Вычислите: 7/9 * 5/6 : 4/15

1. $\frac{7}{9} \cdot \frac{5}{6} : \frac{4}{15} = \frac{7 \cdot 5 \cdot 15}{9 \cdot 6 \cdot 4} = \frac{7 \cdot 5 \cdot 5}{3 \cdot 6 \cdot 4} = \frac{175}{72} = 2\frac{31}{72}$ **Ответ: 2\frac{31}{72}** 2. $(\frac{2}{3} + \frac{4}{9}) \cdot \frac{3}{8} = (\frac{6}{9} + \frac{4}{9}) \cdot \frac{3}{8} = \frac{10}{9} \cdot \frac{3}{8} = \frac{5 \cdot 1}{3 \cdot 4} = \frac{5}{12}$ **Ответ: \frac{5}{12}** 3. $\frac{2}{7} + \frac{3}{8} \cdot \frac{7}{32} = \frac{2}{7} + \frac{21}{256} = \frac{512 + 147}{1792} = \frac{659}{1792}$ **Ответ: \frac{659}{1792}** 4. $\frac{5}{9} : (\frac{7}{9} + \frac{11}{18}) = \frac{5}{9} : (\frac{14}{18} + \frac{11}{18}) = \frac{5}{9} : \frac{25}{18} = \frac{5}{9} \cdot \frac{18}{25} = \frac{1 \cdot 2}{1 \cdot 5} = \frac{2}{5}$ **Ответ: \frac{2}{5}** 5. $1 - \frac{4}{7} \cdot \frac{16}{21} = 1 - \frac{64}{147} = \frac{147 - 64}{147} = \frac{83}{147}$ **Ответ: \frac{83}{147}** 6. $\frac{5}{12} \cdot (\frac{1}{5} + \frac{3}{25}) = \frac{5}{12} \cdot (\frac{5}{25} + \frac{3}{25}) = \frac{5}{12} \cdot \frac{8}{25} = \frac{1 \cdot 2}{3 \cdot 5} = \frac{2}{15}$ **Ответ: \frac{2}{15}** 7. $\frac{7}{39} \cdot (\frac{1}{7} + \frac{6}{49}) = \frac{7}{39} \cdot (\frac{7}{49} + \frac{6}{49}) = \frac{7}{39} \cdot \frac{13}{49} = \frac{1 \cdot 1}{3 \cdot 7} = \frac{1}{21}$ **Ответ: \frac{1}{21}** 8. $\frac{9}{14} \cdot (\frac{17}{24} - \frac{5}{12}) = \frac{9}{14} \cdot (\frac{17}{24} - \frac{10}{24}) = \frac{9}{14} \cdot \frac{7}{24} = \frac{3 \cdot 1}{2 \cdot 8} = \frac{3}{16}$ **Ответ: \frac{3}{16}**