Выполните действия: а) (3 7/30 − 1 5/12) : 18 1/6; б) (1 1/2 + 2 2/3) : 1 2/3; в) (11/18 − 1 7/12) · (2 1/6 + 7/30); г) (3 2/5 − 5) · (31/48 + 7/24).

а)

\(3\frac{7}{30}=\frac{97}{30}\), \(1\frac{5}{12}=\frac{17}{12}\), \(18\frac{1}{6}=\frac{109}{6}\).

\[\left(\frac{97}{30}-\frac{17}{12}\right):\frac{109}{6}=\left(\frac{194}{60}-\frac{85}{60}\right)\cdot\frac{6}{109}=\frac{109}{60}\cdot\frac{6}{109}=\frac{1}{10}.\]

б)

\(1\frac{1}{2}=\frac{3}{2}\), \(2\frac{2}{3}=\frac{8}{3}\), \(1\frac{2}{3}=\frac{5}{3}\).

\[\left(\frac{3}{2}+\frac{8}{3}\right):\frac{5}{3}=\left(\frac{9}{6}+\frac{16}{6}\right)\cdot\frac{3}{5}=\frac{25}{6}\cdot\frac{3}{5}=\frac{5}{2}=2\frac{1}{2}.\]

в)

\(1\frac{7}{12}=\frac{19}{12}\), \(2\frac{1}{6}=\frac{13}{6}\).

\[\left(\frac{11}{18}-\frac{19}{12}\right)\cdot\left(\frac{13}{6}+\frac{7}{30}\right)=\left(\frac{22}{36}-\frac{57}{36}\right)\cdot\left(\frac{65}{30}+\frac{7}{30}\right)=\left(-\frac{35}{36}\right)\cdot\frac{12}{5}=-\frac{7}{3}=-2\frac{1}{3}.\]

г)

\(3\frac{2}{5}=\frac{17}{5}\).

\[\left(\frac{17}{5}-5\right)\cdot\left(\frac{31}{48}+\frac{7}{24}\right)=\left(-\frac{8}{5}\right)\cdot\left(\frac{31}{48}+\frac{14}{48}\right)=\left(-\frac{8}{5}\right)\cdot\frac{45}{48}=-\frac{3}{2}=-1\frac{1}{2}.\]

Ответ: а) \(\frac{1}{10}\); б) \(2\frac{1}{2}\); в) \(-2\frac{1}{3}\); г) \(-1\frac{1}{2}\).