Вычислите: 1 − 4/7 : 16/21; 5/12 · (1/5 + 3/25); 9/14 · (17/24 − 5/12); 24/49 : 6/7 + 1/14.

1) Деление дробей заменяем умножением на обратную дробь: \(1 - \frac{4}{7} : \frac{16}{21} = 1 - \frac{4}{7} \cdot \frac{21}{16} = 1 - \frac{3}{4} = \frac{1}{4}\).

2) \(\frac{5}{12} \cdot \left(\frac{1}{5} + \frac{3}{25}\right) = \frac{5}{12} \cdot \left(\frac{5}{25} + \frac{3}{25}\right) = \frac{5}{12} \cdot \frac{8}{25} = \frac{2}{15}\).

3) \(\frac{9}{14} \cdot \left(\frac{17}{24} - \frac{5}{12}\right) = \frac{9}{14} \cdot \left(\frac{17}{24} - \frac{10}{24}\right) = \frac{9}{14} \cdot \frac{7}{24} = \frac{3}{16}\).

4) \(\frac{24}{49} : \frac{6}{7} + \frac{1}{14} = \frac{24}{49} \cdot \frac{7}{6} + \frac{1}{14} = \frac{4}{7} + \frac{1}{14} = \frac{9}{14}\).

Ответ: 1) \(\frac{1}{4}\); 2) \(\frac{2}{15}\); 3) \(\frac{3}{16}\); 4) \(\frac{9}{14}\).