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

Ответ: 1) \(\frac{6}{7}\); 2) \(\frac{3}{17}\); 3) \(\frac{21}{5}\); 4) \(\frac{105}{28}\)

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

Ответ: 1) \(\frac{6}{7}\); 2) \(\frac{3}{17}\); 3) \(\frac{21}{5}\); 4) \(\frac{105}{28}\)