Decimal Word Problems
Decimal word problems combine practical situations with decimal arithmetic operations. These problems typically involve money calculations, measurements, or unit prices where students must identify the correct operation and apply decimal computation rules. The key challenge lies in translating written scenarios into mathematical expressions whilst maintaining precision with decimal places.
Why it matters
Decimal word problems mirror real-world financial literacy skills that appear daily in shopping, budgeting, and consumer decisions. A shopper calculating whether £50 covers purchases of £12.75 and £31.49 uses the same skills as a Year 5 student solving decimal addition problems. These problems prepare learners for GCSE topics including ratio, proportion, and percentage calculations. In workplace contexts, decimal calculations appear in invoicing, measurements, and unit pricing. Shop assistants calculate change, builders measure materials to 0.1 metres, and restaurant managers determine cost per serving. The problem-solving framework developed through decimal word problems—reading carefully, identifying operations, and checking reasonableness—transfers to more complex mathematical reasoning in algebra and statistics at GCSE level.
How to solve decimal word problems
Decimal Word Problems
- Read the problem carefully and identify the numbers and the operation.
- Line up decimal points when adding or subtracting.
- For multiplication, count the total decimal places in both factors; the answer has the same count.
- Check your answer: does it make sense for the situation?
Example: A notebook costs £2.75. How much do 4 notebooks cost? 2.75 × 4 = £11.00.
Worked examples
You have £200.00. You buy an ice cream for £35.00. How much change do you get?
Answer: £165.00
- Set up the subtraction → 200.00 − 35.00 — Subtract the price from the amount you paid.
- Calculate → 200.00 − 35.00 = 165.00 — Your change is £165.00.
A bottle of soda costs £22.90 and a bag of chips costs £34.90. How much do they cost together?
Answer: £57.80
- Line up the decimal points → 22.90 + 34.90 — Write one number below the other with decimals aligned.
- Add → 22.90 + 34.90 = 57.80 — The total cost is £57.80.
2 kgs of grapes costs £99.80. What is the price per kg?
Answer: £49.90
- Set up the division → 99.80 ÷ 2 — Divide the total cost by the number of units.
- Calculate → 99.80 ÷ 2 = 49.90 — The price per kg is £49.90.
Common mistakes
- Misaligning decimal points during addition or subtraction leads to errors like calculating £12.50 + £3.75 = £15.25 instead of £16.25
- Forgetting to include the decimal point in the final answer results in writing £1250 when the correct answer is £12.50
- Placing the decimal point incorrectly after multiplication, such as calculating 3 × £2.45 = £735 instead of £7.35
- Not checking whether the answer makes sense in context, accepting unrealistic results like £500 change from a £20 purchase