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Multiplication can be defined in the following way: Assume that you have a number $a$ (where $a$ can be any number). If you add $a$ to itself $b$ times, that can be written like this:

$$\underset{\text{}b\text{times}}{\underset{\u23df}{a+a+\cdots +a}}$$ |

This can be tiresome in the long run, especially when $b$ becomes large. That’s where multiplication enters the picture. By definition, the sum above can also be written like this:

$$\underset{\text{}b\text{times}}{\underset{\u23df}{a+a+\cdots +a}}=b\times a$$ |

This means that $a$ added to itself $b$ times is the same as $a$ multiplied by $b$.

The numbers that are multiplied together are called factors, and the answer is called a product.

Rule

$$\text{factor}\times \text{factor}=\text{product}$$ |

This might look a little odd—it might not be how you learned about multiplication before. So here’s an example to clarify.

Example 1

**You want to add 3 to itself 5 times **

This can be written as

$$\underset{\text{5times}}{\underset{\u23df}{3+3+3+3+3}}$$ |

but if you use the definition above, it can also be written as

$$5\times 3=15$$ |

Multiplication problems with whole numbers (integers) between 1 and 10 are organized in the times tables. You should learn this table by heart.

Rule

- 1.
- $a\times b=b\times a$. It does not matter what order the numbers are written in when you multiply—you get the same answer either way!
- 2.
- Anything multiplied by 0 is 0. For example, $5\times 0\times 20=0.$
- 3.
- If you multiply something by 1, it doesn’t change. For example, $32\times 1=32.$