Решение:
а) $-\frac{3}{4} : \frac{5}{6} + \frac{15}{16} * \frac{2}{5} - 1 : \frac{1}{9} = -\frac{3 * 6}{4 * 5} + \frac{15 * 2}{16 * 5} - 1 * 9 = -\frac{3 * 3}{2 * 5} + \frac{3 * 1}{8 * 1} - 9 = -\frac{9}{10} + \frac{3}{8} - 9 = \frac{-36 + 15}{40} - 9 = -\frac{21}{40} - \frac{360}{40} = - \frac{381}{40} = -9\frac{21}{40}$;
б) $2 : (-\frac{3}{5}) + \frac{3}{5} : 2 - \frac{3}{2} : 6 + 6 : \frac{3}{2} = 2 * (-\frac{5}{3}) + \frac{3}{5} * \frac{1}{2} - \frac{3}{2} * \frac{1}{6} + 6 * \frac{2}{3} = -\frac{10}{3} + \frac{3}{10} - \frac{1}{4} + 4 = \frac{-200 + 18 - 15 + 240}{60} = \frac{43}{60}$;
в) $\frac{11}{4} : (\frac{2}{5} - \frac{3}{2}) + (\frac{3}{4} + \frac{5}{6}) : (-\frac{25}{8}) = \frac{11}{4} : \frac{4 - 15}{10} + \frac{9 + 10}{12} : (-\frac{25}{8}) = \frac{11}{4} : \frac{-11}{10} + \frac{19}{12} : (-\frac{25}{8}) = \frac{11}{4} * -\frac{10}{11} + \frac{19}{12} * (-\frac{8}{25}) = -\frac{10}{4} - \frac{19 * 8}{12 * 25} = -\frac{10}{4} - \frac{19 * 2}{3 * 25} = -\frac{5}{2} - \frac{38}{75} = -\frac{375 + 76}{150} = -\frac{451}{150} = -3\frac{1}{150};$
г) $(\frac{2}{15} + \frac{19}{12}) * \frac{30}{103} - (1 : \frac{9}{4}) * (-\frac{9}{16}) = \frac{8 + 95}{60} * \frac{30}{103} - (1 * \frac{4}{9}) * (-\frac{9}{16}) = \frac{103}{60} * \frac{30}{103} + \frac{4}{9} * \frac{9}{16} = \frac{1}{2} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4}.$
Ответ:
а) $-9\frac{21}{40}$;
б) $\frac{43}{60}$;
в) $-3\frac{1}{150};$
г) $\frac{3}{4}.$