Fascinating technique

If you want to multiply any number with 9, 99, 999, so on

Consider the following examples
Example 1
99 X 42 = 4158

Procedure
Step 1 Subtract 1 from 42, we get 41
Step 2 Now, Subtract 41 from 99, we get 58

Answer is 4158

Example 2
999x343=342657

Procedure
Step 1 343 – 1 = 342
Step 2 9-3 = 6, 9-4 = 5, 9-2 = 7

Answer is 342657

Sutra 1

This means "By one more than the previous one"
I am sharing one example where this sutra is applied.
Finding the square of a number ending with 5.
65^2
= [6 X (6+1)] 25 = 4225
For this number , the last digit is 5 and the 'previous' digit is 6. Hence, 'one more than the previous one', that is, 6+1=7.
The Sutra, in this context, gives the procedure 'to multiply the previous digit 6 by one more than itself, that is, by 7'. It becomes the L.H.S of the result, that is, 6 X 7 = 42. The R.H.S of the result 25.

85^2
= [8 X (8+1)] 25 = 7225
For this number , the last digit is 5 and the 'previous' digit is 8. Hence, 'one more than the previous one', that is, 8+1=9. The Sutra, in this context, gives the procedure 'to multiply the previous digit 8 by one more than itself, that is, by 9'. It becomes the L.H.S of the result, that is, 8 X 9 = 72. The R.H.S of the result 25.

Vedic Mathematics

Vedic Mathematics is the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krisna Tirthaji (1884-1960). According to his research all of mathematics is based on sixteen Sutras or word-formulae.