Найдите произведение: a) $$rac{5}{6} \cdot \frac{7}{9} =$$ b) $$rac{11}{28} \cdot \frac{7}{33} =$$ c) $$1\frac{8}{25} \cdot 1\frac{4}{11} =$$ d) $$3\frac{5}{7} \cdot 1\frac{1}{13} =$$ e) $$2\frac{2}{3} \cdot 6 =$$

Для начала переведем все смешанные дроби в неправильные:

• $$1\frac{8}{25} = \frac{1 \cdot 25 + 8}{25} = \frac{33}{25}$$
• $$1\frac{4}{11} = \frac{1 \cdot 11 + 4}{11} = \frac{15}{11}$$
• $$3\frac{5}{7} = \frac{3 \cdot 7 + 5}{7} = \frac{26}{7}$$
• $$1\frac{1}{13} = \frac{1 \cdot 13 + 1}{13} = \frac{14}{13}$$
• $$2\frac{2}{3} = \frac{2 \cdot 3 + 2}{3} = \frac{8}{3}$$

Теперь решим каждый пример:

a) $$\frac{5}{6} \cdot \frac{7}{9} = \frac{5 \cdot 7}{6 \cdot 9} = \frac{35}{54}$$

b) $$\frac{11}{28} \cdot \frac{7}{33} = \frac{11 \cdot 7}{28 \cdot 33} = \frac{11 \cdot 7}{4 \cdot 7 \cdot 3 \cdot 11} = \frac{1}{4 \cdot 3} = \frac{1}{12}$$

c) $$1\frac{8}{25} \cdot 1\frac{4}{11} = \frac{33}{25} \cdot \frac{15}{11} = \frac{33 \cdot 15}{25 \cdot 11} = \frac{3 \cdot 11 \cdot 3 \cdot 5}{5 \cdot 5 \cdot 11} = \frac{3 \cdot 3}{5} = \frac{9}{5} = 1\frac{4}{5}$$

d) $$3\frac{5}{7} \cdot 1\frac{1}{13} = \frac{26}{7} \cdot \frac{14}{13} = \frac{26 \cdot 14}{7 \cdot 13} = \frac{2 \cdot 13 \cdot 2 \cdot 7}{7 \cdot 13} = 2 \cdot 2 = 4$$

e) $$2\frac{2}{3} \cdot 6 = \frac{8}{3} \cdot 6 = \frac{8 \cdot 6}{3} = \frac{8 \cdot 2 \cdot 3}{3} = 8 \cdot 2 = 16$$