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.
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