2.453. Найдите значение выражения: а) 4/5 : 1 1/3 + 2 1/3 · 3/7 − 1 : 1 3/8; б) 2 1/6 : (1 1/15 − 1/5) + (2 1/8 + 3/4) : 5 3/4; в) (1/4 + 1 11/14) · 14/57 − 2/3 : 1 1/6 · 7/32; г) (2 1/2 : 3 1/3 + 3 1/3 : 2 1/2) · 9 3/5; д) (10 5/13 − 7 23/26) : 5/6; е) ((1 1/2)^3 − 3/4) : 7/8.

а)

\(\frac{4}{5}:1\frac{1}{3}+2\frac{1}{3}\cdot\frac{3}{7}-1:1\frac{3}{8}\)

\(=\frac{4}{5}:\frac{4}{3}+\frac{7}{3}\cdot\frac{3}{7}-1:\frac{11}{8}\)

\(=\frac{3}{5}+1-\frac{8}{11}=\frac{48}{55}\)

б)

\(2\frac{1}{6}:(1\frac{1}{15}-\frac{1}{5})+(2\frac{1}{8}+\frac{3}{4}):5\frac{3}{4}\)

\(=\frac{13}{6}:\frac{13}{15}+\frac{23}{8}:\frac{23}{4}\)

\(=\frac{5}{2}+\frac{1}{2}=3\)

в)

\((\frac{1}{4}+1\frac{11}{14})\cdot\frac{14}{57}-\frac{2}{3}:1\frac{1}{6}\cdot\frac{7}{32}\)

\(=\frac{57}{28}\cdot\frac{14}{57}-\frac{2}{3}:\frac{7}{6}\cdot\frac{7}{32}\)

\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

г)

\((2\frac{1}{2}:3\frac{1}{3}+3\frac{1}{3}:2\frac{1}{2})\cdot9\frac{3}{5}\)

\(=(\frac{5}{2}:\frac{10}{3}+\frac{10}{3}:\frac{5}{2})\cdot\frac{48}{5}\)

\(=(\frac{3}{4}+\frac{4}{3})\cdot\frac{48}{5}=\frac{25}{12}\cdot\frac{48}{5}=20\)

д)

\((10\frac{5}{13}-7\frac{23}{26}):\frac{5}{6}\)

\(=(\frac{265}{26}-\frac{205}{26}):\frac{5}{6}=\frac{30}{13}\cdot\frac{6}{5}=\frac{36}{13}\)

е)

\(((1\frac{1}{2})^3-\frac{3}{4}):\frac{7}{8}\)

\(=(\frac{3}{2})^3-\frac{3}{4}\;\Big/\;\frac{7}{8}\)

\(=(\frac{27}{8}-\frac{6}{8}):\frac{7}{8}=\frac{21}{8}\cdot\frac{8}{7}=3\)

Ответ: а) \(\frac{48}{55}\); б) \(3\); в) \(\frac{3}{8}\); г) \(20\); д) \(\frac{36}{13}\); е) \(3\).