15 мая. Подготовка к контрольной работе. №1. 1) \(\frac{7}{5} \cdot \frac{12}{35} =\) 2) \(\frac{14}{5} : \frac{7}{2} =\) 3) \(\frac{23}{10} : \frac{2}{20} =\) 4) \(\frac{4}{25} + \frac{15}{4} =\)

Решение:

1. \(\frac{7}{5} \cdot \frac{12}{35} = \frac{7 \cdot 12}{5 \cdot 35} = \frac{7 \cdot 12}{5 \cdot 7 \cdot 5} = \frac{12}{25}\)
2. \(\frac{14}{5} : \frac{7}{2} = \frac{14}{5} \cdot \frac{2}{7} = \frac{14 \cdot 2}{5 \cdot 7} = \frac{2 \cdot 7 \cdot 2}{5 \cdot 7} = \frac{4}{5}\)
3. \(\frac{23}{10} : \frac{2}{20} = \frac{23}{10} \cdot \frac{20}{2} = \frac{23 \cdot 20}{10 \cdot 2} = \frac{23 \cdot 10 \cdot 2}{10 \cdot 2} = 23\)
4. \(\frac{4}{25} + \frac{15}{4} = \frac{4 \cdot 4}{25 \cdot 4} + \frac{15 \cdot 25}{4 \cdot 25} = \frac{16}{100} + \frac{375}{100} = \frac{16 + 375}{100} = \frac{391}{100} = 3.91\)

Ответ: 1) \(\frac{12}{25}\); 2) \(\frac{4}{5}\); 3) 23; 4) 3.91.