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

а)

1. \(6+\frac{5}{13}=\frac{78}{13}+\frac{5}{13}=\frac{83}{13}=6\frac{5}{13}\).
2. \(\frac{6}{57}+4=\frac{2}{19}+4=4\frac{2}{19}\).
3. \(6\frac{4}{9}+5\frac{2}{9}=11\frac{6}{9}=11\frac{2}{3}\).
4. \(11\frac{8}{11}-3\frac{5}{11}=8\frac{3}{11}\).

б)

1. \(8\frac{7}{18}+7\frac{5}{18}-4\frac{11}{18}=15\frac{12}{18}-4\frac{11}{18}=10\frac{13}{18}\).
2. \(13\frac{6}{10}-5\frac{3}{10}+16\frac{1}{10}=8\frac{3}{10}+16\frac{1}{10}=24\frac{4}{10}=24\frac{2}{5}\).
3. \(3\frac{8}{11}+2\frac{6}{11}=5\frac{14}{11}=6\frac{3}{11}\).
4. \(1-\frac{16}{21}=\frac{21}{21}-\frac{16}{21}=\frac{5}{21}\).
5. \(5-2\frac{3}{8}=4\frac{8}{8}-2\frac{3}{8}=2\frac{5}{8}\).
6. \(8\frac{4}{9}-3\frac{7}{9}=7\frac{13}{9}-3\frac{7}{9}=4\frac{6}{9}=4\frac{2}{3}\).

Уравнение:

\(4\frac{5}{14}-\left(x-7\frac{3}{14}\right)=2\frac{9}{14}\).

Раскроем скобки:

\(4\frac{5}{14}-x+7\frac{3}{14}=2\frac{9}{14}\).

\(11\frac{8}{14}-x=2\frac{9}{14}\).

\(-x=2\frac{9}{14}-11\frac{8}{14}=-9\frac{13}{14}\), поэтому \(x=9\frac{13}{14}\).

Ответ: а) \(6\frac{5}{13};\ 4\frac{2}{19};\ 11\frac{2}{3};\ 8\frac{3}{11}\). б) \(10\frac{13}{18};\ 24\frac{2}{5};\ 6\frac{3}{11};\ \frac{5}{21};\ 2\frac{5}{8};\ 4\frac{2}{3}\). \(x=9\frac{13}{14}\).