5. Вычислите 3$$\frac{35}{36}$$:($$\frac{1}{2}$$+$$\frac{5}{14}$$)$$\cdot$$\frac{5}{6}$$:2$$\frac{10}{27}$$

5. Вычислите 3$$\frac{35}{36}$$:($$\frac{1}{2}$$+$$\frac{5}{14}$$)$$\cdot$$\frac{5}{6}$$:2$$\frac{10}{27}$$

1) $$\frac{1}{2}$$+$$\frac{5}{14}$$ =$$\frac{1\cdot7 + 5}{14}$$=$$\frac{7+5}{14}$$=$$\frac{12}{14}$$=$$\frac{6}{7}$$

2) 3$$\frac{35}{36}$$:($$\frac{6}{7}$$)=$$\frac{3\cdot36+35}{36}$$:($$\frac{6}{7}$$)=$$\frac{143}{36}$$\cdot$$($$\frac{7}{6}$$)=$$\frac{143\cdot7}{36\cdot6}$$=$$\frac{1001}{216}$$

3) 2$$\frac{10}{27}$$=$$\frac{2\cdot27+10}{27}$$=$$\frac{64}{27}$$

4) $$\frac{1001}{216}$$\cdot$$\frac{5}{6}$$:$$\frac{64}{27}$$=$$\frac{1001}{216}$$\cdot$$\frac{5}{6}$$\cdot$$\frac{27}{64}$$=$$\frac{1001\cdot5\cdot27}{216\cdot6\cdot64}$$=$$\frac{1001\cdot5\cdot3}{24\cdot6\cdot64}$$=$$\frac{15015}{9216}$$

Ответ: $$\frac{15015}{9216}$$