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

a) \(\frac{7}{9}:\frac{7}{18}\) = \(\frac{7}{9} \cdot \frac{18}{7}\) = \(\frac{7 \cdot 18}{9 \cdot 7}\) = \(\frac{1 \cdot 2}{1 \cdot 1}\) = 2

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

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

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

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

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

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

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

Ответ: a) 2; б) \(\frac{3}{4}\); в) \(\frac{27}{28}\); г) 6; д) \(\frac{1}{11}\); е) \(\frac{3}{13}\); ж) 5; з) \(\frac{3}{22}\)