Answer
Because the "1" on top of the reciprocal is always positive and thus doesn't change the sign of the overall fraction.
Work Step by Step
If we take the reciprocal of a nonzero number, the sign stays the same:
If $x\gt 0$:
$\frac{1}{x}\gt 0$
If $x\lt 0$:
$\frac{1}{x}\lt 0$
This is because the "1" on top of the reciprocal is always positive and thus doesn't change the sign of the overall fraction (i.e. positive/negative=negative; positive/positive=positive).
