Ekanyunena Purvena:

*By one less than the previous one*
Ekanyunena Purvena is the fourteenth

sutra of

Vedic mathematics. Its corollary is

Dhvajanka. It shares some similarities with the first sutra,

Ekadhikina Purvena, and the twelfth sutra,

Shesanyankena Charamena, although the first and twelfth sutras hold far more practical applications than Ekanyunena Purvena.

This sutra is used when multiplying any number by a number consisting only of nines, such as 9, 99, 999, 9999, etc.

For the smaller numbers consisting of nines, it is usually easier to just round the number up to the nearest power of ten, add that many zeroes to the other number, than subtract the other number. ie. 9 x 5,000 = (10 x 5,000) - 5,000 = 45,000

For the larger numbers consisting of nines, this sutra

*might* save time.

**Example: 9999 x 1016**
The left hand side of the answer will be found by subtracting 1 from 1016, which is

**1015**
The right hand side of the answer will be found by subtracting the bolded number in the previous step (1015) from the number consisting of nines: 9999 - 1015 =

**8984**
Thus, 9999 x 1016 = 10,158,984

**Ekanyunena Purvena can also be used in some problems that call for converting certain fractions to decimals** This will not arrive at every possible decimal point in every case.

*Example: Fractions for which the denominator is 7*
See

Kevalaih Saptakam Gunyat.

*Example: Fractions for which the denominator is 13*
To solve this, we use

*Kalau Kshudasasaih*: "For 13 the multiplicand is 077"

We would solve for 1/13 as follows:

We multiply the

multiplicand (077) by 999. We use 999 because it has the same number of digits as our multiplicand and consists only of nines

077 x 999 =

**076923**
Multiply that number by the

numerator: 1 x 076923 = 076923

Place a decimal point at the beginning: 0.076923

Thus, 1/13 = 0.076923

*Example: Fractions for which the denominator is 17*
To solve this, we use

*Kamse Kshaamadaaha-khalairmalaih*: "For 17 the multiplicand is 05882353" (The

literal translation is "In king Kamsa's reign famine and unhygenic conditions prevailed.")

We would solve for 1/17 as follows:

We multiply the multiplicand (05882353) by 99999999. We use 99999999 because it has the same number of digits as our multiplicand and consists only of nines

05882353 x 99999999 =

**0588235294117647**
Multiply that number by the

numerator: 1 x 0588235294117647 = 0588235294117647

Place a decimal point at the beginning: 0.0588235294117647

Thus, 1/17 = 0.0588235294117647

To learn more about this sutra, check out the resources below:

**RESOURCES:**

*Vedic Mathematics* by Sri Bharati Krisna Tirthaji

http://www.vedamu.org/Mathematics/course.asp

http://www.sanalnair.org/articles/vedmath/intro.htm

http://www.vedicganita.org/ganitsutras.htm

http://hinduism.about.com/library/weekly/aa062901a.htm

http://www.vedicmaths.org/

http://www.hinduism.co.za/vedic.htm

*Mathemagics* by Arthur Benjamin and Michael B. Shermer

http://en.wikipedia.org/wiki/Vedic_math

http://www.tifr.res.in/~vahia/dani-vmsm.pdf

http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html