For the following values of a and b, find q e ℤ and r e ℤ so that a = qb + r and 0 ≤ r < i b i 1. a = 1211 and b = 5 2. a = 7521 and b = - 25 3. a = -8989 and b= 88 4. a = -4225 and b = -9

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?