№4. Вычислите. A) \(\frac{3}{16} + \frac{5}{20}\) б) \(\frac{9}{28} - \(\frac{3}{14}\) в) \(\frac{12}{14} \cdot \(\frac{21}{6}\) г) \(\frac{16}{49} : \(\frac{4}{7}\) д) \(\frac{24}{51} : 3\) е)9:\(\frac{3}{10}\)

Ответ: А) \(\frac{11}{16}\); Б) \(\frac{3}{28}\); В) 3; Г) \(\frac{4}{7}\); Д) \(\frac{8}{51}\); Е) 30

1. А) \(\frac{3}{16} + \frac{5}{20}\)

   \[\frac{3}{16} + \frac{5}{20} = \frac{3 \cdot 5}{16 \cdot 5} + \frac{5 \cdot 4}{20 \cdot 4} = \frac{15}{80} + \frac{20}{80} = \frac{15+20}{80} = \frac{35}{80} = \frac{7}{16}\]

2. Б) \(\frac{9}{28} - \frac{3}{14}\)

   \[\frac{9}{28} - \frac{3}{14} = \frac{9}{28} - \frac{3 \cdot 2}{14 \cdot 2} = \frac{9}{28} - \frac{6}{28} = \frac{9-6}{28} = \frac{3}{28}\]

3. В) \(\frac{12}{14} \cdot \frac{21}{6}\)

   \[\frac{12}{14} \cdot \frac{21}{6} = \frac{12 \cdot 21}{14 \cdot 6} = \frac{2 \cdot 3}{2 \cdot 1} = 3\]

4. Г) \(\frac{16}{49} : \frac{4}{7}\)

   \[\frac{16}{49} : \frac{4}{7} = \frac{16}{49} \cdot \frac{7}{4} = \frac{16 \cdot 7}{49 \cdot 4} = \frac{4}{7}\]

5. Д) \(\frac{24}{51} : 3\)

   \[\frac{24}{51} : 3 = \frac{24}{51} \cdot \frac{1}{3} = \frac{24 \cdot 1}{51 \cdot 3} = \frac{8}{51}\]

6. Е) 9 : \(\frac{3}{10}\)

   \[9 : \frac{3}{10} = 9 \cdot \frac{10}{3} = \frac{9 \cdot 10}{3} = \frac{3 \cdot 10}{1} = 30\]

Ответ: А) \(\frac{11}{16}\); Б) \(\frac{3}{28}\); В) 3; Г) \(\frac{4}{7}\); Д) \(\frac{8}{51}\); Е) 30