2.Выполните деление: a) 6/25 : 18/55; б) 9/17 : 18; в) 2 13/16 : 4 3/8; г) 12/11 : 3/4 * 11/24; g) 3/10 : 9/4 + 16/45 * 1/4

Давай выполним деление дробей по порядку. а) \(\frac{6}{25} : \frac{18}{55}\) = \(\frac{6}{25} \cdot \frac{55}{18}\) = \(\frac{6 \cdot 55}{25 \cdot 18}\) = \(\frac{6 \cdot 5 \cdot 11}{5 \cdot 5 \cdot 6 \cdot 3}\) = \(\frac{11}{5 \cdot 3}\) = \(\frac{11}{15}\). б) \(\frac{9}{17} : 18\) = \(\frac{9}{17} : \frac{18}{1}\) = \(\frac{9}{17} \cdot \frac{1}{18}\) = \(\frac{9 \cdot 1}{17 \cdot 18}\) = \(\frac{9 \cdot 1}{17 \cdot 9 \cdot 2}\) = \(\frac{1}{17 \cdot 2}\) = \(\frac{1}{34}\). в) \(2 \frac{13}{16} : 4 \frac{3}{8}\) = \(\frac{2 \cdot 16 + 13}{16} : \frac{4 \cdot 8 + 3}{8}\) = \(\frac{45}{16} : \frac{35}{8}\) = \(\frac{45}{16} \cdot \frac{8}{35}\) = \(\frac{45 \cdot 8}{16 \cdot 35}\) = \(\frac{5 \cdot 9 \cdot 8}{8 \cdot 2 \cdot 5 \cdot 7}\) = \(\frac{9}{2 \cdot 7}\) = \(\frac{9}{14}\). г) \(\frac{12}{11} : \frac{3}{4} \cdot \frac{11}{24}\) = \(\frac{12}{11} \cdot \frac{4}{3} \cdot \frac{11}{24}\) = \(\frac{12 \cdot 4 \cdot 11}{11 \cdot 3 \cdot 24}\) = \(\frac{12 \cdot 4 \cdot 11}{11 \cdot 3 \cdot 12 \cdot 2}\) = \(\frac{4}{3 \cdot 2}\) = \(\frac{2}{3}\). g) \(\frac{3}{10} : \frac{9}{4} + \frac{16}{45} \cdot \frac{1}{4}\) = \(\frac{3}{10} \cdot \frac{4}{9} + \frac{16}{45} \cdot \frac{1}{4}\) = \(\frac{3 \cdot 4}{10 \cdot 9} + \frac{16 \cdot 1}{45 \cdot 4}\) = \(\frac{3 \cdot 4}{2 \cdot 5 \cdot 3 \cdot 3} + \frac{4 \cdot 4}{45 \cdot 4}\) = \(\frac{2}{5 \cdot 3} + \frac{4}{45}\) = \(\frac{2}{15} + \frac{4}{45}\) = \(\frac{2 \cdot 3}{15 \cdot 3} + \frac{4}{45}\) = \(\frac{6}{45} + \frac{4}{45}\) = \(\frac{10}{45}\) = \(\frac{2}{9}\).

Ответ: а) 11/15; б) 1/34; в) 9/14; г) 2/3; д) 2/9