79. Найдите частное: 1) \(6:\frac{2}{7}\); 2) \(1:\frac{8}{19}\); 3) \(\frac{7}{25}:28\); 4) \(16:\frac{1}{3}:5\frac{5}{6}\); 5) \(2\frac{2}{3}:2\frac{2}{7}\); 6) \(4\frac{4}{9}:\frac{5}{27}\)

Решим примеры на деление смешанных чисел.

1) \(6:\frac{2}{7} = 6 \cdot \frac{7}{2} = \frac{6 \cdot 7}{2} = \frac{3 \cdot 2 \cdot 7}{2} = 3 \cdot 7 = 21\)

2) \(1:\frac{8}{19} = 1 \cdot \frac{19}{8} = \frac{19}{8} = 2\frac{3}{8}\)

3) \(\frac{7}{25}:28 = \frac{7}{25} \cdot \frac{1}{28} = \frac{7}{25 \cdot 28} = \frac{7}{25 \cdot 7 \cdot 4} = \frac{1}{25 \cdot 4} = \frac{1}{100}\)

4) \(16\frac{1}{3}:5\frac{5}{6} = \frac{16 \cdot 3 + 1}{3} : \frac{5 \cdot 6 + 5}{6} = \frac{49}{3} : \frac{35}{6} = \frac{49}{3} \cdot \frac{6}{35} = \frac{49 \cdot 6}{3 \cdot 35} = \frac{7 \cdot 7 \cdot 3 \cdot 2}{3 \cdot 7 \cdot 5} = \frac{7 \cdot 2}{5} = \frac{14}{5} = 2\frac{4}{5}\)

5) \(2\frac{2}{3}:2\frac{2}{7} = \frac{2 \cdot 3 + 2}{3} : \frac{2 \cdot 7 + 2}{7} = \frac{8}{3} : \frac{16}{7} = \frac{8}{3} \cdot \frac{7}{16} = \frac{8 \cdot 7}{3 \cdot 16} = \frac{8 \cdot 7}{3 \cdot 8 \cdot 2} = \frac{7}{3 \cdot 2} = \frac{7}{6} = 1\frac{1}{6}\)

6) \(4\frac{4}{9}:\frac{5}{27} = \frac{4 \cdot 9 + 4}{9} : \frac{5}{27} = \frac{40}{9} : \frac{5}{27} = \frac{40}{9} \cdot \frac{27}{5} = \frac{40 \cdot 27}{9 \cdot 5} = \frac{8 \cdot 5 \cdot 3 \cdot 9}{9 \cdot 5} = 8 \cdot 3 = 24\)

Ответ: 1) 21; 2) \(2\frac{3}{8}\); 3) \(\frac{1}{100}\); 4) \(2\frac{4}{5}\); 5) \(1\frac{1}{6}\); 6) 24