Решение задания 134

а) $$\frac{5m}{6n} : \frac{15m^2}{8} = \frac{5m}{6n} \cdot \frac{8}{15m^2} = \frac{5m \cdot 8}{6n \cdot 15m^2} = \frac{40m}{90nm^2} = \frac{4}{9nm}$$

б) $$\frac{14}{9x^2} : \frac{7x}{2y^2} = \frac{14}{9x^2} \cdot \frac{2y^2}{7x} = \frac{14 \cdot 2y^2}{9x^2 \cdot 7x} = \frac{28y^2}{63x^3} = \frac{4y^2}{9x^3}$$

в) $$\frac{a^2}{12b} : \frac{ab}{36} = \frac{a^2}{12b} \cdot \frac{36}{ab} = \frac{a^2 \cdot 36}{12b \cdot ab} = \frac{36a^2}{12ab^2} = \frac{3a}{b^2}$$

г) $$\frac{3x}{10a^3} : \frac{1}{5a^2} = \frac{3x}{10a^3} \cdot 5a^2 = \frac{3x \cdot 5a^2}{10a^3} = \frac{15xa^2}{10a^3} = \frac{3x}{2a}$$

д) $$\frac{11x}{4y^2} : (22x^2) = \frac{11x}{4y^2} : \frac{22x^2}{1} = \frac{11x}{4y^2} \cdot \frac{1}{22x^2} = \frac{11x}{4y^2 \cdot 22x^2} = \frac{11x}{88x^2y^2} = \frac{1}{8xy^2}$$

е) $$27a^3 : \frac{18a^4}{7b^2} = \frac{27a^3}{1} \cdot \frac{7b^2}{18a^4} = \frac{27a^3 \cdot 7b^2}{18a^4} = \frac{189a^3b^2}{18a^4} = \frac{21b^2}{2a}$$

ж) $$\frac{18c^4}{7d} : (9c^2d) = \frac{18c^4}{7d} : \frac{9c^2d}{1} = \frac{18c^4}{7d} \cdot \frac{1}{9c^2d} = \frac{18c^4}{7d \cdot 9c^2d} = \frac{18c^4}{63c^2d^2} = \frac{2c^2}{7d^2}$$

з) $$35x^5y : \frac{7x^3}{34} = \frac{35x^5y}{1} \cdot \frac{34}{7x^3} = \frac{35x^5y \cdot 34}{7x^3} = \frac{1190x^5y}{7x^3} = 170x^2y$$