Вычислите: а) \(8,\overline{5}-7,\overline{3}\); б) \(4,\overline{7}\cdot12,\overline{3}\); в) \(6,\overline{5}:1,\overline{3}\); г) \(5,\overline{6}+0,\overline{9}\); д) \(2\cdot9,\overline{5}+14\); е) \((10-2,\overline{7}):5\); ж) \(6,\overline{1}\cdot(8,\overline{4}:4)\); з) \((6,\overline{4}+7):2\).

Используем правило: \(0,\overline{a}=\frac{a}{9}\).

1. а) \(8,\overline{5}=\frac{77}{9}\), \(7,\overline{3}=\frac{22}{3}=\frac{66}{9}\).
   \(\frac{77}{9}-\frac{66}{9}=\frac{11}{9}=1\frac{2}{9}\).
2. б) \(4,\overline{7}=\frac{43}{9}\), \(12,\overline{3}=\frac{37}{3}\).
   \(\frac{43}{9}\cdot\frac{37}{3}=\frac{1591}{27}=59\frac{ -2}{27}\).
   Правильная смешанная запись: \(\frac{1591}{27}=58\frac{25}{27}\).
3. в) \(6,\overline{5}=\frac{59}{9}\), \(1,\overline{3}=\frac{4}{3}\).
   \(\frac{59}{9}:\frac{4}{3}=\frac{59}{9}\cdot\frac{3}{4}=\frac{59}{12}=4\frac{11}{12}\).
4. г) \(5,\overline{6}=\frac{17}{3}\), \(0,\overline{9}=1\).
   \(\frac{17}{3}+1=\frac{20}{3}=6\frac{2}{3}\).
5. д) \(9,\overline{5}=\frac{86}{9}\).
   \(2\cdot\frac{86}{9}+14=\frac{172}{9}+\frac{126}{9}=\frac{298}{9}=33\frac{1}{9}\).
6. е) \(2,\overline{7}=\frac{25}{9}\).
   \((10-\frac{25}{9}):5=\frac{65}{9}:5=\frac{13}{9}=1\frac{4}{9}\).
7. ж) \(6,\overline{1}=\frac{55}{9}\), \(8,\overline{4}=\frac{76}{9}\).
   \(\frac{55}{9}\cdot(\frac{76}{9}:4)=\frac{55}{9}\cdot\frac{19}{9}=\frac{1045}{81}=12\frac{73}{81}\).
8. з) \(6,\overline{4}=\frac{58}{9}\).
   \((\frac{58}{9}+7):2=\frac{121}{9}:2=\frac{121}{18}=6\frac{13}{18}\).

Ответ: а) \(1\frac{2}{9}\); б) \(58\frac{25}{27}\); в) \(4\frac{11}{12}\); г) \(6\frac{2}{3}\); д) \(33\frac{1}{9}\); е) \(1\frac{4}{9}\); ж) \(12\frac{73}{81}\); з) \(6\frac{13}{18}\).