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

$1100\times 0.125+625\times 0.4+3.75\times 2$
$=1.1\times 125+125\times 5\times 0.4+125\times 0.03\times 2$
$=125\times (1.1+2+0.06)$
$=125\times 3.16$
$=125\times 8\times 0.395=1000\times 0.395=395$

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

$289÷0.17-1.975\times 120-315÷1.25+8.5\times 46$
$=289÷{\displaystyle \frac{17}{100}}$ ― ${\displaystyle \frac{1975}{1000}}\times 120$ ― $315÷{\displaystyle \frac{125}{100}}+{\displaystyle \frac{85}{10}}\times 46$
$={\cancel{289}}^{17}\times {\displaystyle \frac{100}{\cancel{17}}}$ ― ${\displaystyle \frac{{\cancel{1975}}^{79}}{{\cancel{1000}}^{\cancel{40}}}}\times {\cancel{120}}^3$ ― ${\cancel{315}}^{63}\times {\displaystyle \frac{{\cancel{100}}^4}{{\cancel{125}}^{\cancel{5}}}}+{\displaystyle \frac{{\cancel{85}}^{17}}{{\cancel{10}}^{\cancel{2}}}}\times {\cancel{46}}^{23}$
$=17\times 100$ ― $79\times 3$ ― $63\times 4+17\times 23$
$=1700$ ― $237$ ― $252+391=1602$

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

$150-56÷0.7\times 0.25+420\times 0.55$
$=150$ ― $80\times 0.125\times 2+420\times (0.5+0.05)$
$=150$ ― $10\times 2+420\times 0.5+420\times 0.05$
$=150$ ― $20+210+21=361$

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

$(1.4-2.94÷21)\times 2.5$
$=(1.4–0.14)\times 2.5$
$=1.4\times (1-0.1)\times 2.5$
$=1.4\times 0.9\times 2.5$
$={\displaystyle \frac{14}{10}}\times {\displaystyle \frac{9}{10}}\times {\displaystyle \frac{25}{10}}$
$={\displaystyle \frac{315}{100}}=3.15$

問７

20.22 × 4.7 + 1.011 × 26 – 2.022 × 10 =

ヒント

$=2.022\times 10\times 4.7+1.011\times 2\times 13$ ― $2.022\times 10$

答え

101.1

解き方

$20.22\times 4.7+1.011\times 26-2.022\times 10$
$=2.022\times 10\times 4.7+1.011\times 2\times 13$ ― $2.022\times 10$
$=2.022\times 47+2.022\times 13$ ― $2.022\times 10$
$=2.022\times (47+13-10)$
$=2.022\times 50=101.1$

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

$(1+0.5+0.25+0.125)÷0.625$
$=(1+{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{8}})÷{\displaystyle \frac{5}{8}}$
$=(1+{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{8}})\times {\displaystyle \frac{8}{5}}$
$=(8+4+2+1)\times {\displaystyle \frac{1}{5}}$
$={\displaystyle \frac{15}{5}}=3$

問９

4.2 × 0.072 ÷ 0.0063 =

ヒント

分数に変える

答え

48

解き方

$4.2\times 0.072÷0.0063$
$={\displaystyle \frac{42}{10}}\times {\displaystyle \frac{72}{1000}}÷{\displaystyle \frac{63}{10000}}$
$={\displaystyle \frac{{\cancel{42}}^6}{\cancel{10}}}\times {\displaystyle \frac{{\cancel{72}}^8}{\cancel{1000}}}\times {\displaystyle \frac{\cancel{10000}}{{\cancel{63}}^{{\cancel{9}}^1}}}=6\times 8=48$

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

$2.24\times 2.24+2.24\times 0.76-2.24\times 0.74-0.76\times 0.74$
$=0.76\times (2.24-0.74)+2.24\times (2.24-0.74)$
$=0.76\times 1.5+2.24\times 1.5$
$=1.5\times (0.76+2.24)$
$=1.5\times 3=4.5$

問１１

43 × 0.29 – 0.56 ÷ 0.08 × 0.31 =

答え

10.3

解き方

$43\times 0.29-0.56÷0.08\times 0.31$
$=43\times (0.3-0.01)-7\times (0.3+0.01)$
$=12.9-0.43-2.1-0.07$
$=10.8-0.5=10.3$

問１２

(15.6 ÷ 0.26 – 1.1 ÷ 0.275) × 0.375 =

答え

21

解き方

$(15.6÷0.26-1.1÷0.275)\times 0.375$
$=({\displaystyle \frac{156}{10}}÷{\displaystyle \frac{26}{100}}$ – ${\displaystyle \frac{11}{10}}÷{\displaystyle \frac{275}{1000}})\times {\displaystyle \frac{3}{8}}$
$=({\displaystyle \frac{{\cancel{156}}^6}{\cancel{10}}}\times {\displaystyle \frac{{\cancel{100}}^{10}}{\cancel{26}}}$ – ${\displaystyle \frac{\cancel{11}}{\cancel{10}}}\times {\displaystyle \frac{{\cancel{1000}}^{{\cancel{100}}^4}}{{\cancel{275}}^{\cancel{25}}}})\times {\displaystyle \frac{3}{8}}$
$=(60$ – $4)\times {\displaystyle \frac{3}{8}}$
$={\cancel{56}}^7\times {\displaystyle \frac{3}{\cancel{8}}}=21$

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