1988 AHSME Problem 14

For any real number a and positive integer k, define

{a \choose k} = \frac{a(a-1)(a-2)\cdots(a-(k-1))}{k(k-1)(k-2)\cdots(2)(1)}

What is

{-\frac{1}{2} \choose 100} \div {\frac{1}{2} \choose 100}?

\textbf{(A)}\ -199\qquad \textbf{(B)}\ -197\qquad \textbf{(C)}\ -1\qquad \textbf{(D)}\ 197\qquad \textbf{(E)}\ 199

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.