Order of Operations with Brackets – BODMAS Explained
Brackets are the most powerful tool in arithmetic notation. They override the normal order of operations and must always be evaluated first.
Without vs With Brackets
8 + 4 × 3 = 8 + 12 = 20 (multiply first)
(8 + 4) × 3 = 12 × 3 = 36 (brackets first)
Nested Brackets
When brackets appear inside brackets, work from the innermost outward.
2 × [(3 + 4) × 5 − 6] = 2 × [7 × 5 − 6] = 2 × [35 − 6] = 2 × 29 = 58
Worked Examples
Example 1
(9 − 3) ÷ 2 + 5 = 6 ÷ 2 + 5 = 3 + 5 = 8
Example 2
3 × (2 + 4²) − 10 = 3 × (2 + 16) − 10 = 3 × 18 − 10 = 54 − 10 = 44
Example 3 – Nested
4 × {2 + (3 × 5)} − 7 = 4 × {2 + 15} − 7 = 4 × 17 − 7 = 68 − 7 = 61
Key Takeaways
- Brackets are always evaluated first.
- Nested brackets: innermost first, then outward.
- Changing brackets changes the answer.
- Add brackets to control the order of any calculation.
Practice Questions
- Calculate (7 + 3) × 5 − 4.
- Calculate 10 − (6 − 2) × 3.
- Calculate 2 × [(4 + 3) × 2].
- Insert brackets to make: 5 + 3 × 4 = 32.
- Calculate 3² + (8 − 5)² ÷ 3.