Trick 18 divided by numbers just BELOW 10 or 100. For divisors just ABOVE (11, 12, 13, 102, 112…) write the extra digits with minus signs and use the same columns.
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The trick
Paravartya Yojayet — “transpose and apply”
Write the extra over the base with minus signs: 12 → −2, 112 → −1 −2, 103 → 0 −3.
Split off the last 1 (for 11–13) or 2 (for 102–121) digits as the remainder part.
Bring down each column total, multiply by the transposed digits and add under the next columns.
If the remainder is negative, take 1 from the quotient and add the divisor; if it is too big, divide it again.
Use it for: Dividing by 11, 12, 13, 102, 103, 111, 112, 121.
Worked example: 1467 ÷ 12 = 122 remainder 3
12 → −2. Split 146 | 7.
Total 1 → add −2: 4 − 2 = 2. Total 2 → add −4: 6 − 4 = 2. Total 2 → add −4: 7 − 4 = 3.
Quotient 122, remainder 3.
Answer: 122 remainder 3.
Check: 12 × 122 + 3 = 1464 + 3 = 1467 ✓
✏️ Practice
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