a) $\frac{-1}{5}\times \frac{1}{2} = \frac{(-1)\times 1}{5\times 2} = \frac{-1}{10}$

b) $\frac{-1}{8}\times \frac{8}{-9} = \frac{(-1)\times 8}{8\times (-9)} = \frac{1}{9}$

c) $\frac{-3}{7}\times \frac{14}{15} = \frac{(-3)\times 14}{7\times 15} = \frac{42}{105} = \frac{2}{5}$

d) $\frac{-7}{5}\times \frac{15}{21} = \frac{(-7)\times 15}{5\times 21} = \frac{-105}{105} = -1$

e) $(-4)\times \frac{7}{24} = \frac{(-4)\times 7}{24} = \frac{-28}{24} = \frac{-7}{6}$

f) $\frac{-9}{13}\times \frac{5}{18} = \frac{(-9)\times 5}{13\times 18} = \frac{-45}{234} = \frac{-5}{26}$.