Commutative Property

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Commutative property for addition :

Look at the following Examples.
12 + 18 = 18 + 12 = 30;
345 + 65 = 65 + 345 = 410
45 + 0 = 0 + 45 = 45
From the above examples we can say that during addition we can change the place of the number. The answer remains the same.

For any two elements of the set W, a and b, a + b = b + a This is called the Commutative-Property of Addition for the set of W.

Some solved examples
1) 15 + 6 = 6 + 15

21 = 21

So the property holds true.

2) 85 + 16 = 16 + 85

101 = 101

So the property holds true.

3) 5 + 97 = 97 + 5

102 = 102

So the property holds true.

Commutative-property for multiplication :

If a and b are whole numbers then

a x b = b x a

For any elements of the set W, a x b = b x a This is called the Commutative-Property of multiplication for the set of W.

Some solved examples :

1) 5 x 6 = 6 x 5

30 = 30

So the property holds true.

2) 12 x 5 = 5 x 12 = 60

Regardless of the order in which whole numbers are multiplied,

we will get the same product.

For Division :

6 ÷ 3 = 2 is not same as 3 ÷ 6 = 1/2

If a and b are whole numbers, then a ÷ b is not equal to

b ÷ a. So the commutative-property does not hold

true for whole numbers.

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Whole numbers

• Closure property
• Commutative property
• Associative property
• Additive Identity
• Distributive property
From commutative to Whole numbers

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