1. Выполните действия: a) \(\frac{3}{7} \cdot \frac{5}{11}\) b) \(2\frac{1}{2} \cdot 2\frac{4}{5}\) д) \(\frac{2}{3} : \frac{4}{7}\) б) \(\frac{7}{13} \cdot \frac{39}{56}\) г) \(1\frac{1}{9} : 18\) e) \(\frac{6}{11} : 3\)

Ответ:

a) \(\frac{15}{77}\); б) \(\frac{3}{8}\); в) \(\frac{7}{6}\); г) \(\frac{5}{81}\); д) \(\frac{7}{6}\); e) \(\frac{2}{11}\)

Решение:

a) \(\frac{3}{7} \cdot \frac{5}{11} = \frac{3 \cdot 5}{7 \cdot 11} = \frac{15}{77}\)

б) \(\frac{7}{13} \cdot \frac{39}{56} = \frac{7 \cdot 39}{13 \cdot 56} = \frac{7 \cdot 3 \cdot 13}{13 \cdot 7 \cdot 8} = \frac{3}{8}\)

в) \(\frac{2}{3} : \frac{4}{7} = \frac{2}{3} \cdot \frac{7}{4} = \frac{2 \cdot 7}{3 \cdot 4} = \frac{7}{6}\)

г) \(1\frac{1}{9} : 18 = \frac{10}{9} : 18 = \frac{10}{9} \cdot \frac{1}{18} = \frac{10}{9 \cdot 18} = \frac{2 \cdot 5}{9 \cdot 2 \cdot 9} = \frac{5}{81}\)

д) \(2\frac{1}{2} \cdot 2\frac{4}{5} = \frac{5}{2} \cdot \frac{14}{5} = \frac{5 \cdot 14}{2 \cdot 5} = \frac{14}{2} = 7\)

e) \(\frac{6}{11} : 3 = \frac{6}{11} \cdot \frac{1}{3} = \frac{6}{11 \cdot 3} = \frac{3 \cdot 2}{11 \cdot 3} = \frac{2}{11}\)

Ответ:

a) \(\frac{15}{77}\); б) \(\frac{3}{8}\); в) \(\frac{7}{6}\); г) \(\frac{5}{81}\); д) \(\frac{7}{6}\); e) \(\frac{2}{11}\)