12. Вычислите: 2$$\frac{5}{13}$$ ($$\frac{4}{5}$$-$$\frac{7}{12}$$) -7$$\frac{1}{2}$$ : 3$$\frac{1}{2}$$. Запишите полностью решение и ответ.

12. Вычислите: 2$$\frac{5}{13}$$ ($$\frac{4}{5}$$-$$\frac{7}{12}$$) -7$$\frac{1}{2}$$ : 3$$\frac{1}{2}$$.

Решение:

1. $$\frac{4}{5}$$-$$\frac{7}{12}$$ = $$\frac{4 \cdot 12 - 7 \cdot 5}{60}$$ = $$\frac{48-35}{60}$$ =$$\frac{13}{60}$$
2. 2$$\frac{5}{13}$$ = $$\frac{2 \cdot 13 + 5}{13}$$ = $$\frac{26+5}{13}$$ = $$\frac{31}{13}$$
3. $$\frac{31}{13}$$\cdot$$\frac{13}{60}$$ = $$\frac{31 \cdot 13}{13 \cdot 60}$$ = $$\frac{31}{60}$$
4. 7$$\frac{1}{2}$$ = $$\frac{7 \cdot 2 + 1}{2}$$ = $$\frac{14+1}{2}$$ = $$\frac{15}{2}$$
5. 3$$\frac{1}{2}$$ = $$\frac{3 \cdot 2 + 1}{2}$$ = $$\frac{6+1}{2}$$ = $$\frac{7}{2}$$
6. $$\frac{15}{2}$$ : $$\frac{7}{2}$$ = $$\frac{15}{2}$$\cdot$$\frac{2}{7}$$ = $$\frac{15 \cdot 2}{2 \cdot 7}$$ = $$\frac{15}{7}$$ = 2$$\frac{1}{7}$$
7. $$\frac{31}{60}$$ - 2$$\frac{1}{7}$$ = $$\frac{31}{60}$$ - $$\frac{15}{7}$$ = $$\frac{31 \cdot 7 - 15 \cdot 60}{420}$$ = $$\frac{217 - 900}{420}$$ = $$\frac{-683}{420}$$ = -1$$\frac{263}{420}$$

Ответ: -1$$\frac{263}{420}$$