633. Выполните деление: (23) a) \frac{4}{9}:\frac{3}{8}; б) \frac{8}{7}:\frac{9}{14}; в) \frac{86}{113}:\frac{43}{51'}; г) \frac{27}{64} : 9; д) 8 : \frac{2}{3}; e) 7: 3; ж) 2\frac{1}{7} : 1\frac{11}{14}; з) 3\frac{3}{5} : 1\frac{11}{25}

Ответ:

a) \(\frac{4}{9}:\frac{3}{8}=\frac{4}{9} \cdot \frac{8}{3}=\frac{4 \cdot 8}{9 \cdot 3}=\frac{32}{27}=1\frac{5}{27}\)

б) \(\frac{8}{7}:\frac{9}{14}=\frac{8}{7} \cdot \frac{14}{9}=\frac{8 \cdot 14}{7 \cdot 9}=\frac{8 \cdot 2}{1 \cdot 9}=\frac{16}{9}=1\frac{7}{9}\)

в) \(\frac{86}{113}:\frac{43}{51}=\frac{86}{113} \cdot \frac{51}{43}=\frac{2 \cdot 43 \cdot 51}{113 \cdot 43}=\frac{2 \cdot 51}{113}=\frac{102}{113}\)

г) \(\frac{27}{64} : 9 = \frac{27}{64} \cdot \frac{1}{9} = \frac{3 \cdot 9}{64 \cdot 9} = \frac{3}{64}\)

д) \(8 : \frac{2}{3} = 8 \cdot \frac{3}{2} = \frac{8 \cdot 3}{2} = \frac{4 \cdot 3}{1} = 12\)

e) \(7 : 3 = \frac{7}{3} = 2\frac{1}{3}\)

ж) \(2\frac{1}{7} : 1\frac{11}{14} = \frac{15}{7} : \frac{25}{14} = \frac{15}{7} \cdot \frac{14}{25} = \frac{3 \cdot 5 \cdot 2 \cdot 7}{7 \cdot 5 \cdot 5} = \frac{3 \cdot 2}{5} = \frac{6}{5} = 1\frac{1}{5}\)

з) \(3\frac{3}{5} : 1\frac{11}{25} = \frac{18}{5} : \frac{36}{25} = \frac{18}{5} \cdot \frac{25}{36} = \frac{18 \cdot 5 \cdot 5}{5 \cdot 18 \cdot 2} = \frac{5}{2} = 2\frac{1}{2}\)

Ответ: