Реши примеры с дробями: 5 10/19 : 15/19

Конечно, давай решим эти примеры с дробями! 1) $5\frac{10}{19} : \frac{15}{19} = \frac{5 \cdot 19 + 10}{19} : \frac{15}{19} = \frac{95 + 10}{19} : \frac{15}{19} = \frac{105}{19} : \frac{15}{19} = \frac{105}{19} \cdot \frac{19}{15} = \frac{105 \cdot 19}{19 \cdot 15} = \frac{105}{15} = 7$ 2) $1\frac{1}{4} + 4\frac{9}{10} = \frac{1 \cdot 4 + 1}{4} + \frac{4 \cdot 10 + 9}{10} = \frac{5}{4} + \frac{49}{10} = \frac{5 \cdot 5}{4 \cdot 5} + \frac{49 \cdot 2}{10 \cdot 2} = \frac{25}{20} + \frac{98}{20} = \frac{25 + 98}{20} = \frac{123}{20} = 6\frac{3}{20}$ 3) $3\frac{1}{5} \cdot 1\frac{1}{4} = \frac{3 \cdot 5 + 1}{5} \cdot \frac{1 \cdot 4 + 1}{4} = \frac{16}{5} \cdot \frac{5}{4} = \frac{16 \cdot 5}{5 \cdot 4} = \frac{16}{4} = 4$ 4) $5\frac{5}{6} - 2\frac{1}{21} = \frac{5 \cdot 6 + 5}{6} - \frac{2 \cdot 21 + 1}{21} = \frac{35}{6} - \frac{43}{21} = \frac{35 \cdot 7}{6 \cdot 7} - \frac{43 \cdot 2}{21 \cdot 2} = \frac{245}{42} - \frac{86}{42} = \frac{245 - 86}{42} = \frac{159}{42} = 3\frac{33}{42} = 3\frac{11}{14}$ 5) $4\frac{2}{5} : 1\frac{3}{5} = \frac{4 \cdot 5 + 2}{5} : \frac{1 \cdot 5 + 3}{5} = \frac{22}{5} : \frac{8}{5} = \frac{22}{5} \cdot \frac{5}{8} = \frac{22 \cdot 5}{5 \cdot 8} = \frac{22}{8} = \frac{11}{4} = 2\frac{3}{4}$