50 lines
1.9 KiB
Markdown
50 lines
1.9 KiB
Markdown
# 乘法
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> 乘法（英语：Multiplication），加法的连续运算，同一数的若干次连加，其运算结果称为积（英语：Product）。
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$$ \sum_{k=1}^{n}{m} = \underbrace{m + m + m + \cdots + m}_{n} = m \times n $$
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## 表示法
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- $m \times n$
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- $m \cdot n$
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- $mn$ (代数中，乘号经常省略掉)
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- $m*n$ (计算机程序代码乘号常用*表示)
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## 乘法口诀表
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| $\times$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| -------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
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| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
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| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
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| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
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| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
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| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
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| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
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| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
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| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
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| 10 | 10 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 100 | 110 | 120 |
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| 11 | 11 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 110 | 121 | 132 |
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| 12 | 12 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 120 | 132 | 144 |
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## 竖式计算
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$12 \times 3$ 表示3个12的和。可以用竖式计算乘法：
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$\begin{array}{ccc}
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&1 &2 \\\\
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\times & &3 \\\\
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\hline
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& &6 \\\\
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{+} &3 &0 \\\\
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\hline
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= &3 &6
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\end{array}$
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## 性质
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- 交换律 $a \times b = b \times a$
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- 结合律 $(a \times b) \times c = a \times (b \times c)$
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- 分配律 $a \times (b+c)= a\times b + a\times c$
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