1. Выполните действия: a) \(\frac{5}{6}\cdot\frac{7}{9}\); б) \(\frac{11}{28}\cdot\frac{7}{33}\); в) \(6 \cdot \frac{3}{5}\); г) \(\frac{3}{8}:\frac{9}{16}\); д) \(\frac{15}{16}: 5\); e) \(\frac{9}{14}: 3\).

Ответ: a) \(\frac{35}{54}\); б) \(\frac{1}{12}\); в) \(\frac{18}{5}\); г) \(\frac{2}{3}\); д) \(\frac{3}{16}\); e) \(\frac{3}{14}\)

Решение:

1. a) \(\frac{5}{6}\cdot\frac{7}{9} = \frac{5 \cdot 7}{6 \cdot 9} = \frac{35}{54}\)
2. б) \(\frac{11}{28}\cdot\frac{7}{33} = \frac{11 \cdot 7}{28 \cdot 33} = \frac{1 \cdot 1}{4 \cdot 3} = \frac{1}{12}\)
3. в) \(6 \cdot \frac{3}{5} = \frac{6}{1} \cdot \frac{3}{5} = \frac{6 \cdot 3}{1 \cdot 5} = \frac{18}{5}\)
4. г) \(\frac{3}{8}:\frac{9}{16} = \frac{3}{8} \cdot \frac{16}{9} = \frac{3 \cdot 16}{8 \cdot 9} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3}\)
5. д) \(\frac{15}{16}: 5 = \frac{15}{16} : \frac{5}{1} = \frac{15}{16} \cdot \frac{1}{5} = \frac{15 \cdot 1}{16 \cdot 5} = \frac{3 \cdot 1}{16 \cdot 1} = \frac{3}{16}\)
6. e) \(\frac{9}{14}: 3 = \frac{9}{14} : \frac{3}{1} = \frac{9}{14} \cdot \frac{1}{3} = \frac{9 \cdot 1}{14 \cdot 3} = \frac{3 \cdot 1}{14 \cdot 1} = \frac{3}{14}\)

Ответ: a) \(\frac{35}{54}\); б) \(\frac{1}{12}\); в) \(\frac{18}{5}\); г) \(\frac{2}{3}\); д) \(\frac{3}{16}\); e) \(\frac{3}{14}\)