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Let’s take the following example:
1412 x 14 = 19768
The technique helps you finding digits from left to right as following:
- take the first digits of 1412 (which is 1) and write it down as it is; so the first digit of our product will become 1
- check which is the last digit of the number we are multiplying with (14); so the digit we will use is 4
- basically we will multiply with this “4” every digit in our number (1412) and add the resulting product with the next digit of our number (1412):
- “our 4” x the first digit (which is 1) = 4; this 4 + the next digit (which is 4) = 8; write down this digit
- “our 4” x the second digit (which is 4) = 16; this 16 + the next digit (which is 1) = 17; we write down 7 and the 1 just above the previous calculated digit (which was 8)
- “our 4” x the third digit (which is 1) = 4; this 4 + the next digit (which is 2) = 6; we write down 6
- “our 4” x the fourth and the last digit (which is 2) is 8;
- So basically our product is 18¹768; note that above the 8 we saved a 1 (from 17), so the second digit will be 8+1 instead of 8; that means the final product is 19768
Another example:
321 x 17 = 3²3¹57 = 5457
Note that the ² and ¹ on 3²3¹57 does not mean “power” but the number we saved in memory. How it works:
- we take the first digit from 321 and we write down that digit as it is: 3
- the last digit of the number we are multiplying with is 7; we start using that number from now on;
- 7 x the first digit of our number (3) = 21; we add to this 21 the next digit (which is 2) = 23; we write down the 3 and save into memory the 2
- 7 x the second digit of our number (2) = 14; we add to this 14 the next digit (which is 1) = 15; we write down 5 and save into memory 1
- 7 x the third digit of our number (1) = 7; we write down 7
- now we have something like 3²3¹57; write this number from right to left and get 5457
I was curious to find out which of the following methods works faster: that that we were taught in school or the one above? Well, that that we taught in school works little bit faster (2-3 seconds, maybe), but you need a pen.
The only advantage of the one above is that it allows you to do the same math without the pen and is just 2-3 seconds slower than the other one.