算数【応用】小数を含む四則計算（問題文に）

問１

21 ÷ 0.7 × 0.01 ÷ 0.001 =

答え
300
解き方
21 ÷ 0.7 × 0.01 ÷ 0.001
= 21 ÷ \(\dfrac{7}{10}\) × \(\dfrac{1}{100}\) ÷ \(\dfrac{1}{1000}\)
= \(\cancelto{3}{21}\) × \(\dfrac{10}{\cancel{7}}\) × \(\dfrac{1}{\cancel{100}}\) × \(\cancelto{10}{1000}\)
= 3 × 10 × 10 = 300

問２

605.4 ÷ 30.27 × 16.46 ÷ 0.823 =

答え
400
解き方
605.4 ÷ 30.27 × 16.46 ÷ 0.823
= \(\dfrac{6054}{10}\) ÷ \(\dfrac{3027}{100}\) × \(\dfrac{1646}{100}\) ÷ \(\dfrac{823}{1000}\)
= \(\dfrac{\cancelto{2}{6054}}{\cancel{10}}\) × \(\dfrac{\cancelto{10}{100}}{\cancel{3027}}\) × \(\dfrac{\cancelto{2}{1646}}{\cancel{100}}\) × \(\dfrac{\cancelto{10}{1000}}{\cancel{823}}\)
= 2 × 10 × 2 × 10 = 400

問３

15.4 ÷ 0.7 – 6.8 × 0.5 ÷ 1.7 =

答え
20
解き方
15.4 ÷ 0.7 – 6.8 × 0.5 ÷ 1.7
= \(\dfrac{154}{10}\) ÷ \(\dfrac{7}{10}\) – \(\dfrac{68}{10}\) × \(\dfrac{5}{10}\) ÷ \(\dfrac{17}{10}\)
= \(\dfrac{\cancelto{22}{154}}{\cancel{10}}\) × \(\dfrac{\cancel{10}}{\cancel{7}}\) – \(\dfrac{\cancel{17}\ ×\ \cancelto{2}{4}}{\cancel{10}}\) × \(\dfrac{1}{\cancel{2}}\) × \(\dfrac{\cancel{10}}{\cancel{17}}\)
= 22 – 2 = 20

問４

5 – { 4.5 – 5.2 ÷ ( 6.1 – 4.8 ) + 3.7 } =

答え
0.8
解き方
5 – { 4.5 – 5.2 ÷ ( 6.1 – 4.8 ) + 3.7 }
= 5 – ( 4.5 – 5.2 ÷ 1.3 + 3.7 )
= 5 – ( 4.5 – 4 + 3.7 )
= 5 – 4.2 = 0.8

問５

2.7 × 8 + 3.6 × 4 – 5.4 × 5 =

答え
9
解き方
2.7 × 8 + 3.6 × 4 – 5.4 × 5
= 21.6 + 14.4 – 27
= 36 – 27 = 9

問６

61 – 4.5 × 5.2 ÷ 0.65 =

答え
25
解き方
61 – 4.5 × 5.2 ÷ 0.65
= 61 – \(\dfrac{45}{10}\) × \(\dfrac{52}{10}\) × \(\dfrac{100}{65}\)
= 61 – \(\dfrac{\cancelto{9}{45}}{\cancel{10}}\) × \(\dfrac{\cancel{13}\ ×\ 4}{\cancel{10}}\) × \(\dfrac{\cancel{100}}{\cancel{13}\ ×\ \cancel{5}}\)
= 61 – 9 × 4
= 61 – 36 = 25

問７

23.4 ÷ 1.2 – 2.5 × 4.2 =

答え
9
解き方
23.4 ÷ 1.2 – 2.5 × 4.2
= \(\dfrac{234}{10}\) × \(\dfrac{10}{12}\) – \(\dfrac{25}{10}\) × \(\dfrac{42}{10}\)
= \(\dfrac{\cancelto{39}{117}}{\cancel{5}}\) × \(\dfrac{\cancel{5}}{\cancelto{2}{6}}\) – \(\dfrac{\cancel{5}}{2}\) × \(\dfrac{21}{\cancel{5}}\)
= \(\dfrac{39}{2}\) – \(\dfrac{21}{2}\) = \(\dfrac{18}{2}\) = 9

問８

6.3 – 5.1 ÷ ( 3.13 + 5.37 ) =

答え
5.7
解き方
6.3 – 5.1 ÷ ( 3.13 + 5.37 )
= 6.3 – 5.1 ÷ 8.5
= 6.3 – \(\dfrac{\cancelto{3}{51}}{\cancel{10}}\) × \(\dfrac{\cancel{10}}{\cancelto{5}{85}}\)
= 6.3 – \(\dfrac{3}{5}\) = 6.3 – 0.6 = 5.7

問９

( 13.1 – 5.9 ) × 0.25 + 18.2 – 12.6 + 8.4 =

答え
15.8
解き方
( 13.1 – 5.9 ) × 0.25 + 18.2 – 12.6 + 8.4
= 7.2 × \(\dfrac{1}{4}\) + 18.2 – 12.6 + 8.4
= 1.8 + 18.2 – 12.6 + 8.4 = 15.8

問１０

4.21 + 9.22 – 3.5 × 2.3 =

答え
5.38
解き方
4.21 + 9.22 – 3.5 × 2.3
= 13.43 – \(\dfrac{\cancelto{7}{35}}{\cancelto{2}{10}}\) × \(\dfrac{23}{10}\)
= 13.43 – \(\dfrac{161}{20}\)
= 13.43 – 8.05 = 5.38

問１１

( 1.45 + 2.38 – 0.3 × 3.3 ) ÷ 0.5 =

答え
5.68
解き方
( 1.45 + 2.38 – 0.3 × 3.3 ) ÷ 0.5
= ( 3.83 – 0.99 ) ÷ \(\dfrac{1}{2}\)
= 2.84 × 2 = 5.68

問１２

6.4 ÷ 8 + 16.9 ÷ 13 + 3.6 ÷ 6 =

答え
2.7
解き方
6.4 ÷ 8 + 16.9 ÷ 13 + 3.6 ÷ 6
= 0.8 + 1.3 + 0.6 = 2.7

問１３

( 2.8 + 1.2 ) × 1.8 – ( 3 – 0.018 ) + 1.8 =

答え
6.018
解き方
( 2.8 + 1.2 ) × 1.8 – ( 3 – 0.018 ) + 1.8
= 4 × 1.8 – 2.982 + 1.8
= 7.2 – 2.982 + 1.8
= 9 – 2.982 = 6.018

問１４

0.6 ÷ 0.24 + 1.5 × 0.06 – 0.04 × 2.5 =

答え
2.49
解き方
0.6 ÷ 0.24 + 1.5 × 0.06 – 0.04 × 2.5
= \(\dfrac{60}{24}\) + 0.09 – 0.1
= \(\dfrac{5}{2}\) + 0.09 – 0.1
= 2.5 + 0.09 – 0.1 = 2.49

問１５

3.85 – ( 0.17 + 1.34 ) × 3 + 1.25 =

答え
0.57
解き方
3.85 – ( 0.17 + 1.34 ) × 3 + 1.25
= 3.85 – 1.51 × 3 + 1.25
= 5.1 – 4.53 = 0.57

問１６

2 × 0.8 – ( 0.6 × 0.2 + 2.4 ÷ 4 ) =

答え
0.88
解き方
2 × 0.8 – ( 0.6 × 0.2 + 2.4 ÷ 4 )
= 1.6 – ( 0.12 + 0.6 )
= 1.6 – 0.72 = 0.88

問１７

{ ( 4.2 + 0.9 ) – ( 1.5 – 0.6 ) } ÷ 7.8 =

答え
\(\dfrac{7}{13}\)
解き方
{ ( 4.2 + 0.9 ) – ( 1.5 – 0.6 ) } ÷ 7.8
= ( 5.1 – 0.9 ) ÷ 7.8
= 4.2 ÷ 7.8
= \(\dfrac{\cancelto{7}{42}}{\cancel{10}}\) × \(\dfrac{\cancel{10}}{\cancelto{13}{78}}\) = \(\dfrac{7}{13}\)

問１８

6.79 ÷ ( 4.85 × 0.4 ) – 2.8 =

答え
0.7
解き方
6.79 ÷ ( 4.85 × 0.4 ) – 2.8
= 6.79 ÷ ( \(\dfrac{\cancelto{97}{485}}{\cancelto{50}{100}}\) × \(\dfrac{\cancel{2}}{\cancel{5}}\) ) – 2.8
= \(\dfrac{679}{100}\) ÷ \(\dfrac{97}{50}\) – 2.8
= \(\dfrac{\cancelto{7}{679}}{\cancelto{2}{100}}\) × \(\dfrac{\cancel{50}}{\cancel{97}}\) – 2.8
= \(\dfrac{7}{2}\) – 2.8 = 3.5 – 2.8 = 0.7

問１９

7.8 ÷ ( 2.3 × 6 – 1.52 ÷ 1.9 ) + 6 × 0.4 =

答え
3
解き方
7.8 ÷ ( 2.3 × 6 – 1.52 ÷ 1.9 ) + 6 × 0.4
= 7.8 ÷ ( 13.8 – \(\dfrac{152}{190}\) ) + 2.4
= 7.8 ÷ ( 13.8 – \(\dfrac{\cancel{19}\ ×\ \cancelto{4}{8}}{\cancel{19}\ ×\ \cancelto{5}{10}}\) ) + 2.4
= 7.8 ÷ ( 13.8 – \(\dfrac{4}{5}\) ) + 2.4
= 7.8 ÷ ( 13.8 – 0.8 ) + 2.4
= 7.8 ÷ 13 + 2.4
= 0.6 + 2.4 = 3

問２０

48 ÷ 512 × ( 4.5 + 3.5 ) =

答え
0.75
解き方
48 ÷ 512 × ( 4.5 + 3.5 )
= 48 × \(\dfrac{1}{512}\) × 8
= \(\cancelto{3}{48}\) × \(\dfrac{1}{\cancelto{4}{64}\ ×\ \cancel{8}}\) × \(\cancel{8}\) = \(\dfrac{3}{4}\) = 0.75