Вычислите: a) $$2\frac{1}{3}\cdot3\frac{1}{5}-8\frac{4}{9}:2$$; б) $$5\frac{2}{7}\cdot1\frac{1}{4}+5\frac{2}{7}\cdot1\frac{3}{4}$$.

Вычислите:

a) $$2\frac{1}{3}\cdot3\frac{1}{5}-8\frac{4}{9}:2$$

1. $$2\frac{1}{3} = \frac{2 \cdot 3 + 1}{3} = \frac{6+1}{3} = \frac{7}{3}$$
2. $$3\frac{1}{5} = \frac{3 \cdot 5 + 1}{5} = \frac{15+1}{5} = \frac{16}{5}$$
3. $$\frac{7}{3} \cdot \frac{16}{5} = \frac{7 \cdot 16}{3 \cdot 5} = \frac{112}{15}$$
4. $$8\frac{4}{9} = \frac{8 \cdot 9 + 4}{9} = \frac{72+4}{9} = \frac{76}{9}$$
5. $$\frac{76}{9} : 2 = \frac{76}{9} \cdot \frac{1}{2} = \frac{76 \cdot 1}{9 \cdot 2} = \frac{38}{9}$$
6. $$\frac{112}{15} - \frac{38}{9} = \frac{112 \cdot 3}{15 \cdot 3} - \frac{38 \cdot 5}{9 \cdot 5} = \frac{336}{45} - \frac{190}{45} = \frac{336-190}{45} = \frac{146}{45} = 3\frac{11}{45}$$

Ответ: $$3\frac{11}{45}$$

б) $$5\frac{2}{7}\cdot1\frac{1}{4}+5\frac{2}{7}\cdot1\frac{3}{4}$$

1. $$5\frac{2}{7} = \frac{5 \cdot 7 + 2}{7} = \frac{35+2}{7} = \frac{37}{7}$$
2. $$1\frac{1}{4} = \frac{1 \cdot 4 + 1}{4} = \frac{4+1}{4} = \frac{5}{4}$$
3. $$1\frac{3}{4} = \frac{1 \cdot 4 + 3}{4} = \frac{4+3}{4} = \frac{7}{4}$$
4. $$\frac{37}{7} \cdot \frac{5}{4} + \frac{37}{7} \cdot \frac{7}{4} = \frac{37}{7} \cdot (\frac{5}{4} + \frac{7}{4}) = \frac{37}{7} \cdot \frac{5+7}{4} = \frac{37}{7} \cdot \frac{12}{4} = \frac{37}{7} \cdot 3 = \frac{37 \cdot 3}{7} = \frac{111}{7} = 15\frac{6}{7}$$

Ответ: $$15\frac{6}{7}$$