परावर्त्य योजयेत्

Parāvartya Yojayet

"Transpose and apply"

LearnStep-by-step animation PracticeInteractive problems ProofWhy it works

What this sutra solves

Divide by awkward numbers like 12, 13 or 112 without setting up long division.

You owe ₹1234 and want to spread it over a 12-instalment plan — how much per instalment, and what is left over?

becomes

1234 \div 12

⚡

Flag the divisor (−2) → 102 with ₹10 remaining.

Live Demo— animated step-by-step

transpose & apply

↓

divide by

flag (negated)

-2

Transpose the divisor into a flag

Divisor 12: keep the leading 1 as the divider, transpose the rest (2) to a negative flag (-2).

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⚡ Speed Advantage

Vedic

3 steps

Traditional

12 steps

4× faster with Vedic Mathematics

Best for

• Division by numbers close to a power of 10

Use when

• Divisor has leading digit 1, or is close to 10^k

Avoid when

• Divisor is arbitrary (use standard long division)

Intuition

Division by a near-10 divisor: transpose the sub-digits of the divisor (negate them) and use them as a flag that helps you divide step by step.

Story Mode

Flipping the Divisor

What if you could turn a division problem into a series of additions and single-digit multiplications? Paraavartya does exactly this. The 'flag' — the sub-digit of the divisor — gets transposed (sign-flipped) and applied at each step. The scary long divisor becomes a one-digit helper.

Vedic vs conventional

Conventional long division of $1234\div 12$ : 5 written steps. Paraavartya flag division: 4 mental steps with no written remainders.

Eliminates multi-digit divisor trial — reduces to single-digit operations.

Applications

Flag division

Divide by any number where the leading digit is 1 (or near a power of 10).

1234 \div 12

2356 \div 13

12345 \div 112

Common Mistakes to Avoid

Not negating the flag correctly

Wrong approach

Divisor 12: flag is −2, not +2

Correct approach

✓

The flag is the sub-digit with its sign reversed (transposed).

Why this happens

💡 Students add instead of subtract the flag product.

Why It Works

Split the divisor into leading part and flag part:

D=10m+r

Transposing means moving the smaller part to the other side:

10m\cdot q = N-rq

Each quotient digit uses the same correction:

\text{next partial dividend}=\text{current digits}-r\times\text{previous quotient digit}

The flag method is long division rewritten so the hard multi-digit divisor is replaced by repeated one-digit corrections.

For divisor $D = 10^k + d$ (where |d| < $10^k$ ): flag method transposes d (uses −d). Each step: bring down a digit, subtract flag×quotient-digit from remainder. The transposed coefficients generate the quotient digit by digit.

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