Multi-Step Calculations
Many real problems require more than one arithmetic operation. A multi-step calculation is simply a series of individual steps carried out in the correct order.
Why Order Matters
Different orders of operations can give different answers. Always follow BODMAS/PEMDAS unless brackets specify otherwise.
3 + 4 × 5 = 3 + 20 = 23 (not 35, because × before +)
Strategy for Multi-Step Problems
- Read the problem carefully and identify what information you have.
- Decide which operation to do first.
- Work through one step at a time.
- Check each step before moving to the next.
- Review the final answer in context.
Worked Examples
Easy Two-Step
A book costs £8.50. You buy 3 books and pay with a £30 note. How much change?
Step 1: 3 × £8.50 = £25.50.
Step 2: £30 − £25.50 = £4.50
Medium Three-Step
A rectangle is 12 cm by 7 cm. A square of side 4 cm is cut from one corner. What area remains?
Step 1: rectangle area = 12 × 7 = 84 cm².
Step 2: square area = 4 × 4 = 16 cm².
Step 3: 84 − 16 = 68 cm²
Key Takeaways
- Break problems into single operations.
- Use BODMAS/PEMDAS to determine the correct order.
- Label each step clearly.
- Estimate the final answer before starting to check reasonableness.
Practice Questions
- 5 × (12 − 4) + 6 = ?
- You earn £9.50 per hour and work 8 hours on Monday and 6 on Wednesday. How much do you earn in total?
- A car travels at 60 mph for 2.5 hours, then at 80 mph for 1.5 hours. What is the total distance?
- There are 6 shelves with 24 books each; 37 books are removed. How many books remain?
- Calculate (3² + 4²) × 2 − 10.