Additive Identity
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
Additive identity for multiplication
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
•
Additive Identity
•
Distributive property
Whole Numbers
Home