1) 2) 3) 4) Ответы:

Решение:

1. \( \left[ \left( \frac{15}{28} - \frac{11}{36} \right) : \frac{21}{29} + 6 \frac{6}{7} : 16 \frac{1}{2} \right] = \left[ \left( \frac{15 \cdot 9 - 11 \cdot 7}{252} \right) : \frac{21}{29} + \frac{48}{7} : \frac{33}{2} \right] = \left[ \left( \frac{135 - 77}{252} \right) : \frac{21}{29} + \frac{48}{7} \cdot \frac{2}{33} \right] = \left[ \frac{58}{252} \cdot \frac{29}{21} + \frac{16 \cdot 2}{7 \cdot 11} \right] = \left[ \frac{29}{126} \cdot \frac{29}{21} + \frac{32}{77} \right] = \left[ \frac{841}{2646} + \frac{32}{77} \right] = \frac{841 \cdot 77 + 32 \cdot 2646}{203742} = \frac{64757 + 84672}{203742} = \frac{149429}{203742} \)
2. \( \left[ \left( \frac{5}{7} - \frac{11}{14} \right) \cdot \frac{2}{3} + \left( 3 \frac{2}{9} - 1 \frac{5}{6} \right) \frac{18}{25} \right] : 2 \frac{3}{4} = \left[ \left( \frac{10 - 11}{14} \right) \cdot \frac{2}{3} + \left( \frac{29}{9} - \frac{11}{6} \right) \frac{18}{25} \right] : \frac{11}{4} = \left[ \left( -\frac{1}{14} \right) \cdot \frac{2}{3} + \left( \frac{58 - 33}{18} \right) \frac{18}{25} \right] \cdot \frac{4}{11} = \left[ -\frac{1}{21} + \frac{25}{18} \cdot \frac{18}{25} \right] \cdot \frac{4}{11} = \left[ -\frac{1}{21} + 1 \right] \cdot \frac{4}{11} = \frac{20}{21} \cdot \frac{4}{11} = \frac{80}{231} \)
3. \( \frac{9}{40} \cdot \left[ 7 \frac{5}{7} : 3 \frac{3}{5} - \left( \frac{53}{56} - \frac{29}{35} \right) : \frac{33}{40} \right] = \frac{9}{40} \cdot \left[ \frac{54}{7} : \frac{18}{5} - \left( \frac{53 \cdot 5 - 29 \cdot 8}{280} \right) : \frac{33}{40} \right] = \frac{9}{40} \cdot \left[ \frac{54}{7} \cdot \frac{5}{18} - \left( \frac{265 - 232}{280} \right) : \frac{33}{40} \right] = \frac{9}{40} \cdot \left[ \frac{3 \cdot 5}{7} - \frac{33}{280} \cdot \frac{40}{33} \right] = \frac{9}{40} \cdot \left[ \frac{15}{7} - \frac{1}{7} \right] = \frac{9}{40} \cdot \frac{14}{7} = \frac{9}{40} \cdot 2 = \frac{9}{20} \)
4. \( \left[ \left( \frac{5}{9} - \frac{7}{18} \right) : 35 + \left( \frac{40}{63} - \frac{8}{21} \right) : 2 \right] \cdot 35 = \left[ \left( \frac{10 - 7}{18} \right) : 35 + \left( \frac{40 - 24}{63} \right) : 2 \right] \cdot 35 = \left[ \frac{3}{18} : 35 + \frac{16}{63} : 2 \right] \cdot 35 = \left[ \frac{1}{6 \cdot 35} + \frac{8}{63} \right] \cdot 35 = \left[ \frac{1}{210} + \frac{8}{63} \right] \cdot 35 = \left[ \frac{1 \cdot 3 + 8 \cdot 10}{630} \right] \cdot 35 = \frac{3 + 80}{630} \cdot 35 = \frac{83}{630} \cdot 35 = \frac{83}{18} = 4 \frac{11}{18} \)

Ответ: 1) \( \frac{149429}{203742} \); 2) \( \frac{80}{231} \); 3) \( \frac{9}{20} \); 4) \( 4 \frac{11}{18} \).