# Associative Property

The term “Associative” signifies the grouping of something. And the associative property interprets the multiplication of the numbers and the addition of the numbers by grouping.

## Examples

Here are a few of the examples for associative property:

Example 1: ( 9 * 2 ) * 1000 =  9 * ( 2 * 1000 )

Solution:

Here, on the left-hand side, we are given,

( 9 * 2 ) *1000

On solving this, we will get,

18000

Now, on the right-hand side, we are given,

9 * ( 2 * 1000)

On solving this, we will get,

18000

Example 2: ( 7 + 5 ) + 3 = 7 + ( 5 + 3 )
Solution:

Here, on the left-hand side, we are given,

( 7 + 5 ) + 3

On solving this, we will get,

15

Now, on the right-hand side, we are given,

7 + ( 5 + 3 )

On solving this, we will get,

15

According to the associative property of addition,

When ” a” is added to “b” and “c” , the result will be something always equal to when “b” and “c” is added to “a” , after shifting the places of the values. Shifting the values will not change the resulting values.

We can understand this more clearly by illustrating a few of the example:

Example 1: If this equation is given,

( 5 + 8 ) +100 =  5 + ( 8 + 100 )

Solution:

Here,

Left-hand side = 113

Now,

Right-hand side = 113

Therefore, the left-hand side = the right-hand side.

Example 2: If this equation is given,

( 9 + 1 ) + 200 = 9 + ( 1 + 200)

Solution:

Here,

Left-hand side = 210

Now,

Right-hand side = 210

Therefore, the left-hand side = the right-hand side.

## Associative Property for Multiplication

According to the associative property for multiplication,

( a*b )* 1=  a * ( b*1)

We can understand this more clearly by illustrating a few examples:

Example 1: If this equation is given,

( 3*6 ) * 300 = 3 * ( 6*300)

Solution:
Here,

Left-hand side = 5400

Now,

Right-hand side = 5400

Therefore, the left-hand side = the right-hand side.

Example 2: If this equation is given,

( 8*3 ) * 100 =  8* ( 3*100)

Solution:

Here,

Left-hand side = 2400

Now,

Right-hand side = 2400

Therefore, the left-hand side = the right-hand side.

## Commutative Property

Commutative property is only appropriate for multiplication and addition.  When we do the process of addition or do the process of multiplication, then if the direction of the values is alternated or switched to each other, the result of the processes will never shift or alter. This is interpreted as a commutative property.

The commutative property for the process of the addition can be:

z + v + j = v + j + z

p + u = u + p

The commutative property for the process of multiplication can be illustrated by ;

d * h * j = j * h * d

x * k * y * I = I * x * y * k

l * m * n = n * m * l

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