Вопрос:

13. Вычислите: 1) \(\frac{2}{7} \cdot 5 \frac{1}{4} - \frac{1}{7} \cdot 5 \frac{1}{4}\) 2) \(\frac{1}{3} \cdot 3 \frac{5}{7} + \frac{2}{3} \cdot 3 \frac{5}{7}\) 3) \(4 \frac{5}{9} - \frac{1}{5} \cdot 3 \frac{1}{5}\) 4) \(\frac{3}{5} \cdot 2 \frac{1}{2} + \frac{1}{5} \cdot 2 \frac{1}{2}\)

Ответ:

1) \(\frac{2}{7} \cdot 5 \frac{1}{4} - \frac{1}{7} \cdot 5 \frac{1}{4} = \left( \frac{2}{7} - \frac{1}{7} \right) \cdot 5 \frac{1}{4} = \frac{1}{7} \cdot \frac{21}{4} = \frac{3}{4}\)
2) \(\frac{1}{3} \cdot 3 \frac{5}{7} + \frac{2}{3} \cdot 3 \frac{5}{7} = \left( \frac{1}{3} + \frac{2}{3} \right) \cdot 3 \frac{5}{7} = 1 \cdot 3 \frac{5}{7} = 3 \frac{5}{7}\)
3) \(4 \frac{5}{9} - \frac{1}{5} \cdot 3 \frac{1}{5} = 4 \frac{5}{9} - \frac{1}{5} \cdot \frac{16}{5} = 4 \frac{5}{9} - \frac{16}{25} = \frac{41}{9} - \frac{16}{25} = \frac{1025 - 144}{225} = \frac{881}{225} = 3 \frac{206}{225}\)
4) \(\frac{3}{5} \cdot 2 \frac{1}{2} + \frac{1}{5} \cdot 2 \frac{1}{2} = \left( \frac{3}{5} + \frac{1}{5} \right) \cdot 2 \frac{1}{2} = \frac{4}{5} \cdot \frac{5}{2} = 2\)