Вариант 1 a) \frac{3}{8}:\frac{2}{3}; б) \frac{4}{7}:\frac{4}{9}; в) 11\frac{2}{5}:3\frac{4}{5}; г) \frac{16}{17}:8; д) 12:\frac{6}{7}. e) 2\frac{1}{7}:4\frac{1}{6}\cdot2\frac{1}{3}

Вариант 1

a) $$ \frac{3}{8}:\frac{2}{3} = \frac{3}{8} \cdot \frac{3}{2} = \frac{3 \cdot 3}{8 \cdot 2} = \frac{9}{16} $$

Ответ: $$\frac{9}{16}$$

б) $$ \frac{4}{7}:\frac{4}{9} = \frac{4}{7} \cdot \frac{9}{4} = \frac{4 \cdot 9}{7 \cdot 4} = \frac{9}{7} = 1\frac{2}{7} $$

Ответ: $$1\frac{2}{7}$$

в) $$ 11\frac{2}{5}:3\frac{4}{5} = \frac{11\cdot5+2}{5}:\frac{3\cdot5+4}{5} = \frac{57}{5}:\frac{19}{5} = \frac{57}{5} \cdot \frac{5}{19} = \frac{57 \cdot 5}{5 \cdot 19} = \frac{57}{19} = 3 $$

Ответ: $$3$$

г) $$ \frac{16}{17}:8 = \frac{16}{17}:\frac{8}{1} = \frac{16}{17} \cdot \frac{1}{8} = \frac{16 \cdot 1}{17 \cdot 8} = \frac{2}{17} $$

Ответ: $$\frac{2}{17}$$

д) $$ 12:\frac{6}{7} = \frac{12}{1}:\frac{6}{7} = \frac{12}{1} \cdot \frac{7}{6} = \frac{12 \cdot 7}{1 \cdot 6} = \frac{2 \cdot 7}{1} = 14 $$

Ответ: $$14$$

е) $$ 2\frac{1}{7}:4\frac{1}{6}\cdot2\frac{1}{3} = \frac{2\cdot7+1}{7}:\frac{4\cdot6+1}{6} \cdot \frac{2\cdot3+1}{3} = \frac{15}{7}:\frac{25}{6} \cdot \frac{7}{3} = \frac{15}{7} \cdot \frac{6}{25} \cdot \frac{7}{3} = \frac{15 \cdot 6 \cdot 7}{7 \cdot 25 \cdot 3} = \frac{3 \cdot 6}{25} = \frac{18}{25} $$

Ответ: $$\frac{18}{25}$$