Sarah is joining a craft club and is going to have to pay a one-time initiation fee of $12. After the fee she will have to pay $20 per month for the craft kits she will be using. The question is; is this a direct variation problem?

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?