1. Вычислите, сократите дробь, если возможно a) \(\frac{2}{6} \cdot \frac{2}{3}\); б) \(\frac{5}{14} : \frac{7}{8}\); в) \(\frac{3}{9} \cdot 2\); г) \(\frac{3}{4} : 9\); д) \(1\frac{2}{4} \cdot 5\); e) \(1\frac{1}{4} : 1\frac{2}{5}\); ж) \(\left(\frac{3}{6}\right)^2 : \left(\frac{1}{3}\right)^3\)

Решение:

a) \(\frac{2}{6} \cdot \frac{2}{3} = \frac{2 \cdot 2}{6 \cdot 3} = \frac{4}{18} = \frac{2}{9}\)

б) \(\frac{5}{14} : \frac{7}{8} = \frac{5}{14} \cdot \frac{8}{7} = \frac{5 \cdot 8}{14 \cdot 7} = \frac{40}{98} = \frac{20}{49}\)

в) \(\frac{3}{9} \cdot 2 = \frac{3 \cdot 2}{9} = \frac{6}{9} = \frac{2}{3}\)

г) \(\frac{3}{4} : 9 = \frac{3}{4} \cdot \frac{1}{9} = \frac{3}{36} = \frac{1}{12}\)

д) \(1\frac{2}{4} \cdot 5 = \frac{6}{4} \cdot 5 = \frac{6 \cdot 5}{4} = \frac{30}{4} = \frac{15}{2} = 7\frac{1}{2}\)

e) \(1\frac{1}{4} : 1\frac{2}{5} = \frac{5}{4} : \frac{7}{5} = \frac{5}{4} \cdot \frac{5}{7} = \frac{25}{28}\)

ж) \(\left(\frac{3}{6}\right)^2 : \left(\frac{1}{3}\right)^3 = \left(\frac{1}{2}\right)^2 : \left(\frac{1}{3}\right)^3 = \frac{1}{4} : \frac{1}{27} = \frac{1}{4} \cdot 27 = \frac{27}{4} = 6\frac{3}{4}\)