21061中２・式の計算・計算問題・単項式の乗法と除法1

$\begin{eqnarray}(1)\quad\;8x^{2}\times xy \div (\,-4y\,)\end{eqnarray}\;\;$

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

答$-\,2x^{3}$

$\begin{eqnarray}(2)\quad\;\;20a^{2} \div (\,-5ab\,) \times (\,-b^{2}\,)\end{eqnarray}\;\;$

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

答$4ab$

$\begin{eqnarray}(3)\quad\;\;-5x^{3} \times 4y \div (\,-10xy\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&-5x^{3} \times 4y \times \Bigl(\,-\dfrac{1}{\;10xy\;}\,\Bigr)\\[6pt]&=&+\dfrac{\;\color{silver}\cancelto{1}{\color{black}5} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times x \times x \times \color{silver}\cancelto{2}{\color{black}4} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y}\;}{\;\color{silver}\cancelto{1}{\color{black}10} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \;}\\[6pt]&=&2x^{2}\end{eqnarray}\;\;$

答$2x^{2}$

$\begin{eqnarray}(4)\quad\;\;2ab^{2} \div (\,-8b^{3}\,) \times 12ab\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&2ab^{2} \times \Bigl(\,-\dfrac{\;1\;}{\;8b^{3}\;}\,\Bigr) \times 12ab\\[6pt]&=&-\dfrac{\,\color{silver}\cancelto{1}{\color{black}2} \color{black}\times a \times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{silver}\cancelto{3}{\color{black}12} \color{black}\times a \times \color{aqua}\cancelto{1}{\color{black}b}\;} {\;\color{silver}\cancelto{1}{\color{black}8} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \color{black}\times \color{aqua}\cancelto{1}{\color{black}b} \;}\\[6pt]&=&-3a^{2}\end{eqnarray}\;\;$

答$-\,3a^{2}$

$\begin{eqnarray}(5)\quad\;\;18x^{2}y^{3} \times (\,-5xy\,) \div (\,-10x^{3}y^{2}\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\color{red}\Bigl\{\,\color{black}18 \times (\,-5\,) \times x^{2} \times x \times y^{3} \times y\,\color{red}\Bigr\}\color{black}\div (\,-10x^{3}y^{2}\,) \\[6pt]&=&-90x^{3}y^{4} \div (\,-10x^{3}y^{2}\,) \\[6pt]&=& -90x^{3}y^{4} \times \Bigl(\,-\dfrac{1}{\;10x^{3}y^{2}\;}\Bigr)\\[6pt]&=& +\dfrac{\;90 \times x \times x \times x \times y \times y \times y \times y\;}{\;10 \times x \times x \times x \times y \times y\;}\\[6pt]&=&+\dfrac{\;\color{silver}\cancelto{9}{\color{black}90} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times y \times y\;}{\;\color{silver}\cancelto{1}{\color{black}10} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y}\;} \\[6pt]&=& 9y^{2}\end{eqnarray}\;\;$

答$9y^{2}$