2.278 Выполните действие: a) \(2\frac{3}{4} : \frac{3}{7}\); б) \(\frac{5}{9} : 1\frac{2}{3}\); в) \(3\frac{4}{5} : \frac{5}{11}\); г) \(3\frac{1}{9} : \frac{3}{7}\); д) \(1\frac{5}{8} : \frac{8}{13}\); е) \(\frac{13}{24} : 1\frac{11}{13}\)

a) \(2\frac{3}{4} : \frac{3}{7} = \frac{11}{4} : \frac{3}{7} = \frac{11}{4} \cdot \frac{7}{3} = \frac{11 \cdot 7}{4 \cdot 3} = \frac{77}{12} = 6\frac{5}{12}\)

б) \(\frac{5}{9} : 1\frac{2}{3} = \frac{5}{9} : \frac{5}{3} = \frac{5}{9} \cdot \frac{3}{5} = \frac{5 \cdot 3}{9 \cdot 5} = \frac{3}{9} = \frac{1}{3}\)

в) \(3\frac{4}{5} : \frac{5}{11} = \frac{19}{5} : \frac{5}{11} = \frac{19}{5} \cdot \frac{11}{5} = \frac{19 \cdot 11}{5 \cdot 5} = \frac{209}{25} = 8\frac{9}{25}\)

г) \(3\frac{1}{9} : \frac{3}{7} = \frac{28}{9} : \frac{3}{7} = \frac{28}{9} \cdot \frac{7}{3} = \frac{28 \cdot 7}{9 \cdot 3} = \frac{196}{27} = 7\frac{7}{27}\)

д) \(1\frac{5}{8} : \frac{8}{13} = \frac{13}{8} : \frac{8}{13} = \frac{13}{8} \cdot \frac{13}{8} = \frac{13 \cdot 13}{8 \cdot 8} = \frac{169}{64} = 2\frac{41}{64}\)

е) \(\frac{13}{24} : 1\frac{11}{13} = \frac{13}{24} : \frac{24}{13} = \frac{13}{24} \cdot \frac{13}{24} = \frac{13 \cdot 13}{24 \cdot 24} = \frac{169}{576}\)

Ответ: a) \(6\frac{5}{12}\); б) \(\frac{1}{3}\); в) \(8\frac{9}{25}\); г) \(7\frac{7}{27}\); д) \(2\frac{41}{64}\); e) \(\frac{169}{576}\)