6.66 Найдите значение выражения: a) 37/9 - 13/6 + 7 2/13; б) 21 2/9 + 4 5/6 - 54/9; в) 54 3/11 + 8 5/22 + 3; г) 6 9/10 + 2 7/10 + 4 1/10; д) 14 23/100 - 3 11/100 - 1; e) 10 5/39/100 - 2 56/100;

Ответ (RU):

a) $$37 \frac{9}{13} - 13 \frac{6}{13} + 7 \frac{2}{13} = (37 - 13 + 7) + (\frac{9}{13} - \frac{6}{13} + \frac{2}{13}) = 31 + \frac{9 - 6 + 2}{13} = 31 + \frac{5}{13} = 31 \frac{5}{13}$$

б) $$21 \frac{2}{9} + 4 \frac{5}{6} - 5 \frac{4}{9} = (21 + 4 - 5) + (\frac{2}{9} + \frac{5}{6} - \frac{4}{9}) = 20 + (\frac{4}{18} + \frac{15}{18} - \frac{8}{18}) = 20 + \frac{4 + 15 - 8}{18} = 20 + \frac{11}{18} = 20 \frac{11}{18}$$

в) $$54 \frac{3}{11} + 8 \frac{5}{22} + 3 = (54 + 8 + 3) + (\frac{3}{11} + \frac{5}{22}) = 65 + (\frac{6}{22} + \frac{5}{22}) = 65 + \frac{6 + 5}{22} = 65 + \frac{11}{22} = 65 + \frac{1}{2} = 65 \frac{1}{2}$$

г) $$6 \frac{9}{10} + 2 \frac{7}{10} + 4 \frac{1}{10} = (6 + 2 + 4) + (\frac{9}{10} + \frac{7}{10} + \frac{1}{10}) = 12 + \frac{9 + 7 + 1}{10} = 12 + \frac{17}{10} = 12 + 1 \frac{7}{10} = 13 \frac{7}{10}$$

д) $$14 \frac{23}{100} - 3 \frac{11}{100} - 1 = (14 - 3 - 1) + (\frac{23}{100} - \frac{11}{100}) = 10 + \frac{23 - 11}{100} = 10 + \frac{12}{100} = 10 + \frac{3}{25} = 10 \frac{3}{25}$$

e) $$10 \frac{5}{39}{100} - 2 \frac{56}{100} = (10 - 2) + (\frac{5}{100} - \frac{39}{100} - \frac{56}{100}) = 8 + (\frac{5 - 39 - 56}{100}) = 8 + (\frac{-90}{100}) = 8 - \frac{9}{10} = 7 \frac{10}{10} - \frac{9}{10} = 7 \frac{1}{10}$$

Ответ: a) $$31 \frac{5}{13}$$; б) $$20 \frac{11}{18}$$; в) $$65 \frac{1}{2}$$; г) $$13 \frac{7}{10}$$; д) $$10 \frac{3}{25}$$; e) $$7 \frac{1}{10}$$