# Identity Property of Addition

**Identity property of addition**:

` huge color(purple)(a+0=a) `

What does it mean?

It means, that addition of zero to the number will not change the number.

Indeed, suppose your first friend (let's call it Tom) gave you 3 apples, but your second friend (let's call it Jim) gave you nothing. So, you are left with 3 apples.

Using commutative property of addition, we can write that `a+0=0+a`.

Thus, `huge color(purple)(a+0=0+a=a)`.

This is also true, if we subtract zero: `a-0=a`.

In fact, identity property is true for any real number.

**Example 1**. `3+0=3`.

**Example 2**. `(-sqrt(2))-0=-sqrt(2)`.

**Example 3**. `0+5/8=5/8`.

**Conclusion**. Addition or subtraction of zero doesn't change things.