The reciprocal
of a number x is the number obtained by dividing 1 by x. Thus a
number multiplied by its reciprocal is 1. The reciprocal of a fraction
a/b is b/a since a/b x b/a is 1.

For example 1/4
is the reciprocal of 4;

3/2 is the reciprocal of 2/3

Taking the reciprocal of a number is dividing 1 by the number; so
the reciprocal of four is one quarter, for instance. The reciprocal
is what you have to multiply the number by in order to get 1. If
you take the reciprocal of the reciprocal you get back to where
you started.