Do these have to be double? Ints would be a lot easier. You shouldn't make direct comparisons between doubles, because of the binary fraction representation - not all real numbers can be stored exactly, so direct comparisons quite often fail.
To do this assignment, you also need a Greatest Common Denominator function, so you can rationalise fractions such as 4 / 6 into 2 /3.
I would recommend something like this. Please look up the MODULUS operation (%), as it's very useful for this. It returns the remainder after division. Good luck and hopefully you can stick with your class!
E: You may also wish to modify this to check for a denominator that is ZERO before performing any division with it. Sorry. And don't worry about reducing the fractions -- the prompt gives an example output of "10/12", which is not reduced.