# Power of Vedic Maths With Trigonometry PDF

### TWO SIMPLE TECHNIQUES

We will begin our journey into the fascinating world of Vedic maths with two simple techniques which will lay the foundation for some of the techniques in the following chapters.

I. Subtraction from 100/1000/10000

We will start with a very simple technique wherein we will see the use of the sutra ‘All from 9 and last from 10’.

This is used to subtract a given number from 100, 1000, 10000 etc. It removes the mental strain which is existent in the method taught in schools.

This method is also used later on in the Nikhilam method of multiplication. Consider the subtraction of 7672 from 10000.

a) Normal Method

The normal method is We carry ‘1’ from the left side and continue doing so till we reach the rightmost digit, leaving behind 9 in each column and 10 in the last column.

Then, we subtract the right most digit ‘2’ from 10 and write down ‘8’. Next, we subtract the digit ‘7’ from ‘9’ and write down ‘2’. We repeat this process for all the remaining digits to the left.

Through this operation, the final result is always obtained from right to left.
Mentally, there is a carry operation for every digit, which is time consuming
and slows down the overall process.

b) Vedic Method

The Vedic method uses the sutra ‘All from 9 and last from 10’ and gives a
very simple and powerful technique to achieve the same result.

The result can be obtained from both left to right as well as right to left with
equal ease.
It states that the result can be obtained by subtraction of each digit from ‘9’ and the last digit from ‘10’.

Hence, in the given example, We can get the result from left to right or vice versa from right to left as i.e. all digits except the last one are subtracted from 9, the last digit is subtracted from 10 and the result (2328) is written down directly.

The mental burden of a carry for each column vanishes and the answer can be obtained easily, in a jiffy.

The same technique can be applied for decimal subtraction also, e.g. 2.000 –
0.3436.

The core operation here is subtraction of 3436 from 10000 where 1 is a carry
from left.

VII) Computation of the quotient on division by 9

Let us now see how to get the quotient on dividing a number by 9. In Vedic
maths, the division is converted to a simple addition operation.
a) Method 1

The first method consists of a forward pass followed by a backward pass.
Example : Divide 8132 by 9

Steps:
Place a colon before the last digit, which shows the position separating the
quotient and the remainder.

Start from the left most digit and bring it down as it is.

Carry it (8) to the next column and add it to the digit in that column i.e. 1 + 8 and bring down 9.

Carry 9 to the next column, add it to 3 and bring down 12.

Repeat by carrying 12 to the next (last) column, add to 2 and bring down 14 as shown.

After reaching the end, we work backwards from the right to the left by computing the remainder in the last column and by carrying the surplus digits to the left.

We have to retain only one digit at each location.

Examine the last column, which should hold the remainder. If the number is more than 9, we subtract the maximum multiples of 9 from it, which gives the quotient digit to be carried to the left, leaving the remainder behind.

Since the number in the last column (14) contains one multiple of 9, we carry 1 to the left hand digit (12) and retain 5 (14 – 9) as final remainder.

At the end of the forward pass, the digits looked as follows: 8. 9. 12 : 14