Ekanyunena Purvena

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'. Ekanyunena Sutra is useful in Recurring Decimals.

For instance: 43 × 9.

Divide the multiplicand off by a vertical line into a right hand portion consisting of as many digits as the multiplier; and subtract from the multiplicand one more than the whole excess portion on the left. This gives us the left hand side portion of the product or take the Ekanyuna and subtract it from the previous i.e. the excess portion on the left and subtract the right hand side part of the multiplicand by the Nikhilam rule. This will give you the right hand side of the product 43 × 9 4 : 3 :–5 : 3 3 : 8 : 7

This Ekanyuna Sutra can be utilized for the purpose of postulating mental one-line answers to the question.

The Sutra signifies numbers of which the last digits added up give 10. i.e. The Sutra works in multiplication of numbers

For example: 25 and 25, 47 and 43, 62 and 68, 116 and 114. Note that in each case the sum of the last digit of first number to the last digit of second number is 10. Further the portion of digits or numbers left wards to the last digits remain the same. At that instant use Ekadhikena on left hand side digits. Multiplication of the last digits gives the right hand part of the answer.

Example 2 : 47 X 43

See the end digits sum 7 + 3 = 10 ; then by the Sutras Antyayor Dasakepi and Ekadhikena we have the answer, 47 x 43 = ( 4 + 1 ) x 4/ 7 x 3 = 20 / 21 = 2021.