Mixed Operations & BODMAS

BODMAS — Order of Operations

When a calculation has multiple operations, follow BODMAS:

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

1. Read carefully — identify exactly what is asked.
2. Extract numbers and operations — what does each imply?
3. Work step-by-step — one operation at a time.
4. 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