# Inverse Property of Addition

Inverse property of addition:

$\color{purple}{a+\left(-a\right)=\left(-a\right)+a=0}$

$-a$ is called the additive inverse of ${a}$.

Inverse property is true for any real number ${a}$.

Notice, that we wrote, that ${a}+{\left(-{a}\right)}={\left(-{a}\right)}+{a}$. This is true, according to the commutative property of addition.

Example 1. Additive inverse of $\frac{{5}}{{3}}$ is $-\frac{{5}}{{3}}$, because $\frac{{5}}{{3}}+{\left(-\frac{{5}}{{3}}\right)}={0}$.

Example 2. Additive inverse of $-\sqrt{{{2}}}$ is $\sqrt{{{2}}}$, because ${\left(-\sqrt{{{2}}}\right)}+\sqrt{{{2}}}={0}$.

Example 3. ${2.57}+{\left(-{2.57}\right)}={\left(-{2.57}\right)}+{2.57}={0}$.

Conclusion. Additive inverse of the number $a$ is a number, that has the same value as ${a}$, but different sign, i.e. $-a$.