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Mathematics · Number and place value
KS2 SATs 2024 — Mathematics Papers 2 & 3: Reasoning
A free preview from the Athena Learning Library — the same lesson registered students learn from.
In this lesson: You will learn to switch between fractions, decimals and percentages when a problem uses them in a real-life context.
The idea
Fractions, decimals and percentages are three ways of describing the same part of a whole. A half can be written as 1⁄2, 0.5 or 50%, and confident mathematicians translate between them. To turn a decimal into a percentage, multiply by 100; to turn a percentage into a decimal, divide by 100.
In context problems, first decide what the whole is. A discount of 25% on a £60 jacket means finding a quarter of £60, then subtracting it from the full price — the question asks for the sale price, not just the discount.
Benchmarks help you compare quickly: 0.75 is 75%, which is three-quarters, and 0.4 is 40%. Placing values against halves and quarters lets you judge which is bigger without heavy calculation.
Worked example
A jacket costs £60. It is reduced by 25% in a sale. What is the sale price?
- Find 25% of £60. 25% is a quarter, and 60 ÷ 4 = £15. This is the discount.
- Subtract the discount from the full price: £60 − £15 = £45.
Answer: £45
Watch out
- Giving the discount (£15) as the answer instead of the sale price.
- Reading 0.75 as 75 without realising it equals 75%.
Quick check
Try these on your own first — then reveal each answer.
1. How many pupils are 3⁄5 of a class of 200 pupils? Work out 3⁄5 of 200.
2. Which is larger, 0.75 or 70%?
Practise this concept
Reading is the first step — the concept sticks when your child answers questions on it. Registered students practise graded questions for this lesson, with instant marking and worked explanations, and the lesson is marked complete in their progress.