6. Выполните действия: а) \(6+\frac{5}{13}\); \(\frac{6}{57}+4\); \(6\frac{4}{9}+5\frac{2}{9}\); \(11\frac{8}{11}-3\frac{5}{11}\); \(8\frac{7}{18}+7\frac{5}{18}-4\frac{7}{18}\); \(13\frac{6}{10}-5\frac{3}{10}+16\frac{1}{10}\); \(3\frac{2}{11}+2\frac{6}{11}\); \(1-\frac{16}{21}\); \(5-2\frac{3}{8}\); \(9\frac{4}{9}-3\frac{7}{9}\). б) Решите уравнение: \(4\frac{5}{14}-(x-7\frac{2}{14})=2\frac{9}{14}\).

а)

1. \(6+\frac{5}{13}=6\frac{5}{13}\).
2. \(\frac{6}{57}+4=4\frac{2}{19}\).
3. \(6\frac{4}{9}+5\frac{2}{9}=11\frac{6}{9}=11\frac{2}{3}\).
4. \(11\frac{8}{11}-3\frac{5}{11}=8\frac{3}{11}\).
5. \(8\frac{7}{18}+7\frac{5}{18}-4\frac{7}{18}=11\frac{5}{18}\).
6. \(13\frac{6}{10}-5\frac{3}{10}+16\frac{1}{10}=24\frac{4}{10}=24\frac{2}{5}\).
7. \(3\frac{2}{11}+2\frac{6}{11}=5\frac{8}{11}\).
8. \(1-\frac{16}{21}=\frac{5}{21}\).
9. \(5-2\frac{3}{8}=2\frac{5}{8}\).
10. \(9\frac{4}{9}-3\frac{7}{9}=5\frac{6}{9}=5\frac{2}{3}\).

б) \(4\frac{5}{14}-(x-7\frac{2}{14})=2\frac{9}{14}\).

\(x-7\frac{2}{14}=4\frac{5}{14}-2\frac{9}{14}=1\frac{10}{14}\).

\(x=1\frac{10}{14}+7\frac{2}{14}=8\frac{12}{14}=8\frac{6}{7}\).

Ответ: а) \(6\frac{5}{13};\ 4\frac{2}{19};\ 11\frac{2}{3};\ 8\frac{3}{11};\ 11\frac{5}{18};\ 24\frac{2}{5};\ 5\frac{8}{11};\ \frac{5}{21};\ 2\frac{5}{8};\ 5\frac{2}{3}\). б) \(x=8\frac{6}{7}\).