# Identity Property of Addition

**Identity property of addition**:

$$$\color{purple}{a+0=a}$$$

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, $$$\color{purple}{a+0=0+a=a}$$$.

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.** $$${\left(-\sqrt{{{2}}}\right)}-{0}=-\sqrt{{{2}}}$$$.

**Example 3.** $$${0}+\frac{{5}}{{8}}=\frac{{5}}{{8}}$$$.

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