Задание 5 Параграф 5 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 8 класс (Алгебра)

Выполните деление:

1. $$\frac{8m}{5n}:\frac{24m^2}{25n^3}$$;
2. $$27x^8:\frac{36x^9}{y}$$;
3. $$\frac{12c^6}{p^{12}}:(42c^5p^2)$$;
4. $$-\frac{26a^3b^3}{9c^3p^2}:\left(-\frac{65a^2b^3}{6c^2p^3}\right)$$.

1. $$\frac{8m}{5n}:\frac{24m^2}{25n^3}=\frac{8m}{5n}\cdot\frac{25n^3}{24m^2}$$
   $$=\frac{8\cdot 25\cdot m\cdot n^3}{5\cdot 24\cdot n\cdot m^2}=\frac{5n^2}{3m}.$$
2. $$27x^8:\frac{36x^9}{y}=27x^8\cdot\frac{y}{36x^9}$$
   $$=\frac{27y}{36x}=\frac{3y}{4x}.$$
3. $$\frac{12c^6}{p^{12}}:(42c^5p^2)=\frac{12c^6}{p^{12}}\cdot\frac{1}{42c^5p^2}$$
   $$=\frac{12c^6}{42c^5p^{14}}=\frac{2c}{7p^{14}}.$$
4. $$-\frac{26a^3b^3}{9c^3p^2}:\left(-\frac{65a^2b^3}{6c^2p^3}\right)=\frac{26a^3b^3}{9c^3p^2}\cdot\frac{6c^2p^3}{65a^2b^3}$$
   $$=\frac{26\cdot 6\cdot a\cdot p}{9\cdot 65\cdot c}=\frac{4ap}{15c}.$$

Ответ: 1) $$\frac{5n^2}{3m}$$; 2) $$\frac{3y}{4x}$$; 3) $$\frac{2c}{7p^{14}}$$; 4) $$\frac{4ap}{15c}$$.