Does 8y=2x represent a direct variation

Diane owes $387 to her brother. if she debits her bank account $161.25 a month to pay him back, how many months will it take her to pay off the debt?

5,600 x 10^3 = a) 560 b) 5,000,600 c) 5,600,000 d) 56,000

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?