算数【応用】四則計算（小数・分数なし）
問１
5 + 3 × 7 – ( 20 – 2 × 7 ) =
- 答え
- 20
- 解き方
- 5 + 3 × 7 – ( 20 – 2 × 7 )
= 5 + 21 – ( 20 – 14 )
= 5 + 21 – 6 = 20
問２
14 + 6 × 3 – 35 ÷ 7 + 28 =
- 答え
- 55
- 解き方
- 14 + 6 × 3 – 35 ÷ 7 + 28
= 14 + 18 – 5 + 28 = 55
問３
29 + { 24 – 9 × ( 8 – 6 ) } ÷ 3 =
- 答え
- 31
- 解き方
- 29 + { 24 – 9 × ( 8 – 6 ) } ÷ 3
= 29 + ( 24 – 9 × 2 ) ÷ 3
= 29 + ( 24 – 18 ) ÷ 3
= 29 + 6 ÷ 3
= 29 + 2 = 31
問４
67 – { 10 + 16 × ( 17 – 8 ) ÷ 12 } × 3 =
- 答え
- 1
- 解き方
- 67 – { 10 + 16 × ( 17 – 8 ) ÷ 12 } × 3
= 67 – ( 10 + 16 × 9 ÷ 12 ) × 3
= 67 – ( 10 + 144 ÷ 12 ) × 3
= 67 – ( 10 + 12 ) × 3
= 67 – 22 × 3
= 67 – 66 = 1
問５
42 – ( 65 – 9 ) ÷ ( 4 + 12 ÷ 4 ) =
- 答え
- 34
- 解き方
- 42 – ( 65 – 9 ) ÷ ( 4 + 12 ÷ 4 )
= 42 – 56 ÷ ( 4 + 3 )
= 42 – 56 ÷ 7
= 42 – 8 = 34
問６
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 =
- 答え
- 100
- 解き方
- 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
= ( 1 + 19 ) + ( 3 + 17 ) + ( 5 + 15 ) + ( 7 + 13 ) + ( 9 + 11 )
= 20 + 20 + 20 + 20 + 20
= 20 × 5 = 100
問７
8 + 7 ÷ 5 – 3 × 0 =
- 答え
- 9.4
- 解き方
- 8 + 7 ÷ 5 – 3 × 0
= 8 + 1.4 – 0 = 9.4
問８
128 ÷ { 8 + ( 5 × 3 – 42 ÷ 6 ) } =
- 答え
- 8
- 解き方
- 128 ÷ { 8 + ( 5 × 3 – 42 ÷ 6 ) }
= 128 ÷ { 8 + ( 15 – 7 ) }
= 128 ÷ ( 8 + 8 )
= 128 ÷ 16 = 8
問９
( 5 – 5 ÷ 2 ) × 6 – 5 ÷ ( 2 ÷ 5 ) – 12 ÷ 10 ÷ 2 =
- 答え
- 1.9 ( または、\(1\dfrac{9}{10}\) )
- 解き方
- ( 5 – 5 ÷ 2 ) × 6 – 5 ÷ ( 2 ÷ 5 ) – 12 ÷ 10 ÷ 2
= ( 5 – 2.5 ) × 6 – 5 ÷ 0.4 – 1.2 ÷ 2
= 2.5 × 6 – 12.5 – 0.6
= 15 – 12.5 – 0.6
= 2.5 – 0.6 = 1.9
【別解】分数にして計算する
( 5 – 5 ÷ 2 ) × 6 – 5 ÷ ( 2 ÷ 5 ) – 12 ÷ 10 ÷ 2
= ( 5 – \(\dfrac{5}{2}\) ) × 6 – 5 ÷ \(\dfrac{2}{5}\) – 12 × \(\dfrac{1}{10}\) × \(\dfrac{1}{2}\)
= \(\dfrac{5}{2}\) × 6 – 5 × \(\dfrac{5}{2}\) – \(\dfrac{3}{5}\)
= 15 – \(\dfrac{25}{2}\) – \(\dfrac{3}{5}\)
= \(\dfrac{150\ -\ 125\ -\ 6}{10}\) = \(\dfrac{19}{10}\) = \(1\dfrac{9}{10}\)
※小数で計算するよりも分数で計算する方が楽な場合が多い。
問１０
10 × 9 – 8 ÷ 4 + 2 =
- 答え
- 90
- 解き方
- 10 × 9 – 8 ÷ 4 + 2
= 90 – 2 + 2 = 90
問１１
7 – 14 ÷ 42 × 9 =
- 答え
- 4
- 解き方
- 7 – 14 ÷ 42 × 9
= 7 – 14 × \(\dfrac{1}{42}\) × 9
= 7 – \(\dfrac{1}{3}\) × 9
= 7 – 3 = 4
問１２
9 – 2 × 4 + 10 ÷ 5 =
- 答え
- 3
- 解き方
- 9 – 2 × 4 + 10 ÷ 5
= 9 – 8 + 2 = 3
問１３
5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 =
- 答え
- 140
- 解き方
- 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
= ( 5 + 23 ) + ( 7 + 21 ) + ( 9 + 19 ) + ( 11 + 17 ) + ( 13 + 15 )
= 28 + 28 + 28 + 28 + 28
= 28 × 5 = 140
問１４
7 × 6 + 5 – 102 ÷ 6 =
- 答え
- 30
- 解き方
- 7 × 6 + 5 – 102 ÷ 6
= 42 + 5 – 17 = 30
問１５
( 12 × 7 – 16 × 3 ) ÷ ( 86 – 41 – 39 + 3 ) =
- 答え
- 4
- 解き方
- ( 12 × 7 – 16 × 3 ) ÷ ( 86 – 41 – 39 + 3 )
= ( 84 – 48 ) ÷ ( 86 + 3 – 39 – 41 )
= 36 ÷ ( 89 – 39 – 41 )
= 36 ÷ ( 50 – 41 )
= 36 ÷ 9 = 4
問１６
3 ÷ ( 6 ÷ 7 ) =
- 答え
- 3.5 ( または、\(3\dfrac{1}{2}\) )
- 解き方
- 3 ÷ ( 6 ÷ 7 )
= 3 ÷ \(\dfrac{6}{7}\)
= 3 × \(\dfrac{7}{6}\) = \(\dfrac{7}{2}\) = 3.5
問１７
( 9 – 5 ÷ 6 ) × 3 – ( 8 + 2 × 7 ) ÷ 4 =
- 答え
- 19
- 解き方
- ( 9 – 5 ÷ 6 ) × 3 – ( 8 + 2 × 7 ) ÷ 4
= ( 9 – \(\dfrac{5}{6}\) ) × 3 – ( 8 + 14 ) ÷ 4
= ( \(\dfrac{54}{6}\) – \(\dfrac{5}{6}\) ) × 3 – 22 ÷ 4
= \(\dfrac{49}{6}\) × 3 – \(\dfrac{22}{4}\)
= \(\dfrac{49}{2}\) – \(\dfrac{11}{2}\) = \(\dfrac{38}{2}\) = 19
問１８
32 ÷ 57 ÷ 25 × 95 ÷ 48 =
- 答え
- \(\dfrac{2}{45}\)
- 解き方
- 32 ÷ 57 ÷ 25 × 95 ÷ 48
= 32 × \(\dfrac{1}{57}\) × \(\dfrac{1}{25}\) × 95 × \(\dfrac{1}{48}\)
= \(\dfrac{32}{48}\) × \(\dfrac{95}{57}\) × \(\dfrac{1}{25}\)
= \(\dfrac{2}{3}\) × \(\dfrac{\cancelto{1}{5}}{3}\) × \(\dfrac{1}{\cancelto{5}{25}}\)
= \(\dfrac{2}{3\ ×\ 3\ ×\ 5}\) = \(\dfrac{2}{45}\)
問１９
{ 2202 ÷ 6 – 201 ÷ ( 19 – 8 × 2 ) } ÷ 25 =
- 答え
- 12
- 解き方
- { 2202 ÷ 6 – 201 ÷ ( 19 – 8 × 2 ) } ÷ 25
= { 367 – 201 ÷ ( 19 – 16 ) } ÷ 25
= ( 367 – 201 ÷ 3 ) ÷ 25
= ( 367 – 67 ) ÷ 25
= 300 ÷ 25 = 12
問２０
112 – ( 6 × 19 – 81 ÷ 3 ) ÷ ( 54 ÷ 18 ) =
- 答え
- 83
- 解き方
- 112 – ( 6 × 19 – 81 ÷ 3 ) ÷ ( 54 ÷ 18 )
= 112 – ( 114 – 27 ) ÷ 3
= 112 – 87 ÷ 3
= 112 – 29 = 83
問２１
333 – 3 × ( 82 – 60 ÷ 4 ) – 15 × 4 =
- 答え
- 72
- 解き方
- 333 – 3 × ( 82 – 60 ÷ 4 ) – 15 × 4
= 333 – 3 × ( 82 – 15 ) – 60
= 333 – 3 × 67 – 60
= 333 – 201 – 60 = 72
問２２
( 100 + 8 ) × 7 – ( 31 – 80 ÷ 5 ) × 17 ÷ 5 =
- 答え
- 705
- 解き方
- ( 100 + 8 ) × 7 – ( 31 – 80 ÷ 5 ) × 17 ÷ 5
= 108 × 7 – ( 31 – 16 ) × 17 ÷ 5
= 756 – \(\cancelto{3}{15}\) × 17 × \(\dfrac{1}{\cancel{5}}\)
= 756 – 51 = 705
問２３
21 – { 150 ÷ 25 + ( 113 – 99 ) × 3 ÷ 7 } =
- 答え
- 9
- 解き方
- 21 – { 150 ÷ 25 + ( 113 – 99 ) × 3 ÷ 7 }
= 21 – ( 6 + 14 × 3 ÷ 7 )
= 21 – ( 6 + 6 ) = 21 – 12 = 9
問２４
396 ÷ ( 72 – 6 ) – 6 =
- 答え
- 0
- 解き方
- 396 ÷ ( 72 – 6 ) – 6
= 396 ÷ 66 – 6 = 6 – 6 = 0
問２５
27 – { 154 – 7 × ( 7 – 5 ) } ÷ 7 =
- 答え
- 7
- 解き方
- 27 – { 154 – 7 × ( 7 – 5 ) } ÷ 7
= 27 – ( 154 – 7 × 2 ) ÷ 7
= 27 – ( 154 – 14 ) ÷ 7
= 27 – 140 ÷ 7 = 27 – 20 = 7
問２６
( 17 × 9 + 18 ) ÷ 19 + 18 × 9 =
- 答え
- 171
- 解き方
- ( 17 × 9 + 18 ) ÷ 19 + 18 × 9
= ( 153 + 18 ) ÷ 19 + 18 × 9
= 171 ÷ 19 + 162
= 9 + 162 = 171
問２７
2021 + { 59 – 2 × ( 121 – 92 ) } =
- 答え
- 2022
- 解き方
- 2021 + { 59 – 2 × ( 121 – 92 ) }
= 2021 + ( 59 – 2 × 29 )
= 2021 + ( 59 – 58 ) = 2021 + 1 = 2022
問２８
92 – 378 ÷ { 210 – 9 × ( 14 + 7 ) } =
- 答え
- 74
- 解き方
- 92 – 378 ÷ { 210 – 9 × ( 14 + 7 ) }
= 92 – 378 ÷ ( 210 – 9 × 21 )
= 92 – 378 ÷ ( 210 – 189 )
= 92 – 378 ÷ 21
= 92 – 18 = 74
問２９
16 × 6 – 35 – 84 ÷ 4 =
- 答え
- 40
- 解き方
- 16 × 6 – 35 – 84 ÷ 4
= 96 – 35 – 21
= 61 – 21 = 40
問３０
15 + 4 × { 200 – 48 ÷ 8 × ( 5 + 3 × 9 ) } =
- 答え
- 47
- 解き方
- 15 + 4 × { 200 – 48 ÷ 8 × ( 5 + 3 × 9 ) }
= 15 + 4 × { 200 – 48 ÷ 8 × ( 5 + 27 ) }
= 15 + 4 × ( 200 – 48 ÷ 8 × 32 )
= 15 + 4 × ( 200 – 6 × 32 )
= 15 + 4 × ( 200 – 192 )
= 15 + 4 × 8
= 15 + 32 = 47
問３１
45 + 10 × ( 62 – 56 ÷ 8 ) – 10 × 7 =
- 答え
- 525
- 解き方
- 45 + 10 × ( 62 – 56 ÷ 8 ) – 10 × 7
= 45 + 10 × ( 62 – 7 ) – 10 × 7
= 45 + 10 × 55 – 10 × 7
= 45 + 550 – 70
= 45 + 480 = 525
問３２
52 – 24 ÷ 36 ÷ 4 + 5 × 7 – 8 =
- 答え
- \(78\dfrac{5}{6}\)
- 解き方
- 52 – 24 ÷ 36 ÷ 4 + 5 × 7 – 8
= 52 – \(\dfrac{\cancelto{\cancelto{1}{2}}{24}}{\cancelto{3}{36}\ ×\ \cancelto{2}{4}}\) + 35 – 8
= 52 – \(\dfrac{1}{3\ ×\ 2}\) + 27
= 79 – \(\dfrac{1}{6}\) = \(78\dfrac{5}{6}\)
問３３
8 + 4 × 12 – 120 ÷ ( 7 × 3 + 3 ) =
- 答え
- 51
- 解き方
- 8 + 4 × 12 – 120 ÷ ( 7 × 3 + 3 )
= 8 + 48 – 120 ÷ ( 21 + 3 )
= 8 + 48 – 120 ÷ 24
= 8 + 48 – 5
= 56 – 5 = 51
