How do you find the multplicate inverse of a rational number?

You take its reciprocal, that is you divide 1 by the number.

A rational number can be written as a fraction with integer values in both the numerator and denominator, j/k. The multiplicative inverse of a number is what you have to multiply by to get a product of 1. Putting these ideas together, the multiplicative inverse is the reciprocal, or k/j:

(j/k) * (k/j) = 1.