Вычислите: 1) $$\frac{12}{35} : \frac{2}{5}$$; 2) $$\frac{15}{17} : 5$$; 3) $$4 : \frac{20}{21}$$; 4) $$8\frac{3}{4} : 2\frac{1}{3}$$.

Решение:

1. $$\frac{12}{35} : \frac{2}{5} = \frac{12}{35} * \frac{5}{2} = \frac{12 * 5}{35 * 2} = \frac{60}{70} = \frac{6}{7}$$
2. $$\frac{15}{17} : 5 = \frac{15}{17} : \frac{5}{1} = \frac{15}{17} * \frac{1}{5} = \frac{15 * 1}{17 * 5} = \frac{15}{85} = \frac{3}{17}$$
3. $$4 : \frac{20}{21} = \frac{4}{1} : \frac{20}{21} = \frac{4}{1} * \frac{21}{20} = \frac{4 * 21}{1 * 20} = \frac{84}{20} = \frac{21}{5} = 4\frac{1}{5}$$
4. $$8\frac{3}{4} : 2\frac{1}{3} = \frac{8 * 4 + 3}{4} : \frac{2 * 3 + 1}{3} = \frac{35}{4} : \frac{7}{3} = \frac{35}{4} * \frac{3}{7} = \frac{35 * 3}{4 * 7} = \frac{105}{28} = \frac{15}{4} = 3\frac{3}{4}$$

Ответы:

1. $$\frac{6}{7}$$
2. $$\frac{3}{17}$$
3. $$4\frac{1}{5}$$
4. $$3\frac{3}{4}$$