1. Выполните действие: a) \(\frac{4}{9} : \frac{5}{7}\) б) \(\frac{8}{15} : \frac{3}{32}\) в) \(4\frac{1}{5} - 3\frac{3}{4}\) г) \(2\frac{6}{11} : 22\) д) \(\frac{4}{11} : \frac{8}{33}\) e) \(\frac{15}{17} : 5\)

Решение:

1. \(\frac{4}{9} : \frac{5}{7} = \frac{4}{9} \cdot \frac{7}{5} = \frac{28}{45}\)
2. \(\frac{8}{15} : \frac{3}{32} = \frac{8}{15} \cdot \frac{32}{3} = \frac{256}{45}\)
3. \(4\frac{1}{5} - 3\frac{3}{4} = \frac{21}{5} - \frac{15}{4} = \frac{21 \cdot 4 - 15 \cdot 5}{20} = \frac{84 - 75}{20} = \frac{9}{20}\)
4. \(2\frac{6}{11} : 22 = \frac{28}{11} : 22 = \frac{28}{11 \cdot 22} = \frac{28}{242} = \frac{14}{121}\)
5. \(\frac{4}{11} : \frac{8}{33} = \frac{4}{11} \cdot \frac{33}{8} = \frac{4 \cdot 33}{11 \cdot 8} = \frac{1 \cdot 3}{1 \cdot 2} = \frac{3}{2}\)
6. \(\frac{15}{17} : 5 = \frac{15}{17 \cdot 5} = \frac{3}{17}\)

Ответ: а) \(\frac{28}{45}\); б) \(\frac{256}{45}\); в) \(\frac{9}{20}\); г) \(\frac{14}{121}\); д) \(\frac{3}{2}\); е) \(\frac{3}{17}\).