Proof by Contraposition... (and background hypothesis PLEASE HELP!)

Prove by using proof by contraposition (and background hypothesis) that "the product of a non-zero rational number m and irrational number n is irrational....

im supposed to use contraposition and background hypothesis to change this statement to...

in the background ---> (m not equal to 0): and the proof ---> (if mn is rational, then n is rational)

BUT i do not know where/if im supposed to incorporate the "background" portion of my hypothesis into my proof (because i do know that you cant prove "if mn is rational then n is rational" since such a proof does not exist.)