a) try not to use "fractions" for elements of Z15. what you want to do is notice that 7 generates Z50, since gcd(7,50) = 1. now, usually we think of elements of Z50 as being "multiples" of 1, that is: x = 1+1+...+1 (x times). note that 7^2 = 49 = -1 (mod 50), so 7^4 = 1 (mod 50). this means "1/7" is 7^3 (mod 50), which is 43.

so x = 1x = (43)(7)x = 43x(7) (mod 50). since φ is a homomorphism, φ(43x(7)) = 43xφ(7) = 43x(6) (mod 15).

but mod 15, 43x(6) = 13x(6) = 78x = 3x (mod 15).