Decimal Word Problems
Decimal word problems appear in Year 4 SATs and continue through GCSE Foundation, challenging students to apply decimal operations to real-world scenarios. These problems require students to interpret context, select appropriate operations, and handle money calculations with precision.
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Why it matters
Decimal word problems mirror everyday situations students encounter outside school. When Oliver buys a £3.25 sandwich and pays with a £5 note, he must calculate £1.75 change using decimal subtraction. At the chippy, calculating the cost of 3 portions at £4.60 each requires decimal multiplication, totalling £13.80. Year 6 students working towards SATs need these skills to interpret multi-step problems involving money, measurements, and real-world data. GCSE Foundation papers frequently include decimal problems in consumer contexts, such as calculating unit prices at supermarkets or working out fuel costs. Students who master decimal word problems develop number sense and mathematical reasoning that extends far beyond the classroom, preparing them for financial literacy and practical problem-solving in adult life.
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 £100.00. You buy a bus ticket for £42.50. How much change do you get?
Answer: £57.50
- Set up the subtraction → 100.00 − 42.50 — Subtract the price from the amount you paid.
- Calculate → 100.00 − 42.50 = 57.50 — Your change is £57.50.
A cheese costs £54.90 and a loaf of bread costs £32.90. How much do they cost together?
Answer: £87.80
- Line up the decimal points → 54.90 + 32.90 — Write one number below the other with decimals aligned.
- Add → 54.90 + 32.90 = 87.80 — The total cost is £87.80.
3 metres of fabric costs £269.70. What is the price per metre?
Answer: £89.90
- Set up the division → 269.70 ÷ 3 — Divide the total cost by the number of units.
- Calculate → 269.70 ÷ 3 = 89.90 — The price per metre is £89.90.
Common mistakes
- Students misalign decimal points when adding, writing £3.25 + £1.7 as £4.32 instead of £4.95, forgetting to treat £1.7 as £1.70
- When dividing decimals, students place the decimal point incorrectly, calculating £24.60 ÷ 3 as £0.82 instead of £8.20
- Students ignore decimal places in multiplication, working out 2.5 × 4 as £100 instead of £10.00, forgetting to count decimal places
- Students misinterpret the question, calculating total cost when asked for change, giving £42.50 instead of £57.50 for £100 - £42.50