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Try to solve the following task by mental calculation:
319 x 546 = ?
Multiplication with one-digit numbers is relatively easy. We have learned the multiplication table in school. We can do this in our head without any problems. Multiplication with small two-digit numbers is also possible. This is the multiplication tables from 1x1 to 20x20. It is difficult to do more calculations in our head. In this case, we do the multiplication on paper.
In school we learned written multiplication in the following way:
We start from the right and multiply the numbers 6x9 = 54. 4 can be written in the first line below 6 and we remember 5. Then we multiply 6 by 1 = 6. 6 plus 5 makes 11. Write 1 below 4 in the line to the left of the number 4. Then 6x3 = 18 + 1 = 19. We repeat the procedure with 4 of 546. 4x9 = 36. 6 has to be written below 4 in the second line. Then we transfer the number 3. And so on. Given that many steps are involved here, it is "impossible" to do a multiplication in the head .
How to multiply in your head?
The method used by memory athletes is called Vedic Multiplication. This calculation method comes from India. With this method, it is easier to calculate in the head. I will explain the method by using our example.
The method is also called cross-multiplication method. If you have a look at the graphic you will understand the meaning of the name. First of all, we multiply the two figures on the right. 9x6 = 54. You can write the 4 below and you can memorise 5. The next step is to multiply the last two numbers along the arms of the cross. 9x4 = 36 and 1x6 = 6. If you put the two numbers together, you will get 42 + 5 = 47. Then you have to write down 7 and memorise 4. The third step is to multiply all the figures along the arms of the cross. 1x5 = 5, 3x4 = 12. If you put the two numbers together, you will get 17 +7 = 24. Then you have to note the number 4 and the 2 as a carry. The final step is to multiply the two figures on the right. 3x5 = 15 + 2 (carry) makes 17. You have to note these figures immediately. The big advantage of this method is the following: You can immediately write down the solutions below from the right to the left. There are not intermediate steps which are necessary when using the written method.
At the championships two five-digit numbers are multiplied.
As you can see, it is the same principle we already used for the multiplication 3x3. We multiply from the right to the left along the arms of the cross. To practice, I suggest that you start with the multiplication 2x2 and then practice the multiplication 3x3. If you are familiar with the principle, you can try the multiplication 5x5 in your head. The most important thing is practice practice practice, it is worth doing. If you do calculations in your head, several brain regions are used simultaneously. Therefore, this is a very good brain training!