Solve the examples written on the blackboard.

Question

Вопрос:

Ответ:

Accepted Answer

$$\frac{2}{3} + \frac{5}{7} \cdot \frac{9}{10} = \frac{2}{3} + \frac{5 \cdot 9}{7 \cdot 10} = \frac{2}{3} + \frac{45}{70} = \frac{2}{3} + \frac{9}{14} = \frac{2 \cdot 14 + 9 \cdot 3}{3 \cdot 14} = \frac{28 + 27}{42} = \frac{55}{42} = 1\frac{13}{42}$$
$$\frac{7}{8} \cdot \frac{2}{14} = \frac{7 \cdot 2}{8 \cdot 14} = \frac{14}{112} = \frac{1}{8}$$
$$\frac{9}{11} - \frac{3}{22} = \frac{9 \cdot 2 - 3}{22} = \frac{18 - 3}{22} = \frac{15}{22}$$
$$4\frac{8}{15} : 1\frac{1}{3} = \frac{4 \cdot 15 + 8}{15} : \frac{1 \cdot 3 + 1}{3} = \frac{60 + 8}{15} : \frac{4}{3} = \frac{68}{15} : \frac{4}{3} = \frac{68}{15} \cdot \frac{3}{4} = \frac{68 \cdot 3}{15 \cdot 4} = \frac{204}{60} = \frac{51}{15} = \frac{17}{5} = 3\frac{2}{5}$$
$$\frac{6}{7} - \frac{2}{3} = \frac{6 \cdot 3 - 2 \cdot 7}{7 \cdot 3} = \frac{18 - 14}{21} = \frac{4}{21}$$
$$(\frac{1}{2} + \frac{2}{3}) \cdot \frac{3}{4} = (\frac{1 \cdot 3 + 2 \cdot 2}{6}) \cdot \frac{3}{4} = (\frac{3 + 4}{6}) \cdot \frac{3}{4} = \frac{7}{6} \cdot \frac{3}{4} = \frac{7 \cdot 3}{6 \cdot 4} = \frac{21}{24} = \frac{7}{8}$$
$$\frac{8}{100} \cdot \frac{1}{10} \cdot \frac{100}{640} = \frac{8 \cdot 1 \cdot 100}{100 \cdot 10 \cdot 640} = \frac{800}{640000} = \frac{8}{6400} = \frac{1}{800}$$