Уровень 3: Сложный (две дроби, смешанные ча Цель: полное применение распределение дроби на дробь, работа со смеш 1) (2/3 + 1/5) × 3/4 2) (2 1/4 - 2/3) × 6/7 (2 1/4 = 9/4) 3) (3/8 + 1/4) × 4/5 4) (3 - 5/6) × 9/10 5) (2 1/3 + 1 1/2) × 3/5 (2 1/3 = 7/3, 1 1/2 = 3/2)

1) $$\left(\frac{2}{3} + \frac{1}{5}\right) \times \frac{3}{4} = \left(\frac{2 \times 5}{3 \times 5} + \frac{1 \times 3}{5 \times 3}\right) \times \frac{3}{4} = \left(\frac{10}{15} + \frac{3}{15}\right) \times \frac{3}{4} = \frac{13}{15} \times \frac{3}{4} = \frac{13}{5} \times \frac{1}{4} = \frac{13}{20}$$

Ответ: 13/20

2) $$\left(2\frac{1}{4} - \frac{2}{3}\right) \times \frac{6}{7} = \left(\frac{9}{4} - \frac{2}{3}\right) \times \frac{6}{7} = \left(\frac{9 \times 3}{4 \times 3} - \frac{2 \times 4}{3 \times 4}\right) \times \frac{6}{7} = \left(\frac{27}{12} - \frac{8}{12}\right) \times \frac{6}{7} = \frac{19}{12} \times \frac{6}{7} = \frac{19}{2} \times \frac{1}{7} = \frac{19}{14} = 1\frac{5}{14}$$

Ответ: $$1\frac{5}{14}$$

3) $$\left(\frac{3}{8} + \frac{1}{4}\right) \times \frac{4}{5} = \left(\frac{3}{8} + \frac{1 \times 2}{4 \times 2}\right) \times \frac{4}{5} = \left(\frac{3}{8} + \frac{2}{8}\right) \times \frac{4}{5} = \frac{5}{8} \times \frac{4}{5} = \frac{1}{2} \times \frac{1}{1} = \frac{1}{2}$$

Ответ: 1/2

4) $$\left(3 - \frac{5}{6}\right) \times \frac{9}{10} = \left(\frac{3 \times 6}{1 \times 6} - \frac{5}{6}\right) \times \frac{9}{10} = \left(\frac{18}{6} - \frac{5}{6}\right) \times \frac{9}{10} = \frac{13}{6} \times \frac{9}{10} = \frac{13}{2} \times \frac{3}{10} = \frac{39}{20} = 1\frac{19}{20}$$

Ответ: $$1\frac{19}{20}$$

5) $$\left(2\frac{1}{3} + 1\frac{1}{2}\right) \times \frac{3}{5} = \left(\frac{7}{3} + \frac{3}{2}\right) \times \frac{3}{5} = \left(\frac{7 \times 2}{3 \times 2} + \frac{3 \times 3}{2 \times 3}\right) \times \frac{3}{5} = \left(\frac{14}{6} + \frac{9}{6}\right) \times \frac{3}{5} = \frac{23}{6} \times \frac{3}{5} = \frac{23}{2} \times \frac{1}{5} = \frac{23}{10} = 2\frac{3}{10}$$

Ответ: $$2\frac{3}{10}$$