5.558 Найдите частное: a) \frac{7}{9}:\frac{7}{18}; в) \frac{3}{4}:\frac{7}{9}; д) \frac{6}{11}:6; ж) \frac{5}{7}:\frac{1}{7}; б) \frac{1}{4}:\frac{1}{3}; г) \frac{3}{7}:\frac{1}{14}; е) \frac{9}{13}:3; з) \frac{15}{22}:5.

Решение:

а) \(\frac{7}{9}:\frac{7}{18} = \frac{7}{9} \cdot \frac{18}{7} = \frac{7 \cdot 18}{9 \cdot 7} = \frac{18}{9} = 2\)

в) \(\frac{3}{4}:\frac{7}{9} = \frac{3}{4} \cdot \frac{9}{7} = \frac{3 \cdot 9}{4 \cdot 7} = \frac{27}{28}\)

д) \(\frac{6}{11}:6 = \frac{6}{11} \cdot \frac{1}{6} = \frac{6 \cdot 1}{11 \cdot 6} = \frac{1}{11}\)

ж) \(\frac{5}{7}:\frac{1}{7} = \frac{5}{7} \cdot \frac{7}{1} = \frac{5 \cdot 7}{7 \cdot 1} = 5\)

б) \(\frac{1}{4}:\frac{1}{3} = \frac{1}{4} \cdot \frac{3}{1} = \frac{1 \cdot 3}{4 \cdot 1} = \frac{3}{4}\)

г) \(\frac{3}{7}:\frac{1}{14} = \frac{3}{7} \cdot \frac{14}{1} = \frac{3 \cdot 14}{7 \cdot 1} = \frac{3 \cdot 2}{1} = 6\)

е) \(\frac{9}{13}:3 = \frac{9}{13} \cdot \frac{1}{3} = \frac{9 \cdot 1}{13 \cdot 3} = \frac{3}{13}\)

з) \(\frac{15}{22}:5 = \frac{15}{22} \cdot \frac{1}{5} = \frac{15 \cdot 1}{22 \cdot 5} = \frac{3}{22}\)