An easy question on fraction problems for P4–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
The estate library lends out 3 picture books today.
That is a third of all its picture books.
How many picture books does the library have in all?
Show the hints (2)
💡Hint 1: 1/3 means the whole is split into 3 equal parts, and 3 is 1 of them.
💡Hint 2: The whole is 3 parts, each of them 3.
Worked solution
Have a go first, then read the solution step by step.
1.Split the whole into 3 equal parts: 3 is one of them, so each part is 3.
2.The whole is 3 parts: 3 × 3 = 9 books.
⚠️Common mistake: dividing 3 by 3, or taking 1/3 of 3. 3 is only part of the whole, so the whole must be more than 3.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download