\(\begin{array}{l}
\dfrac{1}{2}:\left( { - 1\dfrac{1}{2}} \right):\left( {1\dfrac{1}{3}} \right):\left( { - 1\dfrac{1}{4}} \right):...:\left( { - 1\dfrac{1}{{100}}} \right)\\
= \dfrac{1}{2}:\dfrac{{ - 1}}{2}:\dfrac{2}{3}:\dfrac{{ - 3}}{4}:...:\dfrac{{ - 99}}{{100}}\\
= {( - 1)^{50}}\dfrac{1}{2}.\dfrac{2}{1}.\dfrac{3}{2}.\dfrac{4}{3}....\dfrac{{100}}{{99}}\\
= \dfrac{1}{2}.100\\
= 50
\end{array}\)