6.66 Найдите значение выражения:

Пошаговое решение:

1. а) \( \frac{37}{13} - \frac{9}{13} + 7 \frac{2}{13} \)
   \( \frac{37 - 9}{13} + \frac{7 \times 13 + 2}{13} \)
   \( \frac{28}{13} + \frac{91 + 2}{13} \)
   \( \frac{28}{13} + \frac{93}{13} \)
   \( \frac{28 + 93}{13} \)
   \( \frac{121}{13} \)
   \( 9 \frac{4}{13} \)
2. б) \( 21 \frac{2}{9} + 4 \frac{5}{6} - 5 \frac{4}{9} \)
   \( (21 + 4 - 5) + (\frac{2}{9} + \frac{5}{6} - \frac{4}{9}) \)
   \( 20 + (\frac{2 \times 2}{18} + \frac{5 \times 3}{18} - \frac{4 \times 2}{18}) \)
   \( 20 + (\frac{4 + 15 - 8}{18}) \)
   \( 20 + \frac{11}{18} \)
   \( 20 \frac{11}{18} \)
3. в) \( 54 \frac{3}{11} + 8 \frac{5}{11} + \frac{3}{22} \)
   \( (54 + 8) + (\frac{3}{11} + \frac{5}{11} + \frac{3}{22}) \)
   \( 62 + (\frac{3 \times 2}{22} + \frac{5 \times 2}{22} + \frac{3}{22}) \)
   \( 62 + (\frac{6 + 10 + 3}{22}) \)
   \( 62 + \frac{19}{22} \)
   \( 62 \frac{19}{22} \)
4. г) \( 6 \frac{9}{10} + 2 \frac{7}{10} + 4 \frac{1}{10} \)
   \( (6 + 2 + 4) + (\frac{9}{10} + \frac{7}{10} + \frac{1}{10}) \)
   \( 12 + \frac{9 + 7 + 1}{10} \)
   \( 12 + \frac{17}{10} \)
   \( 12 + 1 \frac{7}{10} \)
   \( 13 \frac{7}{10} \)
5. д) \( 14 \frac{23}{100} - 3 \frac{11}{100} - 1 \)
   \( (14 - 3 - 1) + (\frac{23}{100} - \frac{11}{100}) \)
   \( 10 + \frac{12}{100} \)
   \( 10 \frac{12}{100} \)
   \( 10 \frac{3}{25} \)
6. е) \( 10 - 5 \frac{39}{100} - 2 \frac{56}{100} \)
   \( 10 - (5 + 2) - (\frac{39}{100} + \frac{56}{100}) \)
   \( 10 - 7 - \frac{95}{100} \)
   \( 3 - \frac{95}{100} \)
   \( 2 + 1 - \frac{95}{100} \)
   \( 2 + \frac{100 - 95}{100} \)
   \( 2 \frac{5}{100} \)
   \( 2 \frac{1}{20} \)