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) $$2 \frac{51}{100}$$