How do I find a counterexample to show the conjecture is false?

Question

I'm doing my homework....It's 1am and I am exhausted. I'm currently working on a few problems I need help with. My mom wont help me with them obviously cause she's asleep. The questions are:

Find one counterexample to show that each conjecture is false.

1) the product of two positive numbers is greater than either number.

2) The Quotient of two proper fractions is a proper fraction.

If you could help me out with these I'd appreciate it. Cause I'm falling asleep, and just trying to figure out how to solve this thing! It's probably simple, but I can't tell if it is or not at this hour.

Answer 1

Hints:

1) What happens when you multiply a number by another positive number less than 1?

2) Make the denominators of the two proper fractions large enough so that you can make the numerators whatever you want.