222. Установите порядок действий и найдите значения выражений: а) (5 − 1 1/3 · 1/6) · 27/31; (2 − 1 2/3) : (1 − 1/3); б) (1 1/3 : 2/3 − 3/25 : 1/2) · 1/2; (2 − 1 2/3 · 3/5) : (1 − 1/3); (2 : 2/3 + 2/3 · 3/5) / (5 − 2/3 : 1/6); в) 3 : 3 3/4 + 2 2/5 · 2 1/2 − 3 5/6; (2 : 2/3 − 2/3 · 3/5) : (1 − 2/3); (2 3/7 · 3/17 + 3/5 : 1 2/5) / (4 4/5 : 1 1/2 − 2).

а) \(\left(5-1\frac{1}{3}\cdot\frac{1}{6}\right)\cdot\frac{27}{31}=\left(5-\frac{4}{3}\cdot\frac{1}{6}\right)\cdot\frac{27}{31}=\left(5-\frac{2}{9}\right)\cdot\frac{27}{31}=\frac{43}{9}\cdot\frac{27}{31}=\frac{129}{31}\).

\(\left(2-1\frac{2}{3}\right):\left(1-\frac{1}{3}\right)=\frac{1}{3}:\frac{2}{3}=\frac{1}{2}\).

б) \(\left(1\frac{1}{3}:\frac{2}{3}-\frac{3}{25}:\frac{1}{2}\right)\cdot\frac{1}{2}=\left(2-\frac{6}{25}\right)\cdot\frac{1}{2}=\frac{44}{25}\cdot\frac{1}{2}=\frac{22}{25}\).

\(\left(2-1\frac{2}{3}\cdot\frac{3}{5}\right):\left(1-\frac{1}{3}\right)=\left(2-1\right):\frac{2}{3}=\frac{3}{2}\).

\(\frac{2:\frac{2}{3}+\frac{2}{3}\cdot\frac{3}{5}}{5-\frac{2}{3}:\frac{1}{6}}=\frac{3+\frac{2}{5}}{5-4}=\frac{\frac{17}{5}}{1}=\frac{17}{5}\).

в) \(3:3\frac{3}{4}+2\frac{2}{5}\cdot2\frac{1}{2}-3\frac{5}{6}=\frac{3}{15/4}+\frac{12}{5}\cdot\frac{5}{2}-\frac{23}{6}=\frac{4}{5}+6-\frac{23}{6}=\frac{19}{30}\).

\(\left(2:\frac{2}{3}-\frac{2}{3}\cdot\frac{3}{5}\right):\left(1-\frac{2}{3}\right)=\left(3-\frac{2}{5}\right):\frac{1}{3}=\frac{13}{5}\cdot3=\frac{39}{5}\).

\(\frac{2\frac{3}{7}\cdot\frac{3}{17}+\frac{3}{5}:1\frac{2}{5}}{4\frac{4}{5}:1\frac{1}{2}-2}=\frac{\frac{17}{7}\cdot\frac{3}{17}+\frac{3}{5}:\frac{7}{5}}{\frac{24}{5}:\frac{3}{2}-2}=\frac{\frac{3}{7}+\frac{3}{7}}{\frac{16}{5}-2}=\frac{\frac{6}{7}}{\frac{6}{5}}=\frac{5}{7}\).

Ответ: а) \(\frac{129}{31};\ \frac{1}{2}\); б) \(\frac{22}{25};\ \frac{3}{2};\ \frac{17}{5}\); в) \(\frac{19}{30};\ \frac{39}{5};\ \frac{5}{7}\).