Выполните действия: а) 7\(\frac{2}{9}\):4\(\frac{1}{3}\)⋅9; б) 5\(\frac{3}{7}\):\(\frac{8}{21}\)⋅2\(\frac{3}{8}\); в) 1\(\frac{11}{21}\)⋅3\(\frac{8}{9}\):1\(\frac{7}{9}\); г) \(\frac{5}{6}:\frac{6}{11}:1\frac{1}{11}\)

Решение:

а) \(7\frac{2}{9}:4\frac{1}{3}\cdot 9 = \frac{65}{9}:\frac{13}{3}\cdot 9=\frac{65}{9}\cdot \frac{3}{13}\cdot 9=\frac{65\cdot 3\cdot 9}{9\cdot 13}=\frac{5\cdot 3\cdot 9}{9}=\frac{135}{9}=15\cdot 3 = 15\)

Ответ: 15

б) \(5\frac{3}{7}:\frac{8}{21}\cdot 2\frac{3}{8} = \frac{38}{7}:\frac{8}{21}\cdot \frac{19}{8} = \frac{38}{7}\cdot \frac{21}{8}\cdot \frac{19}{8} = \frac{38\cdot 21\cdot 19}{7\cdot 8\cdot 8}=\frac{2\cdot 3\cdot 19}{8} = \frac{114}{8}=\frac{57}{4}=14\frac{1}{4}\)

Ответ: 14\(\frac{1}{4}\)

в) \(1\frac{11}{21}\cdot 3\frac{8}{9}:1\frac{7}{9}=\frac{32}{21}\cdot \frac{35}{9}:\frac{16}{9}=\frac{32}{21}\cdot \frac{35}{9}\cdot \frac{9}{16}=\frac{32\cdot 35\cdot 9}{21\cdot 9\cdot 16}=\frac{2\cdot 5}{3}=\frac{10}{3}=3\frac{1}{3}\)

Ответ: 3\(\frac{1}{3}\)

г) \(\frac{5}{6}:\frac{6}{11}:1\frac{1}{11}=\frac{5}{6}:\frac{6}{11}:\frac{12}{11}=\frac{5}{6}\cdot \frac{11}{6}\cdot \frac{11}{12}=\frac{5\cdot 11\cdot 11}{6\cdot 6\cdot 12}=\frac{605}{432}=1\frac{173}{432}\)

Ответ: 1\(\frac{173}{432}\)