## Intermediate Algebra (12th Edition)

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).