## Associative Property Definition

A Property of addition or multiplication in which the altering grouping of the addends or factors does not affect the result of the operations. The associative property of addition and multiplication are as follows.

**Definition of addition in associative property:**

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

Here the brackets are rearranged but the addition result is not affected

** Definition of multiplication in associative property**:

(ab) c = a (bc)

Here the brackets are rearranged but the product result is not affected

## Model Problems

**For associative property of addition:**

** Example: 1**

- (11+12)+13= 11+(12+13)

**Solution:**

L.H.S = (11+12) +13

Here first 11 and 12 are added and then we add 13

= 23+13

= 36

R.H.S = 11+ (12+13)

Here first 12 and 13 are added and then we add 11

= 11+ (25)

= 36

L.H.S= R.H.S

here both sides are equal , by definition of associative property , we can say that associative property for addition is true

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2.(13+14)+15= 13+(14+15)

**Solution:**

L.H.S = (13+14) +15

Here first 13 and 14 are added and then we add 145

= 27+15

= 42

R.H.S = 13+ (14+15)

Here first 14 and 15 are added and then we add 13

= 13+ (29)

= 42

L.H.S= R.H.S

here both sides are equal , by definition of associative property , we can say that associative property for addition is true

From these two examples we can conclude that associative property is true for the addition

## Model problems:

**For associative property of multiplication:**

**Example: 1**

- (11*12)*13= 11*(12*13)

**Solution:**

L.H.S = (11*12) *13

Here first 11 and 12 are multiplied and then we multiply 13

= 132*13

= 1716

R.H.S = 11* (12*13)

Here first 12 and 13 are multiplied and then we multiply 11

= 11* (156)

= 1716

L.H.S= R.H.S

here both sides are equal , by definition of associative property , we can say that associative property for multiplication is true

2.(13*14)*15= 13*(14*15)

**Solution: **

L.H.S = (13*14) *15

Here first 13 and 14 are multiplied and then we multiply 15

= 182*15

= 2730

R.H.S = 13* (14*15)

Here first 14 and 15 are multiplied and then we multiply 13

= 13* (210)

= 2730

L.H.S= R.H.S

here both sides are equal , by definition of associative property , we can say that associative property for multiplication is true

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From these two examples we can conclude that associative property is true for the multiplication