# Vedic Division by Nine

Friends, this time it has been a long time I have written a post. I badly wanted to write one but because of very busy schedule I couldn’t.

This post is one of the many areas where Vedic Mathematics really surpasses traditional methods as you shall soon see. This post is about dividing any number by 9.

We will start by taking an example

Divide 200103002 by 9

We can initiate solving this problem by writing it as below –

9) 2 0 0 1 0 3 0 0 | 2

The symbol in front of the final 2 is not the number “1”, but a vertical bar “|”. This last position will hold the remainder, if any.

There are only two steps in this procedure.

Step 1:  Bring down the 2. It will look like this:

9) 2 0 0 1 0 3 0 0 | 2

2

Step 2:   Add the answer so far, the “2”, to the number on the upper right. For this example, we would add the “2” from the answer to “0”, the number on the above right. So we have:

9) 2 0 0 1 0 3 0 0 | 2

2 2

Now just repeat this process. Add the 2 to the 0, add the 2 to the 1, etc. We will end up with:

9) 2 0 0 1 0 3 0 0 | 2

2 2 2 3 3 6 6 6 | 8

9) 3 2 3 6 0 5 2 | 2

Step 1: Bring down the first number in the divisor.

9) 3 2 3 6 0 5 2 | 2

3

Step 2: Add the number on the above right and repeat. If we get carrys, put them in and don’t worry about them for now. So we will have:

9) 3   2   3   6   0   5   2 |   2

3   5   8 14 14 19  21 | 23

So, what do we do with all this stuff? Any number that has a carry, needs to be added to the left. Let’s do this starting with the “21” just after the bar.

9) 3   2   3   6   0   5   2 |   2

3   5   9   5   6   1    1 | 23

Now, notice that the remainder of 23 needs to be reduced until it is below a 9. There are two multiples of 9 in 23 with 5 left over. Therefore, we carry over 2 to the other side of the bar and add it to the 1. We will then have the answer:

9) 3   2   3   6   0   5   2 |   2

3   5   9   5   6   1    3 |   5

There is a little more work involved, but, still a lot less than the conventional way.

Author – Vineet Patawari