2000 Pascal Problem 13

In the expression \frac{a}{b}+\frac{c}{d}+\frac{e}{f} each letter is replaced by a different digit from 1, 2, 3, 4, 5, and 6. What is the largest possible value of this expression?

\textbf{(A)}\ 8\frac{2}{3}\quad \textbf{(B)}\ 9\frac{5}{6}\quad \textbf{(C)}\ 9\frac{1}{3}\quad \textbf{(D)}\ 9\frac{2}{3}\quad \textbf{(E)}\ 10\frac{1}{3}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.