34. 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)

\(3\frac{7}{30}-1\frac{5}{12}=\frac{197}{30}-\frac{17}{12}=\frac{394-85}{60}=\frac{103}{20}\).

\(18\frac{1}{6}=\frac{109}{6}\), поэтому

\(\frac{103}{20}:\frac{109}{6}=\frac{103}{20}\cdot\frac{6}{109}=\frac{309}{1090}\).

б)

\(1\frac{1}{2}+2\frac{2}{3}=\frac{3}{2}+\frac{8}{3}=\frac{9+16}{6}=\frac{25}{6}\).

\(1\frac{2}{3}=\frac{5}{3}\), поэтому

\(\frac{25}{6}:\frac{5}{3}=\frac{25}{6}\cdot\frac{3}{5}=\frac{5}{2}=2\frac{1}{2}\).

в)

\(\frac{11}{18}-1\frac{7}{12}=\frac{11}{18}-\frac{19}{12}=\frac{22-57}{36}=-\frac{35}{36}\).

\(2\frac{1}{6}+\frac{7}{30}=\frac{13}{6}+\frac{7}{30}=\frac{65+7}{30}=\frac{12}{5}\).

\(-\frac{35}{36}\cdot\frac{12}{5}=-\frac{7}{3}=-2\frac{1}{3}\).

г)

\(3\frac{2}{5}-5=\frac{17}{5}-\frac{25}{5}=-\frac{8}{5}\).

\(\frac{31}{48}+\frac{7}{24}=\frac{31}{48}+\frac{14}{48}=\frac{15}{16}\).

\(-\frac{8}{5}\cdot\frac{15}{16}=-\frac{3}{2}=-1\frac{1}{2}\).

Ответ: а) \(\frac{309}{1090}\); б) \(2\frac{1}{2}\); в) \(-2\frac{1}{3}\); г) \(-1\frac{1}{2}\).