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
Kayee has 240 dollars of pocket money for September.
First she spends a quarter of it on stationery, then half of what is left on books.
How many dollars does Kayee spend on books?
Show the hints (2)
💡Hint 1: How much goes on stationery, and how much is left after that?
💡Hint 2: The second 1/2 is 1/2 of what is left, not of all her pocket money.
Worked solution
Have a go first, then read the solution step by step.
1.Split all her pocket money into 4 equal parts of 240 ÷ 4 = 60. On stationery: 1 part, 60 × 1 = 60 dollars.
2.3 parts are left: 240 − 60 = 180 dollars.
3.The second 1/2 is of what is left: the 180 left is the new whole, split again into 2 equal parts of 180 ÷ 2 = 90.
4.On books: 1 of these part, 90 × 1 = 90 dollars.
⚠️Common mistake: taking 1/2 of all her pocket money: 240 ÷ 2 × 1 = 120.
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