Reciprocal

The reciprocal of a fraction flips it: the reciprocal of a/b is b/a. The reciprocal of 3/4 is 4/3, and the reciprocal of 5 is 1/5.

A number times its reciprocal is always 1, so 3/4 × 4/3 = 1. That is why dividing by a fraction is the same as multiplying by its reciprocal: dividing by 3/4 and multiplying by 4/3 undo each other, so both give the same quotient. For example, 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.