Relations faggotry

I'm going over the study guide my Discrete Math 2 professor gave us, and I've run into somethings that we haven't gone over in class, and aren't in the book. Here's the problem.
Let A = {(a, b)R(c, d) | a, b ϵ Z, b ≠ 0}. Define a binary relation R on the set A by (a, b)R(c, d) ↔ ad = bc where (a, b) ϵ A, (c, d) ϵ A.
(a) Prove that R is an equivalence relation.
(b) Assume that (a, b)R(a', b') and (c, d)R(c', d'). Show that (ad + bc, bd)R(a'd' + b'c', b'd') and (ac, bd)R(a'c', b'd').
Let Ā denote the set of all equivalence classes of R. Therefore, the following "addition" + and "multiplication" * for the equivalence classes are well-defined: [a, b] + [c, d] = [ad + bc, bd] and [a, b] * [c, d] = [ac, bd].
(c) Prove that there is a one-to-one and onto function f from Ā to Q, the set of all rational numbers such that f([a, b] + [c, d]) = f([a, b]) + f([c, d[) and f([a, b] * [c, d]) = f([a, b]) * f([c, d]) for all [a, b] ϵ Ā and [c, d] ϵ Ā.

I've already done (a), but (b) and (c) elude me.

So, what parts of (b) and (c) do you want help with? For the first part of (b), did you try reducing the expression to terms? For (c), do you see the obvious function f for which you can prove the requirements?