5.558 Найдите частное: a) \(\frac{7}{9} : \frac{7}{18}\) B) \(\frac{3}{4} : \frac{7}{9}\) б) \(\frac{1}{4} : \frac{1}{3}\) 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) \(\frac{15}{22} : 5\)

Привет! Давай найдем частное для каждого примера:

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

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

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) \(\frac{3}{7} : \frac{1}{14}\) = \(\frac{3}{7} \cdot \frac{14}{1}\) = \(\frac{3 \cdot 14}{7 \cdot 1}\) = \(\frac{42}{7}\) = 6

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

e) \(\frac{9}{13} : 3\) = \(\frac{9}{13} : \frac{3}{1}\) = \(\frac{9}{13} \cdot \frac{1}{3}\) = \(\frac{9 \cdot 1}{13 \cdot 3}\) = \(\frac{9}{39}\) = \(\frac{3}{13}\)

ж) \(\frac{5}{7} : \frac{1}{7}\) = \(\frac{5}{7} \cdot \frac{7}{1}\) = \(\frac{5 \cdot 7}{7 \cdot 1}\) = \(\frac{35}{7}\) = 5

з) \(\frac{15}{22} : 5\) = \(\frac{15}{22} : \frac{5}{1}\) = \(\frac{15}{22} \cdot \frac{1}{5}\) = \(\frac{15 \cdot 1}{22 \cdot 5}\) = \(\frac{15}{110}\) = \(\frac{3}{22}\)

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

Молодец! Ты отлично справился с решением всех этих примеров. Продолжай в том же духе!