This article presents 10 tricky BODMAS traps with step-by-step solutions to help learners avoid common errors and build strong mathematical reasoning skills.
Contents
What Is BODMAS?
BODMAS stands for:
- B – Brackets
- O – Orders (powers, roots)
- D – Division
- M – Multiplication
- A – Addition
- S – Subtraction
Division and multiplication are performed from left to right,
as are addition and subtraction.
10 Tricky BODMAS Traps (With Answers)
Trap 1
Expression:
8 + 2 × 5Answer: 18
Solution:
2 × 5 = 10
8 + 10 = 18
Trap 2
Expression:
(8 + 2) × 5Answer: 50
Solution:
8 + 2 = 10
10 × 5 = 50
Trap 3
Expression:
20 ÷ 5 × 2Answer: 8
Solution:
20 ÷ 5 = 4
4 × 2 = 8
Trap 4
Expression:
20 ÷ (5 × 2)Answer: 2
Solution:
5 × 2 = 10
20 ÷ 10 = 2
Trap 5
Expression:
6 + 18 ÷ 3Answer: 12
Solution:
18 ÷ 3 = 6
6 + 6 = 12
Trap 6
Expression:
(6 + 18) ÷ 3Answer: 8
Solution:
6 + 18 = 24
24 ÷ 3 = 8
Trap 7
Expression:
3 + 4² × 2Answer: 35
Solution:
4² = 16
16 × 2 = 32
3 + 32 = 35
Trap 8
Expression:
(3 + 4)² × 2Answer: 98
Solution:
3 + 4 = 7
7² = 49
49 × 2 = 98
Trap 9
Expression:
100 − 20 ÷ 5 × 3Answer: 88
Solution:
20 ÷ 5 = 4
4 × 3 = 12
100 − 12 = 88
Trap 10
Expression:
(100 − 20) ÷ 5 × 3Answer: 48
Solution:
100 − 20 = 80
80 ÷ 5 = 16
16 × 3 = 48
Common BODMAS Mistakes to Avoid
- Ignoring brackets
- Not following left-to-right for division and multiplication
- Skipping powers (squares, cubes)
- Adding or subtracting too early
Educational Value
- Designed using real classroom teaching experience
- Encourages conceptual clarity over memorization
- Ideal for Grade 4–8 learners, competitive exams, and mental math practice
Research-Backed Evidence on Order of Operations Practice
Educational research consistently shows that explicit instruction and repeated practice with order-of-operations problems help students reduce calculation errors and strengthen arithmetic reasoning skills.
A study found that students who received focused practice on evaluating numerical expressions using the correct order of operations demonstrated significant improvement in accuracy and procedural understanding compared to memorization alone. [Source: ERIC (U.S. Department of Education)]
Similarly, structured practice with order-of-operations tasks improves students’ conceptual reasoning, helping them understand why operations are performed in a specific sequence. [Source: DOAJ]
Additional practice reduces common precedence errors in arithmetic expressions, leading to better performance.[Source: Journal of Numerical Cognition]
Understanding BODMAS is essential for accurate math problem-solving. These tricky order-of-operations traps help learners slow down, think logically, and apply rules correctly—skills that are vital for academic success and everyday calculations.
Tip: Always solve brackets and powers first, then move left to right.
