3) Выполните действия: a) $$\frac{4}{7}:\frac{8}{21}$$ b) $$1\frac{2}{3}:\frac{4}{15}$$ c) $$\left(5\frac{1}{5}-1\frac{4}{5}\right):\left(2-\frac{13}{15}\right)$$

a)

$$\frac{4}{7}:\frac{8}{21} = \frac{4}{7} \cdot \frac{21}{8} = \frac{4 \cdot 21}{7 \cdot 8} = \frac{4 \cdot 3 \cdot 7}{7 \cdot 4 \cdot 2} = \frac{3}{2} = 1\frac{1}{2}$$

Ответ: $$1\frac{1}{2}$$

b)

$$1\frac{2}{3}:\frac{4}{15} = \frac{5}{3}:\frac{4}{15} = \frac{5}{3} \cdot \frac{15}{4} = \frac{5 \cdot 15}{3 \cdot 4} = \frac{5 \cdot 3 \cdot 5}{3 \cdot 4} = \frac{25}{4} = 6\frac{1}{4}$$

Ответ: $$6\frac{1}{4}$$

c)

1) $$5\frac{1}{5} - 1\frac{4}{5} = 4\frac{6}{5} - 1\frac{4}{5} = 3\frac{2}{5} = \frac{17}{5}$$

2) $$2 - \frac{13}{15} = \frac{30}{15} - \frac{13}{15} = \frac{17}{15}$$

3) $$\frac{17}{5}:\frac{17}{15} = \frac{17}{5} \cdot \frac{15}{17} = \frac{17 \cdot 15}{5 \cdot 17} = \frac{17 \cdot 3 \cdot 5}{5 \cdot 17} = 3$$

Ответ: 3