№3 Выполните действия с дробями: a) 5/9 : 10/27; б) 7/10 - 3/20; в) 6/25 · 5/18; г) 5²/7 - 24/21 + 3²/3.

Решение:

1. a) \( \frac{5}{9} : \frac{10}{27} = \frac{5}{9} \cdot \frac{27}{10} = \frac{5 \cdot 27}{9 \cdot 10} = \frac{1 \cdot 3}{1 \cdot 2} = \frac{3}{2} = 1\frac{1}{2} \)
2. б) \( \frac{7}{10} - \frac{3}{20} = \frac{14}{20} - \frac{3}{20} = \frac{11}{20} \)
3. в) \( \frac{6}{25} \cdot \frac{5}{18} = \frac{6 \cdot 5}{25 \cdot 18} = \frac{1 \cdot 1}{5 \cdot 3} = \frac{1}{15} \)
4. г) \( \frac{5^2}{7} - \frac{24}{21} + \frac{3^2}{3} = \frac{25}{7} - \frac{24}{21} + \frac{9}{3} = \frac{75}{21} - \frac{24}{21} + \frac{63}{21} = \frac{75 - 24 + 63}{21} = \frac{114}{21} = \frac{38}{7} = 5\frac{3}{7} \)

Ответ: а) 1\(\frac{1}{2}\); б) \(\frac{11}{20}\); в) \(\frac{1}{15}\); г) 5\(\frac{3}{7}\).