Mixed Operations – Using All Four Together
When a calculation involves more than one type of operation, you must follow the agreed order of operations to get the correct answer.
BODMAS / PEMDAS Recap
| Order | BODMAS | PEMDAS |
|---|---|---|
| 1 | Brackets (B) | Parentheses (P) |
| 2 | Orders / Indices (O) | Exponents (E) |
| 3 | Division (D) | Multiplication / Division (M/D) |
| 4 | Multiplication (M) | Addition / Subtraction (A/S) |
| 5 | Addition (A) | — |
| 6 | Subtraction (S) | — |
Worked Examples
Example 1
3 + 4 × 2 − 1 = 3 + 8 − 1 = 10
Example 2 – With Brackets
(3 + 4) × 2 − 1 = 7 × 2 − 1 = 14 − 1 = 13
Advanced
5² − (3 × 4 + 2) ÷ 7 = 25 − (12 + 2) ÷ 7 = 25 − 14 ÷ 7 = 25 − 2 = 23
Key Takeaways
- Brackets first — they override everything.
- Division and multiplication before addition and subtraction.
- When operators have equal precedence, work left to right.
- Inserting brackets can completely change the answer.
Practice Questions
- Calculate 8 + 3 × 4.
- Calculate (8 + 3) × 4.
- Calculate 20 − 4² + 6 ÷ 2.
- Calculate 3 × (5 + 2²) − 4.
- Insert brackets to make the following true: 5 + 3 × 2 = 16.