問１ 分配法則
- 分配法則
- ① 共通の数を見つけてひとまとめにする
a × b + a × c = a × ( b + c )
a × b – a × c = a × ( b – c )
② かける数をかっこの中のすべての数に配る
a × ( b + c ) = a × b + a × c
a × ( b – c ) = a × b – a × c
（１）次の計算をしなさい。
① 5 × 82 + 48 × 5 – 5 × 30 =
- 答え（１）- ①
- 500
- 解き方（１）- ①
- 5 × 82 + 48 × 5 – 5 × 30
= 5 × 82 + 5 × 48 – 5 × 30
= 5 × ( 82 + 48 – 30 )
= 5 × ( 130 – 30 )
= 5 × 100 = 500
② 18 + 18 × 9 =
- 答え（１）- ②
- 180
- 解き方（１）- ②
- 18 + 18 × 9
= 18 × 1 + 18 × 9
= 18 × ( 1 + 9 )
= 18 × 10 = 180
③ 25 × 28 – 25 × 27 =
- 答え（１）- ③
- 25
- 解き方（１）- ③
- 25 × 28 – 25 × 27
= 25 × ( 28 – 27 )
= 25 × 1 = 25
④ 12 × 63 + 3 × 4 × 37 =
- 答え（１）- ④
- 1200
- 解き方（１）- ④
- 12 × 63 + 3 × 4 × 37
= 12 × 63 + 12 × 37
= 12 × ( 63 + 37 )
= 12 × 100 = 1200
⑤ 96 – 3 × 8 + 4 × 9 =
- 答え（１）- ⑤
- 108
- 解き方（１）- ⑤
- 96 – 3 × 8 + 4 × 9
= 12 × 8 – 12 × 2 + 12 × 3
= 12 × ( 8 – 2 + 3 )
= 12 × 9 = 108
⑥ 777 × 20 + 777 × 80 =
- 答え（１）- ⑥
- 77700
- 解き方（１）- ⑥
- 777 × 20 + 777 × 80
= 777 × ( 20 + 80 )
= 777 × 100 = 77700
⑦ 13 × 1331 – 13 × 331 =
- 答え（１）- ⑦
- 13000
- 解き方（１）- ⑦
- 13 × 1331 – 13 × 331
= 13 × ( 1331 – 331 )
= 13 × 1000 = 13000
⑧ 37 × 76 + 37 × 68 – 44 × 37 =
- 答え（１）- ⑧
- 3700
- 解き方（１）- ⑧
- 37 × 76 + 37 × 68 – 44 × 37
= 37 × ( 76 + 68 – 44 )
= 37 × ( 144 – 44 )
= 37 × 100 = 3700
⑨ 89 × 101 – 89 =
- 答え（１）- ⑨
- 8900
- 解き方（１）- ⑨
- 89 × 101 – 89
= 89 × ( 101 – 1 )
= 89 × 100 = 8900
⑩ 9 × 22 + 9 × 78 =
- 答え（１）- ⑩
- 900
- 解き方（１）- ⑩
- 9 × 22 + 9 × 78
= 9 × ( 22 + 78 )
= 9 × 100 = 900
（２）次の計算をしなさい。
① 25 × ( 9 + 2 ) =
- 答え（２）- ①
- 275
- 解き方（２）- ①
- 25 × ( 9 + 2 )
= 25 × 9 + 25 × 2
= 225 + 50 = 275
② 12.5 × ( 8 – 0.8 ) =
- 答え（２）- ②
- 90
- 解き方（２）- ②
- 12.5 × ( 8 – 0.8 )
= 12.5 × 8 – 12.5 × 0.8
= 100 – 10 = 90
③ 36 × ( 50 + 5 ) =
- 答え（２）- ③
- 1980
- 解き方（２）- ③
- 36 × ( 50 + 5 )
= 36 × 50 + 36 × 5
= 1800 + 180 = 1980
④ \(\dfrac{3}{5}\) × ( 10 + \(\dfrac{5}{3}\) ) =
- 答え（２）- ④
- 7
- 解き方（２）- ④
- \(\dfrac{3}{5}\) × ( 10 + \(\dfrac{5}{3}\) )
= \(\dfrac{3}{5}\) × 10 + \(\dfrac{3}{5}\) × \(\dfrac{5}{3}\)
= 6 + 1 = 7
⑤ 2.4 × ( 20 – 5 ) =
- 答え（２）- ⑤
- 36
- 解き方（２）- ⑤
- 2.4 × ( 20 – 5 )
= 2.4 × 20 – 2.4 × 5
= 48 – 12 = 36
⑥ 42 × 75 =
- 答え（２）- ⑥
- 3150
- 解き方（２）- ⑥
- 42 × 75
= 42 × ( 70 + 5 )
= 42 × 70 + 42 × 5
= 2940 + 210 = 3150
⑦ 48 × 99 =
- 答え（２）- ⑦
- 4752
- 解き方（２）- ⑦
- 48 × 99
= 48 × ( 100 – 1 )
= 48 × 100 – 48 × 1
= 4800 – 48 = 4752
⑧ 25 × 104 =
- 答え（２）- ⑧
- 2600
- 解き方（２）- ⑧
- 25 × 104
= 25 × ( 100 + 4 )
= 25 × 100 + 25 × 4
= 2500 + 100 = 2600
⑨ 12.5 × 16 =
- 答え（２）- ⑨
- 200
- 解き方（２）- ⑨
- 12.5 × 16
= 12.5 × ( 8 + 8 )
= 12.5 × 8 + 12.5 × 8
= 100 + 100 = 200
問２
次の計算をしなさい。
- ヒント
- 数をばらして計算しやすい順番に並べかえたり、計算しやすいようにまとめましょう！
（１）625 × 16 =
- 答え（１）
- 10000
- 解き方（１）
- 625 × 16
= 25 × 25 × 4 × 4
= 25 × 4 × 25 × 4
= 100 × 100 = 10000
※かけ算は数の順番を入れ替えても答えが変わらない ⇒ 交換法則
（２）75 × 32 – 25 × 36 =
- 答え（２）
- 1500
- 解き方（２）
- 75 × 32 – 25 × 36
= 3 × 25 × 4 × 8 – 25 × 4 × 9
= 24 × 100 – 100 × 9
= 100 × ( 24 – 9 )
= 100 × 15 = 1500
（３）625 × 8 – 125 × 16 + 250 × 4 =
- 答え（３）
- 4000
- 解き方（３）
- 625 × 8 – 125 × 16 + 250 × 4
= 125 × 5 × 8 – 125 × 8 × 2 + 1000
= 1000 × 5 – 1000 × 2 + 1000 × 1
= 1000 × ( 5 – 2 + 1 )
= 1000 × 4 = 4000
※覚えておこう！
625 = 125 × 5
125 × 8 = 1000
（４）25 × 32 × 625 =
- 答え（４）
- 500000
- 解き方（４）
- 25 × 32 × 625
= 25 × 4 × 8 × 125 × 5
= 100 × 1000 × 5 = 500000
※覚えておこう！
25 × 4 = 100
125 × 8 = 1000
（５）125 × 35 – 375 × 9 =
- 答え（５）
- 1000
- 解き方（５）
- 125 × 35 – 375 × 9
= 125 × 35 – 125 × 3 × 9
= 125 × ( 35 – 27 )
= 125 × 8 = 1000
- 覚えておこう！
- 25 × 4 = 100、125 × 8 = 1000はもちろん、その他の25の倍数、125の倍数も覚えておきましょう！
125 = 25 × 5
625 = 25 × 25 = 125 × 5
問３
47 × 48 + 53 × 48 =
- 答え
- 4800
- 解き方
- 47 × 48 + 53 × 48
= 48 × ( 47 + 53 )
= 48 × 100 = 4800
問４
25 × 70 + 250 + 23 =
- 答え
- 2023
- 解き方
- 25 × 70 + 250 + 23
= 250 × 7 + 250 + 23
= 250 × ( 7 + 1 ) + 23
= 250 × 8 + 23
= 2000 + 23 = 2023
問５
225 – { 90 – 3 × ( 31 – 6 ) } × 7 =
- 答え
- 120
- 解き方
- 225 – { 90 – 3 × ( 31 – 6 ) } × 7
= 225 – ( 90 – 3 × 25 ) × 7
= 225 – ( 90 – 75 ) × 7
= 15 × 15 – 15 × 7
= 15 × ( 15 – 7 )
= 15 × 8 = 120
問６
2 + ( 5 × 5 + 3 × 5 ) ÷ 5 =
- 答え
- 10
- 解き方
- 2 + ( 5 × 5 + 3 × 5 ) ÷ 5
= 2 + { ( 5 + 3 ) × 5 } ÷ 5
= 2 + ( 8 × 5 ) ÷ 5
= 2 + 40 ÷ 5
= 2 + 8 = 10
問７
( 90+91+92+93+94+95+96+97+98+99 ) ÷ 45 =
- 答え
- 21
- 解き方
( 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 ) ÷ 45
= { 90 × 10 + ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 ) } ÷ 45
= ( 45 × 2 × 10 + 45 ) ÷ 45
= ( 20 + 1 ) × 45 ÷ 45 = 21
※覚えておこう！
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
問８
43 × 7 – 43 × 4 – 43 × 1 =
- 答え
- 86
- 解き方
- 43 × 7 – 43 × 4 – 43 × 1
= 43 × ( 7 – 4 – 1 )
= 43 × 2 = 86
問９
31 × 7 – 5 × 31 + 2 × 31 × 9 =
- 答え
- 620
- 解き方
- 31 × 7 – 5 × 31 + 2 × 31 × 9
= 31 × ( 7 – 5 + 18 )
= 31 × 20 = 620
問１０
138 – ( 18 + 3 ) × 6 =
- 答え
- 12
- 解き方
- 138 – ( 18 + 3 ) × 6
= 6 × 23 – 21 × 6
= 6 × ( 23 – 21 )
= 6 × 2 = 12
問１１
250 × 9 – 25 × 50 + 23 =
- 答え
- 1023
- 解き方
- 250 × 9 – 25 × 50 + 23
= 250 × 9 – 250 × 5 + 23
= 250 × ( 9 – 5 ) + 23
= 250 × 4 + 23
= 1000 + 23 = 1023
問１２
( 1 + 12 + 123 + 1234 ) ÷ ( 1 + 2 + 3 + 4 ) =
- 答え
- 137
- 解き方
- ( 1 + 12 + 123 + 1234 ) ÷ ( 1 + 2 + 3 + 4 )
= { ( 1 + 2 + 3 + 4 ) + ( 10 + 120 + 1230 ) } ÷ 10
= { 10 + 10 × ( 1 + 12 + 123 ) } ÷ 10
= ( 10 + 10 × 136 ) ÷ 10
= ( 1 + 136 ) × 10 ÷ 10
= 1 + 136 = 137
問１３
921 × 1515 + 921 × 1517 – 32 × 921 =
- 答え
- 2763000
- 解き方
- 921 × 1515 + 921 × 1517 – 32 × 921
= 921 × ( 1515 + 1517 – 32 )
= 921 × 3000 = 2763000
問１４
3021 × 10 + 3021 × 7 + 3021 × 13 =
- 答え
- 90630
- 解き方
- 3021 × 10 + 3021 × 7 + 3021 × 13
= 3021 × ( 10 + 7 + 13 )
= 3021 × 30 = 90630
問１５
4017 × 16 – 25 × 16 + 8 × 16 =
- 答え
- 64000
- 解き方
- 4017 × 16 – 25 × 16 + 8 × 16
= 16 × ( 4017 – 25 + 8 )
= 16 × 4000 = 64000
問１６
374 × 374 + 374 × 626 =
- 答え
- 374000
- 解き方
- 374 × 374 + 374 × 626
= 374 × ( 374 + 626 )
= 374 × 1000 = 374000
問１７
51 × 3 – 255 ÷ 5 =
- 答え
- 102
- 解き方
- 51 × 3 – 255 ÷ 5
= 51 × 3 – 51
= 51 × ( 3 – 1 )
= 51 × 2 = 102
問１８
21 ÷ 4 × 8 – 21 =
- 答え
- 21
- 解き方
- 21 ÷ 4 × 8 – 21
= 21 × 2 – 21
= 21 × ( 2 – 1 ) = 21
問１９
52 × 3.14 + 48 × 3.14 =
- 答え
- 314
- 解き方
- 52 × 3.14 + 48 × 3.14
= ( 52 + 48 ) × 3.14
= 100 × 3.14 = 314
問２０
47 × 6.87 – 47 × 3.23 – 47 × 2.64 =
- 答え
- 47
- 解き方
- 47 × 6.87 – 47 × 3.23 – 47 × 2.64
= 47 × ( 6.87 – 3.23 – 2.64 )
= 47 × 1 = 47
問２１
52 × 49 – 352 =
- 答え
- 2196
- 解き方
- 52 × 49 – 352
= 52 × ( 50 – 1 ) – 352
= 2600 – 52 – 352
= 2600 – ( 52 + 352 )
= 2600 – 404 = 2196
問２２
91 × 46 + 37 × 107 – 37 × 7 + 46 × 9 =
- 答え
- 8300
- 解き方
- 91 × 46 + 37 × 107 – 37 × 7 + 46 × 9
= 46 × ( 91 + 9 ) + 37 × ( 107 – 7 )
= 46 × 100 + 37 × 100
= ( 46 + 37 ) × 100
= 83 × 100 = 8300
問２３
6 + 31.4 × 0.472 + 314 × 0.0002 =
- 答え
- 31.4
- 解き方
- 3.14 × 5.26 + 31.4 × 0.472 + 314 × 0.0002
= 3.14 × 5.26 + 3.14 × 4.72 + 3.14 × 0.02
= 3.14 × ( 5.26 + 4.72 + 0.02 )
= 3.14 × 10 = 31.4
問２４
817 × 454 =
- 答え
- 370918
- 解き方
- 817 × 454
= 817 × ( 400 + 50 + 4 )
= 326800 + 40850 + 3268 = 370918
問２５
{ 7 + ( 8 – 2 ) × 10 } × 63 =
- 答え
- 4221
- 解き方
- { 7 + ( 8 – 2 ) × 10 } × 63
= ( 7 + 6 × 10 ) × 63
= ( 7 + 60 ) × 63
= 7 × 63 + 60 × 63
= 441 + 3780 = 4221