Paravartya Yojayet Sutra

Let's dive into division with the elegant sutra: "Paravartya Yojayet," which means "Transpose and Apply." This is a fantastic method for dividing numbers when your divisor is slightly bigger than a base like 10, 100, or 1000.

The "Transpose and Apply" Rule 🔄

Instead of complex division, we turn the problem into simple multiplication and addition! The key is to find how much "bigger" our divisor is than its base and then use the negative of that number.

Example: 1234 ÷ 112

Divisor is 112 (Base 100). Deviation is +12. Transpose it to -1, -2.

1. Setup: Write 1234. Separate last 2 digits (34) because base 100 has 2 zeros.
2. First Digit: Bring down 1. Multiply by -1, -2. Write under 2 and 3.
3. Second Digit: 2 + (-1) = 1. Multiply this 1 by -1, -2. Write under 3 and 4.
4. Add Columns:
   • 3 + (-2) + (-1) = 0
   • 4 + (-2) = 2
5. Answer: Quotient 11, Remainder 02.