Mixed Operations & BODMAS
Order of operations and multi-step word problems
Explanation
BODMAS — Order of Operations
When a calculation has multiple operations, follow BODMAS:
| Letter | Stands For | Priority |
|---|---|---|
| B | Brackets | 1st |
| O | Orders (powers and roots) | 2nd |
| D / M | Division and Multiplication | 3rd — left to right |
| A / S | Addition and Subtraction | 4th — left to right |
Important: Division and Multiplication share equal priority — work left to right. Same for Addition and Subtraction.
Worked Examples
Example 1: 3 + 4 × 2 = 3 + 8 = 11 (× before +)
Example 2: (3 + 4) × 2 = 7 × 2 = 14 (brackets first)
Example 3: 20 − 4² ÷ 2 = 20 − 16 ÷ 2 = 20 − 8 = 12
Example 4: 18 ÷ 6 × 3 = 3 × 3 = 9 (left to right for ÷ and ×)
Multi-Step Word Problems
- Read carefully — identify exactly what is asked.
- Extract numbers and operations — what does each imply?
- Work step-by-step — one operation at a time.
- Check your answer is reasonable in context.
Example: 3 boxes of 8 apples, each box costs $4.50. How much for 5 boxes?
→ Cost per box = $4.50 → 5 × $4.50 = $22.50
Key Tips
- Use brackets in your working to make order explicit and avoid mistakes
- Underline key numbers and operation words in word problems
- For "find the original" problems, work backwards using inverse operations
- Estimate first (round numbers) to check your final answer is in the right ballpark
Sample Practice Questions
-
Calculate: (5 + 3) × 2 − 4
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Answer: 12
-
What is 10 − 6 ÷ 2?
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Answer: 7
-
Calculate: 100 ÷ (4 + 1)
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Answer: 20
-
Calculate: 48 ÷ 6 + 3 × 2
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Answer: 14
Practice Questions
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What does Mixed Operations & BODMAS cover in the Selective Entry Numerical Reasoning exam?
Order of operations and multi-step word problems.
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