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 \(\frac{5}{9}\) в) 54 \(\frac{3}{11}\) + 8 \(\frac{5}{11}\) + 3 \(\frac{3}{22}\) г) 6 \(\frac{9}{10}\) + 2 \(\frac{7}{10}\) + 4 \(\frac{1}{10}\) д) 14 \(\frac{23}{100}\) - 3 \(\frac{11}{100}\) e) 10 - 5 \(\frac{39}{100}\) - 2 \(\frac{1}{10}\)

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) $$21 \frac{2}{9} + 4 \frac{5}{6} - 5 \frac{5}{9} = (21 + 4 - 5) + (\frac{2}{9} + \frac{5}{6} - \frac{5}{9}) = 20 + (\frac{4}{18} + \frac{15}{18} - \frac{10}{18}) = 20 + \frac{9}{18} = 20 + \frac{1}{2} = 20 \frac{1}{2}$$

в) $$54 \frac{3}{11} + 8 \frac{5}{11} + 3 \frac{3}{22} = (54 + 8 + 3) + (\frac{3}{11} + \frac{5}{11} + \frac{3}{22}) = 65 + (\frac{6}{22} + \frac{10}{22} + \frac{3}{22}) = 65 + \frac{19}{22} = 65 \frac{19}{22}$$

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) $$14 \frac{23}{100} - 3 \frac{11}{100} = (14 - 3) + (\frac{23}{100} - \frac{11}{100}) = 11 + \frac{12}{100} = 11 + \frac{3}{25} = 11 \frac{3}{25}$$

е) $$10 - 5 \frac{39}{100} - 2 \frac{1}{10} = 10 - 5 \frac{39}{100} - 2 \frac{10}{100} = (10 - 5 - 2) + (0 - \frac{39}{100} - \frac{10}{100}) = 3 - \frac{49}{100} = 2 \frac{100}{100} - \frac{49}{100} = 2 \frac{51}{100}$$

Ответ:
a) $$31 \frac{5}{13}$$
б) $$20 \frac{1}{2}$$
в) $$65 \frac{19}{22}$$
г) $$13 \frac{7}{10}$$
д) $$11 \frac{3}{25}$$
е) $$2 \frac{51}{100}$$