**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.

**Identity property** is all about adding number with 0.

It says that adding any number with 0 will produce same number

A + 0 = A

**In Math, do we have identity property of multiplication?**

Yes!!

If we multiply any number with 1, we will get same number as a result.

Since the identity of the number after multiplication is intact, the above expression is called identity property of multiplication