Вычислить: \(\left(\left(1\frac{1}{7}-\frac{23}{49}\right):\frac{22}{147}-\left(0,6:3\frac{3}{4}\right)\right)\frac{1}{2}+3,75:1\frac{1}{2}\right):2,2\).

\[1\frac{1}{7}-\frac{23}{49}=\frac{8}{7}-\frac{23}{49}=\frac{56-23}{49}=\frac{33}{49}.\]

\[\frac{33}{49}:\frac{22}{147}=\frac{33}{49}\cdot\frac{147}{22}=\frac{33\cdot3}{22}=\frac{9}{2}.\]

\[0,6:3\frac{3}{4}=\frac{3}{5}:\frac{15}{4}=\frac{3}{5}\cdot\frac{4}{15}=\frac{4}{25}.\]

\[\left(\frac{9}{2}-\frac{4}{25}\right)\frac{1}{2}=\frac{217}{50}\cdot\frac{1}{2}=\frac{217}{100}.\]

\[3,75:1\frac{1}{2}=\frac{15}{4}:\frac{3}{2}=\frac{15}{4}\cdot\frac{2}{3}=\frac{5}{2}.\]

\[\frac{217}{100}+\frac{5}{2}=\frac{217}{100}+\frac{250}{100}=\frac{467}{100}=4,67.\]

\[4,67:2,2=\frac{467}{100}:\frac{11}{5}=\frac{467}{100}\cdot\frac{5}{11}=\frac{467}{220}.\]

Ответ: \(\frac{467}{220}=2\frac{27}{220}\).