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

a) $$\frac{1}{4} : (1\frac{1}{5} + 2\frac{1}{3}) - 1 : 1\frac{3}{8} = \frac{1}{4} : (\frac{6}{5} + \frac{7}{3}) - 1 : \frac{11}{8} = \frac{1}{4} : (\frac{18}{15} + \frac{35}{15}) - 1 \cdot \frac{8}{11} = \frac{1}{4} : \frac{53}{15} - \frac{8}{11} = \frac{1}{4} \cdot \frac{15}{53} - \frac{8}{11} = \frac{15}{212} - \frac{8}{11} = \frac{165}{2332} - \frac{1696}{2332} = -\frac{1531}{2332}$$

б) $$2\frac{5}{6} : (1\frac{1}{15} - \frac{1}{5}) + (2\frac{3}{4}) : 5\frac{3}{4} = \frac{17}{6} : (\frac{16}{15} - \frac{3}{15}) + (\frac{11}{4}) : \frac{23}{4} = \frac{17}{6} : \frac{13}{15} + \frac{11}{4} \cdot \frac{4}{23} = \frac{17}{6} \cdot \frac{15}{13} + \frac{11}{23} = \frac{17 \cdot 15}{6 \cdot 13} + \frac{11}{23} = \frac{17 \cdot 5}{2 \cdot 13} + \frac{11}{23} = \frac{85}{26} + \frac{11}{23} = \frac{1955}{598} + \frac{286}{598} = \frac{2241}{598} = 3\frac{447}{598}$$

в) $$(1\frac{1}{4} + \frac{11}{14}) : \frac{14}{57} - 2 : 1\frac{7}{32} = (\frac{5}{4} + \frac{11}{14}) : \frac{14}{57} - 2 : \frac{39}{32} = (\frac{35}{28} + \frac{22}{28}) : \frac{14}{57} - 2 \cdot \frac{32}{39} = \frac{57}{28} : \frac{14}{57} - \frac{64}{39} = \frac{57}{28} \cdot \frac{57}{14} - \frac{64}{39} = \frac{3249}{392} - \frac{64}{39} = \frac{126711}{15288} - \frac{20032}{15288} = \frac{106679}{15288} = 6\frac{15931}{15288}$$

г) $$(2\frac{1}{2} : 3\frac{1}{2} + 3\frac{1}{3} : 2\frac{1}{3}) : 9\frac{3}{5} = (\frac{5}{2} : \frac{7}{2} + \frac{10}{3} : \frac{7}{3}) : \frac{48}{5} = (\frac{5}{2} \cdot \frac{2}{7} + \frac{10}{3} \cdot \frac{3}{7}) : \frac{48}{5} = (\frac{5}{7} + \frac{10}{7}) : \frac{48}{5} = \frac{15}{7} : \frac{48}{5} = \frac{15}{7} \cdot \frac{5}{48} = \frac{15 \cdot 5}{7 \cdot 48} = \frac{75}{336} = \frac{25}{112}$$

д) $$(10\frac{5}{13} - 7\frac{23}{26}) : \frac{5}{6} = (\frac{135}{13} - \frac{205}{26}) : \frac{5}{6} = (\frac{270}{26} - \frac{205}{26}) : \frac{5}{6} = \frac{65}{26} : \frac{5}{6} = \frac{5}{2} : \frac{5}{6} = \frac{5}{2} \cdot \frac{6}{5} = \frac{5 \cdot 6}{2 \cdot 5} = \frac{6}{2} = 3$$

e) $$(1\frac{1}{2})^3 - \frac{3}{4} : \frac{7}{8} = (\frac{3}{2})^3 - \frac{3}{4} \cdot \frac{8}{7} = \frac{27}{8} - \frac{3 \cdot 8}{4 \cdot 7} = \frac{27}{8} - \frac{3 \cdot 2}{1 \cdot 7} = \frac{27}{8} - \frac{6}{7} = \frac{189}{56} - \frac{48}{56} = \frac{141}{56} = 2\frac{29}{56}$$

Ответ: а) $$\frac{-1531}{2332}$$; б) $$3\frac{447}{598}$$; в) $$6\frac{15931}{15288}$$; г) $$\frac{25}{112}$$; д) $$3$$; е) $$2\frac{29}{56}$$.