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By one less than the previous one
Ekanyunena Purvena
This sutra means 'by one less than the previous one' and is used to multiply any number by 9, 99, 999, etc. The method: subtract 1 from the multiplicand for the left part, then find the complement from 9 (or 99, etc.) for the right part.
How It Works
- 1.To multiply N by 9: left part = N − 1. Right part = 9 − (N − 1) = 10 − N.
- 2.To multiply N by 99: left part = N − 1. Right part = 99 − (N − 1) = 100 − N.
- 3.Concatenate the two parts.
- 4.Example: 78 × 99 → left = 77, right = 100 − 78 = 22 → 7722.
- 5.This works because N × (10ⁿ − 1) = N × 10ⁿ − N.
Examples
7 × 9
Step 1 / 4
Multiply 7 × 9. The multiplier is all 9s, so use Ekanyunena.
Number7
Multiplier9
Try It Yourself
67 × 99