Signs of fractions and reciprocals

Every fraction has three signs: the numerator's, the denominator's, and the fraction's own sign in front. They aren't always written: in 34 all three are positive.

The key fact: you can change exactly two of the signs and the value stays the same, because two negatives cancel. So these are all equal:

−47 = −47 = 4−7 = −−4−7

Reciprocals

The reciprocal of ab is ba: flip it. A number times its reciprocal is always 1: 29 × 92 = 1. The reciprocal of a whole number 5 is 15. The sign doesn't change: the reciprocal of −35 is −53.

0 has no reciprocal, because 10 is undefined.

The negative reciprocal flips the fraction and changes its sign. The negative reciprocal of −35 is 53, and their product is −1.