The sign of a ratio is determined by the signs of both numerator and denominator.
If both have the same sign, then the ration is positive.
If they have different signs, then the ration is negative.
Below are some examples:
-2/ -3 = 2/3
-4/5 = - 4/5
3/-2 = - 3/2
5/7 = 5/7
So, if both numerator and denominator are positive or negative, then the sign of the ratio is always positive.
On the other hand, if numerator and denominator have opposite signs, then the ratio is always negative.
The sign of the ratio depends on the signs of both, numerator and denominator.
For instance, the ratio is positive, or it has a positive value, if and only if the numerator and denominator are both positive or both negative.
The ratio is negative when the numerator and the denominator have opposite signs, or one is positive and the other is negative.