This type of multiplication can be done accurately and faster by using the VEDIC SUTRA “Antyayoreva“. It means “only the last two digits”. In this sutra every time we add last two digits. We actually do not perform multiplication here. Let’s take an example to understand it.
Example 1: – Find the product of 3475 and 11 (3475 × 11).
Solution: –
STEP 1:- Put one zero on either side of the number.
034750 (Now this new number will be considered for further calculation)
STEP 2: – As per the Vedic Sutra ”Antyayoreva” , keep on adding only the last two digits of the new number every time, until all the digits are used (including zero).
0 + 5 = 5 (Last two digits added) –
Number to be written – 5
STEP 3: – 5 + 7 = 12 (Next last two digits added)
(Here only 2 will be considered and 1 will be carry forwarded to next step)
Now write 2 in the left of 5 (obtained in the previous step)
Now number is 25
STEP 4: – 4 + 7 = 11 (Next last two digits added)
11 + 1 = 12
( Here, 1 is carry forwarded and added to 11. Number to be considered is now 12. 2 will be written and 1 will be again carry forwarded.)
Write 2 in the left of 25 (obtained in the previous step)
Number is 225
STEP 5: – 3 + 4 = 7 (Next last two digits added)
7 + 1 = 8 (1 is carry forwarded and added to 7)
Write 8 in the left of 225 (obtained in previous step)
Now the number is 8225
STEP 6 : – 0 + 3 = 3 (Finally rest of the two digits added)
Write 3 in the left of 8225 (obtained in previous step)
Now the number is 38225.
Ans: – 3475 × 11 = 38225