6.66 Найдите значение выражения: a) $$37\frac{9}{13} - 13\frac{6}{13} + 7\frac{2}{13}$$; б) $$21\frac{2}{9} + 4\frac{5}{6} - 5\frac{4}{9}$$; в) $$54\frac{3}{11} + 8\frac{5}{11} + \frac{3}{22}$$; г) $$6\frac{9}{10} + 2\frac{7}{10} + 4\frac{1}{10}$$; д) $$14\frac{23}{100} - 3\frac{11}{100} - 1$$; е) $$10 - 5\frac{39}{100} - 2\frac{56}{100}$$.

Решение: a) $$37\frac{9}{13} - 13\frac{6}{13} + 7\frac{2}{13} = (37 - 13 + 7) + (\frac{9}{13} - \frac{6}{13} + \frac{2}{13}) = 31 + \frac{5}{13} = 31\frac{5}{13}$$. б) $$21\frac{2}{9} + 4\frac{5}{6} - 5\frac{4}{9} = (21 + 4 - 5) + (\frac{2}{9} + \frac{5}{6} - \frac{4}{9}) = 20 + (\frac{4}{18} + \frac{15}{18} - \frac{8}{18}) = 20 + \frac{11}{18} = 20\frac{11}{18}$$. в) $$54\frac{3}{11} + 8\frac{5}{11} + \frac{3}{22} = (54 + 8) + (\frac{3}{11} + \frac{5}{11} + \frac{3}{22}) = 62 + (\frac{6}{22} + \frac{10}{22} + \frac{3}{22}) = 62 + \frac{19}{22} = 62\frac{19}{22}$$. г) $$6\frac{9}{10} + 2\frac{7}{10} + 4\frac{1}{10} = (6 + 2 + 4) + (\frac{9}{10} + \frac{7}{10} + \frac{1}{10}) = 12 + \frac{17}{10} = 12 + 1\frac{7}{10} = 13\frac{7}{10}$$. д) $$14\frac{23}{100} - 3\frac{11}{100} - 1 = (14 - 3 - 1) + (\frac{23}{100} - \frac{11}{100}) = 10 + \frac{12}{100} = 10\frac{12}{100} = 10\frac{3}{25}$$. е) $$10 - 5\frac{39}{100} - 2\frac{56}{100} = (10 - 5 - 2) + ( -\frac{39}{100} - \frac{56}{100}) = 3 - \frac{95}{100} = 2 + \frac{100}{100} - \frac{95}{100} = 2\frac{5}{100} = 2\frac{1}{20}$$. Ответ: a) $$31\frac{5}{13}$$; б) $$20\frac{11}{18}$$; в) $$62\frac{19}{22}$$; г) $$13\frac{7}{10}$$; д) $$10\frac{3}{25}$$; е) $$2\frac{1}{20}$$.