So, 10 – (5 – 2) ≠ (10 – 5) – 2

Example Division:

(24 ÷ 4) ÷ 2 = 6 ÷ 2 = 3

24 ÷ (4 ÷ 2) = 24 ÷ 2 = 12

So, (24 ÷ 4) ÷ 2 ≠ 24 ÷ (4 ÷ 2)   