1. Выполните деление: 1) $$\frac{7}{15} : \frac{14}{25}$$ 2) $$\frac{8}{13} : 4$$ 3) $$9 : \frac{27}{28}$$ 4) $$2\frac{2}{9} : 1\frac{7}{9}$$

Решение:

1. 1) $$\frac{7}{15} : \frac{14}{25} = \frac{7}{15} \times \frac{25}{14} = \frac{7 \times 25}{15 \times 14} = \frac{7 \times 5 \times 5}{3 \times 5 \times 2 \times 7} = \frac{5}{6}$$
2. 2) $$\frac{8}{13} : 4 = \frac{8}{13} : \frac{4}{1} = \frac{8}{13} \times \frac{1}{4} = \frac{8 \times 1}{13 \times 4} = \frac{2 \times 4}{13 \times 4} = \frac{2}{13}$$
3. 3) $$9 : \frac{27}{28} = \frac{9}{1} : \frac{27}{28} = \frac{9}{1} \times \frac{28}{27} = \frac{9 \times 28}{1 \times 27} = \frac{9 \times 28}{27} = \frac{1 \times 28}{3} = \frac{28}{3} = 9\frac{1}{3}$$
4. 4) $$2\frac{2}{9} : 1\frac{7}{9} = \frac{2 \times 9 + 2}{9} : \frac{1 \times 9 + 7}{9} = \frac{20}{9} : \frac{16}{9} = \frac{20}{9} \times \frac{9}{16} = \frac{20 \times 9}{9 \times 16} = \frac{20}{16} = \frac{5 \times 4}{4 \times 4} = \frac{5}{4} = 1\frac{1}{4}$$

Ответ: 1) $$\frac{5}{6}$$, 2) $$\frac{2}{13}$$, 3) $$9\frac{1}{3}$$, 4) $$1\frac{1}{4}$$