5. Выполните деление: a) \(\frac{3}{7} : \frac{5}{8}\) б) \(\frac{2}{3} : \frac{2}{7}\) в) \(8\frac{1}{3} : 2\frac{2}{3}\) г) \(\frac{6}{11} : 3\) д) \(3\frac{2}{9} : 2\frac{11}{12}\) е) \(6\frac{8}{15}\)

Решение:

1. а) \( \frac{3}{7} : \frac{5}{8} = \frac{3}{7} \cdot \frac{8}{5} = \frac{3 \cdot 8}{7 \cdot 5} = \frac{24}{35} \)
2. б) \( \frac{2}{3} : \frac{2}{7} = \frac{2}{3} \cdot \frac{7}{2} = \frac{7}{3} = 2\frac{1}{3} \)
3. в) \( 8\frac{1}{3} : 2\frac{2}{3} = \frac{8 \cdot 3 + 1}{3} : \frac{2 \cdot 3 + 2}{3} = \frac{25}{3} : \frac{8}{3} = \frac{25}{3} \cdot \frac{3}{8} = \frac{25}{8} = 3\frac{1}{8} \)
4. г) \( \frac{6}{11} : 3 = \frac{6}{11} \cdot \frac{1}{3} = \frac{2 \cdot 3}{11} \cdot \frac{1}{3} = \frac{2}{11} \)
5. д) \( 3\frac{2}{9} : 2\frac{11}{12} = \frac{3 \cdot 9 + 2}{9} : \frac{2 \cdot 12 + 11}{12} = \frac{29}{9} : \frac{35}{12} = \frac{29}{9} \cdot \frac{12}{35} = \frac{29}{3 \cdot 3} \cdot \frac{3 \cdot 4}{35} = \frac{29 \cdot 4}{3 \cdot 35} = \frac{116}{105} = 1\frac{11}{105} \)
6. е) \( 6\frac{8}{15} = \frac{6 \cdot 15 + 8}{15} = \frac{90+8}{15} = \frac{98}{15} \)

Ответ: а) \(\frac{24}{35}\); б) \(2\frac{1}{3}\); в) \(3\frac{1}{8}\); г) \(\frac{2}{11}\); д) \(1\frac{11}{105}\); е) \(\frac{98}{15}\).