№1. Выполните действия: а) \(\frac{7}{16} : \frac{21}{32}\); б) \(2.7 : \frac{9}{14}\); в) \(2\frac{3}{7} : 51\)

Решение:

1. а) \(\frac{7}{16} : \frac{21}{32} = \frac{7}{16} \times \frac{32}{21} = \frac{7 \times 32}{16 \times 21} = \frac{7 \times 2 \times 16}{16 \times 3 \times 7} = \frac{2}{3}\)
2. б) \(2.7 : \frac{9}{14} = \frac{27}{10} : \frac{9}{14} = \frac{27}{10} \times \frac{14}{9} = \frac{27 \times 14}{10 \times 9} = \frac{3 \times 9 \times 2 \times 7}{2 \times 5 \times 9} = \frac{3 \times 7}{5} = \frac{21}{5} = 4.2\)
3. в) \(2\frac{3}{7} : 51 = \frac{17}{7} : 51 = \frac{17}{7} \times \frac{1}{51} = \frac{17}{7 \times 51} = \frac{17}{7 \times 3 \times 17} = \frac{1}{21}\)

Ответ: а) \(\frac{2}{3}\); б) \(4.2\); в) \(\frac{1}{21}\).