344 Выполните действия: a) \frac{9}{52}\cdot 4\frac{1}{3}\cdot \frac{1}{3}+\left(3\frac{2}{3}+2\frac{4}{5}\right)\cdot \frac{60}{97}+\frac{5}{36}\cdot 1\frac{4}{5};

a)

1) $$4\frac{1}{3}=\frac{4 \cdot 3 + 1}{3}=\frac{13}{3}$$

2) $$\frac{9}{52}\cdot \frac{13}{3}\cdot \frac{1}{3}=\frac{9 \cdot 13 \cdot 1}{52 \cdot 3 \cdot 3}=\frac{1 \cdot 1 \cdot 1}{4 \cdot 1 \cdot 1}=\frac{1}{4}$$

3) $$3\frac{2}{3}+2\frac{4}{5}=\frac{3 \cdot 3 + 2}{3}+\frac{2 \cdot 5 + 4}{5}=\frac{11}{3}+\frac{14}{5}=\frac{11 \cdot 5 + 14 \cdot 3}{15}=\frac{55+42}{15}=\frac{97}{15}$$

4) $$\frac{97}{15}\cdot \frac{60}{97}=\frac{97 \cdot 60}{15 \cdot 97}=\frac{1 \cdot 4}{1 \cdot 1}=4$$

5) $$1\frac{4}{5}=\frac{1 \cdot 5 + 4}{5}=\frac{9}{5}$$

6) $$\frac{5}{36}\cdot \frac{9}{5}=\frac{5 \cdot 9}{36 \cdot 5}=\frac{1 \cdot 1}{4 \cdot 1}=\frac{1}{4}$$

7) $$\frac{1}{4}+4+\frac{1}{4}=4+\frac{1+1}{4}=4+\frac{2}{4}=4+\frac{1}{2}=4\frac{1}{2}$$

Ответ: $$4\frac{1}{2}$$