82. Выполните деление:

Решение:

1. \( \frac{4}{9} : \frac{7}{9} = \frac{4}{9} \cdot \frac{9}{7} = \frac{4}{7} \)
2. \( \frac{9}{16} : \frac{5}{7} = \frac{9}{16} \cdot \frac{7}{5} = \frac{63}{80} \)
3. \( \frac{6}{25} : \frac{12}{35} = \frac{6}{25} \cdot \frac{35}{12} = \frac{6 \cdot 35}{25 \cdot 12} = \frac{1 \cdot 7}{5 \cdot 2} = \frac{7}{10} \)
4. \( \frac{5}{6} : \frac{55}{36} = \frac{5}{6} \cdot \frac{36}{55} = \frac{5 \cdot 36}{6 \cdot 55} = \frac{1 \cdot 6}{1 \cdot 11} = \frac{6}{11} \)
5. \( \frac{8}{65} : \frac{4}{13} = \frac{8}{65} \cdot \frac{13}{4} = \frac{8 \cdot 13}{65 \cdot 4} = \frac{2 \cdot 1}{5 \cdot 1} = \frac{2}{5} \)
6. \( \frac{48}{49} : \frac{32}{63} = \frac{48}{49} \cdot \frac{63}{32} = \frac{48 \cdot 63}{49 \cdot 32} = \frac{3 \cdot 9}{7 \cdot 2} = \frac{27}{14} \)

Ответ: 1) \( \frac{4}{7} \); 2) \( \frac{63}{80} \); 3) \( \frac{7}{10} \); 4) \( \frac{6}{11} \); 5) \( \frac{2}{5} \); 6) \( \frac{27}{14} \).