 # Multiplication using the Nikhilam Sutra -Vedic Maths

Vedic Maths, as I have said in my last post is a boon for Math Lovers. Multiplication plays an important role from the elementary class to college to our day to day life.We know that without the 14 sutras ,Vedic Math  wont exists.In fact,the fourteen sutras are  the life line of Vedic system of Mathematics.Now,I am going to explain a simple process of Multiplication using one of the sutra named ” The Nikhilam Sutra – All from 9 and last from 10″.

Example 1:
605 x 504 = ?

The nearest base for the above two numbers are 500.So we fix this 500 as our base.Now,see that the above both numbers are greater than the base

How much deficient are are the above numbers are from base ?

605 -500 = +105
504 -500 = +004

Next,align as follows,

605  + 105
504  + 004
—————-
L.H.S 609  |  ( + 420) R.H.S  —> [the RHS is got by adding diagonally on any one side ,the LHS is the result of multiplying the deficiencies .]
(609 /2) | (+420) since we have fixed base 500 and 500 is half of 1000 .i.e;1000/2 = 500.
304.5 +  420
304.5 | 420
Now see that the L.H.S has a decimal point ,so carry out that half to the R.H.S side from L.H.S .Now R..H.S side becomes 420 +500 =920

304 | 920
Therefore ,605 x 504 = 304920

Example 2
485 x 475 = ?

The nearest base for the above two numbers are 500.So we fix this 500 as our base.Now, see that the above both numbers are less than the base.

How much deficient are are the above numbers are from base ?

485 -500 = -015
475 -500 = -025

485 – 015
475-  025
————–

460 | ( +375) –>the RHS is got by adding diagonally on any one side ,the LHS is the result of multiplying the deficiencies .
230 | 375  —- (Half of 460 is 230)
230 | 375
Therefore 485 x 475 = 230375
Example 3
614 x 495 =?.

The nearest base for the above two numbers are 500.So we fix this 500 as our base.Now, see that the above numbers .One is greater than the base and one is less than the base.

How much deficient are are the above numbers are from base ?

614 – 500 = +114
495 – 500 = -005

614 + 114
495 – 005
————

609 | (-570)—>–>the RHS is got by adding diagonally on any one side ,the LHS is the result of multiplying the deficiencies .
(609 /2) | (-570)
304.5 | (-570) —– > the minus sign is removed by 1000 -570 =430 and remove one from the L.H.S side
303.5 | 430
303| (430+500) —-> the 0.5 when carried to R.H.S, becomes 500 and add it to R.H.S
303| 930

Therefore ,614 x 495= 303930

Note :The above three methods are general rule.When the multipliers are both above or greater we dont have any problems.But when one is greater and one is lesser,we follow the rules in example 3.For all ,the same rules apply.

• The (0.5) on L.H.S is carried as 500 and added to the R.H.S every time you fall into a decimal (1/2).
• The Minus signs resulting on R.H.S is removed by adding 1000 to it.
The theory behind the above rules is beyond my time here on this post.Kindly refer Bharati Krishna Tirtha Vedic Math
Arithmetic Mutiplications becomes very easy if you understand the sutras and the modus operandi involved in these sutras.Yet another popular method of multiplication is by Urdhva-Tiragbhyaam Sutra which uses ‘Vertically and Crosswise’ as its modus operandi.

Try these at home and put them in the comments below with the simple steps as above.
1. 510 x 610
2. 390 x 485
3. 460 x 680