"Vedic mathematics" gained popularity primarily through the work of late
Sankaracharya (Bharti Krisna Tirtha) of Puri (1884 -1960). Swamiji's "Vedic
Mathematics" and the practical demonstrations of *Sixteen Sutras (120 words!)*
stunned the world with their originality and simplicity. The four Vedas
(Rigveda, Samaveda, Yajuraveda, Atharvaveda), the four Upvedas, six Vedangas and
numerous commentaries on them over the centuries are storehouse of great
knowledge. However, many scholars dispute that these Sutras are found in Vedas.

Here we shall describe only one Sutra out of sixteen -the general formula for
multiplication. After learning this, you will never take out calculators for multiplication.

**URDHVA-TIRYAK SUTRA**

This sutra says -**"Vertically and Crosswise".** That's all to multiply
two numbers!

Till now, you were multiplying like this:

*Question*: Multiply 432 by 617.

*Answer*:

432

__ x 617
__ 3024

432

__2592__

__266544__

More the number of digits in the numbers, more lines and time you consume. No more! Using the Sutra "Vertically and Crosswise", you have

Step 1 (mentally, don't write on notebook) : vertically (last digits) :

2x7=14; write 4 carry 1

Step 2 (mentally) : crosswise (last two digits) :

3x7 +2x1 = 23 +carry 1 = 24; write 4 carry 2

Step 3 : vertically and crosswise (three digits) :

4x7 + 3x1 +2x6 = 43 +carry 2 = 45; write 5 carry 4

Step 4 : (move left; first two digits) :

4x1 +3x6 = 22 +carry 4 = 26; write 6 carry 2

Step 5 : (move left; first digit of each number) :

4x6 = 24 +carry 2 = 26. End.

Write answer : 266544

This is how it appears on notebook :

432

__x 617__

__266544__

No matter how big the numbers are, you will need to write only the final answer. All other steps are easily carried out mentally. If the two numbers have different number of digits, write smaller number below the other and pad it on left side with zeros. The

*theory*behind above example is :

*ax² +bx +c*

adx

Observe that coefficient of

__dx__²__+ex +f__adx

^{4}+(ae+bd)x³ +(af+be+cd)x² +(bf+ce)x +cf*x*is

^{0}(units digit)*cf*, which is obtained by multiplying last two coefficients (vertically). The coefficient of

*x*(tens digit) is

^{1}*bf+ce,*which is obtained by crosswise multiplication of last two coefficients. The coefficient of

*x²*(hundreds digit) is

*af+be+cd,*which is obtained by crosswise and vertical multiplication of last three coefficients. Now as all coefficients are used up, we leave last coefficients and use the remaining, and so on.

Here are a few more examples:

*Multiply 92 by 67*

92

__x 67__

(Mentally) 2x7 is 14; write 4 carry 1;

9x7 +2x6 = 75 +carry 1 = 76; write 6, carry 7

9x6 is 54, add carry 7 to get 61 -so

*answer is 6164*

*Multiply 2376 by 4060*

2376

__x 4060__

6x0 = 0; write 0;

7x0 +6x6 = 36; write 6 carry 3;

3x0 +7x6 +6x0 = 42 +carry 3 = 45; write 5 carry 4

2x0 +3x6 +7x0 +6x4 = 42 +carry 4 = 46; write 6 carry 4

2x6 +3x0 +7x4 = 40 +carry 4 = 44; write 4 carry 4

2x0 +3x4 = 12 +carry 4 = 16; write 6 carry 1

2x4 = 8 +carry 1 = 9; write 9. End.

*Answer is 9646560*

Note that all the calculations can be easily done in mind; you just go on writing a digit of answer one at a time (from right to left). So on notebook you will just write:

2376

__x 4060__

__9646560__

Please do the following multiplications by Sutra "Vertically and Crosswise" :

32 x 54?

50 x 98?

123 x 987?

654 x 84?

749 x 302?

3112 x 8735?

3022 x 7004?

This is just a "trailer" from Vedic Mathematics. If you found it useful or interesting (or both), we strongly recommend the book "Vedic Mathematics" by late Sankaracharya (Bharti Krisna Tirtha) of Puri. This book is published by Motilal Banarsidass Publishers. You may also contact APC Books, New Delhi.