Base and Complement are very important in Vedic Mathematics and form the basis of many calculations.

## Base:

As explained above we work in a base 10 number system. In order to ease our calculations we can take any number ending with ‘0’ i.e. any multiple of 10 as our base.

## COMPLEMENT

The Complement of a number is the difference between that number and the next higher power of 10.

### 10’s complement:

This includes all 1 digit numbers. It is the number that should be added to make it 10.

The complement of 6 is 4.

The complement of 7 is 3.

### 100’s complement:

This includes all 2 digit numbers. It is the number that should be added to make it 100.

The complement of 55 is 45.

The complement of 89 is 11.

### Finding a complement of a number:

We use the **Sutra/Rule** **“All from 9 and last from 10”**

As the name suggests we subtract the last digit i.e. the unit’s digit by 10 and the other digits by 9.

Let’s find the complement of 845

(From 9) (From 9) (From 10)

8 4 5

** 1 5 5 **

**845 + 155 = 1000**

If the unit’s digit is ‘0’ then retain it and subtract the other digits by the same rule.

Let’s find the complement of 230

(From 9) (From 10) (Retain)

2 3 0

7 7 0

**230 + 770 = 1000**

In every case the total of two numbers is a base number 10, 100, 1000 etc.

This gives us an easy way of subtracting from numbers like 100,1000,10000 etc.