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

79. Найдите частное:

1) $$10:\frac{5}{9}=10 \cdot \frac{9}{5}=\frac{10}{1} \cdot \frac{9}{5}=\frac{2 \cdot 5}{1} \cdot \frac{9}{5}=\frac{2}{1} \cdot \frac{9}{1}=\frac{18}{1}=18$$

Ответ: 18

2) $$1:\frac{8}{13}=1 \cdot \frac{13}{8}=\frac{13}{8}=1\frac{5}{8}$$

Ответ: $$1\frac{5}{8}$$

3) $$\frac{9}{16}:36=\frac{9}{16}:\frac{36}{1}=\frac{9}{16} \cdot \frac{1}{36}=\frac{9}{16} \cdot \frac{1}{4 \cdot 9}=\frac{1}{16} \cdot \frac{1}{4}=\frac{1}{64}$$

Ответ: $$\frac{1}{64}$$

4) $$2\frac{13}{16}:4=\frac{2 \cdot 16+13}{16}:\frac{4}{1}=\frac{32+13}{16} \cdot \frac{1}{4}=\frac{45}{16} \cdot \frac{1}{4}=\frac{45}{64}$$

Ответ: $$\frac{45}{64}$$

5) $$3\frac{1}{7}:2\frac{6}{7}=\frac{3 \cdot 7+1}{7}:\frac{2 \cdot 7+6}{7}=\frac{21+1}{7}:\frac{14+6}{7}=\frac{22}{7} \cdot \frac{7}{20}=\frac{22}{1} \cdot \frac{1}{20}=\frac{2 \cdot 11}{1} \cdot \frac{1}{2 \cdot 10}=\frac{11}{1} \cdot \frac{1}{10}=\frac{11}{10}=1\frac{1}{10}$$

Ответ: $$1\frac{1}{10}$$

6) $$3\frac{9}{28}:3\frac{6}{7}=\frac{3 \cdot 28+9}{28}:\frac{3 \cdot 7+6}{7}=\frac{84+9}{28}:\frac{21+6}{7}=\frac{93}{28}:\frac{27}{7}=\frac{93}{28} \cdot \frac{7}{27}=\frac{31 \cdot 3}{4 \cdot 7} \cdot \frac{7}{9 \cdot 3}=\frac{31}{4} \cdot \frac{1}{9}=\frac{31}{36}$$

Ответ: $$\frac{31}{36}$$