Multiply numbers near 10, 100 or 1000

From the sutra Nikhilaṃ Navataścaramaṃ Daśataḥ, All from 9 and the last from 10, in Bharati Krishna Tirtha's 1965 book Vedic Mathematics. Deep dive into the sutra

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First number Second number

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When to use it

Both numbers are close to the same power of ten: 97 × 94, 103 × 108, 996 × 989.

The idea

Write how far each number is from the base. Cross-subtract (or add) one distance from the other number for the left part. Multiply the distances for the right part.

Worked example: 97 × 94

1. 97 −3
   94 −6Base 100. 97 is −3 from it and 94 is −6.
2. 91 | Left part: cross 97 with −6: 97 − 6 = 91. (94 − 3 gives the same.)
3. 91 | 18Right part: multiply the distances: −3 × −6 = 18. It gets 2 digits because the base has 2 zeros.
4. 9118So 97 × 94 = 9118.

Practice this trick

All 15 speed tricks, each with its calculator. The speed tricks use sutras from Bharati Krishna Tirtha's 1965 book Vedic Mathematics; the lessons, problems and pictures here are our own.