5.523 Найдите частное: a) 4/5 : 9/11; b) 2/7 : 5/9; r) 5/8 : 7/12; e) 5/9 : 5 1/2; d) 4/7 : 16/49; ж) 12/25 : 8/15; з) 9/14 : 18/35.

• a) \(\frac{4}{5} : \frac{9}{11} = \frac{4}{5} \cdot \frac{11}{9} = \frac{4 \cdot 11}{5 \cdot 9} = \frac{44}{45}\)
• б) \(\frac{2}{7} : \frac{5}{9} = \frac{2}{7} \cdot \frac{9}{5} = \frac{2 \cdot 9}{7 \cdot 5} = \frac{18}{35}\)
• г) \(\frac{5}{8} : \frac{7}{12} = \frac{5}{8} \cdot \frac{12}{7} = \frac{5 \cdot 12}{8 \cdot 7} = \frac{60}{56} = \frac{15}{14} = 1\frac{1}{14}\)
• e) \(\frac{5}{9} : 5 \frac{1}{2} = \frac{5}{9} : \frac{11}{2} = \frac{5}{9} \cdot \frac{2}{11} = \frac{5 \cdot 2}{9 \cdot 11} = \frac{10}{99}\)
• д) \(\frac{4}{7} : \frac{16}{49} = \frac{4}{7} \cdot \frac{49}{16} = \frac{4 \cdot 49}{7 \cdot 16} = \frac{196}{112} = \frac{7}{4} = 1\frac{3}{4}\)
• ж) \(\frac{12}{25} : \frac{8}{15} = \frac{12}{25} \cdot \frac{15}{8} = \frac{12 \cdot 15}{25 \cdot 8} = \frac{180}{200} = \frac{9}{10}\)
• з) \(\frac{9}{14} : \frac{18}{35} = \frac{9}{14} \cdot \frac{35}{18} = \frac{9 \cdot 35}{14 \cdot 18} = \frac{315}{252} = \frac{5}{4} = 1\frac{1}{4}\)

Ответ: а) \(\frac{44}{45}\); б) \(\frac{18}{35}\); г) \(1\frac{1}{14}\); e) \(\frac{10}{99}\); д) \(1\frac{3}{4}\); ж) \(\frac{9}{10}\); з) \(1\frac{1}{4}\)