Antyayor Dasakepi:
Whose last digits together total 10 and whose previous part is exactly the same
Antyayor Dasakepi is the corollary to
Puranapuranabyham, the eighth
sutra of
Vedic mathematics.
What follows is a
brief and
incomplete summary of the math shortcuts this corollary contains:
Multiplying two numbers when the last digit of each adds up to 10, and the first digit(s) of each is the same Such as 43 x 47, 51 x 59, 94 x 96, etc.
Example #1: 61 x 69
Multiply the last digit of each number: 1 x 9 = 9
Multiply the first digit of each number
but add a 1 to one of them: (6 + 1) x 6 = 42
To this number, add the 2 zeros we dropped in the previous step: 4200
Add to this number the result in the first step: 4200 + 9 = 4209
Thus, 61 x 69 =
4209
Example #2: 114 x 116
Multiply the last digit of each number: 4 x 6 = 24
Multiply the first digits of each number but add a 1 to one of them: (11 + 1) x 11 = 132 (Note: you can use the
Trachtenberg system to quickly multiply any number by 11)
Add to this number the 2 zeroes we dropped: 13200
Add to this number the result in the first step: 13200 + 24 =
13224
Multiplying two numbers when the last 2 digits of each adds up to 100 and the first digit(s) of each is the same
Example: 689 x 611
Multiply the last two digits of each number: 89 x 11 = 979 (Note: you can use the
Trachtenberg system to quickly multiply any number by 11)
Multiply the first digit of each number but add a 1 to one of them: (6 + 1) x 6 = 42
Add to this number the 4 zeroes we dropped: 420000
Add to this number the result in the first step: 420000 + 979 =
420979
This sutra is similar to
Ekadhikina Purvena in that it can be used to square numbers ending in 5. This sutra can also be applied when the last 3 digits add up to 1000, the last 4 digits add up to 10000, etc. To learn more about Antyayor Dasakepi, 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