2463 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) : 5/6; e) ((1 1/2)^3 - 3/4) : 7/8.

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

Ответ: 48/55

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

Ответ: -63/4

в) $$(\frac{1}{4} + \frac{11}{14}) \cdot \frac{14}{57} - \frac{2}{3} : 1 \frac{1}{6} \cdot \frac{7}{32} = (\frac{7}{28} + \frac{22}{28}) \cdot \frac{14}{57} - \frac{2}{3} : \frac{7}{6} \cdot \frac{7}{32} = \frac{29}{28} \cdot \frac{14}{57} - \frac{2}{3} \cdot \frac{6}{7} \cdot \frac{7}{32} = \frac{29}{2 \cdot 57} - \frac{2 \cdot 6 \cdot 7}{3 \cdot 7 \cdot 32} = \frac{29}{114} - \frac{2 \cdot 2}{32} = \frac{29}{114} - \frac{1}{4} = \frac{58 - 114}{456} = -\frac{56}{456} = -\frac{14}{114} = -\frac{7}{57}$$

Ответ: -7/57

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

Ответ: 20

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

Ответ: 3

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

Ответ: 3