If I have a fraction that just has a negative number in the numerator or denominator, does this make the whole fraction negative?

Question

For example: -3(negative numerator) over 4 (positive denominator)

Would this whole fraction be considered negative?

Answer 1

Well, in general, given any integers $m,n$ with $n\neq 0,$ we define $\frac m n$ to be the unique number $q$ satisfying $$nq=m.\tag{$\heartsuit$}$$

It is hopefully obvious that if $m=0,$ then we need $q=0.$ Otherwise, let's suppose exactly one of $m,n$ is negative. What sign must $q$ have in order for $(\heartsuit)$ to be true?