4 Найдите разность: a) \(\frac{4}{5} - \frac{3}{4}\); б) \(\frac{3}{10} - \frac{2}{7}\); в) \(\frac{2}{3} - \frac{1}{7}\); г) \(\frac{5}{9} - \frac{1}{3}\); д) \(\frac{5}{6} - \frac{5}{12}\); е) \(\frac{2}{13} - 0\);

Решение:

1. а) \(\frac{4}{5} - \frac{3}{4} = \frac{4 \cdot 4}{5 \cdot 4} - \frac{3 \cdot 5}{4 \cdot 5} = \frac{16}{20} - \frac{15}{20} = \frac{16-15}{20} = \frac{1}{20}\)
2. б) \(\frac{3}{10} - \frac{2}{7} = \frac{3 \cdot 7}{10 \cdot 7} - \frac{2 \cdot 10}{7 \cdot 10} = \frac{21}{70} - \frac{20}{70} = \frac{21-20}{70} = \frac{1}{70}\)
3. в) \(\frac{2}{3} - \frac{1}{7} = \frac{2 \cdot 7}{3 \cdot 7} - \frac{1 \cdot 3}{7 \cdot 3} = \frac{14}{21} - \frac{3}{21} = \frac{14-3}{21} = \frac{11}{21}\)
4. г) \(\frac{5}{9} - \frac{1}{3} = \frac{5}{9} - \frac{1 \cdot 3}{3 \cdot 3} = \frac{5}{9} - \frac{3}{9} = \frac{5-3}{9} = \frac{2}{9}\)
5. д) \(\frac{5}{6} - \frac{5}{12} = \frac{5 \cdot 2}{6 \cdot 2} - \frac{5}{12} = \frac{10}{12} - \frac{5}{12} = \frac{10-5}{12} = \frac{5}{12}\)
6. е) \(\frac{2}{13} - 0 = \frac{2}{13}\)

Ответ: а) \(\frac{1}{20}\); б) \(\frac{1}{70}\); в) \(\frac{11}{21}\); г) \(\frac{2}{9}\); д) \(\frac{5}{12}\); е) \(\frac{2}{13}\).