算数【応用】ばらす・まとめる計算
問１
55 × 338 – 55 × 186 – 55 × 28 =
- 答え
- 6820
- 解き方
- 55 × 338 – 55 × 186 – 55 × 28
= 55 × ( 338 – 186 – 28 )
= 55 × 124
= 11 × 5 × 4 × 31
= 11 × 620 = 6820
問２
1023 × 20 – 10.23 × 1500 – 10230 × 0.5 =
- 答え
- 0
- 解き方
- 1023 × 20 – 10.23 × 1500 – 10230 × 0.5
= 1023 × 20 – 1023 × 15 – 1023 × 5
= 1023 × ( 20 – 15 – 5 )
= 1023 × 0 = 0
問３
3.033 × 1.8 + 0.606 × 18 + 9.07 × 0.18 =
- 答え
- 18
- 解き方
- 3.033 × 1.8 + 0.606 × 18 + 9.07 × 0.18
= 0.3033 × 18 + 0.606 × 18 + 0.0907 × 18
= ( 0.3033 + 0.606 + 0.0907 ) × 18
= 1 × 18 = 18
問４
9.42 × 40 – 6.28 × 30 + 3.14 × 40 =
- 答え
- 314
- 解き方
- 9.42 × 40 – 6.28 × 30 + 3.14 × 40
= 3.14 × 3 × 40 – 3.14 × 2 × 30 + 3.14 × 40
= 3.14 × ( 120 – 60 + 40 )
= 3.14 × 100 = 314
問５
22.5 × 3 – 2.5 × 9 =
- 答え
- 45
- 解き方
- 22.5 × 3 – 2.5 × 9
= 225 × 0.3 – 25 × 0.9
= 15 × 15 × 0.3 – 5 × 5 × 3 × 0.3
= 15 × 4.5 – 15 × 1.5
= 15 × ( 4.5 – 1.5 )
= 15 × 3 = 45
問６
3.9 × 451 + 1.5 × 3 × 451 + ( 5.4 – 3.8 ) × 451 =
- 答え
- 4510
- 解き方
- 3.9 × 451 + 1.5 × 3 × 451 + ( 5.4 – 3.8 ) × 451
= ( 3.9 + 4.5 + 1.6 ) × 451
= 10 × 451 = 4510
問７
\(\dfrac{1}{9}\) × 1.1 + \(\dfrac{1}{12}\) × 11 + \(\dfrac{1}{36}\) × 2.2 =
- 答え
- 1.1
- 解き方
- \(\dfrac{1}{9}\) × 1.1 + \(\dfrac{1}{12}\) × 11 + \(\dfrac{1}{36}\) × 2.2
= ( \(\dfrac{1}{9}\) + \(\dfrac{10}{12}\) + \(\dfrac{2}{36}\) ) × 1.1
= ( \(\dfrac{1}{9}\) + \(\dfrac{5}{6}\) + \(\dfrac{1}{18}\) ) × 1.1
= \(\dfrac{2\ +\ 15\ +\ 1}{18}\) × 1.1
= 1 × 1.1 = 1.1
問８
6.25 + 3.14 × 7.7 – 1.57 × 2 × 1.7 =
- 答え
- 25.09
- 解き方
- 6.25 + 3.14 × 7.7 – 1.57 × 2 × 1.7
= 6.25 + 3.14 × ( 7.7 – 1.7 )
= 6.25 + 3.14 × 6
= 6.25 + 18.84 = 25.09
問９
1.58 × 1700 + 1580 × 2.3 + 79 × 120 =
- 答え
- 15800
- 解き方
- 1.58 × 1700 + 1580 × 2.3 + 79 × 120
= 158 × 17 + 158 × 23 + 79 × 2 × 60
= 158 × ( 17 + 23 + 60 )
= 158 × 100 = 15800
問１０
213 × 99 – 588 × 33 + 297 =
- 答え
- 1980
- 解き方
- 213 × 99 – 588 × 33 + 297
= 213 × 99 – 196 × 3 × 33 + 3 × 99
= ( 213 – 196 + 3 ) × 99
= 20 × 99 = 1980
問１１
\(\dfrac{3}{5\ ×\ 8}\) + \(\dfrac{5}{8\ ×\ 13}\) + \(\dfrac{7}{13\ ×\ 20}\) =
- 答え
- \(\dfrac{3}{20}\)
- 解き方
- \(\dfrac{3}{5\ ×\ 8}\) + \(\dfrac{5}{8\ ×\ 13}\) + \(\dfrac{7}{13\ ×\ 20}\)
= ( \(\dfrac{1}{5}\) – \(\dfrac{1}{8}\) ) + ( \(\dfrac{1}{8}\) – \(\dfrac{1}{13}\) ) + ( \(\dfrac{1}{13}\) – \(\dfrac{1}{20}\) )
= \(\dfrac{1}{5}\) – \(\dfrac{1}{20}\) = \(\dfrac{3}{20}\)
問１２
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 =
- 答え
- 396
- 解き方
- 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88
= 11 × ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 )
= 11 × ( 45 – 9 )
= 11 × 36 = 396
※ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 は覚えておこう！
問１３
( 0.34 × 1200 + 3.4 × 360 + 34 × 52 ) ÷ 100 =
- 答え
- 34
- 解き方
- ( 0.34 × 1200 + 3.4 × 360 + 34 × 52 ) ÷ 100
= ( 34 × 12 + 34 × 36 + 34 × 52 ) ÷ 100
= 34 × ( 12 + 36 + 52 ) ÷ 100
= 34 × 100 ÷ 100 = 34
問１４
1.35 × 6 + 13.5 × 4 – 0.135 × 456 =
- 答え
- 0.54
- 解き方
- 1.35 × 6 + 13.5 × 4 – 0.135 × 456
= 1.35 × 6 + 1.35 × 40 – 1.35 × 45.6
= 1.35 × ( 6 + 40 – 45.6 )
= 1.35 × 0.4
= 1.35 × \(\dfrac{2}{5}\)
= 0.27 × 2 = 0.54
問１５
11 × 11 + 22 × 22 + 33 × 33 + 44 × 44 =
- 答え
- 3630
- 解き方
- 11 × 11 + 22 × 22 + 33 × 33 + 44 × 44
= 11 × 11 + 2 × 11 × 2 × 11 + 3 × 11 × 3 × 11 + 4 × 11 × 4 × 11
= 11 × 11 × (1 + 4 + 9 + 16)
= 121 × 30 = 3630
問１６
21 × 29 + 22 × 28 + 23 × 27 + 24 × 26 + 25 × 25 =
- 答え
- 3095
- 解き方
- 21 × 29 + 22 × 28 + 23 × 27 + 24 × 26 + 25 × 25
= 21 × ( 25 + 4 ) + 22 × ( 25 + 3 ) + 23 × ( 25 + 2 ) + 24 × ( 25 + 1 ) + 25 × 25
= 25 × ( 21 + 22 + 23 + 24 + 25 ) + 21 × 4 + 22 × 3 + 23 × 2 + 24 × 1
= 25 × { 20 × 5 + ( 1 + 2 + 3 + 4 + 5 ) } + 84 + 66 + 46 + 24
= 25 × ( 100 + 10 + 5 ) + 150 + 70
= 2500 + 250 + 125 + 220 = 3095
問１７
\(\dfrac{11}{19}\) × 181 – \(\dfrac{9}{19}\) × 181 + \(\dfrac{2}{19}\) × 9 =
- 答え
- 20
- 解き方
- \(\dfrac{11}{19}\) × 181 – \(\dfrac{9}{19}\) × 181 + \(\dfrac{2}{19}\) × 9
= \(\dfrac{1}{19}\) × ( 11 × 181 – 9 × 181 + 2 × 9 )
= \(\dfrac{1}{19}\) × { ( 11 – 9 ) × 181 + 18 }
= \(\dfrac{1}{19}\) × ( 2 × 181 + 18 )
= \(\dfrac{1}{19}\) × ( 362 + 18 )
= \(\dfrac{1}{19}\) × 380 = 20
問１８
12 × 3.3 – 13 × 3.03 – 15 × 3.03 + 16 × 3.3 =
- 答え
- 7.56
- 解き方
- 12 × 3.3 – 13 × 3.03 – 15 × 3.03 + 16 × 3.3
= 12 × 3.3 + 16 × 3.3 – ( 13 × 3.03 + 15 × 3.03 )
= ( 12 + 16 ) × 3.3 – { ( 13 + 15 ) × 3.03 }
= 28 × 3.3 – 28 × 3.03
= 28 × ( 3.3 – 3.03 )
= 28 × 0.27 = 7.56
問１９
\(\dfrac{5×6×7×8+6×7×8×9+7×8×9×10}{6×7×8}\) =
- 答え
- 29
- 解き方
- \(\dfrac{5\ ×\ 6\ ×\ 7\ ×\ 8\ +\ 6\ ×\ 7\ ×\ 8\ ×\ 9\ +\ 7\ ×\ 8\ ×\ 9\ ×\ 10}{6\ ×\ 7\ ×\ 8}\)
= 5 + 9 + \(\dfrac{7\ ×\ 8\ ×\ 3\ ×\ 3\ ×\ 2\ ×\ 5}{6\ ×\ 7\ ×\ 8}\)
= 14 + 3 × 5 = 29
問２０
( 888 – 88 × 9 ) ÷ 6 + 48 × 15 ÷ 9 =
- 答え
- 96
- 解き方
- ( 888 – 88 × 9 ) ÷ 6 + 48 × 15 ÷ 9
= ( 148 × 6 – 44 × 2 × 3 × 3 ) ÷ 6 + 16 × 3 × 3 × 5 ÷ 9
= ( 148 – 132 ) + 80
= 16 + 80 = 96
問２１
2.15 + 4.6 × 5.7 – 1.9 × 2.3 =
- 答え
- 24
- 解き方
- 2.15 + 4.6 × 5.7 – 1.9 × 2.3
= 1.15 + 1 + 4.6 × 5.7 – 1.9 × 2.3
= 2.3 × 0.5 + 1 + 2.3 × 2 × 5.7 – 1.9 × 2.3
= 2.3 × ( 0.5 + 11.4 – 1.9 ) + 1
= 2.3 × 10 + 1 = 24
問２２
83 × 567 + 86 × 567 – 34 × 567 + 135 × 433 =
- 答え
- 135000
- 解き方
- 83 × 567 + 86 × 567 – 34 × 567 + 135 × 433
= ( 83 + 86 – 34 ) × 567 + 135 × 433
= 135 × 567 + 135 × 433
= 135 × ( 567 + 433 )
= 135 × 1000 = 135000
