а)

Приведём смешанные числа к неправильным дробям:

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

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

б)

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

в)

\[\left(\frac{11}{18}-1\frac{7}{12}\right)\cdot\left(2\frac{1}{6}+\frac{7}{30}\right)=\left(\frac{22}{36}-\frac{55}{36}\right)\cdot\left(\frac{13}{6}+\frac{7}{30}\right).\]

\[=-\frac{11}{12}\cdot\frac{72}{30}=-\frac{11}{12}\cdot\frac{12}{5}=-\frac{11}{5}=-2\frac{1}{5}.\]

г)

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

\[=-\frac{8}{5}\cdot\frac{45}{48}=-\frac{8}{5}\cdot\frac{15}{16}=-\frac{3}{2}=-1\frac{1}{2}.\]

Ответ: а) \(\frac{1}{10}\); б) \(2\frac{1}{2}\); в) \(-2\frac{1}{5}\); г) \(-1\frac{1}{2}\).

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