2.463 Найдите значение выражения: a) 4/5 : 1 1/3 + 2 1/3 · 3/7 - 1 : 1 3/8; б) 2 1/6 : (1/15 - 1/5) + (2 1/8 + 3/4) : 5 3/4; в) (1/4 + 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 5/6; e) ((1 1/2)^3 - 3/4) : 7/8.

Найдем значение выражения.

a) $$ \frac{4}{5} : 1 \frac{1}{3} + 2 \frac{1}{3} \cdot \frac{3}{7} - 1 : 1 \frac{3}{8} = \frac{4}{5} : \frac{4}{3} + \frac{7}{3} \cdot \frac{3}{7} - 1 : \frac{11}{8} = \frac{4}{5} \cdot \frac{3}{4} + \frac{7 \cdot 3}{3 \cdot 7} - 1 \cdot \frac{8}{11} = \frac{3}{5} + 1 - \frac{8}{11} = \frac{3}{5} + \frac{5}{5} - \frac{8}{11} = \frac{8}{5} - \frac{8}{11} = \frac{88 - 40}{55} = \frac{48}{55} $$

б) $$ 2 \frac{1}{6} : (\frac{1}{15} - \frac{1}{5}) + (2 \frac{1}{8} + \frac{3}{4}) : 5 \frac{3}{4} = \frac{13}{6} : (\frac{1}{15} - \frac{3}{15}) + (\frac{17}{8} + \frac{6}{8}) : \frac{23}{4} = \frac{13}{6} : (-\frac{2}{15}) + (\frac{23}{8}) : \frac{23}{4} = \frac{13}{6} \cdot (-\frac{15}{2}) + \frac{23}{8} \cdot \frac{4}{23} = -\frac{13 \cdot 5}{2 \cdot 2} + \frac{1}{2} = -\frac{65}{4} + \frac{2}{4} = -\frac{63}{4} = -15 \frac{3}{4} $$

в) $$ (\frac{1}{4} + \frac{11}{14}) \cdot \frac{14}{57} - \frac{2}{3} : 1 \frac{1}{6} \cdot \frac{7}{32} = (\frac{7}{28} + \frac{22}{28}) \cdot \frac{14}{57} - \frac{2}{3} : \frac{7}{6} \cdot \frac{7}{32} = (\frac{29}{28}) \cdot \frac{14}{57} - \frac{2}{3} \cdot \frac{6}{7} \cdot \frac{7}{32} = \frac{29 \cdot 1}{2 \cdot 57} - \frac{2 \cdot 6 \cdot 7}{3 \cdot 7 \cdot 32} = \frac{29}{114} - \frac{1}{4} = \frac{58 - 114}{228} = -\frac{56}{228} = -\frac{14}{57} $$

г) $$ (2 \frac{1}{2} : 3 \frac{1}{3} + 3 \frac{1}{3} : 2 \frac{1}{2}) \cdot 9 \frac{3}{5} = (\frac{5}{2} : \frac{10}{3} + \frac{10}{3} : \frac{5}{2}) \cdot \frac{48}{5} = (\frac{5}{2} \cdot \frac{3}{10} + \frac{10}{3} \cdot \frac{2}{5}) \cdot \frac{48}{5} = (\frac{3}{4} + \frac{4}{3}) \cdot \frac{48}{5} = (\frac{9 + 16}{12}) \cdot \frac{48}{5} = \frac{25}{12} \cdot \frac{48}{5} = \frac{5}{1} \cdot \frac{4}{1} = 20$$

д) $$(10 \frac{5}{13} - 7 \frac{23}{26}) : 5 \frac{5}{6} = (10 \frac{10}{26} - 7 \frac{23}{26}) : \frac{35}{6} = (9 \frac{36}{26} - 7 \frac{23}{26}) : \frac{35}{6} = 2 \frac{13}{26} : \frac{35}{6} = 2 \frac{1}{2} : \frac{35}{6} = \frac{5}{2} \cdot \frac{6}{35} = \frac{3}{7} $$

е) $$((1 \frac{1}{2})^3 - \frac{3}{4}) : \frac{7}{8} = ((\frac{3}{2})^3 - \frac{3}{4}) : \frac{7}{8} = (\frac{27}{8} - \frac{6}{8}) : \frac{7}{8} = \frac{21}{8} : \frac{7}{8} = \frac{21}{8} \cdot \frac{8}{7} = 3 $$

Ответ: a) $$\frac{48}{55}$$, б) $$-15 \frac{3}{4}$$, в) $$\frac{-14}{57}$$, г) 20, д) $$\frac{3}{7}$$, е) 3.