When a fraction is negative are both the numerator and the denominator negative?

Not necessarily, it could be either the numerator or the denominator. For example, - 3/4 (lets pretend that its one on top of the other) either the three or the four could be negative but not both. If both the numerator and denominator were negative, they would cancel each other out, making it a positive question. So to answer your question, it is no.