A medium question on fraction problems for P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P5 and P6 qualifying rounds and finals; harder ones work backwards through fractions, or need clever shortcuts with fractions.
The question
In Class 6C, a quarter of the pupils are boys, and there are 20 more girls than boys.
How many pupils are there in Class 6C?
Show the hints (2)
💡Hint 1: Think of the class as 4 equal parts, with the boys taking 1. How many parts are girls?
💡Hint 2: How many more parts are girls than boys? Those parts are the 20 pupils.
Worked solution
Have a go first, then read the solution step by step.
1.Think of the class as 4 equal parts: boys 1, girls 4 − 1 = 3.
2.Line them up: the girls have 3 − 1 = 2 more parts, and that is the 20 more.
3.One part = 20 ÷ 2 = 10.
4.The class is 4 parts: 10 × 4 = 40 pupils.
⚠️Common mistake: treating 20 as the number of girls. It is only how many more girls there are than boys: 2 parts.
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