Решебник по алгебре 8 класс Макарычев ФГОС Задание 134

 

\[\boxed{\text{134\ (134).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \frac{6x^{2}}{m^{3}n}\ :\frac{x}{3mn^{2}} = \frac{6x^{2}}{m^{3}n} \cdot \frac{3mn^{2}}{x} =\]

\[= \frac{6x \cdot x \cdot 3n \cdot mn}{m^{2} \cdot mn \cdot x} = \frac{18xn}{m^{2}}\]

\[\textbf{б)}\ \frac{35x^{2}y}{12ab}\ :\frac{7\text{xy}}{8ab^{2}} =\]

\[= \frac{35x^{2}y}{12ab} \cdot \frac{8ab^{2}}{7xy} =\]

\[= \frac{7xy \cdot 5x \cdot 2b \cdot 4ab}{3 \cdot 4ab \cdot 7xy} = \frac{10xb}{3}\]

\[\textbf{в)}\ \frac{8mx^{2}}{3y^{3}}\ :\left( 4m^{2}x \right) =\]

\[= \frac{8mx^{2}}{3y^{3}} \cdot \frac{1}{4m^{2}x} =\]

\[= \frac{2x \cdot 4mx}{3y^{3} \cdot m \cdot 4mx} = \frac{2x}{3my^{3}}\]

\[\textbf{г)}\ 15a^{2}bx\ :\frac{a^{3}b^{2}}{30x^{2}} =\]

\[= \frac{15a^{2}\text{bx}}{1} \cdot \frac{30x^{2}}{a^{3}b^{2}} =\]

\[= \frac{a^{2}b \cdot 15x \cdot 30x^{2}}{a^{2}b \cdot ab} = \frac{450x^{3}}{\text{ab}}\]

\[\boxed{\text{134.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \frac{5m}{6n}\ :\frac{15m^{2}}{8} = \frac{5m}{6n} \cdot \frac{8}{15m^{2}} =\]

\[= \frac{5m \cdot 2 \cdot 4}{3n \cdot 2 \cdot 5 \cdot 3m \cdot m} = \frac{4}{9mn}\]

\[\textbf{б)}\ \frac{14}{9x^{3}}\ :\frac{7x}{2y^{2}} = \frac{14}{9x^{3}} \cdot \frac{2y^{2}}{7x} =\]

\[= \frac{2 \cdot 7 \cdot 2y^{2}}{9x^{3} \cdot x \cdot 7} = \frac{4y^{2}}{9x^{4}}\]

\[\textbf{в)}\ \frac{a^{2}}{12b}\ :\frac{\text{ab}}{36} = \frac{a^{2}}{12b} \cdot \frac{36}{\text{ab}} =\]

\[= \frac{a \cdot 12 \cdot 3}{12 \cdot a \cdot b \cdot b} = \frac{3a}{b^{2}}\ \]

\[\textbf{г)}\ \frac{3x}{10a^{3}}\ :\frac{1}{5a^{2}} = \frac{3x}{10a^{3}} \cdot \frac{5a^{2}}{1} =\]

\[= \frac{3x \cdot 5a^{2}}{5a^{2} \cdot 2a} = \frac{3x}{2a}\ \]

\[\textbf{д)}\ \frac{11x}{4y^{2}}\ :\left( 22x^{2} \right) = \frac{11x}{4y^{2}} \cdot \frac{1}{22x^{2}} =\]

\[= \frac{11x}{4y^{2} \cdot 2x \cdot 11x} = \frac{1}{8xy²}\]

\[\textbf{е)}\ 27a^{3}\ :\frac{18a^{4}}{7b^{2}} = \frac{27a^{3}}{1} \cdot \frac{7b^{2}}{18a^{4}} =\]

\[= \frac{3 \cdot 9a^{3} \cdot 7b^{2}}{2a \cdot 9a^{3}} = \frac{21b^{2}}{2a}\]

\[\textbf{ж)}\frac{18c^{4}}{7d}\ :\left( 9c^{2}d \right) = \frac{18c^{4}}{7d} \cdot \frac{1}{9c^{2}d} =\]

\[= \frac{2c^{2} \cdot 9c^{2}}{7d \cdot d \cdot 9c^{2}} = \frac{2c²}{7d^{2}}\]

\[\textbf{з)}\ 35x^{5}y\ :\frac{7x^{3}}{34} = \frac{35x^{5}y}{1} \cdot \frac{34}{7x^{3}} =\]

\[= \frac{5x^{2}y \cdot 7x^{3} \cdot 34}{7x^{3}} = 170x^{2}\text{y\ }\]