№4. Вычислите. A) \(\frac{2}{25} + \frac{1}{20}\) б) \(\frac{5}{21} - \frac{3}{14}\) в) \(\frac{5}{7} \cdot \frac{14}{19}\) г) \(\frac{15}{8} : \frac{4}{17}\) д) \(\frac{14}{5} : 2\) е)6:\(\frac{3}{5}\)

Ответ: А) \(\frac{13}{100}\); Б) \(\frac{1}{42}\); В) \(\frac{10}{19}\); Г) \(\frac{255}{32}\); Д) \(\frac{7}{5}\); Е) 10

1. А) \(\frac{2}{25} + \frac{1}{20}\)

   \[\frac{2}{25} + \frac{1}{20} = \frac{2 \cdot 4}{25 \cdot 4} + \frac{1 \cdot 5}{20 \cdot 5} = \frac{8}{100} + \frac{5}{100} = \frac{8+5}{100} = \frac{13}{100}\]

2. Б) \(\frac{5}{21} - \frac{3}{14}\)

   \[\frac{5}{21} - \frac{3}{14} = \frac{5 \cdot 2}{21 \cdot 2} - \frac{3 \cdot 3}{14 \cdot 3} = \frac{10}{42} - \frac{9}{42} = \frac{10-9}{42} = \frac{1}{42}\]

3. В) \(\frac{5}{7} \cdot \frac{14}{19}\)

   \[\frac{5}{7} \cdot \frac{14}{19} = \frac{5 \cdot 14}{7 \cdot 19} = \frac{5 \cdot 2}{1 \cdot 19} = \frac{10}{19}\]

4. Г) \(\frac{15}{8} : \frac{4}{17}\)

   \[\frac{15}{8} : \frac{4}{17} = \frac{15}{8} \cdot \frac{17}{4} = \frac{15 \cdot 17}{8 \cdot 4} = \frac{255}{32}\]

5. Д) \(\frac{14}{5} : 2\)

   \[\frac{14}{5} : 2 = \frac{14}{5} \cdot \frac{1}{2} = \frac{14 \cdot 1}{5 \cdot 2} = \frac{7 \cdot 1}{5 \cdot 1} = \frac{7}{5}\]

6. Е) 6 : \(\frac{3}{5}\)

   \[6 : \frac{3}{5} = 6 \cdot \frac{5}{3} = \frac{6 \cdot 5}{3} = \frac{2 \cdot 5}{1} = 10\]

Ответ: А) \(\frac{13}{100}\); Б) \(\frac{1}{42}\); В) \(\frac{10}{19}\); Г) \(\frac{255}{32}\); Д) \(\frac{7}{5}\); Е) 10