Решение:

\(3 \frac{3}{4} : \frac{3}{8} : 1 \frac{1}{7} = \frac{15}{4} : \frac{3}{8} : \frac{8}{7} = \frac{15}{4} \cdot \frac{8}{3} \cdot \frac{7}{8} = \frac{15 \cdot 8 \cdot 7}{4 \cdot 3 \cdot 8} = \frac{5 \cdot 7}{4} = \frac{35}{4} = 8 \frac{3}{4}\)
\(3 \frac{3}{4} : \left( \frac{3}{8} : 1 \frac{1}{7} \right) = \frac{15}{4} : \left( \frac{3}{8} : \frac{8}{7} \right) = \frac{15}{4} : \left( \frac{3}{8} \cdot \frac{7}{8} \right) = \frac{15}{4} : \frac{21}{64} = \frac{15}{4} \cdot \frac{64}{21} = \frac{15 \cdot 64}{4 \cdot 21} = \frac{5 \cdot 16}{7} = \frac{80}{7} = 11 \frac{3}{7}\)
\(1 \frac{7}{9} : \frac{15}{32} : 1 \frac{19}{36} = \frac{16}{9} : \frac{15}{32} : \frac{55}{36} = \frac{16}{9} \cdot \frac{32}{15} \cdot \frac{36}{55} = \frac{16 \cdot 32 \cdot 36}{9 \cdot 15 \cdot 55} = \frac{16 \cdot 32 \cdot 4}{15 \cdot 55} = \frac{2048}{825} \approx 2.48\)
\(1 \frac{7}{9} \cdot \left( \frac{15}{32} : 1 \frac{19}{36} \right) = \frac{16}{9} \cdot \left( \frac{15}{32} : \frac{55}{36} \right) = \frac{16}{9} \cdot \left( \frac{15}{32} \cdot \frac{36}{55} \right) = \frac{16}{9} \cdot \frac{15 \cdot 36}{32 \cdot 55} = \frac{16 \cdot 15 \cdot 36}{9 \cdot 32 \cdot 55} = \frac{15 \cdot 2}{2 \cdot 55} = \frac{15}{55} = \frac{3}{11}\)
\(3 \frac{4}{7} : 1 \frac{1}{7} : \frac{2}{3} = \frac{25}{7} : \frac{8}{7} : \frac{2}{3} = \frac{25}{7} \cdot \frac{7}{8} \cdot \frac{3}{2} = \frac{25 \cdot 7 \cdot 3}{7 \cdot 8 \cdot 2} = \frac{25 \cdot 3}{16} = \frac{75}{16} = 4 \frac{11}{16}\)
\(3 \frac{4}{7} : \left( 1 \frac{1}{7} : \frac{2}{3} \right) = \frac{25}{7} : \left( \frac{8}{7} : \frac{2}{3} \right) = \frac{25}{7} : \left( \frac{8}{7} \cdot \frac{3}{2} \right) = \frac{25}{7} : \frac{12}{7} = \frac{25}{7} \cdot \frac{7}{12} = \frac{25}{12} = 2 \frac{1}{12}\)
\(\left( \frac{5}{12} + \frac{1}{8} \right) : \frac{3}{8} = \left( \frac{10 + 3}{24} \right) : \frac{3}{8} = \frac{13}{24} : \frac{3}{8} = \frac{13}{24} \cdot \frac{8}{3} = \frac{13 \cdot 8}{24 \cdot 3} = \frac{13}{3 \cdot 3} = \frac{13}{9} = 1 \frac{4}{9}\)
\(\frac{5}{12} + \frac{1}{8} : \frac{3}{8} = \frac{5}{12} + \frac{1}{8} \cdot \frac{8}{3} = \frac{5}{12} + \frac{1}{3} = \frac{5 + 4}{12} = \frac{9}{12} = \frac{3}{4}\)
\(2 \frac{6}{7} : \left( \frac{5}{6} - \frac{9}{14} \right) = \frac{20}{7} : \left( \frac{35 - 27}{42} \right) = \frac{20}{7} : \frac{8}{42} = \frac{20}{7} : \frac{4}{21} = \frac{20}{7} \cdot \frac{21}{4} = \frac{20 \cdot 21}{7 \cdot 4} = 5 \cdot 3 = 15\)
\(2 \frac{6}{7} \cdot \frac{5}{6} - \frac{9}{14} = \frac{20}{7} \cdot \frac{5}{6} - \frac{9}{14} = \frac{100}{42} - \frac{9}{14} = \frac{50}{21} - \frac{9 \cdot 3}{14 \cdot 3} = \frac{50}{21} - \frac{27}{42} = \frac{100 - 27}{42} = \frac{73}{42} = 1 \frac{31}{42}\)
\(2 \frac{1}{4} : 1 \frac{4}{11} - \frac{3}{8} \cdot \frac{7}{8} = \frac{9}{4} : \frac{15}{11} - \frac{21}{64} = \frac{9}{4} \cdot \frac{11}{15} - \frac{21}{64} = \frac{99}{60} - \frac{21}{64} = \frac{33}{20} - \frac{21}{64} = \frac{33 \cdot 16 - 21 \cdot 5}{320} = \frac{528 - 105}{320} = \frac{423}{320} = 1 \frac{103}{320}\)
\(\left( 3 \frac{1}{6} - 5 \frac{1}{6} \right) : 4 \frac{2}{15} \cdot \frac{3}{92} = \left( \frac{19}{6} - \frac{31}{6} \right) : \frac{62}{15} \cdot \frac{3}{92} = \left( -\frac{12}{6} \right) : \frac{62}{15} \cdot \frac{3}{92} = -2 : \frac{62}{15} \cdot \frac{3}{92} = -2 \cdot \frac{15}{62} \cdot \frac{3}{92} = -\frac{30}{62} \cdot \frac{3}{92} = -\frac{15}{31} \cdot \frac{3}{92} = -\frac{45}{2852}\)

Ответ: 1) \(8 \frac{3}{4}\) 2) \(11 \frac{3}{7}\) 3) \(\frac{2048}{825}\) 4) \(\frac{3}{11}\) 5) \(4 \frac{11}{16}\) 6) \(2 \frac{1}{12}\) 7) \(1 \frac{4}{9}\) 8) \(\frac{3}{4}\) 9) \(15\) 10) \(\frac{73}{42}\) 11) \(1 \frac{103}{320}\) 12) \(-\frac{45}{2852}\)

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