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 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.

Решение:

1. a) $$\frac{4}{5} : 1 \frac{1}{3} + 2 \frac{1}{3} \cdot \frac{3}{7} - 1 : 1 \frac{3}{8} = \frac{4}{5} : \frac{4}{3} + \frac{7}{3} \cdot \frac{3}{7} - 1 : \frac{11}{8} = \frac{4}{5} \cdot \frac{3}{4} + \frac{7}{3} \cdot \frac{3}{7} - 1 \cdot \frac{8}{11} = \frac{3}{5} + 1 - \frac{8}{11} = \frac{3}{5} + \frac{5}{5} - \frac{8}{11} = \frac{8}{5} - \frac{8}{11} = \frac{88 - 40}{55} = \frac{48}{55}$$
2. б) $$2 \frac{1}{6} : (1 \frac{1}{15} - \frac{1}{5}) + (2 \frac{1}{8} + \frac{3}{4}) : 5 \frac{3}{4} = \frac{13}{6} : (\frac{16}{15} - \frac{3}{15}) + (\frac{17}{8} + \frac{6}{8}) : \frac{23}{4} = \frac{13}{6} : \frac{13}{15} + \frac{23}{8} : \frac{23}{4} = \frac{13}{6} \cdot \frac{15}{13} + \frac{23}{8} \cdot \frac{4}{23} = \frac{15}{6} + \frac{4}{8} = \frac{30}{12} + \frac{6}{12} = \frac{36}{12} = 3$$
3. в) $$(\frac{1}{4} + 1 \frac{11}{14}) \cdot \frac{14}{57} - \frac{2}{3} : 1 \frac{1}{6} \cdot \frac{7}{32} = (\frac{7}{28} + \frac{4 \cdot 25}{4 \cdot 14}) \cdot \frac{14}{57} - \frac{2}{3} : \frac{7}{6} \cdot \frac{7}{32} = (\frac{7}{28} + \frac{50}{28}) \cdot \frac{14}{57} - \frac{2}{3} \cdot \frac{6}{7} \cdot \frac{7}{32} = \frac{57}{28} \cdot \frac{14}{57} - \frac{2 \cdot 6 \cdot 7}{3 \cdot 7 \cdot 32} = \frac{1}{2} - \frac{12}{96} = \frac{1}{2} - \frac{1}{8} = \frac{4}{8} - \frac{1}{8} = \frac{3}{8}$$
4. г) $$(2 \frac{1}{2} : 3 \frac{1}{3} + 3 \frac{1}{3} : 2 \frac{1}{2}) \cdot 9 \frac{3}{5} = (\frac{5}{2} : \frac{10}{3} + \frac{10}{3} : \frac{5}{2}) \cdot \frac{48}{5} = (\frac{5}{2} \cdot \frac{3}{10} + \frac{10}{3} \cdot \frac{2}{5}) \cdot \frac{48}{5} = (\frac{3}{4} + \frac{4}{3}) \cdot \frac{48}{5} = (\frac{9}{12} + \frac{16}{12}) \cdot \frac{48}{5} = \frac{25}{12} \cdot \frac{48}{5} = \frac{25 \cdot 48}{12 \cdot 5} = \frac{5 \cdot 4}{1 \cdot 1} = 20$$
5. д) $$(10 \frac{5}{13} - 7 \frac{23}{26}) : \frac{5}{6} = (\frac{135}{13} - \frac{205}{26}) : \frac{5}{6} = (\frac{270}{26} - \frac{205}{26}) : \frac{5}{6} = \frac{65}{26} : \frac{5}{6} = \frac{65}{26} \cdot \frac{6}{5} = \frac{65 \cdot 6}{26 \cdot 5} = \frac{13 \cdot 3}{13 \cdot 1} = 3$$
6. е) $$((\frac{1}{2})^3 - \frac{3}{4}) : \frac{7}{8} = ((\frac{3}{2})^3 - \frac{3}{4}) : \frac{7}{8} = (\frac{27}{8} - \frac{6}{8}) : \frac{7}{8} = \frac{21}{8} : \frac{7}{8} = \frac{21}{8} \cdot \frac{8}{7} = \frac{21 \cdot 8}{8 \cdot 7} = 3$$

Ответ: а) $$\frac{48}{55}$$; б) $$3$$; в) $$\frac{3}{8}$$; г) $$20$$; д) $$3$$; е) $$3$$