21053中２・式の計算・計算問題・単項式の除法3

$\begin{eqnarray}(1)\quad\;\;20xy^{2} \div \dfrac{5}{\;3\;}xy\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&20xy^{2} \div \dfrac{\;5xy\;}{\;3\;}\\[6pt]&=&20xy^{2} \times \dfrac{3}{\;5xy\;}\\[6pt]&=&\dfrac{\, \color{silver}\cancelto{4}{\color{black}20} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times y \times 3\;\,}{\,\color{silver}\cancelto{1}{\color{black}5} \color{black}\times \color{red}\cancelto{1}{\color{black}x}\color{black}\times \color{aqua}\cancelto{1}{\color{black}y}\,}\\[6pt]&=&12y\end{eqnarray}\;\;$

答$12y$

$\begin{eqnarray}(2)\quad\;\;\Bigl(\,-\dfrac{3}{\;4\;}a^{2}b^{2}\,\Bigr) \div a^{2}b\end{eqnarray}\;\;$

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

答$-\,\dfrac{3}{\;4\;}b$

$\begin{eqnarray}(3)\quad\;\;\Bigl(\,-\dfrac{8}{\;21\;}x^{3}y^{2}\,\Bigr) \div \dfrac{4}{\;7\;}x^{2}y^{2}\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\Bigl(\,-\dfrac{\;8x^{3}y^{2}\;}{\;21\;}\,\Bigr) \div \dfrac{4x^{2}y^{2}}{\;7\;}\\[6pt]&=&\Bigl(\,-\dfrac{\;8x^{3}y^{2}\;}{\;21\;}\,\Bigr) \times \dfrac{\;7\;}{4x^{2}y^{2}}\\[6pt]&=&-\dfrac{\,\color{silver}\cancelto{2}{\color{black}8} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times x \times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times \color{silver}\cancelto{1}{\color{black}7}\,}{\,\color{silver}\cancelto{3}{\color{black}21} \color{black}\times \color{silver}\cancelto{1}{\color{black}4} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{red}\cancelto{1}{\color{black}x} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y} \color{black}\times \color{aqua}\cancelto{1}{\color{black}y}\,}\\[6pt]&=&-\dfrac{2}{\;3\;}x\end{eqnarray}\;\;$

答$-\,\dfrac{2}{\;3\;}x$

$\begin{eqnarray}(4)\quad\;\;\Bigl(\,-\dfrac{9}{\;16\;}a^{2}b^{3}c\,\Bigr) \div \Bigl(\,-\dfrac{15}{\;16\;}ab^{2}c\,\Bigr)\end{eqnarray}\;\;$

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

答$\dfrac{3}{\;5\;}ab$