№4. Вычислите. A) \(\frac{4}{25} + \frac{2}{20}\) Б) \(\frac{1}{6} - \frac{5}{21}\) В) \(\frac{5}{7} \cdot \frac{14}{19}\) Г) \(\frac{15}{8} : \frac{5}{4}\) Д) \(\frac{14}{17} : 2\) Е) \(6 : \frac{3}{5}\)

Решение:

• А) \[\frac{4}{25} + \frac{2}{20} = \frac{4 \cdot 4}{25 \cdot 4} + \frac{2 \cdot 5}{20 \cdot 5} = \frac{16}{100} + \frac{10}{100} = \frac{26}{100} = \frac{13}{50}\]
• Б) \[\frac{1}{6} - \frac{5}{21} = \frac{1 \cdot 7}{6 \cdot 7} - \frac{5 \cdot 2}{21 \cdot 2} = \frac{7}{42} - \frac{10}{42} = -\frac{3}{42} = -\frac{1}{14}\]
• В) \[\frac{5}{7} \cdot \frac{14}{19} = \frac{5 \cdot 14}{7 \cdot 19} = \frac{70}{133} = \frac{10}{19}\]
• Г) \[\frac{15}{8} : \frac{5}{4} = \frac{15}{8} \cdot \frac{4}{5} = \frac{15 \cdot 4}{8 \cdot 5} = \frac{60}{40} = \frac{3}{2} = \frac{15}{10}\]
• Д) \[\frac{14}{17} : 2 = \frac{14}{17} : \frac{2}{1} = \frac{14}{17} \cdot \frac{1}{2} = \frac{14 \cdot 1}{17 \cdot 2} = \frac{14}{34} = \frac{7}{17}\]
• Е) \[6 : \frac{3}{5} = \frac{6}{1} : \frac{3}{5} = \frac{6}{1} \cdot \frac{5}{3} = \frac{6 \cdot 5}{1 \cdot 3} = \frac{30}{3} = 10\]