*By*Gaurav Tiwari- Study Notes,Research,Recreations,Real Analysis,Problems,Number Theory,Math
- Comments (14)

Multiplication is probably the most important elementary operation in mathematics; even more important than usual addition. Every math-guy has its own style of multiplying numbers. But have you ever tried multiplicating by this way?

Exercise: $ 88 \times 45$ =?

Ans: as usual :- 3960 but I got this using a particular way:

88 45

176 22

352 11

704 5

1408 2

2816 1

Thus, $ 88 \times 45=3960$ (as usual).

You might be thinking that what did I do here. Okay, let we understand this method by illustrating another multiplication, of 48 with 35.

Step 1. Write the numbers in two separate columns.

$ 48 \\ 35$

Step 2. Now, double the number in left column and half the number in right column such that the number in right column reduces to 1. If the number [remaining] in right column is odd, then leave the fractional part and only write integer part.

$ 48 35 \\ 96 17 \\192 8 \\ 384 4 \\ 768 2 \\ 1536 1$

Step 3: Cancel out any number in the left column whose corresponding number in the right column is even.

48 35

96 17

192 8

384 4

768 2

1536 1

Step 4:Sum all the numbers in the left column which are not cancelled. This sum is the required product.

$ =1680$

I agree this method of multiplying numbers is not easy and you’re not going to use this in your every day math. It’s a bit boring and very long way of multiplication. But you can use this way to tease your friends, teach juniors and can write this into your own NOTEBOOK for future understandings. Remember, knowing more is getting more in mathematics. Have Fun.

**Tagged:** Column vector, Elementary math, LaTeX, Multiplication, Number

## 14 Comments on Just another way to Multiply

## Matt George -

I do love Math, however I'm not very good at it. I need more practice. I was wondering how you enabled the posts on your index after the first post to be all underneath each other with only the titles.

## Gaurav Tiwari -

Hi Matt! Thanks for dropping by. That's theme dependent. Twenty Eleven theme has a showcase template. You can set a static page with showcase template and enjoy this way. All sticky posts will work like slideshows. See here: http://wpbtips.wordpress.com/2011/05/04/workings-of-duster/

## Matt George -

Thanks for your reply.

## Abhi -

I don't think we need to tease our friends Gaurav.And of course it is really typical ,cannot be used in daily lives.It will take more time to solve relatively to the normal one.

## Gaurav Tiwari -

I think I already said it in last paragraph of the post. It is not for everyday multiplication. It's just another way to multiply.

## shivnadimpalli -

we can even prove this using basic number theory .........

## Vishwas Sethi (@VishLovesIndia) -

Btw whats the logic behind leaving those numerals wid even corresponding numbers?

## Gaurav Tiwari -

We convert one of the two numbers into binary (the number which is halved on

every line) and then do the required calculation.

## Vishwas Sethi (@VishLovesIndia) -

Yet again, why do we do this?

## Gaurav Tiwari -

Let's look at a different way of doing the same calculation by converting "35" into binary.

In binary 35=100011=

$ 1times 2^5 + 0times 2^4 +0 times 2^3 +0 times 2^2+1 times 2^1+1 times 2^0$.

So to multiply 35 by 48 we could work out the following:

$ 48 times 35=48 times 1 times 2^5 + 48 times 0 times 2^4 +48 times 0 times 2^3 +48 times 0 times 2^2+48 times 1 times 2^1 + 48 times 1 times 2^0$

The zeros belonging to binary of 35 (even part indeed) cancel out doubled part of 48 and vice-versa. And the actual summation reaches to $ 48 times 35= 48 times 1 times 2^5 +48 times 1 times 2^1 + 48 times 1 times 2^0$.

P.S. If, still, you're not satisfied, you may comment again. Your comments are heartly welcomed.

[Comment edited once.]

## Gaurav Tiwari -

Updates and CorrectionsUpdate I: (Really, I didn't know about this.)

rhlewis from reddit told that it's called the Russian Peasant Algorithm.

Russian Peasant Algorithm : Math Forum FAQ http://mathforum.org/dr.math/faq/faq.peasant.html

Update II:

Wikipedia Page for Multiplication Algorithm

[Thanks to r/math friends for Improving MY DIGITAL NOTEBOOK.]

## David Radcliffe -

Here's another way to look at it (instead of using binary numbers):

$ 88 times 45 \ = 88 + 88 times 44 \ = 88 + 176 times 22 \ = 88 + 352 times 11 \ = 88 + 352 + 352 times 10 \ = 88 + 352 + 704 times 5 \ = 88 + 352 + 704 + 704 times 4 \ = 88 + 352 + 704 + 1408 times 2 \ = 88 + 352 + 704 + 2816 \ = 3960$

## Petersim -

Ur 2much my man