Multiplication Techniques Using Vedic Maths Part 1

There is no change when any number is multiplied by 1.When we multiply one number by another then it is increased and becomes further away from one. When 4 is multiplies by 5 it becomes 20 which is further away from 4 and 5. Using our multiplication techniques, we relate each number very close to another number called base. The difference between the number and the base is termed as deviation. Deviation may be positive or negative. Positive deviation is written without the positive sign and the negative deviation, is written using a bar or negative sign on the number

A - Multiplication by using base 10

Let N1 and N2 be two numbers near to a given base in powers of 10, and D1 and D2 are their respective deviations from the base. Then N1 X N2 can be represented as

This is the formula = (N1+D2) or (N2+D1) / D1 x D2

Example 1:      Multiply 7 by 8. base number as 10. Here we compare this multiplication with the formula N1 = 7 , N2 = 8 and Deviation D1 = -3 & D2 = -2 

7 -3

8 -2

(7+(-2)) or (8+(-3)) / 3 x 2 =56

B - Multiplication by using base 100

Formula is same like part or section A but base are changed

Example 2:    Multiply 98 by 97

Compare this multiplication with the formula N1 = 98 , N2 = 97 and Deviation D1 = -02 & D2 = -03 Since the base is 100 than D1 x D2 = 06

98 -02 

97 -03 

(98+(-03)) or (97+(-02)) / 03 x 02 = 9506

Example3 :    Multiply 75 by 95

Compare this multiplication with the formula N1 = 75 , N2 = 95 and Deviation D1 = -25 & D2 = -05. Since the base is 100 than D1xD2 = 125 written 25 & 1 carry to left

75 -25

 95 -05

(75+(-05)) or (95+(-25)) / 25 x 05 = 70/125

C - Multiplication by using base 1000

Example 3:    Multiply 786 by 998

Compare multiplication with the formula N1 = 786 , N2 = 998 & Deviation D1 = -214 & D2 = -002

786 -214

998 -002

(786+(-002)) or (998+(-214)) / 214 x 002 = 784/428 = 784428

D - Multiplication whose first figure are same And whose last figure add up to 10, 100 ,1000 etc.

Example.1 : Find 43 X 47

Check for  R.H.S :  3 + 7 = 10,  L.H.S. portion remains the same i.e.,, 4.

Multiply 4 ( the same figure in both the numbers ) by the next number up 5. This gives 4 X 5 = 20 as the first part of the answer and the last part is 3 X 7 = 21 so the answer is 2021

4 3

4 7

4 X 5 / 3 X 7  =  2021

Example.3 : Find 127 X 123     

Check for : 7 + 3 = 10, L.H.S. portion remains the same

12 7

12 3

12 X 13 / 7 X 3 = 15621

E - Numbers of which the last 2 or 3 or 4 digits added up gives 100, 1000, 10000 etc.

The same rule works when the sum of the last 2, last 3, last 4 digits added respectively equal to 100, 1000, 10000

Example.1 : Find 292 X 208 

Here 92 + 08 = 100, L.H.S portion is same i.e. 2

2 92

2 08

2 X 3 / 92 X 08 = 60/736

Example.2 : Find 693 X 607

Check for : 93 + 07 = 100, L.H.S. portion remains the same i.e., 6

6 93

6 07

420651

Now R.H.S product 93 X 07 can be obtained mentally. 693 x 607 = 6 x 7 / 93 x 07 = 420 / 651 (for 100 raise the L.H.S. product by 0 i.e. 42 X 10) = 420651.

F - Multiplication by using other base

Example.1 : Find 213 X 203     [Base is 200 ]

Complement of 213 is 13  Complement of 203 is 03.

213 / 13

203 / 03

213+3 / 39 = 216 x 2 / 39 

since the base is 200 i e 2 X 100.  The numbers are close to 200 which is 100 X 2 we multiply only the left hand part of the answer by 2 to get 43239.

G - Numbers are close to different bases 10,000, 100 etc..

Example.6 : Find 9998 X 94

Numbers are close to different bases 10,000 and 100

9998 / 02  [Base 10000]

94    / - 06[Base 100]   

9398 /   12   =  939812

Note that 6 is not subtracted from 8, but from the 9 above the 4 in 94  Second column from left. So 9998 becomes 9398.Right hand side will as lower base 100.