2.463 Найдите значение выражения: 1 3 a) 5:1+2--1:10: 3 7 1 1 6) 2:-1--+(-+\5:3 15 584 1 11 14 2 1 7 B) (-+1)- --:1--: 4 14 57 3 6 32 e) (-): 2 48 д) (10--7):5 13 26 6

a) $$5\frac{4}{5}:1\frac{1}{3}+2\frac{1}{3}-1:1\frac{3}{7} = \frac{29}{5} : \frac{4}{3} + \frac{7}{3} - 1 : \frac{10}{7} = \frac{29}{5} \cdot \frac{3}{4} + \frac{7}{3} - 1 \cdot \frac{7}{10} = \frac{87}{20} + \frac{7}{3} - \frac{7}{10} = \frac{87 \cdot 3 + 7 \cdot 20 - 7 \cdot 6}{60} = \frac{261 + 140 - 42}{60} = \frac{359}{60} = 5 \frac{59}{60}$$

б) $$2\frac{1}{6}:(\frac{11}{15}-\frac{1}{5}) + (2\frac{1}{8}+\frac{3}{4}):5\frac{3}{4} = \frac{13}{6}:(\frac{11-3}{15}) + (\frac{17}{8}+\frac{6}{8}):\frac{23}{4} = \frac{13}{6}:\frac{8}{15} + \frac{23}{8}:\frac{23}{4} = \frac{13}{6} \cdot \frac{15}{8} + \frac{23}{8} \cdot \frac{4}{23} = \frac{13 \cdot 5}{2 \cdot 8} + \frac{1}{2} = \frac{65}{16} + \frac{8}{16} = \frac{73}{16} = 4 \frac{9}{16}$$

в) $$(\frac{1}{4}+1\frac{11}{14}) \cdot \frac{14}{57} - 2\frac{1}{3}:1\frac{1}{6}:32\frac{1}{7} = (\frac{1}{4}+\frac{25}{14}) \cdot \frac{14}{57} - \frac{7}{3}:\frac{7}{6}:\frac{225}{7} = (\frac{7+50}{28}) \cdot \frac{14}{57} - \frac{7}{3} \cdot \frac{6}{7} \cdot \frac{7}{225} = \frac{57}{28} \cdot \frac{14}{57} - \frac{7 \cdot 6 \cdot 7}{3 \cdot 7 \cdot 225} = \frac{1}{2} - \frac{2 \cdot 7}{225} = \frac{1}{2} - \frac{14}{225} = \frac{225 - 28}{450} = \frac{197}{450}$$

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

е) $$((\frac{11}{2})^3-\frac{3}{4}):\frac{7}{8} = (\frac{1331}{8}-\frac{6}{8}):\frac{7}{8} = \frac{1325}{8} \cdot \frac{8}{7} = \frac{1325}{7} = 189 \frac{2}{7}$$

Ответ: a) $$5 \frac{59}{60}$$, б) $$4 \frac{9}{16}$$, в) $$\frac{197}{450}$$, д) $$3$$, е) $$189 \frac{2}{7}$$