11. Найдите значение выражения: а) 9 − 3 1/2 · (1 3/7 + 2 1/2) : 2 1/7; б) 3 7/19 · (5/12 + 3/8) : 1 1/3 − 1 1/8 : (1 1/5 − 1/4).

а)

Преобразуем смешанные числа в неправильные дроби:

\(3\frac{1}{2}=\frac{7}{2}\), \(1\frac{3}{7}=\frac{10}{7}\), \(2\frac{1}{2}=\frac{5}{2}\), \(2\frac{1}{7}=\frac{15}{7}\).

\[9-\frac{7}{2}\cdot\left(\frac{10}{7}+\frac{5}{2}\right):\frac{15}{7}\]

\[\frac{10}{7}+\frac{5}{2}=\frac{20}{14}+\frac{35}{14}=\frac{55}{14}\]

\[\frac{7}{2}\cdot\frac{55}{14}:\frac{15}{7}=\frac{7}{2}\cdot\frac{55}{14}\cdot\frac{7}{15}=\frac{77}{12}\]

\[9-\frac{77}{12}=\frac{108}{12}-\frac{77}{12}=\frac{31}{12}=2\frac{7}{12}\]

б)

Преобразуем смешанные числа:

\(3\frac{7}{19}=\frac{64}{19}\), \(1\frac{1}{3}=\frac{4}{3}\), \(1\frac{1}{8}=\frac{9}{8}\), \(1\frac{1}{5}=\frac{6}{5}\).

\[\frac{64}{19}\cdot\left(\frac{5}{12}+\frac{3}{8}\right):\frac{4}{3}-\frac{9}{8}:\left(\frac{6}{5}-\frac{1}{4}\right)\]

\[\frac{5}{12}+\frac{3}{8}=\frac{10}{24}+\frac{9}{24}=\frac{19}{24}\]

\[\frac{64}{19}\cdot\frac{19}{24}:\frac{4}{3}=\frac{8}{3}\cdot\frac{3}{4}=2\]

\[\frac{6}{5}-\frac{1}{4}=\frac{24}{20}-\frac{5}{20}=\frac{19}{20}\]

\[\frac{9}{8}:\frac{19}{20}=\frac{9}{8}\cdot\frac{20}{19}=\frac{45}{38}\]

\[2-\frac{45}{38}=\frac{76}{38}-\frac{45}{38}=\frac{31}{38}\]

Ответ: а) \(2\frac{7}{12}\); б) \(\frac{31}{38}\).