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