Inverse Property of Addition

Inverse property of addition:

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

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

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

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

Example 1. Additive inverse of 53\frac{{5}}{{3}} is 53-\frac{{5}}{{3}}, because 53+(53)=0\frac{{5}}{{3}}+{\left(-\frac{{5}}{{3}}\right)}={0}.

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

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

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