### Theory:

Negative numbers are numbers that are less than zero.
For example, The negative of $$2$$ is $$-2$$ because $$2 + (-2) = (-2) + 2 = 0$$.

Important!
Negative number symbol: Negative numbers are indicated by placing a dash or minus ($$-$$) sign in front, such as $$–5$$, $$–12.77$$. A negative number, such as $$-1$$, is termed as 'negative one'.
An integer $$a$$, we have, $$a + (-a) = (-a) + a = 0$$; So, $$a$$ is the negative of $$-a$$, and $$-a$$ is the negative of $$a$$.

For example, $$2 + (-2) = (-2) + 2 = 0$$, So we say $$2$$ is the negative or additive inverse of $$-2$$ and vice-versa.
Rational Number: A number can be made by dividing two integers. (Note: An integer is a number with no fractional part.)
For example, 1.5 is a rational number because 1.5 $$=$$ $\frac{3}{2}$   (3 and 2 are both integers.)
Negative numbers: A rational number is supposed to be negative if its numerator and denominator are of opposite signs such that, one of them is a positive integer, and another one is a negative integer. In additional words, a rational number is negative, if its numerator and denominator are of the opposite signs.
Example:
Each of the rational numbers  $$2/-8$$, $$-30/16$$, $$13/-18$$, $$-15/24$$ are negative rationals, but $$-11/-17$$, $$2/9$$, $$-3/-7$$, $$1/7$$ are not negative rationals.
For example, The rational number $\frac{2}{3}$.

$\frac{2}{3}$ $$+$$ $-\frac{2}{3}$ $$=$$ $\frac{\left(2+\left(-2\right)\right)}{3}$ $$=$$ 0.

Also, $-\frac{2}{3}$ $$+$$ $\frac{2}{3}$ $$=$$ $$0$$.

Similarly, $\frac{-8}{9}$ $$+$$ $\frac{8}{9}$ $$=$$ $\frac{8}{9}$ $$+$$$\frac{-8}{9}$ $$=$$ $$0$$.

$\frac{11}{6}$ $$+$$ $-\frac{11}{6}$ $$=$$ $-\frac{11}{6}$ $$+$$ $\frac{11}{6}$ $$=$$ $$0$$.

In general, for a rational number $\frac{a}{b}$, we have, $\frac{a}{b}$ $$+$$ $\frac{-a}{b}$ $$=$$ $\frac{-a}{b}$ $$+$$ $\frac{a}{b}$ $$=$$ $$0$$.

We say that $\frac{-a}{b}$ is the additive inverse of $\frac{a}{b}$ and $\frac{a}{b}$ is the additive inverse of $\frac{-a}{b}$.