Subtraction Made Easy

Subtraction is one of the basic operations in mathematics. It is opposite of addition. Subtraction means the difference between minuend and subtrahend. If minuend is larger than subtrahend, the difference is positive. If the subtrahend is larger than minuend, the difference is negative.

 If there is no borrowing, the method is very easy. Generally students are bored when there is borrowing or regrouping in subtraction. There is some difficulty in understanding. It requires abstract thinking and drilling.

 There are several methods of subtraction in arithmetic. The subtraction by Vedic mathematics method is one of the easy and simple methods. It is based on the principle, “All from nine and the last from ten”. It is called NIKHILAM. Nikhilam is one of the 16 main sutras of Vedic mathematics.
To apply Nikhilam to a number, subtract each digit from 9, except the last digit. The last digit is to be subtracted from 10.

Example of subtraction
IF SUBTRAHEND IS LESS THAN MINUEND

Example #1
3 6 2 5 - 1 7 8 9
Here the Subtrahend is 1 7 8 9.
Apply the sutra “all from nine and the last from ten” to the subtrahend number.

9-1      9-7      9-8     10-9
8          2         1          1
Now, add the result to the minuend.
3 6 2 5 + 8 2 1 1
= 1 1 3 8 6
Drop the first digit that is 1 from the left.
The result is 1 3 8 6. This is the answer

Example # 2
4 5 2 9 - 2 3 8 0
As per Nikhilam the subtrahend will be
              
9-2    9-3    10-8    0
7        6        2        0
When the last digit at subtrahend is 0, keep 0 as it is.Therfore in the above problem 8 is to be subtracted from 10.
Now add 7  6  2  0 to 4  5  2  9.The result is 1  2  1  4  9.
Drop the first digit to the left the answer is 2 1 4 9.This is the answer.
Therefore  4  5  2  9  -  2  3  8  0  =  2  1  4  9.

Example #3
4  5  8  2  7  -  3  9  8.
Arrange this as , 4  5  8  2  7  -  0  0  3  9  8.
Applying Nikhilam to the subtrahend
9-0     9-0     9-3     9-9     10-8
9         9         6        0         2
The Subtrahend will be 9 9 6 0 2.
Add 9 9 6 0 2 to the minuend.
4  5  8  2  7  +  9  9  6  0  2  =  1  4  5  4  2  9.
Drop the first digit to the left, the answer is 4 5 4 2 9.
Therefore   4  5  8  2  7  -  3  9  8  =  4  5  4  2  9.

IF MINUEND IS GREATER THAN SUBTRAHEND

Example #1
3 5 1 - 4 9 7
Apply Nikhilam to the minuend.
9-3   9-5   10-1
6       4        9
The result is 6 4 9
Add 6 4 9 to the subtrahend.
4  9  7  + 6  4  9 = 1  1  4  6.
Drop the first digit to the left the result is 1 4 6.
Therefore  3  51  -  4  9  7  =  -  1  4  6.

ADVANTAGES.
• The method is easy to understand.
• No need of borrowing and carrying.
• It is a shortcut method.
• No frustration.
• Comfortable.