7. Найдите значение выражения: а) 3 3/5 · 1/3 + 6 4/9 : 2; б) 2/3 − 8/23 · (3/4 + 1 1/6); в) 2 5/6 − 1 1/5 · 1 1/9 + 1 5/7 : 1 1/7; г) 5 2/9 : (3 − 1 1/9 · 2 2/5) + 4/5.

а) \(3\frac{3}{5} \cdot \frac{1}{3}+6\frac{4}{9}:2\)

\(\frac{18}{5}\cdot\frac{1}{3}+\frac{58}{9}:2=\frac{6}{5}+\frac{29}{9}=\frac{54}{45}+\frac{145}{45}=\frac{199}{45}=4\frac{19}{45}\).

б) \(\frac{2}{3}-\frac{8}{23}\cdot\left(\frac{3}{4}+1\frac{1}{6}\right)\)

\(\frac{3}{4}+1\frac{1}{6}=\frac{3}{4}+\frac{7}{6}=\frac{23}{12}\).

\(\frac{2}{3}-\frac{8}{23}\cdot\frac{23}{12}=\frac{2}{3}-\frac{2}{3}=0\).

в) \(2\frac{5}{6}-1\frac{1}{5}\cdot1\frac{1}{9}+1\frac{5}{7}:1\frac{1}{7}\)

\(\frac{17}{6}-\frac{6}{5}\cdot\frac{10}{9}+\frac{12}{7}:\frac{8}{7}=\frac{17}{6}-\frac{4}{3}+\frac{3}{2}\).

\(\frac{17}{6}-\frac{8}{6}+\frac{9}{6}=\frac{18}{6}=3\).

г) \(5\frac{2}{9}:\left(3-1\frac{1}{9}\cdot2\frac{2}{5}\right)+\frac{4}{5}\)

\(\frac{10}{9}\cdot\frac{12}{5}=\frac{8}{3}\), поэтому \(3-\frac{8}{3}=\frac{1}{3}\).

\(\frac{47}{9}:\frac{1}{3}+\frac{4}{5}=\frac{47}{3}+\frac{4}{5}=\frac{235}{15}+\frac{12}{15}=\frac{247}{15}=16\frac{7}{15}\).

Ответ: а) \(4\frac{19}{45}\); б) \(0\); в) \(3\); г) \(16\frac{7}{15}\).