分数の計算

■問題

次の計算をしなさい．

$3$\displaystyle{ \frac{\hspace{2} 3.54\div 2.95 \hspace{2}}{\hspace{2} 5.04\div 1.05 \hspace{2}} }$

■答

$3$\displaystyle{ 0.25 }$

■ヒント

小数を分数に変換する．

■答

$3$\displaystyle{ \frac{\hspace{2} 3.54\div 2.95 \hspace{2}}{\hspace{2} 5.04\div 1.05 \hspace{2}} }$

小数を分数に変換する．

$3$\displaystyle{ =\frac{\hspace{2} \frac{\hspace{2} 354 \hspace{2}}{\hspace{2} 100 \hspace{2}}\div \frac{\hspace{2} 295 \hspace{2}}{\hspace{2} 100 \hspace{2}} \hspace{2}}{\hspace{2} \frac{\hspace{2} 504 \hspace{2}}{\hspace{2} 100 \hspace{2}}\div \frac{\hspace{2} 105 \hspace{2}}{\hspace{2} 100 \hspace{2}} \hspace{2}} }$

$3$\displaystyle{ =\frac{\hspace{2} \frac{\hspace{2} 354 \hspace{2}}{\hspace{2} 100 \hspace{2}}\times \frac{\hspace{2} 100 \hspace{2}}{\hspace{2} 295 \hspace{2}} \hspace{2}}{\hspace{2} \frac{\hspace{2} 504 \hspace{2}}{\hspace{2} 100 \hspace{2}}\times \frac{\hspace{2} 100 \hspace{2}}{\hspace{2} 105 \hspace{2}} \hspace{2}} }$

$3$\displaystyle{\frac{\hspace{2} \frac{\hspace{2}A\hspace{2}}{\hspace{2}B\hspace{2}} \hspace{2}}{\hspace{2} \frac{\hspace{2}C\hspace{2}}{\hspace{2}D\hspace{2}} \hspace{2}}=\frac{\hspace{2}A\hspace{2}}{\hspace{2}B\hspace{2}}\div \frac{\hspace{2}C\hspace{2}}{\hspace{2}D\hspace{2}}=\frac{\hspace{2}A\hspace{2}}{\hspace{2}B\hspace{2}}\times \frac{\hspace{2}D\hspace{2}}{\hspace{2}C\hspace{2}}}$ の性質を利用する

$3$\displaystyle{ =\frac{\hspace{2} 354 \hspace{2}}{\hspace{2} 100 \hspace{2}}\times \frac{\hspace{2} 100 \hspace{2}}{\hspace{2} 295 \hspace{2}}\times \frac{\hspace{2} 100 \hspace{2}}{\hspace{2} 504 \hspace{2}}\times \frac{\hspace{2} 105 \hspace{2}}{\hspace{2} 100 \hspace{2}} }$

$3$\displaystyle{=\frac{\hspace{2} 354\times 105 \hspace{2}}{\hspace{2} 295\times 504 \hspace{2}}}$

各数値を素因数分解する

$3$\displaystyle{\begin{array}{lll}2\)354& \vspace{6}\\ 3\bar{ \)177 }& \vspace{6}\\ \text{ }\text{ }\bar{ \text{ }59 }& \vspace{6}\\ \end{array}}$
TeXに変換設定していない数学記号や，特殊文字が含まれています。今後直していきます。
， $3$\displaystyle{\begin{array}{lll}5\)295& \vspace{6}\\ \text{\hspace{5}}\bar{ 59 }& \vspace{6}\\ \end{array}}$ ， $3$\displaystyle{\begin{array}{lll}5\)105& \vspace{6}\\ \text{ }3\bar{ \)21 }& \vspace{6}\\ \text{\hspace{5}}\bar{ \text{ }7 }& \vspace{6}\\ \end{array}}$
TeXに変換設定していない数学記号や，特殊文字が含まれています。今後直していきます。
， $3$\displaystyle{\begin{array}{lll}2\)504& \vspace{6}\\ 2\bar{ \)252 }& \vspace{6}\\ 2\bar{ \)126 }& \vspace{6}\\ 3\bar{ \)63 }& \vspace{6}\\ 3\bar{ \)21 }& \vspace{6}\\ \text{ }\text{ }\bar{ \text{ }7\text{ } }& \vspace{6}\\ \end{array}}$
TeXに変換設定していない数学記号や，特殊文字が含まれています。今後直していきます。

$3$\displaystyle{=\frac{\hspace{2} \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\} \hspace{2}}{\hspace{2} \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\}\times 2\times 2\times \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\}\times \{\red{\text{there is tag which can't be converted to TeX}}\} \hspace{2}}}$

$3$\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2} 2\times 2 \hspace{2}}}$

$3$\displaystyle{ =0.25 }$

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最終更新日：2023年7月19日