Найдите частное: a) \(\frac{4}{7} : \frac{16}{49}\) б) \(\frac{5}{9} : 1\frac{1}{2}\) в) \(\frac{12}{25} : \frac{8}{15}\) г) \(\frac{9}{14} : \frac{18}{35}\)

Решение:

a) \( \frac{4}{7} : \frac{16}{49} = \frac{4}{7} \cdot \frac{49}{16} = \frac{4 \cdot 49}{7 \cdot 16} = \frac{4 \cdot (7 \cdot 7)}{(7) \cdot (4 \cdot 4)} = \frac{7}{4} = 1\frac{3}{4} \)

б) \( \frac{5}{9} : 1\frac{1}{2} = \frac{5}{9} : \frac{3}{2} = \frac{5}{9} \cdot \frac{2}{3} = \frac{5 \cdot 2}{9 \cdot 3} = \frac{10}{27} \)

в) \( \frac{12}{25} : \frac{8}{15} = \frac{12}{25} \cdot \frac{15}{8} = \frac{12 \cdot 15}{25 \cdot 8} = \frac{(3 \cdot 4) \cdot (3 \cdot 5)}{(5 \cdot 5) \cdot (2 \cdot 4)} = \frac{3 \cdot 3}{5 \cdot 2} = \frac{9}{10} \)

г) \( \frac{9}{14} : \frac{18}{35} = \frac{9}{14} \cdot \frac{35}{18} = \frac{9 \cdot 35}{14 \cdot 18} = \frac{(9) \cdot (5 \cdot 7)}{(2 \cdot 7) \cdot (2 \cdot 9)} = \frac{5}{2 \cdot 2} = \frac{5}{4} = 1\frac{1}{4} \)

Ответ: а) \(1\frac{3}{4}\); б) \(\frac{10}{27}\); в) \(\frac{9}{10}\); г) \(1\frac{1}{4}\).