Vedic Math: Multiplication of numbers nearer to bases like 10,100,1000 etc

Difference between the number and the base is called the deviation. For example, if the number is 15, the deviation is (15 – 10) = +5 or simply 5. For the number 6 the deviation is (6 – 10) = -4.

Lets take a very simple multiplication ( 7 x 8 ) = 56.

Step 1: Write the numbers and their deviations from the base 10 which is the nearest base for both,

7 -3

8 -2
_____

Step 2: Now add any number with the deviation of the other.
In this case you can add 7 with -2 which will give 5 or,
add 8 with -3 to get 5. Note that in both case there should be the same result.

Write the result like this,

7 -3

8 -2
_____
5/

Step 3: Now multiply the two deviations which are -3 and -2 in this case.
The product is +6
Write the product as,

7 -3

8 -2
_____
5 /6

Hence the result is 5/6 or simply 56.

Now Lets work on a slightly more complicated problem.
( 94 x 108 )

Take the base 100.

94 -6

108 8
_______

Now the Left hand side will be ( 94 + 8 ) or (108 – 6) which is 102

So,

94 -6

108 8
_______
102/

Now the product of the deviation in this case is ( -6 x 8 ) = -48 which is negative.
Remember that we have chosen the base as 100.

94 -6

108 8
________
102/-48

Multiply the right hand side result with the base and subtract 48 to get the result.

102 X 100 = 10200
10200 – 48 =10152

Hence the result is 10152. (We have actually done the same thing in the first example which is, 5 x 10 + 6 = 56)

Now take another example (16 x 13) = 208. Here we take 10 as the base.

16 6

13 3
______
19/18

Here if you add 18 with the right hand side result, the multiplication will be a mess.
Remember we have taken 10 as the base and look at the deviations each of which has one digit. So you must put 8 in the right hand side and carry 1.

16 6

13 3
______
19/18

Now add the carry to the right hand side result to get (19 + 1) = 20.

16 6

13 3
______
20 /8

Hence the result is 20/8 or simply 208.

Exercise: Verify the results

1. 1003 x 997 (Take 1000 as base)
2. 97 x 89 (Take 100 as base)

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