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.

📜 History Corner

Anurupyena comes from the Sanskrit word for "proportionality" or "similarity". Ancient mathematicians realized that if you can't solve a problem directly, you can solve a similar, easier problem (like using base 50 instead of 100) and then adjust the result proportionally.

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.

Example: Multiply 46 × 48

These numbers are close to 50. We can treat 50 as 100 ÷ 2.

Working Base: 50 (100 ÷ 2)

- 4

- 2

Cross-Subtract: 46 - 2 = 44

Adjust (÷ 2): 44 ÷ 2 = 22

Multiply Deviations: -4 × -2 = 08

2208

Find Deviations: Base 50. 46 is -4, 48 is -2.
Right Side: (-4) × (-2) = 08.
Left Side (Raw): 46 - 2 = 44.
Adjust Left Side: Since 50 is 100/2, we divide 44 by 2 to get 22.
Combine: 22 and 08 gives 2208.

🔬The Proportionality Lab

Enter two 2-digit numbers that are close to each other (like 46 and 48) to see the method work!

🎓Graduation Quiz!

Get 20 practice problems with answer key

Frequently Asked Questions

What if my numbers are close to 50, not 100?

You use the Anurupyena (Proportionality) Sutra. Treat 50 as 100/2. Perform the calculation using base 100, then divide your final left-hand side by 2.

Can I use this for numbers near 200 or 500?

Yes. For 200, you multiply the left side by 2. For 500, you multiply by 5 (or divide by 2 if treating as 1000/2).

Interactive Practice Lab & Online Test