Решение:
а) $-\frac{1}{2} * \frac{2}{5} = \frac{-1}{2} * \frac{2}{5} = \frac{-1 * \overset{1}{\cancel{2}}}{\underset{1}{\cancel{2}} * 5} = \frac{-1 * 1}{1 * 5} = \frac{-1}{5} = -\frac{1}{5};$
б) $\frac{3}{4} * (-\frac{2}{9}) = \frac{3}{4} * \frac{-2}{9} = \frac{\overset{1}{\cancel{3}} * \overset{-1}{\cancel{(-2)}}}{\underset{2}{\cancel{4}} * \underset{3}{\cancel{9}}} = \frac{1 * (-1)}{2 * 3} = \frac{-1}{6} = -\frac{1}{6};$
в) $-\frac{4}{5} * (-\frac{10}{3}) = \frac{-4}{5} * \frac{-10}{3} = \frac{-4 * \overset{-2}{\cancel{(-10)}}}{\underset{1}{\cancel{5}} * 3} = \frac{-4 * (-2)}{1 * 3} = \frac{8}{3};$
г) $-\frac{1}{7} * (-\frac{3}{4}) = \frac{-1}{7} * \frac{-3}{4} = \frac{-1 * (-3)}{7 * 4} = \frac{3}{28};$
д) $\frac{2}{5} * (-\frac{3}{4}) = \frac{2}{5} * \frac{-3}{4} = \frac{\overset{1}{\cancel{(2)}} * (-3)}{5 * \underset{2}{\cancel{4}}} = \frac{1 * (-3)}{5 * 2} = \frac{-3}{10} = -\frac{3}{10};$
е) $-\frac{3}{8} * \frac{4}{5} = \frac{-3}{8} * \frac{4}{5} = \frac{-3 * \overset{1}{\cancel{4}}}{\underset{2}{\cancel{8}} * 5} = \frac{-3 * 1}{2 * 5} = \frac{-3}{10} = -\frac{3}{10}.$
Ответ:
а) $-\frac{1}{5};$
б) $-\frac{1}{6};$
в) $2\frac{2}{3};$
г) $\frac{3}{28};$
д) $-\frac{3}{10};$
е) $-\frac{3}{10}.$