24. Вычислите: $$\frac{6}{5}$$ : $$\frac{4}{15}$$-8$$\frac{1}{4}$$+1$$\frac{5}{16}$$ : $$\frac{4}{7}$$. Запишите полностью решение и ответ.

24. Вычислите: $$\frac{6}{5}$$ : $$\frac{4}{15}$$-8$$\frac{1}{4}$$+1$$\frac{5}{16}$$ : $$\frac{4}{7}$$.

Решение:

1. $$\frac{6}{5}$$ : $$\frac{4}{15}$$ = $$\frac{6}{5}$$\cdot$$\frac{15}{4}$$ = $$\frac{6 \cdot 15}{5 \cdot 4}$$ = $$\frac{3 \cdot 3}{1 \cdot 2}$$ = $$\frac{9}{2}$$ = 4$$\frac{1}{2}$$
2. 8$$\frac{1}{4}$$ = $$\frac{8 \cdot 4 + 1}{4}$$ = $$\frac{32 + 1}{4}$$ = $$\frac{33}{4}$$
3. 1$$\frac{5}{16}$$ = $$\frac{1 \cdot 16 + 5}{16}$$ = $$\frac{16+5}{16}$$ = $$\frac{21}{16}$$
4. $$\frac{21}{16}$$ : $$\frac{4}{7}$$ = $$\frac{21}{16}$$\cdot$$\frac{7}{4}$$ = $$\frac{21 \cdot 7}{16 \cdot 4}$$ = $$\frac{147}{64}$$
5. 4$$\frac{1}{2}$$-$$\frac{33}{4}$$+$$\frac{147}{64}$$ = $$\frac{9}{2}$$ - $$\frac{33}{4}$$ + $$\frac{147}{64}$$ = $$\frac{9 \cdot 32 - 33 \cdot 16 + 147}{64}$$ = $$\frac{288 - 528 + 147}{64}$$ = $$\frac{-93}{64}$$ = -1$$\frac{29}{64}$$

Ответ: -1$$\frac{29}{64}$$