1. (6 баллов) Выполните действия: a) \(\frac{3}{7}\cdot\frac{5}{11}\), б) \(\frac{6}{25}\cdot\frac{5}{18}\); в) \(\frac{4}{7}\cdot 2\); г) \(\frac{5}{9}\cdot\frac{10}{27}\), д) \(\frac{12}{13}: 6\); е) \(4:\frac{6}{13}\).

a) \(\frac{3}{7}\cdot\frac{5}{11} = \frac{3\cdot 5}{7 \cdot 11} = \frac{15}{77}\)

б) \(\frac{6}{25}\cdot\frac{5}{18} = \frac{6\cdot 5}{25 \cdot 18} = \frac{1\cdot 1}{5 \cdot 3} = \frac{1}{15}\)

в) \(\frac{4}{7}\cdot 2 = \frac{4 \cdot 2}{7} = \frac{8}{7} = 1\frac{1}{7}\)

г) \(\frac{5}{9}\cdot\frac{10}{27} = \frac{5\cdot 10}{9 \cdot 27} = \frac{50}{243}\)

д) \(\frac{12}{13}: 6 = \frac{12}{13} \cdot \frac{1}{6} = \frac{12 \cdot 1}{13 \cdot 6} = \frac{2 \cdot 1}{13 \cdot 1} = \frac{2}{13}\)

е) \(4:\frac{6}{13} = 4 \cdot \frac{13}{6} = \frac{4 \cdot 13}{6} = \frac{2 \cdot 13}{3} = \frac{26}{3} = 8\frac{2}{3}\)

Ответ: a) \(\frac{15}{77}\); б) \(\frac{1}{15}\); в) \(1\frac{1}{7}\); г) \(\frac{50}{243}\); д) \(\frac{2}{13}\); е) \(8\frac{2}{3}\)