6. 1) 2) 3)

Решение:

1. \( \left( 20 \frac{8}{15} \cdot 1 \frac{7}{2} - 54 \frac{3}{5} : 2 \frac{1}{2} \right) : \left( 3 \frac{13}{21} \cdot 8 \frac{2}{5} - 29 \frac{2}{5} \right) - \frac{5}{6} \cdot 1 \frac{1}{5} + \frac{21}{25} = \left( \frac{308}{15} \cdot \frac{15}{2} - \frac{273}{5} : \frac{5}{2} \right) : \left( \frac{91}{21} \cdot \frac{42}{5} - \frac{147}{5} \right) - \frac{5}{6} \cdot \frac{6}{5} + \frac{21}{25} = \left( 154 - \frac{273}{5} \cdot \frac{2}{5} \right) : \left( \frac{13 \cdot 2}{1} \cdot \frac{2}{5} - \frac{147}{5} \right) - 1 + \frac{21}{25} = \left( 154 - \frac{546}{25} \right) : \left( \frac{52}{5} - \frac{147}{5} \right) - 1 + \frac{21}{25} = \left( \frac{3850 - 546}{25} \right) : \left( \frac{-95}{5} \right) - 1 + \frac{21}{25} = \frac{3304}{25} : \left( -19 \right) - 1 + \frac{21}{25} = \frac{3304}{25} \cdot \left( -\frac{1}{19} \right) - 1 + \frac{21}{25} = -\frac{3304}{475} - \frac{475}{475} + \frac{418}{475} = \frac{-3304 - 475 + 418}{475} = -\frac{3361}{475} \)
2. \( \frac{7}{9} \cdot 1 \frac{2}{7} + 43 \frac{3}{4} : 11 \frac{2}{3} - 3 \frac{18}{25} + 1 \frac{1}{45} \cdot \left( 37 \frac{1}{2} : 2 \frac{1}{12} - 1 \frac{3}{23} \cdot 9 \right) + \frac{21}{25} = \frac{7}{9} \cdot \frac{9}{7} + \frac{175}{4} : \frac{35}{3} - \frac{78}{25} + \frac{46}{45} \cdot \left( \frac{75}{2} : \frac{25}{12} - \frac{26}{23} \cdot 9 \right) + \frac{21}{25} = 1 + \frac{175}{4} \cdot \frac{3}{35} - \frac{78}{25} + \frac{46}{45} \cdot \left( \frac{75}{2} \cdot \frac{12}{25} - \frac{234}{23} \right) + \frac{21}{25} = 1 + \frac{5 \cdot 3}{4} - \frac{78}{25} + \frac{46}{45} \cdot \left( 3 \cdot 6 - \frac{234}{23} \right) + \frac{21}{25} = 1 + \frac{15}{4} - \frac{78}{25} + \frac{46}{45} \cdot \left( 18 - \frac{234}{23} \right) + \frac{21}{25} = \frac{15}{4} - \frac{57}{25} + \frac{46}{45} \cdot \left( \frac{414 - 234}{23} \right) = \frac{15}{4} - \frac{57}{25} + \frac{46}{45} \cdot \frac{180}{23} = \frac{15}{4} - \frac{57}{25} + \frac{46 \cdot 4}{23} = \frac{15}{4} - \frac{57}{25} + \frac{184}{23} = \frac{15 \cdot 575 - 57 \cdot 92 + 184 \cdot 100}{2300} = \frac{8625 - 5244 + 18400}{2300} = \frac{21781}{2300} \)
3. \( 11 \frac{2}{5} + 7 \frac{1}{2} \cdot \left( 285 \frac{3}{5} : 14 - 1 \frac{23}{30} + \frac{13}{50} \right) : \left( 24 \frac{2}{5} - 10 \frac{23}{100} \right) = \frac{57}{5} + \frac{15}{2} \cdot \left( \frac{1428}{5} : 14 - \frac{53}{30} + \frac{13}{50} \right) : \left( \frac{122}{5} - \frac{1023}{100} \right) = \frac{57}{5} + \frac{15}{2} \cdot \left( \frac{1428}{5 \cdot 14} - \frac{53}{30} + \frac{13}{50} \right) : \left( \frac{2440 - 1023}{100} \right) = \frac{57}{5} + \frac{15}{2} \cdot \left( \frac{102}{5} - \frac{53}{30} + \frac{13}{50} \right) : \frac{1417}{100} = \frac{57}{5} + \frac{15}{2} \cdot \left( \frac{6120 - 530 + 78}{300} \right) \cdot \frac{100}{1417} = \frac{57}{5} + \frac{15}{2} \cdot \frac{5668}{300} \cdot \frac{100}{1417} = \frac{57}{5} + \frac{15 \cdot 5668 \cdot 100}{2 \cdot 300 \cdot 1417} = \frac{57}{5} + \frac{15 \cdot 5668}{6 \cdot 1417} = \frac{57}{5} + \frac{5 \cdot 5668}{2 \cdot 1417} = \frac{57}{5} + \frac{5 \cdot 4}{2} = \frac{57}{5} + 10 = \frac{57+50}{5} = \frac{107}{5} \)

Ответ: 1) \( -\frac{3361}{475} \); 2) \( \frac{21781}{2300} \); 3) \( \frac{107}{5} \).