06 Найдите частное: a) \(\frac{4}{7} : \frac{16}{49}\) B) \(\frac{12}{25} : \frac{8}{15}\) 6) \(\frac{5}{9} : \frac{1}{2}\) a) \(\frac{9}{14} : \frac{18}{35}\)

Решение:

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

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

6) \(\frac{5}{9} : \frac{1}{2} = \frac{5}{9} \cdot \frac{2}{1} = \frac{10}{9}\)

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

Ответ: a) \(\frac{7}{4}\); B) \(\frac{9}{10}\); 6) \(\frac{10}{9}\); a) \(\frac{5}{4}\).