乗算 は、同じ項の和として表すことができる数学演算です。

コンテンツ

乗算の一般原理

例えば、 a・b (「a 回 b」と読みます) は、項を合計することを意味します。 a、その数はに等しい b. 乗算の結果は積と呼ばれます。

九九をすばやく簡単に学ぶ方法

例：

  • 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

    (XNUMX かける XNUMX)

  • 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20

    (XNUMX かける XNUMX)

  • 3 ⋅ 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24

    (XNUMX かける XNUMX)

私たちが知っているように、因子の場所の順列から、積は変化しません。 上記の例では、次のことがわかります。

  • 6 ⋅ 2 = 6 + 6 = 12

    (XNUMX かける XNUMX)

  • 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20

    (XNUMX かける XNUMX)

  • 8 ⋅ 3 = 8 + 8 + 8 = 24

    (XNUMX かける XNUMX)

実用的なメリット

乗算のおかげで、同じ種類のアイテムの総数などを大幅に減らすことができます。たとえば、それぞれに 7 本のペンが含まれる 5 つのパッケージがある場合、ペンの総数はこれらを乗算することによって求められます。 XNUMX つの数字:

5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35

(XNUMXペンXNUMX回)

0を掛ける

結果は常にゼロです。

  • 0・0 = 0
  • 1 ⋅ 0 = 0 ⋅ 1 = 0
  • 2 ⋅ 0 = 0 ⋅ 2 = 0 + 0 = 0
  • 3 ⋅ 0 = 0 ⋅ 3 = 0 + 0 + 0 = 0
  • 4 ⋅ 0 = 0 ⋅ 4 = 0 + 0 + 0 + 0 = 0
  • 5 ⋅ 0 = 0 ⋅ 5 = 0 + 0 + 0 + 0 + 0 = 0
  • 6 ⋅ 0 = 0 ⋅ 6 = 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 7 ⋅ 0 = 0 ⋅ 7 = 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 8 ⋅ 0 = 0 ⋅ 8 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 9 ⋅ 0 = 0 ⋅ 9 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 10 ⋅ 0 = 0 ⋅ 10 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0

1を掛ける

積は、XNUMX 以外の別の乗数に等しくなります。

  • 1・1 = 1
  • 2 ⋅ 1 = 2 ⋅ 1 = 2
  • 3 ⋅ 1 = 3 ⋅ 1 = 3
  • 4 ⋅ 1 = 4 ⋅ 1 = 4
  • 5 ⋅ 1 = 5 ⋅ 1 = 5
  • 6 ⋅ 1 = 6 ⋅ 1 = 6
  • 7 ⋅ 1 = 7 ⋅ 1 = 7
  • 8 ⋅ 1 = 8 ⋅ 1 = 8
  • 9 ⋅ 1 = 9 ⋅ 1 = 9
  • 10 ⋅ 1 = 10 ⋅ 1 = 10

2を掛ける

最初の要素をそれ自体に追加します。

  • 1 ⋅ 2 = 1 + 1 = 2
  • 2 ⋅ 2 = 2 + 2 = 4
  • 3 ⋅ 2 = 3 + 3 = 6
  • 4 ⋅ 2 = 4 + 4 = 8
  • 5 ⋅ 2 = 5 + 5 = 10
  • 6 ⋅ 2 = 6 + 6 = 12
  • 7 ⋅ 2 = 7 + 7 = 14
  • 8 ⋅ 2 = 8 + 8 = 16
  • 9 ⋅ 2 = 9 + 9 = 18
  • 10 ⋅ 2 = 10 + 10 = 20

3を掛ける

最初の係数に 2 を掛けてから、結果に加算します。

  • 1・3 = (1・2) + 1 = 2 + 1 = 3
  • 2・3 = (2・2) + 2 = 4 + 2 = 6
  • 3・3 = (3・2) + 3 = 6 + 3 = 9
  • 4・3 = (4・2) + 4 = 8 + 4 = 12
  • 5・3 = (5・2) + 5 = 10 + 5 = 15
  • 6・3 = (6・2) + 6 = 12 + 6 = 18
  • 7・3 = (7・2) + 7 = 14 + 7 = 21
  • 8・3 = (8・2) + 8 = 16 + 8 = 24
  • 9・3 = (9・2) + 9 = 18 + 9 = 27
  • 10・3 = (10・2) + 10 = 20 + 10 = 30

4を掛ける

同じ量を XNUMX 倍の最初の要素に追加します。

  • 1・4 = (1・2) + (1・2) = 2 + 2 = 4
  • 2・4 = (2・2) + (2・2) = 4 + 4 = 8
  • 3・4 = (3・2) + (3・2) = 6 + 6 = 12
  • 4・4 = (4・2) + (4・2) = 8 + 8 = 16
  • 5・4 = (5・2) + (5・2) = 10 + 10 = 20
  • 6・4 = (6・2) + (6・2) = 12 + 12 = 24
  • 7・4 = (7・2) + (7・2) = 14 + 14 = 28
  • 8・4 = (8・2) + (8・2) = 16 + 16 = 32
  • 9・4 = (9・2) + (9・2) = 18 + 18 = 36
  • 10・4 = (10・2) + (10・2) = 20 + 20 = 40

5を掛ける

もう一方の乗数が偶数の場合、結果は 5 で終わり、奇数の場合は XNUMX になります。

  • 1 ⋅ 5 = 5 ⋅ 1 = 5
  • 2 ⋅ 5 = 5 ⋅ 2 = 5 + 5 = 10
  • 3 ⋅ 5 = 5 ⋅ 3 = (5 ⋅ 2) + 5 = 15
  • 4・5=5・4=(5・2)+(5・2)=20
  • 5 ⋅ 5 = 5 + 5 + 5 + 5 + 5 = 25
  • 6 ⋅ 5 = 5 ⋅ 6 = (5 ⋅ 5) + 5 = 30
  • 7 ⋅ 5 = 5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
  • 8・5=5・8=(5・4)+(5・4)=40
  • 9 ⋅ 5 = 5 ⋅ 9 = (5 ⋅ 10) – 5 = 45
  • 10 ⋅ 5 = 5 ⋅ 10 = 50

6を掛ける

最初の因数に 5 を掛けてから、その結果を足します。

  • 1・6 = (1・5) + 1 = 5 + 1 = 6
  • 2・6 = (2・5) + 2 = 10 + 2 = 12
  • 3・6 = (3・5) + 3 = 15 + 3 = 18
  • 4・6 = (4・5) + 4 = 20 + 4 = 24
  • 5・6 = (5・5) + 5 = 25 + 5 = 30
  • 6・6 = (6・5) + 6 = 30 + 6 = 36
  • 7・6 = (7・5) + 7 = 35 + 7 = 42
  • 8・6 = (8・5) + 8 = 40 + 8 = 48
  • 9・6 = (9・5) + 9 = 45 + 9 = 54
  • 10・6 = (10・5) + 10 = 50 + 10 = 60

7を掛ける

7 を掛けるための単純化されたアルゴリズムはないため、他の要素に適用できる方法を使用します。

  • 1 ⋅ 7 = 7 ⋅ 1 = 7
  • 2 ⋅ 7 = 7 ⋅ 2 = 7 + 7 = 14
  • 3 ⋅ 7 = 7 ⋅ 3 = (7 ⋅ 2) + 7 = 21
  • 4・7=7・4=(7・2)+(7・2)=28
  • 5 ⋅ 7 = 7 ⋅ 5 = 7 + 7 + 7 + 7 + 7 = 35
  • 6 ⋅ 7 = 7 ⋅ 6 = (7 ⋅ 5) + 7 = 42
  • 7 ⋅ 7 = 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49
  • 8・7=7・8=(7・4)+(7・4)=56
  • 9 ⋅ 7 = 7 ⋅ 9 = (7 ⋅ 10) – 7 = 63
  • 10・7 = 70

8を掛ける

最初の係数に 4 を掛けてから、同じ量を結果に追加します。

  • 1・8 = (1・4) + (1・4) = 8
  • 2・8 = (2・4) + (2・4) = 16
  • 3・8 = (3・4) + (3・4) = 24
  • 4・8 = (4・4) + (4・4) = 32
  • 5・8 = (5・4) + (5・4) = 40
  • 6・8 = (6・4) + (6・4) = 48
  • 7・8 = (7・4) + (7・4) = 56
  • 8・8 = (8・4) + (8・4) = 64
  • 9・8 = (9・4) + (9・4) = 72
  • 10・8 = (10・4) + (10・4) = 80

9を掛ける

最初の係数に 10 を掛けて、得られた結果から引きます。

  • 1 ⋅ 9 = (1 ⋅ 10) – 1 = 10 – 1 = 9
  • 2 ⋅ 9 = (2 ⋅ 10) – 2 = 20 – 2 = 18
  • 3 ⋅ 9 = (3 ⋅ 10) – 3 = 30 – 3 = 27
  • 4 ⋅ 9 = (4 ⋅ 10) – 4 = 40 – 4 = 36
  • 5 ⋅ 9 = (5 ⋅ 10) – 5 = 50 – 5 = 45
  • 6 ⋅ 9 = (6 ⋅ 10) – 6 = 60 – 6 = 54
  • 7 ⋅ 9 = (7 ⋅ 10) – 7 = 70 – 7 = 63
  • 8 ⋅ 9 = (8 ⋅ 10) – 8 = 80 – 8 = 72
  • 9 ⋅ 9 = (9 ⋅ 10) – 9 = 90 – 9 = 81
  • 10 ⋅ 9 = (10 ⋅ 10) – 10 = 100 – 10 = 90

10を掛ける

もう一方の乗数の末尾にゼロを追加します。

  • 1 ⋅ 10 = 10 ⋅ 1 = 10
  • 2 ⋅ 10 = 10 ⋅ 2 = 20
  • 3 ⋅ 10 = 10 ⋅ 3 = 30
  • 4 ⋅ 10 = 10 ⋅ 4 = 40
  • 5 ⋅ 10 = 10 ⋅ 5 = 50
  • 6 ⋅ 10 = 10 ⋅ 6 = 60
  • 7 ⋅ 10 = 10 ⋅ 7 = 70
  • 8 ⋅ 10 = 10 ⋅ 8 = 80
  • 9 ⋅ 10 = 10 ⋅ 9 = 90
  • 10 ⋅ 10 = 10 ⋅ 10 = 100

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