Identity Property of Addition

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. $$${0}+\frac{{5}}{{8}}=\frac{{5}}{{8}}$$$.