VEDIC MATHEMATICS FOR BEGINNERS

Lesson 2
 

Complements

OUR NUMERATION SYSTEM  is called the  Base Ten system since we use ten basic symbols to represent any number. The ten basic symbols, which we call digits, are:

0,  1,  2,  3,  4,  5,  6,  7,  8   and   9.

Complements of Single Digit  Numbers

When two numbers add up to 10,  the two numbers are called complements of each other.

Thus,              

                        Complement of 1 is 9 since 1 + 9 =10

                        Complement of 2 is 8 since 2 + 8 =10

                        Complement of 3 is 7 since 3 + 7=10

                        Complement of 4 is 6 since 4 + 6 =10

                        Complement of 5 is 5 since 5 + 5 =10

                        Complement of 6 is 4 since 6 + 4 =10

                        Complement of 7 is 3 since 7 + 3 =10

                        Complement of 8 is 2 since 8 + 2 =10

                        Complement of 9 is 1 since 9 + 1 =10

Also,

  1 and 9 are complements of each other since  1 + 9 = 9+1=10

  2 and 8 are complements of each other since  2 + 8 = 8+2=10

  3 and 7 are complements of each other since  3 + 7 =7+3 =10

  4 and 6 are complements of each other since  4 + 6 = 6+4=10         

  5 is complement of itself  since 5+5 = 10

Using complements

  We can find the  sum of 10 and any single digit number mentally.

For example : 10+6= 16;   10+4 = 14 etc.

  Sum of two one digit numbers that involve carrying can be done mentally by using their complements.

Example 1 : Add  7 and 9  mentally.

Solution:

Mental method 1.   The complement of 7 is 3.

                               Subtract 3 from 9 and add it to 7 to make 10.

                                Now add 10 and 6. 

                                The sum is 16.

                    ( 7+9  = 7+3+6 = =10 +6 = 16)

Mental method 2. The complement of 9 is 1.

                               Subtract 1 from 7 and add it to 9 to make 10.

                                Now add 6 and 10.  The sum is 16.

                 ( 7+9  = 6+1+9 = 6+10 = 16)

Important:-

Example Find the complements of

a) 370
b) 66700

Solution

a) 3      7       0
          
    6      2        10
          
    6      3        0           ( 62 + 1 = 63 )

b)

       6      6    7     0

       3      3    2     10

         3      3     3     0        ( 332 + 1 = 333)

An easier way :

When the last digit or digits are zero, you may ignore them and apply Nikhilam to the remaining digits and write the ignored number of zeros to get the complement. For example :

a) Complement of 3370 ?
Complement of 337 is 663
Therefore, the complement of 3370 is 6630 Answer

b) Complement of 56800 ?
Complement of 568 is 432
Therefore, the complement of 56800 is 43200 Answer
 

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