3. Выполните деление: a) \(\frac{3}{4} : \frac{5}{7}\) б) \(\frac{9}{16} : \frac{3}{64}\) в) \(\frac{25}{72} : \frac{45}{63}\) r) \(8 : \frac{4}{5}\) д) \(1 : \frac{7}{16}\) е) \(\frac{8}{15} : 24\) ж) \(12\frac{1}{2} : 3\frac{3}{4}\) з) \(1\frac{3}{5} : 5\frac{1}{3}\)

Решение:

• а) \(\frac{3}{4} : \frac{5}{7} = \frac{3}{4} \cdot \frac{7}{5} = \frac{3 \cdot 7}{4 \cdot 5} = \frac{21}{20}\)
• б) \(\frac{9}{16} : \frac{3}{64} = \frac{9}{16} \cdot \frac{64}{3} = \frac{9 \cdot 64}{16 \cdot 3} = \frac{3 \cdot 3 \cdot 4 \cdot 16}{16 \cdot 3} = 12\)
• в) \(\frac{25}{72} : \frac{45}{63} = \frac{25}{72} \cdot \frac{63}{45} = \frac{25 \cdot 63}{72 \cdot 45} = \frac{5 \cdot 5 \cdot 7 \cdot 9}{8 \cdot 9 \cdot 5 \cdot 9} = \frac{35}{72}\)
• г) \(8 : \frac{4}{5} = \frac{8}{1} \cdot \frac{5}{4} = \frac{8 \cdot 5}{1 \cdot 4} = \frac{2 \cdot 4 \cdot 5}{4} = 10\)
• д) \(1 : \frac{7}{16} = \frac{1}{1} \cdot \frac{16}{7} = \frac{16}{7}\)
• е) \(\frac{8}{15} : 24 = \frac{8}{15} \cdot \frac{1}{24} = \frac{8}{15 \cdot 24} = \frac{8}{15 \cdot 3 \cdot 8} = \frac{1}{45}\)
• ж) \(12\frac{1}{2} : 3\frac{3}{4} = \frac{25}{2} : \frac{15}{4} = \frac{25}{2} \cdot \frac{4}{15} = \frac{25 \cdot 4}{2 \cdot 15} = \frac{5 \cdot 5 \cdot 2 \cdot 2}{2 \cdot 3 \cdot 5} = \frac{10}{3}\)
• з) \(1\frac{3}{5} : 5\frac{1}{3} = \frac{8}{5} : \frac{16}{3} = \frac{8}{5} \cdot \frac{3}{16} = \frac{8 \cdot 3}{5 \cdot 16} = \frac{8 \cdot 3}{5 \cdot 2 \cdot 8} = \frac{3}{10}\)

Ответ: а) \(\frac{21}{20}\), б) 12, в) \(\frac{35}{72}\), г) 10, д) \(\frac{16}{7}\), е) \(\frac{1}{45}\), ж) \(\frac{10}{3}\), з) \(\frac{3}{10}\)