№2 Выполните действие: a) $$4\frac{3}{16} + 13\frac{9}{16}$$; б) $$19\frac{5}{6} - 3\frac{4}{15}$$; в) $$4\frac{2}{7} \cdot 2\frac{4}{5}$$; г) $$14 : \frac{7}{8}$$

Решение:

а) $$4\frac{3}{16} + 13\frac{9}{16} = (4 + 13) + (\frac{3}{16} + \frac{9}{16}) = 17 + \frac{12}{16} = 17 + \frac{3}{4} = 17\frac{3}{4}$$

б) $$19\frac{5}{6} - 3\frac{4}{15} = (19 - 3) + (\frac{5}{6} - \frac{4}{15}) = 16 + (\frac{5 \cdot 15 - 4 \cdot 6}{6 \cdot 15}) = 16 + (\frac{75 - 24}{90}) = 16 + \frac{51}{90} = 16 + \frac{17 \cdot 3}{30 \cdot 3} = 16 + \frac{17}{30} = 16\frac{17}{30}$$

в) $$4\frac{2}{7} \cdot 2\frac{4}{5} = \frac{4 \cdot 7 + 2}{7} \cdot \frac{2 \cdot 5 + 4}{5} = \frac{30}{7} \cdot \frac{14}{5} = \frac{30 \cdot 14}{7 \cdot 5} = \frac{6 \cdot 5 \cdot 2 \cdot 7}{7 \cdot 5} = 6 \cdot 2 = 12$$

г) $$14 : \frac{7}{8} = 14 \cdot \frac{8}{7} = \frac{14 \cdot 8}{7} = \frac{2 \cdot 7 \cdot 8}{7} = 2 \cdot 8 = 16$$

Ответ:

а) $$17\frac{3}{4}$$

б) $$16\frac{17}{30}$$

в) $$12$$

г) $$16$$