SUTRA:- The Sutra Ekanyunena Purvena comes as a sub-sutra to Nikhilam, which gives the meaning ‘ One less than the previous’ OR ‘One less than the one before’. This Sutra has limited applications and is applicable with a mandatory condition. i.e. a number (multiplicand/multiplier) to be multiplied consists of only 9s. For example- 999, 99999, 99999999 etc.
There are three possible cases with the above mentioned mandatory condition.
Case 1:- When the number of digits in both the numbers are same. Eg- 999
× 237
Case 2:- When the number of digits in one of the numbers is less than the number of 9s in the second number. Eg- 365 × 99999
Case 3:- When the number of digits in one of the numbers is more than the number of 9s in the second number. Eg- 48765 × 999
Case 1:- When the number of digits in both the numbers are same.
Example 1:- Multiply 2464 by 9999
Solution:- The answer will be obtained in two parts.
STEP 1:- The left part of the answer will be obtained by applying the Ekanyunena Purvena i. e by deducting 1 from the Multiplicand.
2464 -1 = 2463
STEP 2:- The right part of the answer will be obtained by subtracting the left part of the answer obtained in step 1 from the multiplier.
9999 – 2463 = 7536
Hence, 2464 × 9999 = 24637536
Answer – 24637536
Example 2:- Multiply 5684326 by 9999999
Solution:- The answer will be obtained in two parts.
STEP 1:- The left part of the answer will be obtained by applying the Ekanyunena Purvena i. e by deducting 1 from the Multiplicand.
5684326 -1 = 5684325
STEP 2:- The right part of the answer will be obtained by subtracting the left part of the answer obtained in step 1 from the multiplier.
9999999 – 5684325 = 4315674
Hence, 5684326 × 9999999 = 56843254315674
Answer – 56843254315674
Case 2:- When the number of digits in one of the numbers is less than the number of 9s in the second number.
Example 1:- Multiply 348 by 9999
Solution:- The answer will be obtained in two parts.
STEP 1:- The left part of the answer will be obtained by applying the Ekanyunena Purvena i. e by deducting 1 from the Multiplicand.
348 -1 = 347
STEP 2:- The right part of the answer will be obtained by subtracting the left part of the answer obtained in step 1 from the multiplier.
9999 – 347 = 9652
Hence, 348 × 9999 = 3479652
Example 2:- Multiply 2485 by 999999
Solution:- The answer will be obtained in two parts.
STEP 1:- The left part of the answer will be obtained by applying the Ekanyunena Purvena by deducting 1 from the Multiplicand.
2485 -1 = 2484
STEP 2:- The right part of the answer will be obtained by subtracting the left part of the answer obtained in step 1 from the multiplier.
999999 – 2484 = 997515
Hence, 2485 × 999999 = 2484997515
Case 3:- When the number of digits in one of the numbers is more than the number of 9s in the second number.
Example 1:- Multiply 268 by 99
Solution:- The answer will be obtained in two simple steps.
STEP 1:- Since there are two 9s in multiplier, we multiply the multiplicand by 100 (two zeroes here)
268 × 100 = 26800
STEP 2:- Now subtract the multiplicand from the product obtained in step 1.
26800 – 268 = 26532
Hence, 268 × 99 =26532
Example 2:- Multiply 848567 by 9999
Solution:- The answer will be obtained in two simple steps.
STEP 1:- Since there are four 9s in the multiplier, we multiply the multiplicand by 10000 (four zeroes here)
848567 × 10000 = 8485670000
STEP 2:- Now subtract the multiplicand from the product obtained in step 1.
8485670000 – 848567 = 8484821433
Hence, 848567 × 9999 = 8484821433
NOTE:- The same formula could be used to multiply any number with 9 or 99 or 999 or 9999 and so on.
HAPPY LEARNING…………………..