Вычислить: \(\dfrac{6\frac{1}{7}:\left((1\frac{5}{6}-7\frac{1}{5}:2,7)\cdot5,4-\frac{1}{2}\right)+\frac{1}{8}}{5,2+1\frac{11}{20}}:\left(-\frac{5}{36}\right)\).

Question

Accepted Answer

\(7\frac{1}{5}:2,7=\frac{36}{5}:\frac{27}{10}=\frac{8}{3}\).
\(1\frac{5}{6}-\frac{8}{3}=\frac{11}{6}-\frac{16}{6}=-\frac{5}{6}\).
\(-\frac{5}{6}\cdot5,4-\frac{1}{2}=-\frac{5}{6}\cdot\frac{27}{5}-\frac{1}{2}=-\frac{9}{2}-\frac{1}{2}=-5\).
\(6\frac{1}{7}:(-5)+\frac{1}{8}=\frac{43}{7}:(-5)+\frac{1}{8}=-\frac{43}{35}+\frac{1}{8}=-\frac{309}{280}\).
\(5,2+1\frac{11}{20}=\frac{27}{4}\), поэтому
\(\left(-\frac{309}{280}:\frac{27}{4}\right):\left(-\frac{5}{36}\right)=-\frac{41}{252}\cdot\left(-\frac{36}{5}\right)=\frac{41}{35}\).

Ответ: \(\frac{41}{35}=1\frac{6}{35}\).