Ekādhikena Pūrvena, ("By one more than the previous one") This sūtra means that the prescribed arithmetical operation is either multiplication or division. Both are implied since we may proceed leftward and multiply (and carry-over the excess value to the next leftward column) or we may go rightward and divide (while prefixing the remainder). When dividing by a nine's family denominator, the digit to the left of the nine (previous) is increased by one to obtain the multiplier.
.Examples:
(Proof) This is a simple application of
when 
and 
, i.e.
It can also be applied in multiplications when the last digit is not 5 but the sum of the last digits is the base (10) and the previous parts are the same. Examples:
twice combined with the previous result to produce:
We illustrate this sūtra by its application to conversion of fractions into their equivalent decimal form. Consider fraction 1/19. Using this formula, this can be converted into a decimal form in a single step. This can be done by applying the formula for either a multiplication or division operation, thus yielding two methods.
.Examples:
- 35×35 = ((3×3)+3),25 = 12,25 and 125×125 = ((12×12)+12),25 = 156,25
- 35×35 = ((3×4),25 = 12,25 and 125×125 = ((12×13),25 = 156,25
(Proof) This is a simple application of
when and , i.e.
It can also be applied in multiplications when the last digit is not 5 but the sum of the last digits is the base (10) and the previous parts are the same. Examples:
- 37 × 33 = (3 × 4),7 × 3 = 12,21
- 29 × 21 = (2 × 3),9 × 1 = 6,09 ?
twice combined with the previous result to produce:- .
We illustrate this sūtra by its application to conversion of fractions into their equivalent decimal form. Consider fraction 1/19. Using this formula, this can be converted into a decimal form in a single step. This can be done by applying the formula for either a multiplication or division operation, thus yielding two methods.