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The **Multiplication** is a **mathematical operation**, of elementary **Aritmetic**, that consists of adding several times a same number.

Thus, 3 x 4, indicate that we must add 3, 4 times, that is to say, 3 + 3 + 3 + 3. Therefore, the multiplication can be considered like a repeated sum.

We verify that the result is the same: 3 x 4 = 12 and 3 + 3 + 3 + 3 = 12.

The terms of multiplication are called **factors** and the result is called **product**.

When the multiplication has only two factor, we called **multiplying** to the number that we are going add, and
**multiplier** to the times we are going that it to add, and the result is called **product**.

In our example, 3 is the multiplying, 4 is the multiplier and the product is 12, which is the result of adding 3 + 3 + 3 + 3 or multiply 3 x 4

To multiply two **two multi-digit** numbers, we are going to put the multiplying and **below** the multiplier, and draw a **line** under both.
We began to multiply, **from right to left**, the first digit of the multiplier for each of the multiplying and we put the units of each product under the line, also from right to left,
and add the tens to the next product. (As you can see in the example, the first product is 6 x 3 = 18, we put the 8 y and we "store" (carry) 1 that will add to the next
product 3 x 5 = 15 + 1 = 16).

Then, we do the same with **each** of the remaining digits of the multiplier, placing under the previous row, **displaced** one place to the left.

When we finish of multiply the **last digit** of multiplier by **all digits** of multiplying, draw a line under the last row
(we will have so many rows as digits have the multiplier) and we proceed to **orderly add ** all the rows. The result is the
**product ** of the multiplication.

3 | 2 | 5 | 6 | ||||

x | 4 | 2 | 3 | ||||

__________ | |||||||

9 | 7 | 6 | 8 | ||||

6 | 5 | 1 | 2 | ||||

+ | 1 | 3 | 0 | 2 | 4 | ||

__________________ | |||||||

1 | 3 | 7 | 7 | 2 | 8 | 8 |

**3 x 6 = 18**, we put the**8**and "store" (carry) 1, that will add to the next product.**3 x 5 = 15**, 15 + 1 (which we carried) =**16**, we put the**6**and carry 1 , that will add to the next product.**3 x 2 = 6**, 6 + 1 (which we carried) =**7**, we put the**7**(as 7 is less than 10 now we carry none).**3 x 3 = 9**, as we carry none, we put the**9**.**2 x 6 = 12**, we put the**2**and carry 1 , that will add to the next product.**2 x 5 = 10**, 10 + 1 (which we carried) =**11**, we put the**1**and carry 1 , that will add to the next product.**2 x 2 = 4**, 4 + 1 (which we carried) =**5**, we put the**5**(as 5 is less than 10 we carry none).**2 x 3 = 6**, as we carry none, we put the**6**.**4 x 6 = 24**, we put the**4**and carry 2 , that will add to the next product.**4 x 5 = 20**, 20 + 2 (which we carried) =**22**, we put the**2**and carry 2 , that will add to the next product.**4 x 2 = 8**, 8 + 2 (which we carried) =**10**, we put the**0**and carry 1 , that will add to the next product.**4 x 3 = 12**, 12 + 1 (which we carried) =**13**, as no longer we have more digits, we put the**13**.- the first column only has 8, so we put down 8.
- the second column 6 + 2 = 8 , so we put down another 8.
- the third column 7 + 1 + 4 = 12 , so we put the 2 (and carry 1).
- the fourth column 9 + 5 + 2 = 16 , 16 + 1 (which we carried) = 17, we put the 7 (and carry 1).
- the fifth column 6 + 0 = 6 , 6 + 1 (which we carried) = 7, put down 7 (we carry none).
- the sixth column has only a 3, so we put down 3.
- the seventh column has only a 1, so we put down 1.

We have multiplied 3 by 3256, continue now with the 2.

We have multiplied 2 by 3256, continue now with the 4.

We have multiplied the last digit of the multiplier 4 by 3256.

As the multiplying has 4 digits (3256) and the multiplier 3 (423), the multiplication is done in 12 steps (4 x 3 = 12).

Finally, we proceed to add all the columns.

And we have already finished. ** 3.256 x 423 = 1 _{1} 377 . 288**

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