Common BODMAS Mistakes and How to Avoid Them

📅 2025-09-05 ⏱ 6 min read

There are 8 common BODMAS mistakes students make, including left-to-right errors, bracket mistakes, and exponent confusion. Learn each mistake with wrong vs right examples.

8 Common BODMAS Mistakes

There are 8 common BODMAS mistakes that cause wrong answers in math expressions. Each mistake below includes a wrong vs right comparison and a clear explanation of the correct approach. If you ever need to verify a tricky equation, use our BODMAS calculator to view each calculation step clearly.

Mistake 1: Adding Before Multiplying

The most common BODMAS mistake is performing addition before multiplication.

✗ Wrong 3 + 4 × 2
= 7 × 2
= 14
✓ Correct 3 + 4 × 2
= 3 + 8
= 11

Fix: Perform multiplication and division before addition and subtraction.

Mistake 2: Assuming Division Always Comes Before Multiplication

BODMAS lists D before M, but division and multiplication have equal priority.

✗ Wrong 8 × 2 ÷ 4
= 8 × 0.5 (dividing first)
= 4 (sometimes wrong order)
✓ Correct 8 × 2 ÷ 4
= 16 ÷ 4 (left to right)
= 4

Fix: Solve D and M from left to right, not D before M.

Mistake 3: Forgetting Brackets Change Everything

✗ Wrong (3 + 4) × 2
= 3 + 8 (ignoring brackets)
= 11
✓ Correct (3 + 4) × 2
= 7 × 2
= 14

Fix: Always solve brackets first, before any other operation.

Mistake 4: Solving Outer Brackets Before Inner Brackets

✗ Wrong 2 × [10 − (3 + 2)]
= 2 × [10 − 3] + 2
= wrong grouping
✓ Correct 2 × [10 − (3 + 2)]
= 2 × [10 − 5]
= 2 × 5 = 10

Fix: Solve the innermost brackets first, then work outward.

Mistake 5: Ignoring Exponents (Orders)

✗ Wrong 2 + 3² × 4
= 2 + 3 × 4 (treating 3² as 3)
= 2 + 12 = 14
✓ Correct 2 + 3² × 4
= 2 + 9 × 4
= 2 + 36 = 38

Fix: Solve exponents (orders) right after brackets, before multiplication.

Mistake 6: Applying Exponent to the Wrong Part

✗ Wrong 2 × 3² = (2 × 3)²
= 6² = 36
✓ Correct 2 × 3² = 2 × 9
= 18

Fix: Exponents apply only to the number they are attached to, not to the preceding multiplication.

Mistake 7: Subtraction Before Addition (Same Priority Error)

✗ Wrong 10 − 3 + 2
= 10 − 5 (adding first)
= 5
✓ Correct 10 − 3 + 2
= 7 + 2 (left to right)
= 9

Fix: Addition and subtraction have equal priority. Solve from left to right.

Mistake 8: Confusing Negative Signs With Subtraction

✗ Wrong −3² = (−3)²
= 9
✓ Correct −3² = −(3²)
= −9

Fix: −3² means −(3²) = −9. Use brackets (−3)² to square the negative number and get 9.

Prevention Checklist

  1. Scan for brackets first and solve the innermost bracket before anything else.
  2. Solve exponents second — apply exponents only to the number they are attached to.
  3. Solve D and M left to right — do not assume division comes before multiplication.
  4. Solve A and S left to right — do not assume subtraction comes after addition.
  5. Use brackets for negative numbers — write (−3)² to square a negative.