Learn to Multiply
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.
We are going to see an example:
| 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
(A million three hundred seventy-seven thousands two hundred and eighty-eight)
