1. Вычислите: a) 2/3 * 1 2/7; г) 5/6 : 2 2/9; 6) 3 1/8 * 2; д) 3 3/5 : 9; B) 1 1/7 * 1 3/4; e) 7 3/5 : 1 9/10.

Решение:

1. a) $$\frac{2}{3} \cdot 1\frac{2}{7} = \frac{2}{3} \cdot \frac{9}{7} = \frac{2 \cdot 9}{3 \cdot 7} = \frac{2 \cdot 3}{1 \cdot 7} = \frac{6}{7}$$
2. б) $$3\frac{1}{8} \cdot 2 = \frac{25}{8} \cdot 2 = \frac{25 \cdot 2}{8} = \frac{25}{4} = 6\frac{1}{4}$$
3. в) $$1\frac{1}{7} \cdot 1\frac{3}{4} = \frac{8}{7} \cdot \frac{7}{4} = \frac{8 \cdot 7}{7 \cdot 4} = \frac{8}{4} = 2$$
4. г) $$\frac{5}{6} : 2\frac{2}{9} = \frac{5}{6} : \frac{20}{9} = \frac{5}{6} \cdot \frac{9}{20} = \frac{5 \cdot 9}{6 \cdot 20} = \frac{1 \cdot 3}{2 \cdot 4} = \frac{3}{8}$$
5. д) $$3\frac{3}{5} : 9 = \frac{18}{5} : 9 = \frac{18}{5} \cdot \frac{1}{9} = \frac{18 \cdot 1}{5 \cdot 9} = \frac{2 \cdot 1}{5 \cdot 1} = \frac{2}{5}$$
6. е) $$7\frac{3}{5} : 1\frac{9}{10} = \frac{38}{5} : \frac{19}{10} = \frac{38}{5} \cdot \frac{10}{19} = \frac{38 \cdot 10}{5 \cdot 19} = \frac{2 \cdot 2}{1 \cdot 1} = 4$$

Ответ: а) 6/7; б) 6 1/4; в) 2; г) 3/8; д) 2/5; е) 4