## What is identity property of Addition?

According to the property if any number is added with number 0, the result will be the same number.

Example
5 + 0 = 5

Here number 5 is added with 0 which results in same number 5.

But why its called Identity Property?

Because on adding any number with zero, the identity of the number remain unchanged.

The mathematical expression for identity property of addition can be written as:

where A can be any number possible

### Identity Property of Addition Examples

Some of the example of identity property are:

(a) Adding positive integer with 0

11 + 0 = 11

The end result is same positive integer 11

(b) Adding negative integer with 0
-87 + 0 = – 87

The end results is same negative integer -87

(c) Adding decimal number with 0
8.5 + 0 = 8.5

After addition we got the same decimal number 8.5

(d) Adding fraction number with zero
\mathtt{\frac{2}{5} \ +\ 0\ =\ \frac{2}{5}}

We got the same fraction (2/5)

In all the examples, you can observe that even after addition the end result have the same identity and value as before.

### Understand identity property using number line

Let us add number 6 with 0

The mathematical expression can be written as:
6 + 0 = 0

This addition can be shown in number line as follows:

## Frequently asked Questions – Identity Property

### Does identity property works in subtraction?

Yes!!
It works because on subtracting any number with zero we get the same result

Some examples of identity property of subtraction are:
⟹ 6 – 0 = 6

⟹ – 9 – 0 = – 9

### How identity property is different from commutative property of addition

Commutative property says that in addition the order of number can be changed without any effect of end result.

A + B = B + A

Where A & B are set of positive numbers.

While the identity property says that if you add any number with zero, the result will be the same number.

Hence, any number with zero results in no change in identity of number.

A + 0 = A

### Is multiplication of number with 0 called Identity Property of Multiplication?

NO!!
Multiplication of any number with 0 results in 0

A x 0 = 0

Here the identity of number is not preserved and we get number 0 at the end of operation.

### Does identity property works in division?

No!!

If we divide any number with zero we get infinity (i.e not defined)

\mathtt{\frac{A}{0} \ =\ \infty }

You can see that division with number 0 produced completely different result. Hence, identity property does not work with division

### How is identity property of addition is different from associative property?

Associative property says that forming different groups in addition will not change the end result.

(A + B) + C = A + (B + C)

Where A, B & C are different integer numbers.