Jake has 145 bottle caps and daniel has 143 bottle caps. how many bottle caps do they have in all? 145 143 = 288 which of the following problems could be solved in the same way?
a. ed has 76 model trains and mike has 121 model trains. how many trains do they have altogether?
b. henry has to write 32 you letters. he has written 13 so far. how many more letters must he write?
c. mary had 19 oranges. she gave 12 oranges to amy. how many oranges does mary have now?

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?