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