The townsends, a family of five are going to the local movie theater the family consists off two adults and threw children. mr. townsends wants to calculate the cost of the night out. he looks up the admission prices online. before leaving mr townsends decides that he will get some items at the the theater concession stand, a large drink for each person and a large tub of popcorn for everyone to share. he will not know the prices of the items an the concession stand until they arrive

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?