Arithmetic Word Problems – How to Solve Them
Word problems translate real-life situations into mathematics. A reliable strategy makes them manageable every time.
The RUCSAC Strategy
- Read the problem carefully.
- Underline key information.
- Choose the operation(s).
- Solve step by step.
- Answer the question in context.
- Check using the inverse.
Identifying Operations from Key Words
| Words | Operation |
|---|---|
| total, sum, more than, increase, combined | Addition |
| difference, less, fewer, reduce, take away | Subtraction |
| times, product, each, per, groups of | Multiplication |
| share, split, each, per, how many in each | Division |
Worked Examples
Easy
Tom has 24 stickers and gives 8 to his friend. How many does he have left? 24 − 8 = 16
Medium
Boxes hold 12 apples. There are 7 boxes. 15 apples are eaten. How many remain? 7 × 12 = 84. 84 − 15 = 69 apples
Hard
Concert tickets cost £15 each. A group of 8 friends buys tickets and each person pays an equal share of the total cost plus a £3 booking fee per person. What does each person pay? 8 × £15 = £120. Each person: £120 ÷ 8 + £3 = £15 + £3 = £18
Key Takeaways
- Read twice before calculating.
- Key words signal which operation to use.
- Answer with units and in context.
- Check your answer makes sense.
Practice Questions
- A cinema has 320 seats arranged in 16 equal rows. How many seats per row?
- Sara earns £11.50 per hour and works 7 hours. How much does she earn?
- There are 5 shelves with 32 books each; 18 books are borrowed. How many remain?
- Petrol costs £1.65 per litre. A tank holds 45 litres. How much to fill it from empty?
- A field is 85 m long and 60 m wide. What is the perimeter?