Common Arithmetic Mistakes – A Complete Checklist
Even confident mathematicians make errors. This page brings together the most common mistakes across all four operations so you can identify and eliminate them.
Order of Operations Errors
3 + 4 × 2 wrongly calculated as 14. Correct: 3 + 8 = 11 (multiply before add)
Carrying and Borrowing Errors
- Adding a carry to the wrong column.
- Forgetting to reduce the digit when borrowing in subtraction.
Decimal Point Mistakes
- Misaligning decimal points in addition or subtraction.
- Wrong number of decimal places in multiplication.
- Forgetting to shift digits when dividing by powers of 10.
Sign Errors
- Forgetting that subtracting a negative = adding a positive.
- Multiplying/dividing with mixed signs and getting the sign wrong.
Fraction Mistakes
- Adding fractions without a common denominator.
- Forgetting to flip in fraction division (KCF rule).
- Not simplifying the final answer.
Mental Maths Pitfalls
- Doing steps out of order when working left to right.
- Confusing ×10 with adding a zero (wrong for decimals).
The Master Checklist
- Follow BODMAS/PEMDAS: brackets first, then indices, then ×÷, then +−.
- Carry and borrow to the correct column.
- Align decimal points; count decimal places in multiplication.
- Same signs → positive; different signs → negative.
- Common denominator before adding/subtracting fractions.
- KCF for fraction division.
- Estimate every answer before accepting it.
- Check using the inverse operation.
Practice Questions
- Calculate 5 + 3 × 4 correctly.
- Calculate 8.3 − 4.67.
- Calculate (−6) × (−5).
- Calculate 3/4 + 1/6.
- Calculate 2/3 ÷ 4/9.