Paraavartya Yojayet:

*Transpose and adjust*
Paraavartya Yojayet is the fourth

sutra of

Vedic mathematics. Its corollary is

Kevalaih Saptakam Gunyat.

This method is related to the

Chinese remainder theorem and the

Horner's rule of

synthetic division, but arguably has even more applications.

What follows is a

*brief* and

*incomplete* summary of the math shortcuts this sutra contains:

**Divisor is more than one digit and ***slightly higher* than a power of 10
*Example: 12345 divided by 12*
Subtract the divisor (12) from the nearest power of ten: 10 - 12 =

**-2**
We will need to keep

**-2** in mind for the next steps.

Separate the last digit (5) from the preceeding digits (1234). The last digit will be used later to calculate the

remainder, while the preceeding digits will be used to calculate the

quotient.

The first digit of the

dividend will be the same (in most cases) as the first digit of the quotient, so for now we will assume it is. So the quotient we have so far is

**1xxx**
Multiply this first digit of the quotient (1) by

**-2**. 1 x -2 = -2

Add that number to the second digit of 1234: -2 + 2 =

**0**
So the quotient we have now is

**10xx**
Multiply this second digit of the quotient (0) by -2. That equals 0. Add that number to the third digit of 1234. That equals

**3**
So the quotient we have now is

**103x**
Multiply this third digit of the quotient (3) by -2. This equals -6. Add this number to the fourth digit of 1234. -6 + 4 =

**-2**
Since this is a negative number, we will write the quotient as 1030 and then add this negative number: 1030 + -2 =

**1028**. This is the quotient.

Now let's return to the last digit of the dividend that we set aside: 5

Multiply the last digit of the quotient by -2.

*Important Note:* always use the first number we arrived at before adding the negative number to 1030:

**-2**
-2 x -2 = 4

Add this to 5

4 + 5 =

**9**
Thus, the quotient is 1028 and the remainder is 9.

This method can also be used for numbers

*slightly higher than* 100, 1000, etc.

For a more detailed explaination of Paravartya - Yojayet, see:

http://www.vedamu.org/Mathematics/MathematicalFormulae/Sutras/Paravartyayogayet.asp
**Applications in algebra**
This sutra can be used to simplify algebraic equations. For information on that method visit the link above or 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