FP Flagpole Division
Write down only the first digit of the divisor — the flag — and carry a running remainder. Trial division disappears; every step is deterministic.
1. The naming logic
- Pole (杆): the leading digit of the divisor — the only digit you divide by.
- Flag (旗): the remaining digits — used to subtract what the quotient has already claimed.
- Each round: divide by the pole → subtract the flag product → bring down the next digit.
Why it beats long division
Column division has to guess each quotient digit and then check it, and the checking is exactly the wasted work. Flagpole division fixes the digit from the leading part and subtracts the flag product from the running remainder, so the step is a computation rather than a guess.
2. Step-by-step: 2829 ÷ 123 = 23
- 123 splits into pole = 1, flag = 23. Dividend 2829.
- First quotient digit: 282 ÷ 123 → 2.
- Verify and subtract: 2 × 123 = 246; 282 − 246 = 36.
- Bring down the next digit: 36 with the 9 → 369.
- Second quotient digit: 369 ÷ 123 = 3, remainder 0.
- Answer: 23
When it does not divide exactly: pad with zeros
Append a 0 to the remainder and keep walking right — the digits produced after the append are the decimals. Example: 3517 ÷ 127 → 127 × 27 = 3429, remainder 88; 88 becomes 880, 880 ÷ 127 ≈ 6 → 27.69…
3. The special divisors worth memorising
For divisors 25, 125, 5 or 8, do not divide at all — convert to a multiplication: ÷25 = ×4 ÷ 100, ÷125 = ×8 ÷ 1000, ÷5 = ×2 ÷ 10. Faster than any division technique.
Example: 5578 ÷ 25 = 5578 × 4 ÷ 100 = 22312 ÷ 100 = 223.12
4. Practice
- 2829 ÷ 123 (exact)
- 3517 ÷ 127, two decimal places
- 5578 ÷ 25
- 8480 ÷ 125
- 347 ÷ 5, then check the quotient with DS
Answers
The nine maths techniques are complete. Head to the practice centre for a 20-question set, or take a timed test to see your grade.
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