# 乘法

> 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）。

$$ \sum_{k=1}^{n}{m} = \underbrace{m + m + m + \cdots + m}_{n} = m \times n $$

## 表示法

- $ m \times n $
- $ m \cdot n $
- $ m * n $
- $ mn $ (代数中，乘号经常省略掉)

## 性质

- 交换律 $a \times b = b \times a$
- 结合律 $ (a \times  b) \times c = a \times (b \times c)$
- 分配律 $a \times (b+c)= a\times b + a\times c$

## 乘法口诀表

| X   | 1   | 2   | 3   | 4   | 5   | 6   | 7   | 8   | 9   |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 1   | 1   | 2   | 3   | 4   | 5   | 6   | 7   | 8   | 9   |
| 2   | 2   | 4   | 6   | 8   | 10  | 12  | 14  | 16  | 18  |
| 3   | 3   | 6   | 9   | 12  | 15  | 18  | 21  | 24  | 27  |
| 4   | 4   | 8   | 12  | 16  | 20  | 24  | 28  | 32  | 36  |
| 5   | 5   | 10  | 15  | 20  | 25  | 30  | 35  | 40  | 45  |
| 6   | 6   | 12  | 18  | 24  | 30  | 36  | 42  | 48  | 54  |
| 7   | 7   | 14  | 21  | 28  | 35  | 42  | 49  | 56  | 63  |
| 8   | 8   | 16  | 24  | 32  | 40  | 48  | 56  | 64  | 72  |
| 9   | 9   | 18  | 27  | 36  | 45  | 54  | 63  | 72  | 81  |