Why Do We Need an Order?
When a calculation contains more than one operation, different people could get different answers if they calculated left to right without any rules. The BODMAS rule tells everyone the correct order to follow.
BODMAS
Brackets → Orders (powers/roots) → Division → Multiplication → Addition → Subtraction
The BODMAS Rules
| Step | Stands for | What to do |
|---|---|---|
| B | Brackets | Evaluate everything inside ( ) first |
| O | Orders | Calculate powers and roots |
| D | Division | Divide, working left to right |
| M | Multiplication | Multiply, working left to right |
| A | Addition | Add, working left to right |
| S | Subtraction | Subtract, working left to right |
Step-by-Step Examples
- 1
Identify all brackets
Work out anything in brackets first, using BODMAS inside those brackets too. - 2
Handle orders
Calculate any powers or square roots next. - 3
Divide and multiply
Work through the expression left to right, performing divisions and multiplications as you meet them. - 4
Add and subtract
Finally work left to right performing additions and subtractions.
Calculate 3 + 4 × 2
Without BODMAS (wrong): 3 + 4 = 7, then 7 × 2 = 14 ✗
With BODMAS (correct): multiplication first → 4 × 2 = 8, then 3 + 8 = 11 ✓
Calculate (10 − 4) × 3 + 8 ÷ 2
B: (10 − 4) = 6 → expression becomes 6 × 3 + 8 ÷ 2
D/M (left to right): 6 × 3 = 18, then 8 ÷ 2 = 4 → expression becomes 18 + 4
A/S: 18 + 4 = 22
Calculate 50 − 3 × (4 + 2) + 12 ÷ 6
B: (4 + 2) = 6 → 50 − 3 × 6 + 12 ÷ 6
D/M: 3 × 6 = 18 and 12 ÷ 6 = 2 → 50 − 18 + 2
A/S (left to right): 50 − 18 = 32, then 32 + 2 = 34
Real-World Applications
Real world: calculating total cost with a discount
Three friends each buy a sandwich for 2 € and a drink for 1 €. They also share one dessert for 3 €. What is the total cost?
Total = 3 × (2 + 1) + 3
B: (2 + 1) = 3
M: 3 × 3 = 9
A: 9 + 3 = 12 €
Real world: ticket pricing
An adult ticket costs 8 €, a child ticket costs 5 €. A family of 2 adults and 3 children buys tickets and gets a 4 € group discount. How much do they pay?
Total = 2 × 8 + 3 × 5 − 4
M: 2 × 8 = 16 and 3 × 5 = 15
A/S: 16 + 15 − 4 = 27 €
Real world: time planning
A student has 60 minutes. She spends 10 minutes reading, then does 3 exercises each taking 8 minutes, and finishes with 5 minutes of notes. How many minutes are left?
Remaining = 60 − 10 − 3 × 8 − 5
M: 3 × 8 = 24
A/S (left to right): 60 − 10 = 50, then 50 − 24 = 26, then 26 − 5 = 21 minutes left
Common Mistakes
- Adding or subtracting before multiplying or dividing
- Treating division and multiplication as if division always comes before multiplication — they are equal priority, so go left to right
- Forgetting to apply BODMAS inside brackets
Practice Problems
Calculate 24 ÷ (2 + 4) × 3 − 1.
Show answer
A shop sells pens for 1 € each and notebooks for 3 €. Maya buys 5 pens and 2 notebooks, and uses a 2 € voucher. How much does she pay?