Why do we need rules?
What is 3 + 4 × 2?
- If you go left to right: (3 + 4) × 2 = 14
- If you multiply first: 3 + (4 × 2) = 11
Two different answers! We need a rule so everyone gets the same result.
BODMAS / PEMDAS
The agreed order is:
| Step | Letter | Meaning | Example |
|---|---|---|---|
| 1 | B / P | Brackets (Parentheses) | (3 + 4) first |
| 2 | O / E | Orders (Exponents) | 2² = 4 |
| 3 | DM | Division & Multiplication | left to right |
| 4 | AS | Addition & Subtraction | left to right |
Key idea: Multiplication and division have the same priority — do them left to right. Same for addition and subtraction.
Worked examples
Example 1: 3 + 4 × 2
- Multiply first: 4 × 2 = 8
- Then add: 3 + 8 = 11
Example 2: (5 + 3) × 2 − 4
- Brackets first: 5 + 3 = 8
- Multiply: 8 × 2 = 16
- Subtract: 16 − 4 = 12
Example 3: 20 − 12 ÷ 4 + 1
- Division first: 12 ÷ 4 = 3
- Left to right: 20 − 3 + 1 = 18
Brackets first
Multiply
Divide
Add
Follow BODMAS strictly: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
Practice
What is 6 + 3 × 5?
Multiply first: 3 × 5 = 15. Then add: 6 + 15 = 21.
Calculate (8 + 2) × (7 − 3).
Brackets first: 8 + 2 = 10 and 7 − 3 = 4. Then multiply: 10 × 4 = 40.
What is 24 ÷ 6 + 2 × 3?
Division: 24 ÷ 6 = 4. Multiplication: 2 × 3 = 6. Then add: 4 + 6 = 10.
Calculate 100 − 4 × (3 + 7).
Brackets: 3 + 7 = 10. Multiply: 4 × 10 = 40. Subtract: 100 − 40 = 60.
What is 2 × (3 + 5) − 4?
Brackets first: 3 + 5 = 8. Multiply: 2 × 8 = 16. Subtract: 16 − 4 = 12.
Calculate 5 + 15 ÷ 3 − 2.
Division first: 15 ÷ 3 = 5. Then left to right: 5 + 5 − 2 = 8.
Challenge
Quick-Fire Round