Вычислите значение выражения: а) \((1\frac{1}{3}-2\frac{5}{6}):(0,75-1\frac{1}{6})\); б) \(4-(4\frac{21}{40}-5,25):1\frac{9}{20}\); в) \((1,2-1\frac{7}{15})\cdot(-\frac{5}{8})-1\frac{1}{6}:2\frac{1}{3}\); г) \((-2,5+2\frac{1}{3})\cdot(-5\frac{1}{7})+1\frac{1}{3}:(-5,6)\); д) \((1,25-1\frac{1}{3})\cdot(-5\frac{1}{7})-1\frac{1}{6}:5\frac{4}{9}\).

а)

\(1\frac{1}{3}=\frac{4}{3}\), \(2\frac{5}{6}=\frac{17}{6}\), \(0,75=\frac{3}{4}\), поэтому

\((\frac{4}{3}-\frac{17}{6}):(\frac{3}{4}-\frac{7}{6})=(-\frac{3}{2}):(-\frac{5}{12})=\frac{18}{5}=3,6\).

б)

\(4\frac{21}{40}=\frac{181}{40}\), \(5,25=\frac{21}{4}=\frac{210}{40}\).

\(4-(\frac{181}{40}-\frac{210}{40}):\frac{29}{20}=4+\frac{29}{40}\cdot\frac{20}{29}=4+\frac{1}{2}=4\frac{1}{2}\).

в)

\(1,2=\frac{6}{5}=\frac{18}{15}\), \(1\frac{7}{15}=\frac{22}{15}\), \(2\frac{1}{3}=\frac{7}{3}\).

\((\frac{18}{15}-\frac{22}{15})\cdot(-\frac{5}{8})-\frac{7}{6}:\frac{7}{3}=(-\frac{4}{15})\cdot(-\frac{5}{8})-\frac{1}{2}=\frac{1}{6}-\frac{1}{2}=-\frac{1}{3}\).

г)

\(-2,5=-\frac{5}{2}\), \(5\frac{1}{7}=\frac{36}{7}\), \(-5,6=-\frac{28}{5}\).

\((-\frac{5}{2}+\frac{7}{3})\cdot(-\frac{36}{7})+\frac{4}{3}:(-\frac{28}{5})=(-\frac{1}{6})\cdot(-\frac{36}{7})-\frac{5}{21}=\frac{6}{7}-\frac{5}{21}=\frac{13}{21}\).

д)

\(1,25=\frac{5}{4}\), \(5\frac{4}{9}=\frac{49}{9}\).

\((\frac{5}{4}-\frac{4}{3})\cdot(-\frac{36}{7})-\frac{7}{6}:\frac{49}{9}=(-\frac{1}{12})\cdot(-\frac{36}{7})-\frac{7}{6}\cdot\frac{9}{49}=\frac{3}{7}-\frac{3}{14}=\frac{3}{14}\).

Ответ: а) \(3,6\); б) \(4\frac{1}{2}\); в) \(-\frac{1}{3}\); г) \(\frac{13}{21}\); д) \(\frac{3}{14}\).