Associative property
Associative Property of Addition :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.
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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. |
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
• Additive Identity
• Distributive property
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