算数【入試】小数を含む四則計算（問題文に）
次の計算をしましょう。
問１
1100 × 0.125 + 625 × 0.4 + 3.75 × 2 =
- ヒント
- 125 × 8 = 1000
- 答え
- 395
- 解き方
- \(1100\times0.125+625\times0.4+3.75\times2\)
\(=1.1\times125+125\times5\times0.4+125\times0.03\times2\)
\(=125\times(1.1+2+0.06)\)
\(=125\times3.16\)
\(=125\times8\times0.395=1000\times0.395=395\)
問２
781 × 5.6 + 45 × 2.1 － 63 × 3.2 － 1230 × 0.55 =
- 答え
- 3590
問３
289 ÷ 0.17 – 1.975 × 120 – 315 ÷ 1.25 + 8.5 × 46 =
- ヒント
- 分数に変える
- 答え
- 1602
- 解き方
- \(289\div0.17-1.975\times120-315\div1.25+8.5\times46\)
\(=289\div\dfrac{17}{100}\) ― \(\dfrac{1975}{1000}\times120\) ― \(315\div\dfrac{125}{100}+\dfrac{85}{10}\times46\)
\(=\cancelto{17}{289}\times\dfrac{100}{\cancel{17}}\) ― \(\dfrac{\cancelto{79}{1975}}{\cancelto{\cancel{40}}{1000}}\times\cancelto{3}{120}\) ― \(\cancelto{63}{315}\times\dfrac{\cancelto{4}{100}}{\cancelto{\cancel{5}}{125}}+\dfrac{\cancelto{17}{85}}{\cancelto{\cancel{2}}{10}}\times\cancelto{23}{46}\)
\(=17\times100\) ― \(79\times3\) ― \(63\times4+17\times23\)
\(=1700\) ― \(237\) ― \(252+391=1602\)
問４
65 × 2.1 + 72 × 3.5 – 0.31 × 50 + 45 ÷ 0.15 =
- 答え
- 673
問５
150 – 56 ÷ 0.7 × 0.25 + 420 × 0.55 =
- 答え
- 361
- 解き方
- \(150-56\div0.7\times0.25+420\times0.55\)
\(=150\) ― \(80\times0.125\times2+420\times(0.5+0.05)\)
\(=150\) ― \(10\times2+420\times0.5+420\times0.05\)
\(=150\) ― \(20+210+21=361\)
問６
(1.4 – 2.94 ÷ 21) × 2.5 =
- ヒント
- \(= (1.4 – 0.14) \times 2.5\)
\(= 1.4\times(1-0.1) \times 2.5\)
- 答え
- 3.15
- 解き方
- \((1.4-2.94\div21)\times2.5\)
\(=(1.4 – 0.14)\times2.5\)
\(=1.4\times(1-0.1)\times2.5\)
\(= 1.4 \times 0.9 \times 2.5\)
\(= \dfrac{14}{10} \times \dfrac{9}{10} \times \dfrac{25}{10}\)
\(= \dfrac{315}{100} = 3.15\)
問７
20.22 × 4.7 + 1.011 × 26 – 2.022 × 10 =
- ヒント
- \(=2.022\times10\times4.7+1.011\times2\times13\) ― \(2.022\times10\)
- 答え
- 101.1
- 解き方
- \(20.22\times4.7+1.011\times26-2.022\times10\)
\(=2.022\times10\times4.7+1.011\times2\times13\) ― \(2.022\times10\)
\(=2.022\times47+2.022\times13\) ― \(2.022\times10\)
\(=2.022\times(47+13-10)\)
\(=2.022\times50=101.1\)
問８
(1 + 0.5 + 0.25 + 0.125) ÷ 0.625 =
- ヒント
- 分数に変える
- 答え
- 3
- 解き方
- \((1+0.5+0.25+0.125)\div0.625\)
\(=(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8})\div\dfrac{5}{8}\)
\(=(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8})\times\dfrac{8}{5}\)
\(=(8+4+2+1)\times\dfrac{1}{5}\)
\(=\dfrac{15}{5}=3\)
問９
4.2 × 0.072 ÷ 0.0063 =
- ヒント
- 分数に変える
- 答え
- 48
- 解き方
- \(4.2\times0.072\div0.0063\)
\(=\dfrac{42}{10}\times\dfrac{72}{1000}\div\dfrac{63}{10000}\)
\(=\dfrac{\cancelto{6}{42}}{\cancel{10}}\times\dfrac{\cancelto{8}{72}}{\cancel{1000}}\times\dfrac{\cancel{10000}}{\cancelto{\cancelto{1}{9}}{63}}=6\times8=48\)
問１０
2.24 × 2.24 + 2.24 × 0.76 – 2.24 × 0.74 – 0.76 × 0.74 =
- 答え
- 4.5
- 解き方
- \(2.24\times2.24+2.24\times0.76-2.24\times0.74-0.76\times0.74\)
\(=0.76\times(2.24-0.74)+2.24\times(2.24-0.74)\)
\(=0.76\times1.5+2.24\times1.5\)
\(=1.5\times(0.76+2.24)\)
\(=1.5\times3=4.5\)
問１１
43 × 0.29 – 0.56 ÷ 0.08 × 0.31 =
- 答え
- 10.3
- 解き方
- \(43\times0.29-0.56\div0.08\times0.31\)
\(=43\times(0.3-0.01)-7\times(0.3+0.01)\)
\(=12.9-0.43-2.1-0.07\)
\(=10.8-0.5=10.3\)
問１２
(15.6 ÷ 0.26 – 1.1 ÷ 0.275) × 0.375 =
- 答え
- 21
- 解き方
- \((15.6\div0.26-1.1\div0.275)\times0.375\)
\(=(\dfrac{156}{10}\div\dfrac{26}{100}\) – \(\dfrac{11}{10}\div\dfrac{275}{1000})\times\dfrac{3}{8}\)
\(=(\dfrac{\cancelto{6}{156}}{\cancel{10}}\times\dfrac{\cancelto{10}{100}}{\cancel{26}}\) – \(\dfrac{\cancel{11}}{\cancel{10}}\times\dfrac{\cancelto{\cancelto{4}{100}}{1000}}{\cancelto{\cancel{25}}{275}})\times\dfrac{3}{8}\)
\(=(60\) – \(4)\times\dfrac{3}{8}\)
\(=\cancelto{7}{56}\times\dfrac{3}{\cancel{8}}=21\)
問１３
3.14 + 6.28 – 9.42 – 12.54 + 15.7 =
- 答え
- 3.16
- 解き方
- 3.14 + 6.28 – 9.42 – 12.54 + 15.7
= 3.14 × (1 + 2 – 3 + 5) – 12.54
= 3.14 × 5 -12.54
=15.7 – 12.54 = 3.16
