# 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. $$$-a$$$.