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Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
Lower Bound
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Age 14 to 16 Short Challenge Level:
Two thirds of five sixths of a number $X$ is the same as three quarters of four fifths of a number $Y$.
What is the value of $\frac{X}{Y}$ as a fraction in its lowest terms?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.