12044中１・正の数と負の数・計算問題・乗法4
banno計算問題 》乗法④
次の式を，工夫して計算しなさい。
(1) $\;\;(\,-5\,) \times (\,+4.7\,) \times (\,-2\,)$
(2) $\;\;(\,-25\,) \times (\,-13\,) \times (\,+4\,)$
(3) $\;\;(\,+2\,) \times (\,-4\,) \times (\,-5\,) \times (\,+25\,)$
(4) $\;\;(\,-29\,) \times (\,+2\,) \times (\,-2\,) \times (\,-25\,)$
(5) $\;\;(\,-0.36\,) \times (\,+12.5\,) \times (\,-16\,) \times \Bigl(\,-\dfrac{1}{\;2\;}\,\Bigr)$
(6) $\;\;\Bigl(\,+\dfrac{2}{\;3\;}\,\Bigr) \times \Bigl(\,-\dfrac{4}{\;5\;}\,\Bigr) \times \Bigl(\,-\dfrac{3}{\;4\;}\,\Bigr) \times \Bigl(\,+\dfrac{5}{\;2\;}\,\Bigr)$
解答・解説
$\;\;\begin{eqnarray}(1)\quad\;\;(\,-5\,) \times (\,+4.7\,) \times (\,-2\,)\end{eqnarray}\;\;$
$\qquad\begin{eqnarray}&=&\color{red}+\color{black}\;(\,5 \times 4.7 \times 2\,)\\[6pt]&=&+(\,5 \times \color{red}2\color{black} \times \color{red}4.7\color{black}\,)\\[6pt]&=&+(\,10 \times 4.7\,)\\[6pt]&=&+47\end{eqnarray}\;\;$
答$+\,47$
$\;\;\begin{eqnarray}(2)\quad\;\;(\,-25\,) \times (\,-13\,) \times (\,+4\,)\end{eqnarray}\;\;$
$\qquad\begin{eqnarray}&=&\color{red}+\color{black}\;(\,25 \times 13 \times 4\,)\\[6pt]&=&+(\,25 \times \color{red}4\color{black} \times \color{red}13\color{black}\,)\\[6pt]&=&+(\,100 \times 13\,)\\[6pt]&=&+1300\end{eqnarray}\;\;$
答$+\,1300$
$\;\;\begin{eqnarray}(3)\quad\;\;(\,+2\,) \times (\,-4\,) \times (\,-5\,) \times (\,+25\,)\end{eqnarray}\;\;$
$\qquad\begin{eqnarray}&=&\color{red}+\color{black}\;(\,2 \times 4 \times 5 \times 25\,)\\[6pt]&=&+(\,2 \times \color{red}5\color{black} \times \color{red}4\color{black} \times 25\,)\\[6pt]&=&+\{\,\color{red}(\color{black}\,2 \times 5\,\color{red})\color{black} \times \color{red}(\color{black}\,4 \times 25\,\color{red})\color{black}\}\\[6pt]&=&+(\,10 \times 100\,)\\[6pt]&=&+1000\end{eqnarray}\;\;$
答$+\,1000$
$\;\;\begin{eqnarray}(4)\quad\;\;(\,-29\,) \times (\,+2\,) \times (\,-2\,) \times (\,-25\,)\end{eqnarray}\;\;$
$\qquad\begin{eqnarray}&=&\color{red}-\color{black}\;(\,29 \times 2 \times 2 \times 25\,)\\[6pt]&=&-\{29 \times \color{red}(\,\color{black}2 \times 2\color{red}\,)\color{black} \times 25\,\}\\[6pt]&=&-(\,29 \times 4 \times 25\,)\\[6pt]&=&-\{\,29 \times \color{red}(\,\color{black}4 \times 25\color{red}\,)\color{black}\,\}\\[6pt]&=&-(\,29 \times 100\,)\\[6pt]&=&-2900\end{eqnarray}\;\;$
答$-\,2900$
$\;\;\begin{eqnarray}(5)\quad\;\;(\,-0.36\,) \times (\,+12.5\,) \times (\,-16\,) \times \Bigl(\,-\dfrac{1}{\;2\;}\,\Bigr)\end{eqnarray}\;\;$
$\qquad\begin{eqnarray}&=&\color{red}-\color{black}\Bigl(\,0.36 \times 12.5 \times 16 \times \dfrac{1}{\;2\;}\,\Bigr)\\[6pt]&=&-\Bigl\{\,0.36 \times 12.5 \times \color{red}\Bigl(\,\color{black}16 \times \dfrac{1}{\;2\;}\,\color{red}\Bigr)\color{black}\Bigr\}\\[6pt]&=&-(\,0.36 \times 12.5 \times 8\,)\\[6pt]&=&-\Bigl\{\,0.36 \times \color{red}(\,\color{black}12.5 \times 8 \,\color{red})\color{black}\Bigr\}\\[6pt]&=&-(\,0.36 \times 100\,)\\[6pt]&=&-36\end{eqnarray}\;\;$
答$-\,36$
$\;\;\begin{eqnarray}(6)\quad\;\;\Bigl(\,+\dfrac{2}{\;3\;}\,\Bigr) \times \Bigl(\,-\dfrac{4}{\;5\;}\,\Bigr) \times \Bigl(\,-\dfrac{3}{\;4\;}\,\Bigr) \times \Bigl(\,+\dfrac{5}{\;2\;}\,\Bigr)\end{eqnarray}\;\;$
$\qquad\begin{eqnarray}&=&\color{red}+\color{black}\;\Bigl(\,\dfrac{2}{\;3\;} \times \dfrac{4}{\;5\;} \times \dfrac{3}{\;4\;} \times\dfrac{5}{\;2\;}\,\Bigr)\\[6pt]&=&+\Bigl(\,\dfrac{2}{\;3\;} \times \color{red}\dfrac{3}{\;4\;}\color{black} \times \color{red}\dfrac{4}{\;5\;}\color{black} \times\dfrac{5}{\;2\;}\,\Bigr)\\[6pt]&=&+\Bigl\{\color{red}\Bigl(\color{black}\,\dfrac{2}{\;3\;} \times \dfrac{3}{\;4\;}\,\color{red}\Bigr)\color{black} \times \color{red}\Bigl(\color{black}\,\dfrac{4}{\;5\;} \times \dfrac{5}{\;2\;}\,\color{red}\Bigr)\color{black}\Bigr\}\\[6pt]&=&+\Bigl(\,\dfrac{1}{\;2\;} \times 2\,\Bigr)\\[6pt]&=&+1\end{eqnarray}\;\;$
答$+\,1$
