If anyone could help that’d be cool

My math teacher told my class to "steal" a 6th grade fraction word problem from the internet, word problems? : -p requirements: only a 1 step word problem. needs to be complex.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Determine which postulate or theorem can be used to prove that lmn =nmo