Anurupyena Sutra

What if you want to multiply numbers that aren't close to 100 or 1000? The Anurupyena Sutra, meaning "Proportionally," is the perfect tool. It lets us pick a convenient "working base" to make our calculations super easy.

The "Proportionality" Rule ⚖️

This method extends the Nikhilam (base) method. We pick a multiple of 10 close to our numbers and then adjust our answer at the end.

Let's Multiply 42 × 43

These numbers are close to 40, so our working base is 40.

1. Find Surpluses: How far are the numbers from 40? 42 is +2 and 43 is +3.
2. Right Side of Answer: Multiply surpluses: 2 × 3 = 6.
3. Left Side of Answer: Add crosswise (42 + 3 = 45). Then, multiply by the working base's first digit (4). So, 45 × 4 = 180.
4. Combine: The left part is 180, right part is 6. The answer is 1806.