Найдите значение выражения: а) \(\frac{4}{5}:1\frac{1}{3}+2\frac{1}{3}\cdot \frac{3}{7}-1:1\frac{3}{8}\); б) 2\(\frac{1}{6}:(\frac{1}{15}-\frac{1}{5})+(2\frac{1}{8}+\frac{3}{4}):5\frac{3}{4}\); в) (\(\frac{1}{4}+\frac{11}{14}\))⋅\(\frac{14}{57}-\frac{2}{3}:1\frac{1}{6}⋅\frac{7}{32}\); г) (2\(\frac{1}{2}:3\frac{1}{3}+3\frac{1}{3}:2\frac{1}{2}\))⋅9\frac{3}{5}\); д) (10\(\frac{5}{13}-7\frac{23}{26}\)):\(\frac{5}{6}\); е) ((1\(\frac{1}{2}\))^3-\frac{3}{4}\):\(\frac{7}{8}\)

Решение:

а) \(\frac{4}{5}:1\frac{1}{3}+2\frac{1}{3}\cdot \frac{3}{7}-1:1\frac{3}{8}=\frac{4}{5}:\frac{4}{3}+2\frac{1}{3}\cdot \frac{3}{7}-1:\frac{11}{8}=\frac{4}{5}\cdot \frac{3}{4}+\frac{7}{3}\cdot \frac{3}{7}-\frac{8}{11}=\frac{3}{5}+1-\frac{8}{11}=\frac{3}{5}+\frac{3}{1}-\frac{8}{11}=\frac{33+55-40}{55}=\frac{48}{55}\)

Ответ: \(\frac{48}{55}\)

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

Ответ: -15\(\frac{3}{4}\)

в) \((\frac{1}{4}+\frac{11}{14})\cdot \frac{14}{57}-\frac{2}{3}:1\frac{1}{6}\cdot \frac{7}{32}=(\frac{7+22}{28})\cdot \frac{14}{57}-\frac{2}{3}:\frac{7}{6}\cdot \frac{7}{32}=\frac{29}{28}\cdot \frac{14}{57}-\frac{2}{3}\cdot \frac{6}{7}\cdot \frac{7}{32}=\frac{29}{2\cdot 57}-\frac{2\cdot 6\cdot 7}{3\cdot 7\cdot 32}=\frac{29}{114}-\frac{12}{96}=\frac{29}{114}-\frac{1}{8}=\frac{29\cdot 4-57}{456}=\frac{116-57}{456}=\frac{59}{456}\)

Ответ: \(\frac{59}{456}\)

г) \((2\frac{1}{2}:3\frac{1}{3}+3\frac{1}{3}:2\frac{1}{2})\cdot 9\frac{3}{5}=(\frac{5}{2}:\frac{10}{3}+3\frac{1}{3}:2\frac{1}{2})\cdot \frac{48}{5}=(\frac{5}{2}\cdot \frac{3}{10}+\frac{10}{3}:\frac{5}{2})\cdot \frac{48}{5}=(\frac{3}{4}+\frac{10}{3}\cdot \frac{2}{5})\cdot \frac{48}{5}=(\frac{3}{4}+\frac{4}{3})\cdot \frac{48}{5}=(\frac{9+16}{12})\cdot \frac{48}{5}=\frac{25\cdot 48}{12\cdot 5}=\frac{25\cdot 4}{5}=\frac{100}{5}=20\)

Ответ: 20

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

Ответ: 3

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: 3