$(-2\frac{5}{6} + 3\frac{5}{24}) : 4\frac{1}{2} = (-2\frac{20}{24} + 2\frac{29}{24}) : \frac{9}{2} = \frac{9}{24} * \frac{2}{9} = \frac{1}{12} * \frac{1}{1} = \frac{1}{12}$

$(1\frac{2}{3} + 2\frac{5}{9}) : (-21\frac{3}{4} + 7\frac{1}{2}) = (1\frac{6}{9} + 2\frac{5}{9}) : (-21\frac{3}{4} + 7\frac{2}{4}) = 3\frac{11}{9} : (-14\frac{1}{4}) = \frac{38}{9} : (-\frac{57}{4}) = \frac{38}{9} * (-\frac{4}{57}) = \frac{2}{9} * (-\frac{4}{3}) = -\frac{8}{27}$