Arithmetic Operations
Common Division Mistakes to Avoid
Division errors are common but avoidable. Knowing where mistakes tend to happen means you can prevent them before they occur.
Mistake 1 – Forgetting to Account for the Remainder
Wrong
29 ÷ 6 = 4 (forgetting remainder 5). Correct: 4 r 5
Mistake 2 – Misplacing the Decimal Point
9.6 ÷ 4 written incorrectly as 24. Correct: align decimal → 2.4
Mistake 3 – Sign Errors with Integers
(−48) ÷ (−6) wrongly = −8. Correct: same signs → +8
Mistake 4 – Not Flipping in Fraction Division
3/4 ÷ 2/5 wrongly = 6/20. Correct: KCF → 3/4 × 5/2 = 15/8
Mistake 5 – Dropping the Placeholder Zero in Long Division
Example: 1,224 ÷ 12
12 into 12 = 1. Bring down 2: 12 into 02 = 0 (write 0 as placeholder). Bring down 4: 12 into 24 = 2. Answer: 102, not 12.
Mistake 6 – Interpreting the Remainder Incorrectly
Always read the question context: sometimes round up, sometimes round down, sometimes express as fraction or decimal.
Checklist
- Write the remainder explicitly if the answer is not exact.
- Align decimal point carefully when dividing decimals.
- Remember sign rules: same signs → positive quotient.
- KCF for fractions — never forget to flip.
- Write placeholder zeros in long division.
- Verify: quotient × divisor + remainder = dividend.
Practice: Spot and Fix the Mistake
Find the correct answer.