>The Multiplication Table>The Times Tables

The Times Tables

The times tables for 1 to 10

What Is Multiplication?

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{b times}{\underset{⏟}{a + a + \dots + 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{b times}{\underset{⏟}{a + a + \dots + 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

Multiplication

factor \times factor = 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{5 times}{\underset{⏟}{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

Three Important Rules for Multiplication

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, $32 \times 1 = 32 .$

Activities 1