$\frac{((6\frac{2}{3} + 2\frac{4}{15} + 5\frac{1}{2}) : \frac{1}{15} - 30 : \frac{5}{28}) : 2\frac{3}{4}}{(5 * \frac{4}{5} - \frac{3}{5} * \frac{5}{22}) : 42\frac{1}{2}} = \frac{((13 + \frac{2 * 10 + 4 * 2 + 1 * 15}{30}) * \frac{15}{1} - 5 * 6 * \frac{28}{5}) : \frac{11}{4}}{(4 - \frac{3}{2}) : \frac{85}{2}} = \frac{((13 * 15 + \frac{15 * (20 + 8 + 15)}{2 * 15}) - 6 * 28) * \frac{4}{11}}{(3\frac{22}{22} - \frac{3}{22}) : \frac{85}{2}} = \frac{((195 + \frac{43}{2}) - 168) * \frac{4}{11}}{3\frac{19}{22} : \frac{85}{2}} = \frac{(195\frac{43}{2} - 168) * \frac{4}{11}}{\frac{85}{22} * \frac{2}{85}} = \frac{27\frac{43}{2} * \frac{4}{11}}{\frac{85}{11 * 2} * \frac{2}{85}} = \frac{\frac{97}{2} * \frac{4}{11}}{\frac{1}{11}} = \frac{97}{2} * \frac{4}{11} * \frac{11}{1} = 97 * 2 = 194$