# Subtraction from base numbers of 10 using Vedic maths

Does your child find it difficult to solve subtractions? This second lesson of Vedic Mathematics will help your child to subtract from base numbers within seconds. Read this illustrative article on vedic maths for learning the trick.

## Lesson 2 : Subtraction from 10, 100, 1000 using Vedic maths

Generally children find it difficult when they have to subtract a number from 100, 1000 or 10000. Since they have to borrow from the first digit and strike all the zeros make it no. 9 and so on. Finally the sum looks so shabby and the original number might not be seen. Here is an easy method using Vedic math no more mess or striking out, just a few seconds required to answer.

### Sutra

Nikhilam Navatascaramam Dasatah:

### Meaning : All from 9 the last from 10.

This sutra is used in subtraction from base numbers like 10,100,1000,10000 and so on.

For example 1000 – 876 = 124.

Here the last number is 6, so friend of 6 is 4 or 6 is 4 short of 10.
According to this sutra the last digit is subtracted from 10, and the rest from 9.

Example 1
100
- 52
-----
48
-----

Example 2

1000
- 759
------
241
------

Example 3

10000
- 6543
-------
3457
-------

In all the above cases the last digit is subtracted from 10 and remaining from 9.

Applying the second sutra the subtraction can be done from left to right. Except the last number the other numbers are subtracted from 9 and the last digit from 10.

If we apply the friends concept to this, the last number is the friend of 10 and remaining is the number short of 9.

10000
5486 (here friend of 6 is 4)
-------
4514
--------

The remaining numbers are written using the base 9,from 9 -8 is short of 1, similarly from 9 ---- 4 is short of 5 and like wise.

In all the above cases we saw that the number that get subtracted is one digit short of the above number. Subtracting 5486 from 10000, here 10000 is a 5 digit number and 5486 is a four digit number finding the answer is not a problem.

In all of the above sums you may have noticed that the number of zeros in the first number is the same as the number of figures in the number being subtracted.

For example 1000–571 has three zeros and 571 has three figures.

Suppose if we subtract 54 from 1000 , here 54 is a two digit number and 1000 is a four digit number, the above sutra can be applied here by adding a zero in front of 54.

1000
054
------
946 ( here the last digit is subtracted from 10 and remaining from 9)
-------

Before applying this sutra remember that the number to be subtracted must be only one digit short of the larger number. Else add zero in front of the digits.

1000
009 Here two zeros are added to make 9 a 3 digit number.
------
991 Last from 10 and remaining from 9.
------

### Mental Problems for practice:

In the following exercise you will need to insert zeros, but you can do that mentally.

### Subtract the following:

a. 1000 – 57 b. 1000 – 95 c. 1000 – 15 d. 10000 – 668

## Numbers starting with other than 1

Now Let us look at one more variation

This method otherwise known as 'One Less'

500 – 46.

You have 500 instead of 100.

In fact the 46 will come off from one of the five hundreds, so that 400 will be left.

So 500 – 46 = 454
The 5 is reduced by one to 4,(one less) and the All from 9 . . . formula is applied to 46 to give 54

3000 – 113 = 2887. The 3 is reduced by one to 2, (one Less)
and the formula converts 113 to 887.

Next Variation is called "One More"

Consider the example 6000 - 3485 = 2515

Considering the thousands, the 6 will be reduced by 4 (one more than 3)
because you are taking over 4 thousand away.

All from 9. . . is then applied to the 485 to give 515.

Here the first digit 3 is made 4 by adding 1 and this is reduced from 6.

When you have a sum like 6000-3485 where both numbers have the same number of digits reduce the first digit of the first number by one more than the first digit of the second number to get the first digit of the answer.
And apply the formula to the remaining digits.

Next variation in subtraction

Find 7000 – 27.
You will see here that you have a 2-digit number to subtract from 7000 which has three zeros.

The sum can be written 7000 – 027.
Then 7000 – 027 = 6973.

The 7 is reduced to 6, and the formula converts 027 to 973.

This is a very good article that seek to educate the kids about subtraction and addition at base 10 level. I will like to add my own questions and answer to buttress the above article.

Subtraction

123 - 100 = 23

352- 200= 152

890-500=490