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

1) \(\frac{12}{35}:\frac{2}{5}=\frac{12}{35}\cdot \frac{5}{2}=\frac{12\cdot 5}{35 \cdot 2}=\frac{6\cdot 1}{7\cdot 1}=\frac{6}{7}\)

2) \(\frac{15}{17}:5=\frac{15}{17}:\frac{5}{1}=\frac{15}{17}\cdot \frac{1}{5}=\frac{15 \cdot 1}{17\cdot 5}=\frac{3 \cdot 1}{17 \cdot 1}=\frac{3}{17}\)

3) \(4:\frac{20}{21}=\frac{4}{1}:\frac{20}{21}=\frac{4}{1}\cdot \frac{21}{20}=\frac{4 \cdot 21}{1 \cdot 20}=\frac{1 \cdot 21}{1 \cdot 5}=\frac{21}{5}=4\frac{1}{5}\)

4) \(8\frac{3}{4}:2\frac{1}{3}=\frac{8\cdot 4+3}{4}:\frac{2\cdot 3+1}{3}=\frac{35}{4}:\frac{7}{3}=\frac{35}{4}\cdot \frac{3}{7}=\frac{35 \cdot 3}{4 \cdot 7}=\frac{5 \cdot 3}{4 \cdot 1}=\frac{15}{4}=3\frac{3}{4}\)

Ответ: 1) \(\frac{6}{7}\); 2) \(\frac{3}{17}\); 3) \(4\frac{1}{5}\); 4) \(3\frac{3}{4}\)