# Associative property

If a, b and c are three whole numbers, then

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

In other words, in the addition of whole numbers, the sum does not

change even if the grouping is changed.

 For any three whole numbers a, b and c, a + (b + c) = (a + b) + c This is called the Associative-Property of Addition for the set of W.

Some solved examples :

1) (15 + 27) + 18 = 15 + (27 + 18)

(42) + 18 = 15 + (45)

60 = 60

2) (3 + 6) + 1 = 3 + (6 + 1)

(9) + 1 = 3 + (7)

10 = 10

3) 36 + 94 + 6

= 36 + ( 94 + 6 )

= 36 + 100

= 100

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Consider the following example

(12 - 4) - 3 = 8 - 3 = 5

12 - ( 4 - 3)= 12 - 1 = 11

Hence (12 - 4) - 3 ≠ 12 - ( 4 - 3)

If a, b and c are whole numbers, then (a - b) - c is not equal to a - ( b - c)

So the associative-property does not hold true for subtraction.

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Associative-property for multiplication:

If a , b and c are whole numbers then

a x ( b x c ) = (a x b ) x c

 For any two elements of the set W, a, b and c a x ( b x c ) = (a x b ) x c This is called the Associative-Property of Multiplication for the set of W.
Examples :

1) 3 x ( 4 x 6) = (3 x 4 ) x 6

3 x ( 24) = (12) x 6

72 = 72

2) 12 x 20 x 5

= 12 x ( 20 x 5)

= 12 x 100

= 1200

Associative-property of division :

( 81 ÷ 9) ÷ 3 = 3

81 ÷ ( 9 ÷ 3) = 27

Hence, ( 81 ÷ 9) ÷ 3 ≠ 81 ÷ ( 9 ÷ 3)

So associative-property of division is not true.

Whole numbers

Closure property
Commutative property
Associative property