Решение заданий Варианта 2, задание 1

a) $$\frac{1}{4} + \frac{5}{6} = \frac{1 \cdot 3}{4 \cdot 3} + \frac{5 \cdot 2}{6 \cdot 2} = \frac{3}{12} + \frac{10}{12} = \frac{3+10}{12} = \frac{13}{12} = 1\frac{1}{12}$$

б) $$\frac{5}{6} - \frac{5}{9} = \frac{5 \cdot 3}{6 \cdot 3} - \frac{5 \cdot 2}{9 \cdot 2} = \frac{15}{18} - \frac{10}{18} = \frac{15-10}{18} = \frac{5}{18}$$

в) $$\frac{24}{25} \cdot \frac{35}{36} = \frac{24 \cdot 35}{25 \cdot 36} = \frac{6 \cdot 4 \cdot 7 \cdot 5}{5 \cdot 5 \cdot 6 \cdot 6} = \frac{4 \cdot 7}{5 \cdot 6} = \frac{2 \cdot 2 \cdot 7}{5 \cdot 2 \cdot 3} = \frac{2 \cdot 7}{5 \cdot 3} = \frac{14}{15}$$

г) $$3\frac{1}{5} : 2\frac{2}{15} = \frac{3 \cdot 5 + 1}{5} : \frac{2 \cdot 15 + 2}{15} = \frac{16}{5} : \frac{32}{15} = \frac{16}{5} \cdot \frac{15}{32} = \frac{16 \cdot 15}{5 \cdot 32} = \frac{16 \cdot 5 \cdot 3}{5 \cdot 16 \cdot 2} = \frac{3}{2} = 1\frac{1}{2}$$