乘法 是一種數學運算，可以表示為相同項的總和。
內容
乘法的一般原理
例如， 一個 · 乙 （讀作“a乘以b”）意味著我們將這些術語相加 a, 其中的數量等於 b. 乘法的結果稱為乘積。
例子：
- 2 × 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12
（六乘二）
- 5 × 4 = 5 + 5 + 5 + 5 = 20
（四乘五）
- 3 × 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24
（八乘三）
眾所周知，從因素的位置排列來看，乘積是不變的。 對於上面的例子，結果是：
- 6 × 2 = 6 + 6 = 12
（二乘六）
- 4 × 5 = 4 + 4 + 4 + 4 + 4 = 20
（五乘四）
- 8 × 3 = 8 + 8 + 8 = 24
（三乘八）
實際好處
多虧了乘法，你可以顯著減少相同類型的物品總數的計數等等。例如，如果我們有 7 個包裹，每個包裹包含 5 支筆，那麼通過將這些相乘找到筆的總數兩個數字：
5 × 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
（五筆七次）
乘以 0
結果始終為零。
- 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
乘以 1
乘積等於除一以外的另一個乘數。
- 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
乘以 2
將第一個因素添加到自身。
- 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
乘以 3
我們將第一個因子乘以 2，然後將其添加到結果中。
- 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
乘以 4
我們將相同的數量添加到雙倍的第一個因素。
- 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
乘以 5
如果另一個乘數是偶數，則結果將以零結尾，如果是奇數，則在數字 5 中。
- 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
乘以 6
我們將第一個因子乘以 5，然後將結果添加到其中。
- 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
乘以 7
乘以 7 沒有簡化算法，所以我們使用適用於其他因素的方法。
- 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
乘以 8
我們將第一個因子乘以 4，然後將相同的數量添加到結果中。
- 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
乘以 9
我們將第一個因子乘以 10，然後從獲得的結果中減去它。
- 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
乘以 10
將零添加到另一個乘數的末尾。
- 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