What is the preimage?

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?

Last month, a 770 g box of cereal was sold at a grocery store for $3.10. however, this month, the cereal manufacturer launched the same cereal in a 640 g box, which is being sold at $2.50. what is the percent change in the unit price?

John has 1/2 pound of oranges to share with julie. if they share the oranges equally, how much will each of them have?