6.59 Найдите разность:

Решение:

1. \( 7 \frac{3}{5} - 1 \frac{2}{5} = (7-1) + (\frac{3}{5} - \frac{2}{5}) = 6 + \frac{1}{5} = 6 \frac{1}{5} \)
2. \( 28 \frac{6}{13} - 7 \frac{1}{13} = (28-7) + (\frac{6}{13} - \frac{1}{13}) = 21 + \frac{5}{13} = 21 \frac{5}{13} \)
3. \( 6 - \frac{2}{5} = \frac{6 \cdot 5}{5} - \frac{2}{5} = \frac{30}{5} - \frac{2}{5} = \frac{30-2}{5} = \frac{28}{5} \)
4. \( 21 - \frac{5}{9} = \frac{21 \cdot 9}{9} - \frac{5}{9} = \frac{189}{9} - \frac{5}{9} = \frac{189-5}{9} = \frac{184}{9} \)
5. \( 4 \frac{1}{7} - 1 \frac{4}{7} = \frac{4 \cdot 7 + 1}{7} - \frac{1 \cdot 7 + 4}{7} = \frac{29}{7} - \frac{11}{7} = \frac{29-11}{7} = \frac{18}{7} \)
6. \( 12 \frac{2}{5} - 1 \frac{4}{5} = \frac{12 \cdot 5 + 2}{5} - \frac{1 \cdot 5 + 4}{5} = \frac{62}{5} - \frac{9}{5} = \frac{62-9}{5} = \frac{53}{5} \)
7. \( 4 \frac{1}{2} - 3 \frac{1}{4} = \frac{4 \cdot 2 + 1}{2} - \frac{3 \cdot 4 + 1}{4} = \frac{9}{2} - \frac{13}{4} = \frac{9 \cdot 2}{4} - \frac{13}{4} = \frac{18}{4} - \frac{13}{4} = \frac{18-13}{4} = \frac{5}{4} \)
8. \( 5 \frac{1}{7} - 3 \frac{20}{21} = \frac{5 \cdot 7 + 1}{7} - \frac{3 \cdot 21 + 20}{21} = \frac{36}{7} - \frac{63+20}{21} = \frac{36 \cdot 3}{21} - \frac{83}{21} = \frac{108}{21} - \frac{83}{21} = \frac{108-83}{21} = \frac{25}{21} \)

Ответ: 1) \( 6 \frac{1}{5} \); 2) \( 21 \frac{5}{13} \); 3) \( \frac{28}{5} \); 4) \( \frac{184}{9} \); 5) \( \frac{18}{7} \); 6) \( \frac{53}{5} \); 7) \( \frac{5}{4} \); 8) \( \frac{25}{21} \).