641. Выполните действия: a) \(\frac{3}{4}:\frac{5}{6}+2\frac{1}{2}:\frac{2}{5}-1:1\frac{1}{1} \); б) \(2\frac{3}{4}:(\frac{11}{2}-\frac{2}{5})+\frac{3}{6}:3\frac{1}{6} \); в) \((\frac{2}{15}+\frac{7}{12})\cdot \frac{30}{43}-2:2\frac{1}{32} \); г) \((3\frac{1}{2}:4+\frac{4}{5}:2\frac{2}{3})\cdot 4\frac{4}{5} \); д) \((11\frac{5}{11}-8\frac{21}{22}):1\frac{1}{2} \); е) \(((1\frac{1}{2})^3-\frac{3}{4}):\frac{3}{8} \);

a)

$$\frac{3}{4}:\frac{5}{6}+2\frac{1}{2}:\frac{2}{5}-1:1\frac{1}{1} = \frac{3}{4} \cdot \frac{6}{5} + \frac{5}{2} \cdot \frac{5}{2} - 1 : \frac{2}{1} = \frac{18}{20} + \frac{25}{4} - \frac{1}{2} = \frac{9}{10} + \frac{25}{4} - \frac{1}{2} = \frac{18}{20} + \frac{125}{20} - \frac{10}{20} = \frac{18+125-10}{20} = \frac{133}{20} = 6\frac{13}{20}$$

б)

$$2\frac{3}{4}:(\frac{11}{2}-\frac{2}{5})+\frac{3}{6}:3\frac{1}{6} = \frac{11}{4} : (\frac{55}{10} - \frac{4}{10}) + \frac{1}{2} : \frac{19}{6} = \frac{11}{4} : \frac{51}{10} + \frac{1}{2} \cdot \frac{6}{19} = \frac{11}{4} \cdot \frac{10}{51} + \frac{6}{38} = \frac{110}{204} + \frac{6}{38} = \frac{55}{102} + \frac{3}{19} = \frac{55}{102} + \frac{18}{102} = \frac{55+18}{102} = \frac{73}{102}$$

в)

$$ (\frac{2}{15}+\frac{7}{12})\cdot \frac{30}{43}-2:2\frac{1}{32} = (\frac{8}{60} + \frac{35}{60}) \cdot \frac{30}{43} - 2 : \frac{65}{32} = \frac{43}{60} \cdot \frac{30}{43} - 2 \cdot \frac{32}{65} = \frac{30}{60} - \frac{64}{65} = \frac{1}{2} - \frac{64}{65} = \frac{65}{130} - \frac{128}{130} = -\frac{63}{130} $$

г)

$$ (3\frac{1}{2}:4+\frac{4}{5}:2\frac{2}{3})\cdot 4\frac{4}{5} = (\frac{7}{2} : 4 + \frac{4}{5} : \frac{8}{3}) \cdot \frac{24}{5} = (\frac{7}{2} \cdot \frac{1}{4} + \frac{4}{5} \cdot \frac{3}{8}) \cdot \frac{24}{5} = (\frac{7}{8} + \frac{12}{40}) \cdot \frac{24}{5} = (\frac{7}{8} + \frac{3}{10}) \cdot \frac{24}{5} = (\frac{35}{40} + \frac{12}{40}) \cdot \frac{24}{5} = \frac{47}{40} \cdot \frac{24}{5} = \frac{47 \cdot 24}{40 \cdot 5} = \frac{47 \cdot 3 \cdot 8}{5 \cdot 8 \cdot 5} = \frac{141}{25} = 5\frac{16}{25} $$

д)

$$ (11\frac{5}{11}-8\frac{21}{22}):1\frac{1}{2} = (\frac{126}{11} - \frac{197}{22}) : \frac{3}{2} = (\frac{252}{22} - \frac{197}{22}) : \frac{3}{2} = \frac{55}{22} : \frac{3}{2} = \frac{5}{2} : \frac{3}{2} = \frac{5}{2} \cdot \frac{2}{3} = \frac{5}{3} = 1\frac{2}{3} $$

е)

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

Ответ: a) \(6\frac{13}{20}\); б) \(\frac{73}{102}\); в) -\(\frac{63}{130}\); г) \(5\frac{16}{25}\); д) \(1\frac{2}{3}\); е) 7.