12061中１・正の数と負の数・計算問題・乗法と除法1

$\;\;\begin{eqnarray}(1)\quad\;\;3 \times (\,-8\,) \div (\,-6\,)\end{eqnarray}\;\;$

$\qquad\begin{eqnarray}&=&3 \times (\,-8\,) \times \Bigl(\,-\dfrac{1}{\;6\;}\,\Bigr)\\[6pt]&=&+\Bigl(\,3 \times 8 \times \dfrac{1}{\;6\;}\,\Bigr)\\[6pt]&=&+\Bigl(\,24 \times \dfrac{1}{\;6\;}\,\Bigr)\\[6pt]&=&4\end{eqnarray}\;\;$

答$4$

$\;\;\begin{eqnarray}(2)\quad\;\;(\,-6\,) \div \dfrac{3}{\;4\;} \times (\,-4\,)\end{eqnarray}\;\;$

$\qquad\begin{eqnarray}&=&(\,-6\,) \times \dfrac{4}{\;3\;} \times (\,-4\,)\\[6pt]&=&+\Bigl(\,6 \times \dfrac{4}{\;3\;} \times 4\,\Bigr)\\[6pt]&=&+(\,8 \times 4\,)\\[6pt]&=&32\end{eqnarray}\;\;$

答$32$

$\;\;\begin{eqnarray}(3)\quad\;\;(\,-5\,) \div (\,-7\,) \div (\,-9\,)\end{eqnarray}\;\;$

$\qquad\begin{eqnarray}&=&(\,-5\,) \times \Bigl(\,-\dfrac{1}{\;7\;}\,\Bigr) \times \Bigl(\,-\dfrac{1}{\;9\;}\,\Bigr)\\[6pt]&=&-\Bigl(\,5 \times \dfrac{1}{\;7\;} \times \dfrac{1}{\;9\;}\,\Bigr)\\[6pt]&=&-\dfrac{5}{\;63\;}\end{eqnarray}\;\;$

答$-\,\dfrac{5}{\;63\;}$

$\;\;\begin{eqnarray}(4)\quad\;\;\dfrac{3}{\;4\;} \div (\,-2\,) \div \dfrac{3}{\;5\;}\times (\,-8\,)\end{eqnarray}\;\;$

$\qquad\begin{eqnarray}&=&\dfrac{3}{\;4\;} \times \Bigl(\,-\dfrac{1}{\;2\;}\,\Bigr) \times \dfrac{5}{\;3\;}\times (\,-8\,)\\[6pt]&=&+\Bigl(\,\dfrac{3}{\;4\;} \times \dfrac{1}{\;2\;} \times \dfrac{5}{\;3\;} \times 8\,\Bigr)\\[6pt]&=&+\Bigl(\,\dfrac{\color{red}\cancelto{1}{\color{black}3}}{\;\color{blue}\cancelto{1}{\color{black}8}\;} \times \dfrac{\,5\,}{\color{red}\cancelto{1}{\color{black}3}} \times \color{blue}\cancelto{1}{8}\,\Bigr)\\[6pt]&=&5\end{eqnarray}\;\;$

答$5$

$\;\;\begin{eqnarray}(5)\quad\;\;(\,-0.5\,) \div (\,-0.3\,) \times (\,-3.9\,) \times (\,-0.6\,)\end{eqnarray}\;\;$

$\qquad\begin{eqnarray}&=&\Bigl(\,-\dfrac{1}{\;2\;}\,\Bigr) \div \Bigl(\,-\dfrac{3}{\;10\;}\,\Bigr) \times (\,-3.9\,) \times\Bigl(\,-\dfrac{3}{\;5\;}\,\Bigr)\\[6pt]&=&+\Bigl(\,\dfrac{1}{\color{red}\cancelto{1}{\color{black}2}} \times \dfrac{\color{red}\cancelto{5}{\color{black}10}}{\;3\;} \times 3.9 \times \dfrac{3}{\;5\;}\,\Bigr)\\[6pt]&=&+\Bigl(\,\dfrac{5}{\;3\;} \color{red} \times \dfrac{\,3\,}{5} \times 3.9\color{black}\,\Bigr)\\[6pt]&=&+(\,1 \times 3.9\,)\\[6pt]&=&3.9\end{eqnarray}\;\;$

答$3.9$

$\;\;\begin{eqnarray}(6)\quad\;\;\Bigl(\,-\dfrac{5}{\;7\;} \,\Bigr) \times 1.5 \div \Bigl(\,-\dfrac{9}{\;4\;} \,\Bigr) \times (\,-0.7\,)\end{eqnarray}\;\;$

$\qquad\begin{eqnarray}&=&\Bigl(\,-\dfrac{5}{\;7\;}\,\Bigr) \times \dfrac{3}{\;2\;} \times \Bigl(\,-\dfrac{4}{\;9\;}\,\Bigr) \times\Bigl(\,-\dfrac{7}{\;10\;}\,\Bigr)\\[6pt]&=&-\Bigl(\,\dfrac{5}{\;7\;} \times \dfrac{3}{\;2\;} \times \dfrac{4}{\;9\;} \color{red}\times \dfrac{7}{\;10\;}\color{black}\,\Bigr)\\[6pt]&=&-\Bigl(\,\dfrac{5}{\;7\;} \color{red}\times \dfrac{7}{\;10\;} \color{black}\times \dfrac{3}{\;2\;} \times \dfrac{4}{\;9\;}\,\Bigr)\\[6pt]&=&-\Bigl\{\Bigl(\,\dfrac{5}{\;7\;} \times \dfrac{7}{\;10\;} \,\Bigr)\times \Bigl(\,\dfrac{3}{\;2\;} \times \dfrac{4}{\;9\;}\,\Bigr)\Bigr\}\\[6pt]&=&-\Bigl(\,\dfrac{1}{\;2\;} \times \dfrac{\,2\,}{3}\,\Bigr)\\[6pt]&=&-\dfrac{1}{\;3\;}\end{eqnarray}\;\;$

答$-\,\dfrac{1}{\;3\;}$