79. Найдите частное: 1) 10 : 5/9; 2) 1 : 8/13; 3) 9/16 : 36; 4) 2 13/16 : 4 3/8; 5) 3 1/3 : 2 6/7; 6) 3 6/7 : 9/28.

Решение:

1. \( 10 : \frac{5}{9} = 10 \times \frac{9}{5} = 2 \times 9 = 18 \)
2. \( 1 : \frac{8}{13} = 1 \times \frac{13}{8} = \frac{13}{8} \)
3. \( \frac{9}{16} : 36 = \frac{9}{16} \times \frac{1}{36} = \frac{1}{16} \times \frac{1}{4} = \frac{1}{64} \)
4. \( 2 \frac{13}{16} : 4 \frac{3}{8} = \frac{2 \times 16 + 13}{16} : \frac{4 \times 8 + 3}{8} = \frac{45}{16} : \frac{35}{8} = \frac{45}{16} \times \frac{8}{35} = \frac{45}{2} \times \frac{1}{35} = \frac{9}{2} \times \frac{1}{7} = \frac{9}{14} \)
5. \( 3 \frac{1}{3} : 2 \frac{6}{7} = \frac{3 \times 3 + 1}{3} : \frac{2 \times 7 + 6}{7} = \frac{10}{3} : \frac{20}{7} = \frac{10}{3} \times \frac{7}{20} = \frac{1}{3} \times \frac{7}{2} = \frac{7}{6} \)
6. \( 3 \frac{6}{7} : \frac{9}{28} = \frac{3 \times 7 + 6}{7} : \frac{9}{28} = \frac{27}{7} : \frac{9}{28} = \frac{27}{7} \times \frac{28}{9} = 3 \times 4 = 12 \)

Ответ: 1) 18; 2) \( \frac{13}{8} \); 3) \( \frac{1}{64} \); 4) \( \frac{9}{14} \); 5) \( \frac{7}{6} \); 6) 12.