21062中２・式の計算・計算問題・単項式の乗法と除法2

$\begin{eqnarray}(1)\quad\;12x^{2}y \div \dfrac{3}{\;4\;}xy \times \Bigl(\,-\dfrac{3}{\;2\;}x\,\Bigr)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&12x^{2}y \div \dfrac{\;3xy\;}{\;4\;} \times \Bigl(\,-\dfrac{\;3x\;}{\;2\;}\,\Bigr)\\[6pt]&=&\Bigl(\, 12x^{2}y \times \dfrac{4}{\;3xy\;} \,\Bigr) \times \Bigl(\,-\dfrac{\;3x\;}{\;2\;}\,\Bigr) \\[6pt]&=& \dfrac{\; \color{silver}\cancelto{4}{\color{black}12} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times x \times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times 4\;}{\;\color{silver}\cancelto{1}{\color{black}3} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \;} \times \Bigl(\,-\dfrac{\;3x\;}{\;2\;}\,\Bigr) \\[6pt]&=& 16x \times \Bigl(\,-\dfrac{\;3x\;}{\;2\;}\,\Bigr) \\[6pt]&=& -\dfrac{\;\color{silver}\cancelto{8}{\color{black}16} \color{black}\times x \times 3x\;}{\;\color{silver}\cancelto{1}{\color{black}2}\;} \\[6pt]&=&-24x^{2} \end{eqnarray}\;\;$

答$-\,24x^{2}$

$\begin{eqnarray}(2)\quad\;\;\dfrac{3}{\;5\;}a^{3}b^{4} \div \Bigl(\,-\dfrac{8}{\;15\;}ab^{3}\,\Bigr) \times 16a^{2}b\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\dfrac{\;3a^{3}b^{4}\;}{\;5\;} \div \Bigl(\,-\dfrac{\;8ab^{3}\;}{\;15\;}\,\Bigr) \times 16a^{2}b \\[6pt]&=& \color{red}\Bigl\{\color{black}\, \dfrac{\;3a^{3}b^{4}\;}{\;5\;} \times \Bigl(\,-\dfrac{\;15\;}{\;8ab^{3}\;}\,\Bigr)\,\color{red}\Bigr\}\color{black} \times 16a^{2}b \\[6pt]&=&-\dfrac{\;3 \times \color{red}\cancelto{1}{\color{black}a} \color{black}\times a \times a \times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times b \times \color{silver}\cancelto{3}{\color{black}15}\;} {\;\color{silver}\cancelto{1}{\color{black}5} \color{black}\times 8 \times \color{red}\cancelto{1}{\color{black}a} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \;} \times 16a^{2}b \\[6pt]&=&-\dfrac{\;9a^{2}b\;}{8} \times 16a^{2}b \\[6pt]&=&-\dfrac{\;9a^{2}b \times \color{silver}\cancelto{2}{\color{black}16} \color{black}\times a^{2}b\;}{\color{silver}\cancelto{1}{\color{black}8}} \\[6pt]&=&-18a^{4}b^{2} \end{eqnarray}\;\;$

答$-\,18a^{4}b^{2}$

$\begin{eqnarray}(3)\quad\;\;\dfrac{5}{\;18\;}xy^{2} \times (\,-12x^{2}y\,) \div \Bigl(\,-\dfrac{5}{\;9\;}x^{3}y^{2}\,\Bigr)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\color{red}\Bigl\{\color{black}\, \dfrac{\;5xy^{2}\;}{\;18\;} \times (\,-12x^{2}y\,) \,\color{red}\Bigr\}\color{black} \div \Bigl(\,-\dfrac{\;5x^{3}y^{2}\;}{\;9\;}\,\Bigr) \\[6pt]&=&-\dfrac{\;5xy^{2} \times \color{silver}\cancelto{2}{\color{black}12} \color{black}\times x^{2}y\;}{\;\color{silver}\cancelto{3}{\color{black}18}\;} \div \Bigl(\,-\dfrac{5x^{3}y^{2}}{\;9\;}\,\Bigr) \\[6pt]&=&-\dfrac{\;10x^{3}y^{3}\;}{\;3\;} \times \Bigl(\,-\dfrac{\;9\;}{\;5x^{3}y^{2}\;}\,\Bigr) \\[6pt]&=& +\Bigl(\, \dfrac{\; \color{silver}\cancelto{2}{\color{black}10} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times y \times \color{silver}\cancelto{3}{\color{black}9} \;}{\; \color{silver}\cancelto{1}{\color{black}3} \color{black}\times \color{silver}\cancelto{1}{\color{black}5} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \;} \,\Bigr) \\[6pt]&=&6y\end{eqnarray}\;\;$

答$6y$

$\begin{eqnarray}(4)\quad\;\;20a^{4}b^{3} \times \Bigl(\,-\dfrac{3}{\;8\;}ab\,\Bigr) \div \Bigl(\,-\dfrac{\;15\;}{\;4\;}a^{3}b^{4}\,\Bigr)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\color{red}\Bigl\{\,\color{black}20a^{4}b^{3} \times \Bigl(\,-\dfrac{\;3ab\;}{\;8\;}\,\Bigr)\color{red}\Bigr\}\color{black} \div \Bigl(\,-\dfrac{\;15a^{3}b^{4}\;}{\;4\;}\,\Bigr)\\[6pt]&=&-\dfrac{\; \color{silver}\cancelto{5}{\color{black}20} \color{black}\times a^{4}b^{3} \times 3ab \;} {\; \color{silver}\cancelto{2}{\color{black}8} \color{black} \;} \div \Bigl(\,-\dfrac{\;15a^{3}b^{4}\;}{\;4\;}\,\Bigr) \\[6pt]&=&-\dfrac{\;15a^{5}b^{4}\;}{2} \times \Bigl(\,-\dfrac{4}{\;15a^{3}b^{4}\;} \,\Bigr) \\[6pt]&=&+\Bigl(\;\dfrac{\;\color{silver}\cancelto{1}{\color{black}15} \color{black}\times \color{red}\cancelto{1}{\color{black}a} \color{black}\times \color{red}\cancelto{1}{\color{black}a} \color{black}\times \color{red}\cancelto{1}{\color{black}a} \color{black}\times a \times a \times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{silver}\cancelto{2}{\color{black}4} \color{black}\;} {\;\color{silver}\cancelto{1}{\color{black}2} \color{black}\times \color{silver}\cancelto{1}{\color{black}15} \color{black}\times \color{red}\cancelto{1}{\color{black}a} \color{black}\times \color{red}\cancelto{1}{\color{black}a} \color{black}\times \color{red}\cancelto{1}{\color{black}a} \color{black}\times \times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \;} \;\Bigr) \\[6pt]&=&2a^{2}\end{eqnarray}\;\;$

答$2a^{2}$