Решение:

\(9 \cdot \frac{1}{4} - 8 \cdot \frac{3}{5} \cdot \frac{4}{7} \cdot \frac{1}{2} = \frac{9}{4} - \frac{24}{5} \cdot \frac{4}{7} \cdot \frac{1}{2} = \frac{9}{4} - \frac{12}{5} \cdot \frac{4}{7} = \frac{9}{4} - \frac{48}{35} = \frac{9 \cdot 35 - 48 \cdot 4}{140} = \frac{315 - 192}{140} = \frac{123}{140}\)
\(1 \frac{1}{3} \cdot 3 \frac{2}{3} - (2 \frac{5}{6} + 3 \frac{7}{5}) \cdot \frac{3}{5} = \frac{4}{3} \cdot \frac{11}{3} - (\frac{17}{6} + \frac{22}{5}) \cdot \frac{3}{5} = \frac{44}{9} - (\frac{17 \cdot 5 + 22 \cdot 6}{30}) \cdot \frac{3}{5} = \frac{44}{9} - \frac{85 + 132}{30} \cdot \frac{3}{5} = \frac{44}{9} - \frac{217}{30} \cdot \frac{3}{5} = \frac{44}{9} - \frac{217}{50} = \frac{44 \cdot 50 - 217 \cdot 9}{450} = \frac{2200 - 1953}{450} = \frac{247}{450}\)
\((3 \frac{1}{4} - 2 \frac{3}{5}) : 2 \frac{4}{6} = (\frac{13}{4} - \frac{13}{5}) : \frac{14}{6} = \frac{13 \cdot 5 - 13 \cdot 4}{20} : \frac{7}{3} = \frac{65 - 52}{20} : \frac{7}{3} = \frac{13}{20} \cdot \frac{3}{7} = \frac{39}{140}\)
\(5.07 : \frac{1}{20} - 23.4 : \frac{1}{50} + 0.074 \cdot 1 = 5.07 \cdot 20 - 23.4 \cdot 50 + 0.074 = 101.4 - 1170 + 0.074 = -1068.6 + 0.074 = -1068.526\)
\((-31.7 : 63.4) - (23.4 : (-11.7)) \cdot (-2.4) = (-0.5) - (-2) \cdot (-2.4) = -0.5 - 4.8 = -5.3\)
\((-1.2 + 4.32 : (-1.8)) : (-0.001) \cdot (-0.3) = (-1.2 + (-2.4)) : (-0.001) \cdot (-0.3) = (-3.6) : (-0.001) \cdot (-0.3) = 3600 \cdot (-0.3) = -1080\)
\((\frac{7}{16} - (-\frac{5}{24})) : (-\frac{15}{16}) = (\frac{7}{16} + \frac{5}{24}) : (-\frac{15}{16}) = (\frac{7 \cdot 3 + 5 \cdot 2}{48}) : (-\frac{15}{16}) = \frac{21 + 10}{48} : (-\frac{15}{16}) = \frac{31}{48} \cdot (-\frac{16}{15}) = \frac{31}{3} \cdot (-\frac{1}{15}) = -\frac{31}{45}\)
\((\frac{10}{21} - \frac{25}{28}) : (-\frac{11}{14}) = (\frac{10 \cdot 4 - 25 \cdot 3}{84}) : (-\frac{11}{14}) = \frac{40 - 75}{84} : (-\frac{11}{14}) = \frac{-35}{84} \cdot (-\frac{14}{11}) = \frac{-5 \cdot 7}{12 \cdot 7} \cdot (-\frac{14}{11}) = \frac{-5}{12} \cdot (-\frac{14}{11}) = \frac{5}{12} \cdot \frac{14}{11} = \frac{5 \cdot 7}{6 \cdot 11} = \frac{35}{66}\)
\(-2 \frac{2}{3} - (\frac{15}{3} - \frac{4}{15}) \cdot \frac{3}{7} = -\frac{8}{3} - (\frac{15 \cdot 5 - 4}{15}) \cdot \frac{3}{7} = -\frac{8}{3} - \frac{75-4}{15} \cdot \frac{3}{7} = -\frac{8}{3} - \frac{71}{15} \cdot \frac{3}{7} = -\frac{8}{3} - \frac{71}{5} \cdot \frac{1}{7} = -\frac{8}{3} - \frac{71}{35} = \frac{-8 \cdot 35 - 71 \cdot 3}{105} = \frac{-280 - 213}{105} = \frac{-493}{105}\)

Ответ: 1) \(\frac{123}{140}\) 2) \(\frac{247}{450}\) 3) \(\frac{39}{140}\) 4) \(-1068.526\) 5) \(-5.3\) 6) \(-1080\) 7) \(-\frac{31}{45}\) 8) \(\frac{35}{66}\) 9) \(-\frac{493}{105}\)

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