Вопрос:

11. Найдите значение выражения: а) \(9-3\frac{1}{2}\cdot\left(1\frac{3}{7}+2\frac{1}{2}\right):2\frac{1}{7}\); б) \(3\frac{7}{19}\cdot\left(\frac{5}{12}+\frac{3}{8}\right):1\frac{1}{3}-1\frac{1}{8}:\left(1\frac{1}{5}-\frac{1}{4}\right)\); в) \(2:3\frac{1}{5}+\left(3\frac{1}{4}-\frac{2}{3}\right):\frac{2}{3}-\left(2\frac{5}{18}-\frac{17}{36}\right)\cdot\frac{18}{65}\); г) \(\frac{4}{75}:\left(\frac{4}{5}\cdot1\frac{1}{4}\right):\left(\frac{23}{25}-\frac{13}{15}\right)\cdot1\frac{1}{15}-\frac{1}{15}\).

Ответ:

а) \(9-\frac{7}{2}\cdot\left(\frac{10}{7}+\frac{5}{2}\right):\frac{15}{7}=9-\frac{7}{2}\cdot\frac{55}{14}\cdot\frac{7}{15}=9-\frac{11}{4}=\frac{25}{4}=6\frac{1}{4}\).

б) \(\frac{64}{19}\cdot\frac{19}{24}:\frac{4}{3}-\frac{9}{8}:\frac{19}{20}=2-\frac{45}{38}=\frac{31}{38}\).

в) \(\frac{5}{16}+\frac{31}{12}\cdot\frac{3}{2}-\left(\frac{41}{36}\right)\cdot\frac{18}{65}=\frac{5}{16}+\frac{31}{8}-\frac{41}{130}=\frac{1323}{416}\).

г) \(\frac{4}{75}:1:\frac{2}{5}\cdot\frac{16}{75}-\frac{1}{15}=\frac{4}{75}\cdot\frac{5}{2}\cdot\frac{16}{75}-\frac{1}{15}=\frac{32}{225}-\frac{15}{225}=\frac{17}{225}\).

Ответ: а) \(6\frac{1}{4}\); б) \(\frac{31}{38}\); в) \(\frac{1323}{416}\); г) \(\frac{17}{225}\).