Vedic maths : Complements

 COMPLEMENTS

A complement is a number which must be added to a number to make it to 10, 100, 1000 and so on. You can also call it a deficiency from a power of 10.

eg. Complement  of 6 for 10 is 4
       As 6+4=10
      Complement of 93 for 100 is 7
       As 93+7=100
      Complement of 992 for 1000 is 8
       As 992+8=1000

We can also say that
992 is the complement of 8 and 8 is the complement  of 992.
6 is the complement  of 4 and vice versa.

How  to find a complement

The easy way to find the complement of a number from 100 is to subtract first number from 9 and last number from 10.
eg. For 83,
       9-8=1
     10-3=7
So the complement of 83 from 100 is 17.

       For 74,
       9-7=2
     10-4=6
So 26 is the complement of 74 and 74 is the complement of 26.

If the number is more than 2 digits even then the same rule applies " all from 9 and last from10 ".

eg.  876
       9-8=1
       9-7=2
     10-6=4
So,  124 is the complement of 876.

See the number 3400, What do we do here?
In the cases like this when number ends in zero,  take the last number before zero and subtract from 10 and rest from 9.
For no 3400,
             9-3=6
           10-4=6
Two zeroes will be placed at end.
So the complement of 3400 is 6600 as 6600+3400=1000.

For 1030,
Complement is 8970
As, 9-1=8
       9-0=9
     10-3=7 followed by 0.

This concept of complements is used for nikhilam multiplication in vedic maths which will be discussed in detail in my next blog.