6.66 Найдите значение выражения: a) 37-13+7 13 13 2 6) 21 +40-5 9 6 9 2 ; 13 в) 54 3 11 + г) 6 9 10 +8 3. 5 ; 11 22' + д) 14 23 100 11 3 100 1; +2 7 10 +4 1 10 ; e) 10 39 5 100 56 2 100

Решение:

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