Fast counting method. How in the old days multidigit numbers were multiplied without multiplication tables? (peasant method)

  • Dec 11, 2020
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Good afternoon, dear guests!
Can you multiply two numbers, for example 255 by 316 without knowing the multiplication table, or easier, at least 32 by 17? Rather, you will have to think about these examples, and in this article I will tell and show how in a few completely simple steps to find a solution, and you don't even know the multiplication table will need ...
I am sure that 15 minutes of practice and you will love it! The main thing is to bring it to automatism a little, since these techniques are not similar to our school
An old book on arithmetic
An old book on arithmetic

I confess that when there is no calculator at hand, I myself use this calculation system without any column multiplication. It has a lot of names: "Russian peasant method", "Ancient Egyptian", "peasant multiplication", etc.

The method is based on multiple doubling and dividing by two or two factors, for example, we have two numbers X and Y, we double X, and Y we divide in half! Agree that with this approach, the result of the work will never change.

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Do you agree that 32 * 17 is the same as 16 * 34? Here we divided 32 by 2 and doubled 17. Further 16 * 34 is nothing but 8 * 68, then 4 * 136, then 2 * 272 and the answer is 544! No columns and no calculators.

For simplicity, it is written like this:

Simply put, division by two continues until we get the value of the first factor equal to 1.

If our task is to multiply 45 * 64, for simplicity, in order not to perform a calculation with an odd number, we swap the factors and solve:

64*45, 32*90, 16*180, 8*360, 4*720, 2*1440, 1*2880 = 2880 !!!

Now about the odd numbers

An ancient rule says that when an odd number is multiplied by any number, it is required to discard one from the first factor, and divide the remainder by 2, but by add the last final number to the numbers that were obtained during the calculation and are in the column opposite the odd ones (sounds difficult, but the example is simpler simple):

The previous example is 45 * 64, but we start calculating without changing the factors.

Now look, it is logical that we lost some of the numbers along the way, since we threw one off the first factor three times. Therefore, the rule says that to the result of 2048 we need to add those numbers that stand opposite the odd first factor:

Friends, in reality, this method takes very little time, try to take any example from your head and make a system of calculations according to this method.

And I think we should be more attentive to the ancient arithmetic, because the used counting systems simplify life. I will definitely have similar articles on my channel that simplify the algorithms for various calculations at times. After all, you must admit that calculations that you previously could not do without a pencil and a sheet of paper may be available to you - in your mind!

I really hope that you liked the article, and moreover, it has become useful in terms of application in life situations!

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