Russian Multiplication

[pyost 0]

Today I learned an interesting way to multiply numbers in school. While it's not practical if you have a calculator, or the numbers are small, it is a quite interesting method.

 

You take two numbers for this operation - I will be using 24 and 56 - that's 1344. In order to use this method, we need to create a two-column table. On the top of the left column write one number, and on the top of the right the other one. Then start dividing the left number by 2 (if it's an odd number, reduce it by 1 - 12 instead of 13) and multiplying the right by 2 at the same time. You would get something like this:

 

24 | 56

12 | 112

6 | 224

3 | 448

1 | 896

0 | 1792

 

Now, cross out every line that has an even number in the left column.

 

24 | 56

12 | 112

6 | 224

3 | 448

1 | 896

0 | 1792

 

Now add up the numbers in the right columns, the ones that are not crossed out. 448+896=1344. Interesting, huh? There is also Russian division, but I'm not quite into that one Also, I will try to put up how this works as soon as possible. Or if someone else would like to do that, be my guest

[Arbitrary 0]

I learned this one from some kind of puzzles/math tricks book. I thought it was quite interesting; it was labeled in the book as the Russian Peasant method of Multiplication (guess it was developed by the peasants) And even normal multiplication methods are not practical with small numbers or if you have a calculator, so I guess this could be a good replacement for regular methods. Though, of course, the practitioner would have to have some basic knowledge of division, or else it gets us nowhere.

[kaputnik 0]

Wow, now that's something I really have to try out in my free time someday. What really bugs me is my Math skills - and being in client servicing, I'm having to grapple with cost sheets on a daily basis and it really takes a toll. This looks like interesting stuff. I also once read a book called "Surely you're joking Mr. Fynman" in which Richard Fynman actually writes about how he goes about getting the better of a guy who was a whiz at the abacus - while doing math in his head alone. Now that really would be something. For now, I'll just try to remember my tables and prowl the internet for more fascinating methods to do math.

[Omkar™ 0]

That's a nice method, now that the Russains use it! Its up to us to decide whether we just and to multiply or BOTH multiply and divide at the same time! And how do we decide which number goes to the right and which goes to the left?

By the way, has anyone tried doing that method to multiply a number by 2 (Though pyost told us not to use this for small numbers, I'm still doing it )?

 

2 | 456

1 | 912

 

Answer ---> 912

 

I hope that satisfyies your question, pyost - it works that simple You're just doing the multiplication in terms of 2, and balancing the remainders on the left side... If you don't get it, I'll write a more rigid explaination next time, I have to run right now...

[mitchellmckain 0]

24 | 56

12 | 112

6 | 224

3 | 448

1 | 896

0 | 1792

 

Now, cross out every line that has an even number in the left column.

 

24 | 56

12 | 112

6 | 224

3 | 448

1 | 896

0 | 1792

 

Now add up the numbers in the right columns, the ones that are not crossed out. 448+896=1344. Interesting, huh? There is also Russian division, but I'm not quite into that one Also, I will try to put up how this works as soon as possible. Or if someone else would like to do that, be my guest

 

I think it is related to the binary representation of the first number.

 

for example, 24 in binary is 11000.

But this binary representation just means (2^4 + 2^3)

Now the multiplication becomes

(2^5 + 2^4) 56 = (16 + 8) 56

which using the distributive property is just 896 + 448

 

Since all the non-zero digits in a binary number represent powers of 2, using the binary form of the number in multiplication reduces the multiplication to a sum of products with these powers of 2.

Edited September 23, 2006 by mitchellmckain (see edit history)

[KDEWolf 0]

I hope that satisfyies your question, pyost - it works that simple You're just doing the multiplication in terms of 2, and balancing the remainders on the left side... If you don't get it, I'll write a more rigid explaination next time, I have to run right now...

 

Simple as that.