311. 1) \(\frac{5}{6}\cdot 8\); \(\frac{23}{20}\cdot 10\); \(\frac{23}{40}\cdot 8\); \(\frac{11}{12}\cdot 6\); \(\frac{8}{15}\cdot 3\); \(\frac{9}{35}\cdot 7\); \(\frac{8}{9}: 4\); \(\frac{3}{4}: 6\); \(\frac{2}{7}: 2\); \(\frac{8}{15}: 4\); \(\frac{2}{5}: 3\); \(\frac{6}{7}: 6.\)

1) \(\frac{5}{6}\cdot 8\); \(\frac{23}{20}\cdot 10\); \(\frac{23}{40}\cdot 8\); \(\frac{11}{12}\cdot 6\); \(\frac{8}{15}\cdot 3\); \(\frac{9}{35}\cdot 7\);

1. \(\frac{5}{6} \cdot 8 = \frac{5 \cdot 8}{6} = \frac{40}{6} = \frac{20}{3} = 6\frac{2}{3}\)
2. \(\frac{23}{20} \cdot 10 = \frac{23 \cdot 10}{20} = \frac{230}{20} = \frac{23}{2} = 11\frac{1}{2}\)
3. \(\frac{23}{40} \cdot 8 = \frac{23 \cdot 8}{40} = \frac{184}{40} = \frac{23}{5} = 4\frac{3}{5}\)
4. \(\frac{11}{12} \cdot 6 = \frac{11 \cdot 6}{12} = \frac{66}{12} = \frac{11}{2} = 5\frac{1}{2}\)
5. \(\frac{8}{15} \cdot 3 = \frac{8 \cdot 3}{15} = \frac{24}{15} = \frac{8}{5} = 1\frac{3}{5}\)
6. \(\frac{9}{35} \cdot 7 = \frac{9 \cdot 7}{35} = \frac{63}{35} = \frac{9}{5} = 1\frac{4}{5}\)

\(\frac{8}{9}: 4\); \(\frac{3}{4}: 6\); \(\frac{2}{7}: 2\); \(\frac{8}{15}: 4\); \(\frac{2}{5}: 3\); \(\frac{6}{7}: 6.\)

1. \(\frac{8}{9} : 4 = \frac{8}{9} \cdot \frac{1}{4} = \frac{8 \cdot 1}{9 \cdot 4} = \frac{8}{36} = \frac{2}{9}\)
2. \(\frac{3}{4} : 6 = \frac{3}{4} \cdot \frac{1}{6} = \frac{3 \cdot 1}{4 \cdot 6} = \frac{3}{24} = \frac{1}{8}\)
3. \(\frac{2}{7} : 2 = \frac{2}{7} \cdot \frac{1}{2} = \frac{2 \cdot 1}{7 \cdot 2} = \frac{2}{14} = \frac{1}{7}\)
4. \(\frac{8}{15} : 4 = \frac{8}{15} \cdot \frac{1}{4} = \frac{8 \cdot 1}{15 \cdot 4} = \frac{8}{60} = \frac{2}{15}\)
5. \(\frac{2}{5} : 3 = \frac{2}{5} \cdot \frac{1}{3} = \frac{2 \cdot 1}{5 \cdot 3} = \frac{2}{15}\)
6. \(\frac{6}{7} : 6 = \frac{6}{7} \cdot \frac{1}{6} = \frac{6 \cdot 1}{7 \cdot 6} = \frac{6}{42} = \frac{1}{7}\)

Ответ: 1) \(6\frac{2}{3}\), 2) \(11\frac{1}{2}\), 3) \(4\frac{3}{5}\), 4) \(5\frac{1}{2}\), 5) \(1\frac{3}{5}\), 6) \(1\frac{4}{5}\), 7) \(\frac{2}{9}\), 8) \(\frac{1}{8}\), 9) \(\frac{1}{7}\), 10) \(\frac{2}{15}\), 11) \(\frac{2}{15}\), 12) \(\frac{1}{7}\)