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Forgot the Numbers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

If you are a teacher click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on ...



On my calculator I divided one whole number by another whole number and got the answer $3.125$.

I know that both numbers were less than $50$, but can't remember what they were.

Can you work out what they were?




Once you've had a chance to think about it, click below to see how four different pupils began working on the task.

Here is Gemma and Flo's work:


Richard wrote the following:

He explained:

"I multiplied $3.125$ by $1$, then I tried multiplying $3.125$ by $2$, then I multiplied $3.125$ by $3$ ..."


Here is the start of Thomas' work:

I first looked at the number $0.125$ and worked out what fraction of $1$ it is. It turned out that it was an eighth.


Can you take each of these starting ideas and develop it into a solution?

Click here for a poster of this problem.