4.309 Найдите частное: a) \(\frac{7}{9} : \frac{2}{3}\); б) \(\frac{3}{13} : (\frac{9}{26}\); в) \(\frac{16}{35} : (\frac{4}{25}\); г) \(\frac{5}{8} : (\frac{15}{64}\); д) \(\frac{4}{5} : (-16)\); e) \(-9 : \frac{9}{11}\).

Ответ:

1. a) \(\frac{7}{9} : \frac{2}{3} = \frac{7}{9} \cdot \frac{3}{2} = \frac{7 \cdot 3}{9 \cdot 2} = \frac{7 \cdot 1}{3 \cdot 2} = \frac{7}{6} = 1\frac{1}{6}\)

2. б) \(\frac{3}{13} : (\frac{9}{26}) = \frac{3}{13} \cdot \frac{26}{9} = \frac{3 \cdot 26}{13 \cdot 9} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3}\)

3. в) \(\frac{16}{35} : (\frac{4}{25}) = \frac{16}{35} \cdot \frac{25}{4} = \frac{16 \cdot 25}{35 \cdot 4} = \frac{4 \cdot 5}{7 \cdot 1} = \frac{20}{7} = 2\frac{6}{7}\)

4. г) \(\frac{5}{8} : (\frac{15}{64}) = \frac{5}{8} \cdot \frac{64}{15} = \frac{5 \cdot 64}{8 \cdot 15} = \frac{1 \cdot 8}{1 \cdot 3} = \frac{8}{3} = 2\frac{2}{3}\)

5. д) \(\frac{4}{5} : (-16) = \frac{4}{5} \cdot (-\frac{1}{16}) = -\frac{4 \cdot 1}{5 \cdot 16} = -\frac{1 \cdot 1}{5 \cdot 4} = -\frac{1}{20}\)

6. e) \(-9 : \frac{9}{11} = -9 \cdot \frac{11}{9} = -\frac{9 \cdot 11}{9} = -11\)

Ответ: