What is the use of a negative sign before the fractional bar if it is equal to attaching a negative sign before the numerator or denominator

Question

What is the use of a negative sign before the fractional bar like -(1/2) if it is equal to -1/2 and 1/-2

Answer 1

Intentionally these are three numbers that happen to be equal extensionally.

To elaborate: we know every rational number $q$, there is a unique rational number $r$ where $q+r=0$. we denote that unique $r$ with $-q$.

The same is true for integers. on the other hand for every two integer $a, b$, where $b \neq 0$, we know that $a/b$ is a rational number.

Hence $-(1/2)$ is the notation for the fist intention. $-1/2$ and $1/-2$ are constructed by the second method.

Indeed it is a theorem, which is proved in algebra that these three numbers are equal.