It would good be if reader is aware of both the article. After learning this method you can easily do
1. 1234 x 99
2. 2343 x 999
3. 63164 x 9999 and so on...
Note this method is applied to numbers in which 99... has lesser number of digits when compared to other number. Other variation are already covered before.
Vedic Method is as follows.
1. Two part method is used with slight variation.
2. First part calculation is as before, where 1 is subtracted from the number.
3. Only as many digits in 99.. is used to find the 10's complement.
4. Remaining most significant digits are carried directly.
5. Both parts are written in overlap fashion.
6. Overlap region has as many digit as the difference of digits in the number.
7. Overlap region is subtracted to get final answer
Example will explain the method in better way. Lets calculate 2343 x 999
Mathematical proof is as follows
xyz * 99
xyz can be value can be written as x * 100 + y * 10 + z * 1
= (100x + 10y + z) * 99
= (100x + 10y + z) * (100 - 1)
= 10000x + 1000y + 100z - 100x - 10y - z
= 10000x + 1000y + 100(z - x) - 10y - z
= 10000x + 1000y + 100(z - x - 1) + 100 - 10y - z
= 10000x + 1000y + 100(z - x - 1) + (100 - yz)
= 100(100x + 10y) + (z - x - 1) + (100 - yz)
= 1 st part + overlap + 10's complement of yz
This method applies to number as big as 12345678 * 999.
Links
Next Article - Vedic Maths #05: Navashesha - remainder of 9
Previous Article - Vedic Maths #03: Multiplication by 999.... [with greater number of digits]
All Articles - Vedic Maths
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