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Additive Identity : It is the number which when added to another number gives you the number itself.

Look at the following Examples.

19 + 0 = 0 + 19 = 19 ;

1345 + 0 = 0 + 1345 = 1345

Here we find that adding a 0 to the whole number 19 and 1345 does not change the value of the whole number.

If a is a whole number then a + 0 = 0 + a = a.
 For every whole number a, a + 0 = 0 + a = a. 0 is called the Identity element for addition in the set of W.

This property is not true for subtraction.

863 - 0 = 863

0 - 863 = - 863

863 - 0 ≠ 0 - 863

If 10 apples each are given to 5 children, the total number

of apples given = 10 x 5 = 50 apples.

If we give 10 apples to one child, the number of apples given

away will be 10 x 1 = 10. That is the number of apples remains the same.

Thus when you multiply any whole number by 1, the answer is the whole

number itself.

10 x 1 = 1 x 10

672 x 1 = 1 x 672

0 x 1 = 1 x 0 = 0

When any whole number a is multiplied by 1 the product is the same number a.

 For every whole number a, a x 1 = 1 x a = a 1 is called the multiplicative identity for whole numbers.

Zero Property of Multiplication :

Look at the following Examples.

234 x 0 = 0 x 234 = 0 ;

5647 x 0 = 0 x 5647 = 0

What is seen to be true for in these examples, is true for any element of W.

So, we can say :
 For every whole number a, a x 0 = 0 x a = 0 This is called the Zero Property of Multiplication for the set of W.
Division with 1 of any number gives that number :

Look at the following Examples.

19 ÷ 1 = 19 ;

9776 ÷ 1 = 9776

What is seen to be true for in these examples, is true for any element of W.

So, we can say :
 For every whole number a, a ÷ 1 = a.
Note : Division by zero is not defined.

Whole numbers

Closure property
Commutative property
Associative property