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Nikhilam or Base Multiplication

As I was working on my presentation “Nikhilam or Base Multiplication” for tomorrow’s Session 3 of the Vedic Math Webinars, Series #2, I received this link from Manny Nadela, a UP Tau Rho Xi Fraternity Brother and also an Area Facilitator for Metro Cebu in the 2nd Philippine National Vedic Mathematics Olympiad:

This video show that compared to the conventional method, the Vedic Math Base Multiplication is simpler, much faster, and less prone to mistakes.

While many were quick to dismiss it as a “trick” like other Vedic Math Techniques, there are plenty of Algebraic and geometric proofs to show its derivation. (Some of these proofs can be found in pp 61, 63 and 68 of my book “25 Math Short Cuts”.)

It got its name, “Nikhilam” Multiplication from the Vedic Math Sutra or word formula “Nikhilam Navatashcaramam Dasahtaha” meaning “All from 9 and the Last from 10” which is used to quickly determine how far a number is from a higher power of multiple of 10.

This method is most useful with multiplicands having large digits like 96, 997 or 8,889. This implies that their differences from the next “bases” or higher powers of 10, are small (4, 3 or 1,111 respectively). Using differences or “deficiencies” as they are referred to in Vedic Math, will make calculations definitely easier.

Aside from multiplying numbers below bases, like 98 x 94, this technique can also be applied for numbers above the base like 106 x 108, which is the example used in the video and for one number above and one number below a base like 1321 x 997.

In our Session 3, we will apply the same principles to numbers having different bases like 9788 x 98, bases other than multiples of 10 like 321 x 302 and to numbers with decimals like 98 x 0.0097.

All sessions are recorded and uploaded in our site so that they can be viewed anytime, anywhere.

Fee is P250 per session or P1,500 for the whole series of 8 sessions.

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