13. Вычислите: 2$$\frac{4}{13}$$ ($$\frac{3}{8}$$-$$\frac{4}{15}$$) -11$$\frac{5}{6}$$. Запишите полностью решение и ответ.

13. Вычислите: 2$$\frac{4}{13}$$ ($$\frac{3}{8}$$-$$\frac{4}{15}$$) -11$$\frac{5}{6}$$.

Решение:

1. $$\frac{3}{8}$$-$$\frac{4}{15}$$ = $$\frac{3 \cdot 15 - 4 \cdot 8}{120}$$ = $$\frac{45 - 32}{120}$$ = $$\frac{13}{120}$$
2. 2$$\frac{4}{13}$$ = $$\frac{2 \cdot 13 + 4}{13}$$ = $$\frac{26+4}{13}$$ = $$\frac{30}{13}$$
3. $$\frac{30}{13}$$\cdot$$\frac{13}{120}$$ = $$\frac{30 \cdot 13}{13 \cdot 120}$$ = $$\frac{30}{120}$$ = $$\frac{1}{4}$$
4. 11$$\frac{5}{6}$$ = $$\frac{11 \cdot 6 + 5}{6}$$ = $$\frac{66+5}{6}$$ = $$\frac{71}{6}$$
5. $$\frac{1}{4}$$ - $$\frac{71}{6}$$ = $$\frac{1 \cdot 3 - 71 \cdot 2}{12}$$ = $$\frac{3 - 142}{12}$$ = $$\frac{-139}{12}$$ = -11$$\frac{7}{12}$$

Ответ: -11$$\frac{7}{12}$$