Решение:
а) $-\frac{3}{7} : \frac{5}{6} = -\frac{3}{7} * \frac{6}{5} = -\frac{3 * 6}{7 * 5} = -\frac{18}{35}$;
б) $\frac{16}{-25} : (-\frac{8}{15}) = \frac{16}{-25} * (-\frac{15}{8}) = \frac{\overset{2}{\cancel{16}} * \overset{3}{\cancel{15}}}{\underset{5}{\cancel{25}} * \underset{1}{\cancel{8}}} = \frac{2 * 3}{5 * 1} = \frac{6}{5} = 1\frac{1}{5}$;
в) $-\frac{9}{20} : (-\frac{18}{25}) = -\frac{9}{20} * (-\frac{25}{18}) = \frac{\overset{1}{\cancel{9}} * \overset{5}{\cancel{25}}}{\underset{4}{\cancel{20}} * \underset{2}{\cancel{18}}} = \frac{1 * 5}{4 * 2} = \frac{5}{8}$;
г) $\frac{28}{63} : (-\frac{9}{7}) = \frac{28}{63} * (-\frac{7}{9}) = -\frac{28 * \overset{1}{\cancel{7}}}{\underset{9}{\cancel{63}} * 9} = -\frac{28 * 1}{9 * 9} = -\frac{28}{81}$;
д) $-\frac{15}{16} : (-\frac{10}{24}) = -\frac{15}{16} * (-\frac{24}{10}) = \frac{\overset{3}{\cancel{15}} * \overset{3}{\cancel{24}}}{\underset{2}{\cancel{16}} * \underset{2}{\cancel{10}}} = \frac{3 * 3}{2 * 2} = \frac{9}{4} = 2\frac{1}{4}$;
е) $-\frac{15}{17} : \frac{25}{34} = -\frac{15}{17} * \frac{34}{25} = -\frac{\overset{3}{\cancel{15}} * \overset{2}{\cancel{34}}}{\underset{1}{\cancel{17}} * \underset{5}{\cancel{25}}} = -\frac{3 * 2}{1 * 5} = -\frac{6}{5} = -1\frac{1}{5}$.
Ответ:
а) $-\frac{18}{35}$;
б) $1\frac{1}{5}$;
в) $\frac{5}{8}$;
г) $-\frac{28}{81}$;
д) $2\frac{1}{4}$;
е) $-1\frac{1}{5}$.