5. Найдите значение выражения: 1) \(4\frac{1}{7} \cdot 14 - 1\frac{1}{4} \cdot 1\frac{1}{6} - 1\frac{2}{9} \cdot 2\frac{5}{8}\); 2) \(1\frac{31}{32} \cdot 3\frac{1}{5} + (8\frac{5}{9} \cdot \frac{6}{35} + 3\frac{8}{15}) \cdot \frac{7}{50}\)

1) \(4\frac{1}{7} \cdot 14 - 1\frac{1}{4} \cdot 1\frac{1}{6} - 1\frac{2}{9} \cdot 2\frac{5}{8} = \frac{4 \cdot 7 + 1}{7} \cdot 14 - \frac{1 \cdot 4 + 1}{4} \cdot \frac{1 \cdot 6 + 1}{6} - \frac{1 \cdot 9 + 2}{9} \cdot \frac{2 \cdot 8 + 5}{8} = \frac{29}{7} \cdot 14 - \frac{5}{4} \cdot \frac{7}{6} - \frac{11}{9} \cdot \frac{21}{8} = \frac{29}{1} \cdot 2 - \frac{5}{4} \cdot \frac{7}{6} - \frac{11}{9} \cdot \frac{21}{8} = 58 - \frac{35}{24} - \frac{231}{72} = 58 - \frac{35 \cdot 3}{24 \cdot 3} - \frac{231}{72} = 58 - \frac{105}{72} - \frac{231}{72} = 58 - \frac{105 + 231}{72} = 58 - \frac{336}{72} = 58 - \frac{56}{12} = 58 - \frac{14}{3} = 58 - 4\frac{2}{3} = 53\frac{1}{3}\)

2) \(1\frac{31}{32} \cdot 3\frac{1}{5} + (8\frac{5}{9} \cdot \frac{6}{35} + 3\frac{8}{15}) \cdot \frac{7}{50} = \frac{1 \cdot 32 + 31}{32} \cdot \frac{3 \cdot 5 + 1}{5} + (\frac{8 \cdot 9 + 5}{9} \cdot \frac{6}{35} + \frac{3 \cdot 15 + 8}{15}) \cdot \frac{7}{50} = \frac{63}{32} \cdot \frac{16}{5} + (\frac{77}{9} \cdot \frac{6}{35} + \frac{53}{15}) \cdot \frac{7}{50} = \frac{63}{2} \cdot \frac{1}{5} + (\frac{11}{3} \cdot \frac{2}{5} + \frac{53}{15}) \cdot \frac{7}{50} = \frac{63}{10} + (\frac{22}{15} + \frac{53}{15}) \cdot \frac{7}{50} = \frac{63}{10} + \frac{75}{15} \cdot \frac{7}{50} = \frac{63}{10} + 5 \cdot \frac{7}{50} = \frac{63}{10} + \frac{7}{10} = \frac{70}{10} = 7\)

Ответ: 1) \(53\frac{1}{3}\); 2) \(7\)