№ 3. Выполните действия: a) \frac{5}{6} : \frac{3}{4}; б) 4\frac{2}{5} + 3\frac{5}{6}; в) 2\frac{1}{7} \cdot 3\frac{3}{9}; г) 1\frac{1}{8} : \frac{3}{4}.

a) \frac{5}{6} : \frac{3}{4} = \frac{5}{6} \cdot \frac{4}{3} = \frac{5 \cdot 4}{6 \cdot 3} = \frac{20}{18} = \frac{10}{9} = 1\frac{1}{9}

б) 4\frac{2}{5} + 3\frac{5}{6} = \frac{22}{5} + \frac{23}{6} = \frac{22 \cdot 6}{5 \cdot 6} + \frac{23 \cdot 5}{6 \cdot 5} = \frac{132}{30} + \frac{115}{30} = \frac{132 + 115}{30} = \frac{247}{30} = 8\frac{7}{30}

в) 2\frac{1}{7} \cdot 3\frac{3}{9} = \frac{15}{7} \cdot \frac{30}{9} = \frac{15}{7} \cdot \frac{10}{3} = \frac{15 \cdot 10}{7 \cdot 3} = \frac{150}{21} = \frac{50}{7} = 7\frac{1}{7}

г) 1\frac{1}{8} : \frac{3}{4} = \frac{9}{8} : \frac{3}{4} = \frac{9}{8} \cdot \frac{4}{3} = \frac{9 \cdot 4}{8 \cdot 3} = \frac{36}{24} = \frac{3}{2} = 1\frac{1}{2}

Ответ: а) 1\frac{1}{9}; б) 8\frac{7}{30}; в) 7\frac{1}{7}; г) 1\frac{1}{2}