# Divide by 11 Trick — Free Timed Vedic Maths Practice | Quant Daily > Practise the divide by 11 trick free and timed: bring down the first digit, then subtract the running quotient at each step. Real worked vedic maths solutions. Source: https://quantdaily.app/drill-types/paravartya-division --- Paravartya Yojayet ## The divide by 11 trick — one subtraction per digit The divide by 11 trick, Paravartya Yojayet, replaces long division with one subtraction per digit. Bring down the dividend's first digit as the first quotient digit, then at each next digit subtract the previous quotient digit instead of adding it — 11's flag digit is 1, negated to −1. The last digit gives the remainder the same way. Division has no other Vedic shortcut on this site — every other technique here speeds up multiplication or squaring. This one earns its place because 11 shows up constantly in bank exam quant sets, and the method turns a full long-division layout into a single row of subtractions. **Try it against the clock.** Paravartya Division runs at 20s easy, 30s medium and 45s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading. [Start a timed Paravartya Division drill →](https://quantdaily.app/?drill=paravartya_division&src=seo-paravartya-division) ### How the divide by 11 trick works, digit by digit - Find the flag digit and negate it 11 is 10 + 1, so the flag digit is 1. Paravartya's rule is to always negate the flag digit before using it, which is why every later step subtracts rather than adds. - Bring down the first digit as-is For 1364 ÷ 11, the first quotient digit is simply the first dividend digit: 1. Nothing is calculated here — it is a straight copy. - At each next digit, subtract the previous quotient digit The second digit gives 3 − 1 = 2, the next quotient digit. The third digit gives 6 − 2 = 4. Each step uses only the dividend digit in that position and the quotient digit just produced — never one further back. - The last digit gives the remainder The same subtraction on the final digit produces the remainder: 4 − 4 = 0, so 1364 ÷ 11 = 124 exactly. A nonzero result there is a genuine remainder, not an error — 2786 ÷ 11 works out to 253 remainder 3. ### Reading 1364 ÷ 11 step by step | Step | What happens | | --- | --- | | Dividend digits | 1, 3, 6, 4 | | First quotient digit | Copy the first digit: 1 | | Second quotient digit | 3 − 1 = 2 | | Third quotient digit | 6 − 2 = 4 | | Remainder digit | 4 − 4 = 0 | | Result | 1364 ÷ 11 = 124, remainder 0 | ### 3 real divide by 11 trick questions, with worked solutions Generated by the same engine that mints the Quant Daily daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers. #### Question 1 3869 ÷ 11 — what is the QUOTIENT? Dividing by 11 — beat the clock. - 341 - 351 - 338 - 347 - 317 - 3869 ÷ 11 — Paravartya: 11 = 10 + 1, so the flag digit is 1; negate it to −1. - Bring down the first digit as-is: 3 (first quotient digit). - 8 + (−1 × 3) = 5 (next quotient digit). - 6 + (−1 × 5) = 1 (next quotient digit). - Last digit gives the remainder the same way: 9 + (−1 × 1) = 8. - Quotient 351, remainder 8 — check: 351 × 11 + 8 = 3869. - Answer: 351. #### Question 2 9999 ÷ 11 = ? Dividing by 11 — beat the clock. - 9090 - 987 - 900 - 999 - 909 - 9999 ÷ 11 — Paravartya: 11 = 10 + 1, so the flag digit is 1; negate it to −1. - Bring down the first digit as-is: 9 (first quotient digit). - 9 + (−1 × 9) = 0 (next quotient digit). - 9 + (−1 × 0) = 9 (next quotient digit). - Last digit gives the remainder the same way: 9 + (−1 × 9) = 0. - Quotient 909, remainder 0 — check: 909 × 11 + 0 = 9999. - Answer: 909. #### Question 3 2788 ÷ 11 — what is the QUOTIENT? Dividing by 11 — beat the clock. - 283 - 297 - 253 - 2535 - 239 - 2788 ÷ 11 — Paravartya: 11 = 10 + 1, so the flag digit is 1; negate it to −1. - Bring down the first digit as-is: 2 (first quotient digit). - 7 + (−1 × 2) = 5 (next quotient digit). - 8 + (−1 × 5) = 3 (next quotient digit). - Last digit gives the remainder the same way: 8 + (−1 × 3) = 5. - Quotient 253, remainder 5 — check: 253 × 11 + 5 = 2788. - Answer: 253. ### Common mistakes this drill is built from The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks. #### Adding instead of subtracting Forgetting to negate the flag digit and adding the previous quotient digit instead of subtracting it is the single most common slip, and it cascades wrong from the second digit onward. #### Reaching back further than one step Each step subtracts the quotient digit that was just produced, not an earlier one. Using a digit from two steps back gives a plausible-looking but wrong answer. #### Treating the remainder step as optional The final subtraction is not a bonus check — it is where the remainder comes from. Stopping one digit early silently drops it. ### Why your answer came out wrong The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here. #### Dividing by 11, do I add the previous digit or subtract it? Subtract. The transposed form of 11 is −1, so each new quotient digit is the next digit of the dividend minus the digit you have just written. Adding makes the quotient grow instead of settling, and you usually only notice when the remainder comes out larger than 11 itself. #### How far back do I look at each step? Exactly one step, because 11 has a single digit after its leading 1. Reaching two digits back is the rule for a three-digit divisor such as 101, not for 11. Going further back than the divisor allows is what produces a quotient that drifts wider with every column. #### Can I stop before the last column? No — the last column is the remainder, and skipping it is how a question that asked for the remainder gets answered with the quotient. 4257 ÷ 11 gives a quotient of 387 and a remainder of 0. If that final column comes out negative, borrow one from the quotient and add 11 back. ### FAQ #### What is the divide by 11 trick? It is Paravartya Yojayet applied to a base-plus-one divisor. Because 11 is 10 + 1, its flag digit is 1, negated to −1. Bring the first dividend digit straight down as the first quotient digit, then at each following digit subtract the quotient digit you just produced. The final subtraction gives the remainder. #### Does the divide by 11 trick work for any dividend? Yes — it works for any whole-number dividend, of any length, and handles a nonzero remainder the same way as an exact division. The one thing fixed about it is the divisor: this method is specific to dividing by 11, since that is what makes the flag digit a clean 1. #### How is this different from ordinary long division? Ordinary long division estimates how many times 11 fits, then multiplies and subtracts a full row for each digit. This method skips the estimate entirely: one small subtraction produces each quotient digit directly, which is why it is faster once it is automatic. #### Does the same idea work for dividing by 101? The underlying sutra generalises to any divisor of the form base-plus-one, such as 101 or 1001, with the pattern shifting one place further left each time. The timed drill on this page focuses on division by 11, the version that shows up in bank exam quant sections. ### Practise the next topic - [All 23 drill types](https://quantdaily.app/drill-types) — the full rotation with every published time limit. - [Multiply numbers near 50 — cross-add](https://quantdaily.app/drill-types/anurupyena-multiplication) — multiply numbers near 50, timed. - [Nikhilam multiplication — two numbers near a base](https://quantdaily.app/drill-types/nikhilam-multiplication) — nikhilam multiplication, timed. - [Vedic maths shortcuts](https://quantdaily.app/vedic-maths) — the seven sutras that make a 15-second answer possible. - [How to improve calculation speed](https://quantdaily.app/calculation-speed) — the six-week arc these drills fit into. Quant Daily is free, needs no account, and is not affiliated with IBPS, SBI, SSC, RRB or any exam authority.