Order of Operations – BODMAS / PEMDAS / BIDMAS
When a calculation contains more than one operation, you cannot just work from left to right. There is a strict set of rules that tells you which operation to perform first. These rules go by several names: BODMAS in the UK, PEMDAS in the US, and BIDMAS in some other countries. All three refer to exactly the same priority order.
What Does BODMAS Stand For?
| Letter | Stands for | Example |
|---|---|---|
| B | Brackets (parentheses) | (3 + 4) |
| O | Orders (powers and roots) | 2³, √9 |
| D | Division | 12 ÷ 4 |
| M | Multiplication | 3 × 5 |
| A | Addition | 7 + 2 |
| S | Subtraction | 10 − 3 |
Important: Division and Multiplication have equal priority and are worked left to right. The same applies to Addition and Subtraction.
Step-by-Step Method
- Work out everything inside brackets first.
- Evaluate any powers or roots.
- Work any division and multiplication from left to right.
- Finally, work any addition and subtraction from left to right.
Worked Examples
Calculate 3 + 4 × 2
Step 1: No brackets or powers.
Step 2: Multiply first: 4 × 2 = 8
Step 3: Add: 3 + 8 = 11
Calculate (5 + 3) × 2 − 4 ÷ 2
Step 1: Brackets: (5 + 3) = 8
Step 2: 8 × 2 − 4 ÷ 2
Step 3: Multiply and divide left to right: 8 × 2 = 16, then 4 ÷ 2 = 2
Step 4: Subtract: 16 − 2 = 14
Calculate 2³ + (12 − 4) ÷ 4 × 3
Step 1: Brackets: (12 − 4) = 8 → gives 2³ + 8 ÷ 4 × 3
Step 2: Powers: 2³ = 8 → gives 8 + 8 ÷ 4 × 3
Step 3: Division and multiplication left to right: 8 ÷ 4 = 2, then 2 × 3 = 6
Step 4: Addition: 8 + 6 = 14
Common Mistakes
- Working left to right without checking priorities — 3 + 4 × 2 is 11, not 14.
- Treating division as always coming before multiplication — they have equal priority and must be worked left to right.
- Forgetting that operations inside nested brackets must be resolved from the innermost bracket outwards.
Key Takeaways
- BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction.
- Always resolve brackets first, then powers, then division/multiplication, then addition/subtraction.
- Division and multiplication share equal priority; so do addition and subtraction — work these left to right.
Practice Questions
- Calculate 10 − 2 × 3.
- Calculate (10 − 2) × 3.
- Calculate 18 ÷ 6 + 4 × 2.
- Calculate 5² − (3 + 2) × 4.
- Calculate 3 × (2 + 5) − 4 ÷ 2.