ラサール中学 2022年出題問題 3問紹介
【ヒント】1.7が2回でてくるので、まとめますが、、、うまくいきません。
というものの、そのまま解くのは大変そうです。。
各数字を分解してみると、3.09=1.03×3,4.9=7×0.7とかでしょうか。
【解答】1.7×3×1.03+4.9×1.03+1.7
=5.1×1.03+4.9×1.03+1.7=(5.1+4.9)×1.03+1.7
=10×1.03+1.7=10.3+1.7=12・・・(答え)
【問題2】\(\displaystyle\left\{4×(2.1-\frac{5}{6})-4\frac{1}{6}\right\} ÷(4\frac{2}{5}-1.025)\)=?
【解答】
\(\displaystyle\left\{ \right\} \)内の \(\displaystyle 4×(2.1-\frac{5}{6})\) から計算していきます。
\(\displaystyle 4×(2.1-\frac{5}{6})\) =\(\displaystyle4×(\frac{21}{10}-\frac{5}{6})\) =\(\displaystyle 4×(\frac{126}{60}-\frac{50}{60})\)=\(\displaystyle4×\frac{76}{60}\)=\(\displaystyle \frac{76}{15}\)
\(\displaystyle \frac{76}{15}-4\frac{1}{6}\)= \(\displaystyle \frac{76}{15}-\frac{25}{6}\)=\(\displaystyle \frac{152-125}{30}\)=\(\displaystyle \frac{27}{30}\)=\(\displaystyle \frac{9}{10}\) ‥・①
(後半部分)=\(\displaystyle4\frac{2}{5}-1.025\)=\(\displaystyle\frac{22}{5}-1\frac{1}{40}\)=\(\displaystyle\frac{176-41}{40}\)=\(\displaystyle\frac{135}{40}\)=\(\displaystyle\frac{27}{8}\) ・・・②
①②より
\(\displaystyle \frac{9}{10}\) ÷\(\displaystyle\frac{27}{8}\)=\(\displaystyle \frac{9}{10}\) ×\(\displaystyle\frac{8}{27}\)=\(\displaystyle \frac{8}{30}\) =\(\displaystyle \frac{4}{15}\) ・・・(答え)
【問題3】\(\displaystyle 8\frac{7}{11}\)÷(0.2+ ア)÷2\(\displaystyle\frac{3}{11}\)=17
【ヒント】まず、わり算をかけ算に、帯分数を仮分数に変更します。
\(\displaystyle \frac{95}{11}\)×\(\displaystyle \frac{1}{0.2+ア}\) ×\(\displaystyle\frac{11}{25}\)=17
【解答】
\(\displaystyle \frac{1}{0.2+ア}\)=17×\(\displaystyle \frac{5}{19}\) =\(\displaystyle \frac{85}{19}\)
0.2+ ア=\(\displaystyle \frac{19}{85}\)
ア=\(\displaystyle \frac{19}{85}\)-\(\displaystyle \frac{2}{10}\) =\(\displaystyle\frac{190-170}{850}\)=\(\displaystyle \frac{20}{850}\)=\(\displaystyle \frac{2}{85}\) ・・・(答え)
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