Решение:
а) $1\frac{1}{2} : (-1\frac{1}{6}) = \frac{3}{2} : (-\frac{7}{6}) = \frac{3}{2} * (-\frac{6}{7}) = -\frac{3 * 6}{2 * 7} = -\frac{3 * 3}{1 * 7} = -\frac{9}{7} = -1\frac{2}{7};$
б) $-2\frac{1}{3} : (-1\frac{5}{6}) = -\frac{7}{3} : (-\frac{11}{6}) = -\frac{7}{3} * (-\frac{6}{11}) = \frac{7 * 6}{3 * 11} = \frac{7 * 2}{1 * 11} = \frac{14}{11} = 1\frac{3}{11};$
в) $-1\frac{1}{3} : 2\frac{7}{8} = -\frac{4}{3} : \frac{23}{8} = -\frac{4}{3} * \frac{8}{23} = -\frac{4 * 8}{3 * 23} = -\frac{32}{69};$
г) $-2\frac{1}{8} : (-3\frac{1}{16}) = -\frac{17}{8} : (-\frac{49}{16}) = -\frac{17}{8} : (-\frac{16}{49}) = \frac{17 * 16}{8 * 49} = \frac{17 * 2}{1 * 49} = \frac{34}{49};$
д) $1\frac{13}{15} : (-1\frac{2}{5}) = \frac{28}{15} : (-\frac{7}{5}) = \frac{28}{15} * (-\frac{5}{7}) = -\frac{28 * 5}{15 * 7} = -\frac{4 * 1}{3 * 1} = -\frac{4}{3} = -1\frac{1}{3};$
е) $(-2\frac{2}{21}) : (-1\frac{4}{7}) = (-\frac{44}{21}) : (-\frac{11}{7}) = (-\frac{44}{21}) * (-\frac{7}{11}) = \frac{44 * 7}{21 * 11} = \frac{4 * 1}{3 * 1} = \frac{4}{3} = 1\frac{1}{3}.$
Ответ:
а) $-1\frac{2}{7};$
б) $1\frac{3}{11};$
в) $-\frac{32}{69};$
г) $\frac{34}{49};$
д) $-1\frac{1}{3};$
е) $1\frac{1}{3}.$