Решение:
а) $\frac{32}{75} : (-\frac{48}{25}) = \frac{32}{75} * (-\frac{25}{48}) = -\frac{\overset{4}{\cancel{32}} * \overset{1}{\cancel{25}}}{\underset{3}{\cancel{75}} * \underset{6}{\cancel{48}}} = -\frac{\overset{2}{\cancel{4}} * 1}{3 * \underset{3}{\cancel{6}}} = -\frac{2 * 1}{3 * 3} = -\frac{2}{9}$;
б) $-\frac{38}{75} : (-\frac{19}{100}) = -\frac{38}{75} * (-\frac{100}{19}) = \frac{\overset{2}{\cancel{38}} * \overset{4}{\cancel{100}}}{\underset{3}{\cancel{75}} * \underset{1}{\cancel{19}}} = \frac{2 * 4}{3 * 1} = \frac{8}{3} = 2\frac{2}{3}$;
в) $-\frac{32}{77} : (-\frac{64}{55}) = -\frac{32}{77} * (-\frac{55}{64}) = \frac{\overset{1}{\cancel{32}} * \overset{5}{\cancel{55}}}{\underset{7}{\cancel{77}} * \underset{2}{\cancel{64}}} = \frac{1 * 5}{7 * 2} = \frac{5}{14}$;
г) $-\frac{125}{196} : \frac{50}{52} = -\frac{125}{196} * \frac{52}{50} = -\frac{\overset{5}{\cancel{125}} * \overset{13}{\cancel{52}}}{\underset{49}{\cancel{196}} * \underset{2}{\cancel{50}}} = -\frac{5 * 13}{49 * 2} = -\frac{65}{98}$;
д) $\frac{228}{245} : (-\frac{57}{125}) = \frac{228}{245} * (-\frac{125}{57}) = -\frac{\overset{4}{\cancel{228}} * \overset{25}{\cancel{5}}}{\underset{49}{\cancel{245}} * \underset{1}{\cancel{57}}} = -\frac{4 * 25}{49 * 1} = -\frac{100}{49} = -2\frac{2}{49}$;
е) $-\frac{132}{1000} : (-\frac{143}{1000}) = -\frac{132}{1000} * (-\frac{1000}{143} = \frac{\overset{12}{\cancel{132}} * \overset{1}{\cancel{1000}}}{\underset{1}{\cancel{1000}} * \underset{13}{\cancel{143}}} = \frac{12 * 1}{1 * 13} = \frac{12}{13}$.
Ответ:
а) $-\frac{2}{9}$;
б) $2\frac{2}{3}$;
в) $\frac{5}{14}$;
г) $-\frac{65}{98}$;
д) $-2\frac{2}{49}$;
е) $\frac{12}{13}$.