Divide without long division
Divide by 12, 13 or 112 without setting up long division
Long division by a multi-digit divisor means repeated trial multiplication — the slowest operation on the page.
Spot it when
The divisor is just above a power of 10 (12, 13, 21, 112…).
Watch it solved
Transpose the divisor into a flag
Divisor 12: keep the leading 1 as the divider, transpose the rest (2) to a negative flag (-2).
⚡ Speed Advantage
4× faster with Vedic Mathematics
When you’ll actually hit this
Real moments — exams, homework, competitions — where this shortcut earns its keep.
Splitting ₹1234 into a 12-instalment plan and you need the per-month figure and the leftover.
Flag the divisor (−2) and sweep left to right → 102, remainder 10.
A data-interpretation set needs 2356 ÷ 13 fast to compare two ratios.
Flag −3, one-digit corrections each step → 181, remainder 3.
A three-digit divisor near 100 appears in a competition — 12345 ÷ 112.
Flag −12 (work with the leading 1), single-digit corrections → 110, remainder 25.
The method behind it
परावर्त्य योजयेत्
Parāvartya Yojayet
“Transpose and apply”
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.
Conventional long division of : 5 written steps. Paraavartya flag division: 4 mental steps with no written remainders.
Use when
- • Divisor has leading digit 1, or is close to 10^k
Avoid when
- • Divisor is arbitrary (use standard long division)