Решение:
$\frac{20 : 2\frac{2}{15} + 25\frac{5}{7} : 2\frac{2}{35}}{20\frac{7}{9} : 4\frac{2}{5} - \frac{5}{9}} = \frac{20 : \frac{32}{15} + \frac{180}{7} : \frac{72}{35}}{\frac{187}{9} : \frac{22}{5} - \frac{5}{9}} = \frac{20 * \frac{15}{32} + \frac{180}{7} * \frac{35}{72}}{\frac{187}{9} * \frac{5}{22} - \frac{5}{9}} = \frac{\frac{75}{8} + \frac{100}{8}}{\frac{85}{18} - \frac{5}{9}} = \frac{\frac{175}{8}}{\frac{85 - 10}{18}} = \frac{175}{8} : \frac{75}{18} = \frac{175}{8} * \frac{18}{75} = \frac{21}{4} = 5\frac{1}{4}$
Ответ: $5\frac{1}{4}$

Решение:
$\frac{6\frac{3}{4} : 9 + 24 : \frac{6}{7} - \frac{1}{9} : \frac{4}{21}}{53\frac{2}{3} - 22\frac{14}{15} : 2\frac{2}{3}} = \frac{\frac{27}{4} * \frac{1}{9} + 24 * \frac{7}{6} - \frac{1}{9} * \frac{21}{4}}{53\frac{10}{15} - \frac{344}{15} * \frac{3}{8}} = \frac{\frac{3}{4} + 28 - \frac{7}{12}}{53\frac{10}{15} - \frac{129}{15}} = \frac{28\frac{1}{6}}{53\frac{10}{15} - 8\frac{9}{15}} = \frac{\frac{169}{6}}{45\frac{1}{15}} = \frac{169}{6} * \frac{15}{676} = \frac{1 * 5}{2 * 4} = \frac{5}{8}$
Ответ: $\frac{5}{8}$