"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.
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. Thetheory behind above example is :
ax² +bx +c dx ² +ex +f adx4 +(ae+bd)x³ +(af+be+cd)x² +(bf+ce)x +cf
Observe that coefficient of x0 (units digit) is cf, which is obtained by multiplying last two coefficients (vertically). The coefficient of x1 (tens digit) is 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 6164
(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?
- Will add more in the Future***