परावर्त्य योजयेत्

Parāvartya Yojayet - "Transpose and Apply"

A universal method for fast division

What does it mean?

This sutra simplifies division by transforming the divisor and applying it step-by-step to the dividend. It’s especially useful when the divisor is slightly more than a power of 10, like 11, 101, or 1001.

The Method

  • Identify the base (10, 100, etc.) close to the divisor
  • Transpose the excess digit(s) to negative
  • Apply the transposed digits to the dividend step-by-step
  • Use multiplication and subtraction to find quotient and remainder

Example: Divide 1234 by 12

Base = 10 → 12 is 10 + 2
Transpose 2 → –2
Step-by-step:
1 × –2 = –2 → 2 – 2 = 0
0 × –2 = 0 → 3 – 0 = 3
3 × –2 = –6 → 4 – 6 = –2
✅ Quotient: 103
✅ Remainder: –2

Why it matters

Parāvartya Yojayet reveals how division can be simplified using transformation and pattern recognition. It’s ideal for mental math, competitive exams, and algebraic manipulation.