# Multiplication: The Vedic Way

What would 873 x 982 look like? Lots of lines. But still intriguing. Thanks Allison for sending this our way. Feel free to suggest a good link here

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• Alan Miesch says:

My Japanese wife says she has never seen such a way of multiplying. But very interesting anyway!

• Ines says:

Vedic Maths!

• Tony says:

Yeah apparently it’s not Japanese, but Vedic.. check out this wikipedia article: http://en.wikipedia.org/wiki/Vedic_mathematics

• Dr Silverrose says:

This is really no different from multiplying the way we (westerners) do it with digits: multiply each digit in one number by each digit in the other, and carry over as needed. It seems to be a bit faster our way, especially for multi-digit multiplication, because you don’t have to draw all those lines.

• Dr Silverrose says:

Actually, it’s not really multi-digit multiplication that is a pain to do this way (with lines), it’s high-digit multiplication. Try multiplying 89 x 78 using lines, and you’ll quickly go back to multiplying the way you were taught.

• Jen says:

This is not a Japanese means of teaching multiplication, but Vedic.

• Ramasubramaniyan says:

This method is ok for small numbers such from 1 to 5 but for 6,7… it is tedious to work out but this method of multiplicaion is suitable to teach for kids so that don’t get out of maths

• Sarah says:

Don’t be silly, Doctor.
It’s not the lines that make this easier and faster, it’s the orientation of the multiplicands, the order that you do the multiplication and adding.
In the western way, you make a large intermediate answer for every place in your multiplicand. So for 193×16, you get the answers for 193×6 and 193×10 before you get anything.
The flaw in this is that you’re always going to be adding the result of every one place digit by another one place digit, ten place multiplied by a one place together, then adding every ten by ten and hundred by one together and so on, but instead of performing *those* operations relevant to the final answer, we make a series of intermediate answers that are spaced with place holding zeros. When you’re doing a three digit number by a three digit number, the amount of added steps is really slow and cumbersome, and except for the first operation, these intermediate answers don’t give you any of the digits in the answer.
In this version, the vedic version, regardless of whether or not you draw any lines, you get the answers for each place digit individually.
So, typical western way goes like this: multiply, carry, add, carry, get the answer.
The vedic way, you multiply, add, carry, and then you have a digit from the answer. Each intermediate answer is simply another digit of your final answer, not a strange large number that serves merely as an opportunity to make a mistake. The third time I tried the vedic way, I got an answer pretty quickly, then I checked my work using the way I’d grown up with, and the answers didn’t match. I used a calculator–the vedic way was correct, the western way had several mistakes, even though I took longer to do it.

• Allie says:

Brilliant. I think that this is a lot faster than long multiplication for 3 or 4 digit numbers. As long as you draw it at the correct angle and carry the tens over correctly there are no mistakes. Really great!!
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• Kc says:

The kids at the school where. I worked did their homework so they could find where it would fail.

• Daniel says:

It’s nice, but it’s obvious it’s not faster than “Western” multiplication”.

• Zannr1 says:

well here is the thing. math is math is math. you can make proofs of different concepts in many ways due to the nature of math. myself, i help my daughter with her school work and she is just now learning multiplication, shes in 2nd grade. one of the techniques i taught her was the finger trick when multiplying numbers 1-9 by 9. i also showed her some other tricks. anyway when i saw this Japanese/Vedic way i couldn’t believe it. LOL I looked in to how it works with larger numbers like 1234X1232 etc… and it works. so i emailed her teacher with the link saying that I think that it is a technique that should supplement the times table. the reason is easy. when i was learning my times table it was a slow process. you don’t just learn them all right away. it takes practice. So, with this technique kids can use it as a proof of correctness while they are learning their times table. All kids have to do is know how to add. ITS GREAT!! when i saw this i felt stupid for not knowing this technique…lol and i pretty much minored in math. lol anyway that’s that on that..lol

• Spencer says:

This is the same way I was taught to multiply polynomials. For two digits we called it FOIL (first outer inner last). 21×13= (2x+1)*(x+3)=2x^2+(1+6)x+3 where x=10. The only difference is the visualization.

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