Vedic Math (100)

Nikhilam is the sutra "all from 9 and the last from 10": numbers close to 100 are multiplied through their deviations from the base. 94×98: the deficits are 6 and 2. Left part — subtract the other number's deficit from either factor: 94−2=92 (or 98−6=92, the result is the same). Right part — the product of the deficits: 6×2=12. Answer: 9212. Above the base the deviations are added instead: 103×104 = (103+4) and 3×4 → 10712.

For base 100 the right part must occupy exactly two digits: in 98×99 the deficits are 2 and 1, so their product 2 is written as 02, giving 97|02 → 9702. The method is really the identity (100−a)(100−b) = 100(100−a−b) + ab — by applying it, a child is quietly doing genuine algebra.

• Age: 10+, with solid subtraction and multiplication.
• Common mistake: writing the right part with the wrong number of digits — 2 instead of 02.
• Practice tip: begin in the 91-99 range, where the deficits are small, before trying numbers above the base.