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Vedic Multiplication
Welcome to Vedic Multiplication, one of the fastest ways to multiply!
1.Multiplication of two 2-digit numbers
Here, a, b, c, and d are face values of of the 2-digit numbers.
So if ab is the first number and cd is the other, the answer to this will be a*c | (a*d) + (b*c) | b*d
We can then put the values in and get the answer using the balancing rule. If you do not know what the Balancing rule is, please do click here and read it.
Example - 23 * 45
Here, a = 2, b = 3, c = 4 and d = 5.
Therefore, 23 * 45 = 2 * 4 | (2 * 5) + (3 * 4) | 3 * 5
= 08 | 22 | 15
Now, using the balancing rule, we get the answer to be 1035.
* Please note that when the '*' sign is used, Multiplication is to be done
2. 2-digits multiplied by 3-digits
This time, instead of the 4 variables, we need 5 variables. They will be a, b, c, d, e.
ab is the 2-digit number, while cde is the 3-digit number.
The answer to this is: a*c | (a*d) + (b*c) | (b*d) + (a*e) | b*e
and then, of course, the balancing rule.
Example - 174 * 51
Here, a = 5, b = 1, c = 1, d = 7 and e = 4.
Now, we can use the formula above, which gives us-
5 * 1 | (5 * 7) + (1 * 1) | (7 * 1) + (5 * 4) | 4 * 1
= 05 | 36 | 27 | 04
We get 8874 as the answer using the balancing rule.
3. 3-digit number * 3-digit number
We need 6 variables, namely a, b, c, d, e, f this time.
Let abc be the first number and def be the second number.
Formula : a*d | (d*b) + (a*e) | (d*c) + (a*f) + (e*b) | (e*c) + (f*b) | f*c
Then, Balancing rule to get the answer.
Example - 351 * 426
Here, a = 3, b = 5, c = 1, d = 4, e = 2, f = 6
The formula gives us-
3 * 4 | (4 * 5) + (3 * 2) | (4 * 1) + (6 * 3) + (2 * 5) | (2 * 1) + (6 * 5) | 6 * 1
= 12 | 26 | 32 | 32 | 06
= 149526
Tip - Write the 2 numbers which you want to multiply on a paper (one below the other), and observe the formulae given above. Notice patterns to make memorization easy. The sutra being used here is 'Vertically and Crosswise'.
4. 4-digit number * 4-digit number
Here, we will use 8 variables to solve the problem, a , b, c, d, e, f, g, h.
If the 2 numbers were abcd and efgh, then the formula is-
a*e | (a*f) + (e*b) | (b*f) + (a*g) + (c*e) | (a*h) + (d*e) + (b*g) + (c*f) | (b*h) + (d*f) + (c*g) | (c*h) + (g*d) | d*h and then the balancing rule
Example - 4312 * 2654
a = 4, b = 3, c = 1, d = 2, e = 2, f = 6, g = 5 and h = 4.
Using the formula, we have-
4*2 | (4*6) + (3*2) | (3*6) + (4*5) + (2*1) | (4*4) + (2*2) + (3*5) + (1*6) | (3*4) + (2*6) + (1*5) | (1*4) + (5*2) | 2*4
= 08 | 30 | 40 | 41 | 29 | 14 | 08
= 11444048
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