Identity Property of Addition

Identity property of addition:

a+0=a\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+aa+0=0+a.

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

This is also true, if we subtract zero: a0=aa-0=a.

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

Example 1. 3+0=3{3}+{0}={3}.

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

Example 3. 0+58=58{0}+\frac{{5}}{{8}}=\frac{{5}}{{8}}.

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