№4. Вычислите. A) \(\frac{3}{16} + \frac{5}{20}\) Б) \(\frac{9}{28} - \frac{3}{14}\) В) \(\frac{12}{14} : \frac{21}{6}\) Г) \(\frac{16}{49} : \frac{4}{7}\) Д) \(\frac{24}{51} : 3\) E) \(9 : \frac{3}{10}\)

Решение:

• А) \[\frac{3}{16} + \frac{5}{20} = \frac{3 \cdot 5}{16 \cdot 5} + \frac{5 \cdot 4}{20 \cdot 4} = \frac{15}{80} + \frac{20}{80} = \frac{35}{80} = \frac{7}{16}\]
• Б) \[\frac{9}{28} - \frac{3}{14} = \frac{9}{28} - \frac{3 \cdot 2}{14 \cdot 2} = \frac{9}{28} - \frac{6}{28} = \frac{3}{28}\]
• В) \[\frac{12}{14} : \frac{21}{6} = \frac{12}{14} \cdot \frac{6}{21} = \frac{12 \cdot 6}{14 \cdot 21} = \frac{72}{294} = \frac{12}{49}\]
• Г) \[\frac{16}{49} : \frac{4}{7} = \frac{16}{49} \cdot \frac{7}{4} = \frac{16 \cdot 7}{49 \cdot 4} = \frac{112}{196} = \frac{4}{7}\]
• Д) \[\frac{24}{51} : 3 = \frac{24}{51} : \frac{3}{1} = \frac{24}{51} \cdot \frac{1}{3} = \frac{24}{153} = \frac{8}{51}\]
• Е) \[9 : \frac{3}{10} = \frac{9}{1} : \frac{3}{10} = \frac{9}{1} \cdot \frac{10}{3} = \frac{90}{3} = 30\]