Решение:
а) $-\frac{3}{7} * \frac{5}{9} = \frac{-3}{7} * \frac{5}{9} = \frac{\overset{-1}{\cancel{-3}} * 5}{7 * \underset{3}{\cancel{9}}} = \frac{-1 * 5}{7 * 3} = \frac{-5}{21} = -\frac{5}{21};$
б) $\frac{-3}{8} * \frac{-4}{5} = \frac{-3 * \overset{-1}{\cancel{(-4)}}}{\underset{2}{\cancel{8}} * 5} = \frac{-3 * (-1)}{2 * 5} = \frac{3}{10};$
в) $\frac{-9}{10} * \frac{-1}{-2} = \frac{-9 * (-1)}{10 * (-2)} = \frac{9}{-20} = -\frac{9}{20};$
г) $\frac{-7}{2} * \frac{4}{-35} = \frac{\overset{1}{\cancel{-7}} * 4}{2 * \underset{5}{\cancel{(-35)}}} = \frac{1 * \overset{2}{\cancel{(4)}}}{\underset{1}{\cancel{2}} * 5} = \frac{1 * 2}{1 * 5} = \frac{2}{5};$
д) $\frac{-5}{6} * \frac{3}{10} = \frac{\overset{-1}{\cancel{(-5)}} * \overset{1}{\cancel{3}}}{\underset{2}{\cancel{6}} * \underset{2}{\cancel{10}}} = \frac{-1 * 1}{2 * 2} = \frac{-1}{4} = -\frac{1}{4};$
е) $\frac{-7}{32} * \frac{4}{-21} = \frac{\overset{1}{\cancel{-7}} * \overset{1}{\cancel{4}}}{\underset{8}{\cancel{32}} * \underset{3}{\cancel{(-21)}}} = \frac{1 * 1}{8 * 3} = \frac{1}{24};$
ж) $-\frac{2}{5} * (-\frac{75}{2}) = \frac{-2}{5} * \frac{-75}{2} = \frac{\overset{-1}{\cancel{-2}} * \overset{-15}{\cancel{(-75)}}}{\underset{1}{\cancel{5}} * \underset{1}{\cancel{2}}} = \frac{-1 * (-15)}{1 * 1} = \frac{15}{1} = 15;$
з) $\frac{4}{3} * (-\frac{9}{16}) = \frac{4}{3} * \frac{-9}{16} = \frac{\overset{1}{\cancel{4}} * \overset{-3}{\cancel{(-9)}}}{\underset{1}{\cancel{3}} * \underset{4}{\cancel{16}}} = \frac{1 * (-3)}{1 * 4} = \frac{-3}{4} = -\frac{3}{4};$
и) $-\frac{18}{5} * (-\frac{4}{81}) = \frac{-18}{5} * \frac{-4}{81} = \frac{\overset{-2}{\cancel{-18}} * (-4)}{\underset{9}{\cancel{81}} * 5} = \frac{-2 * (-4)}{9 * 5} = \frac{8}{45}.$
Ответ:
а) $-\frac{5}{21};$
б) $-\frac{9}{20};$
г) $\frac{2}{5};$
д) $-\frac{1}{4};$
е) $\frac{1}{24};$
ж) $15;$
з) $-\frac{3}{4};$
и) $\frac{8}{45}.$