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Rationals Between

What fractions can you find between the square roots of 56 and 58?

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Peaches Today, Peaches Tomorrow....

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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Canny Fraction

Weekly Problem 4 - 2012
What fraction of the volume of this can is filled with lemonade?

Stretching Fractions

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

This problem benefits from a systematic treatment.

Please see the Hint for useful categories when constructing a systematic approach.

The interest in this problem is the structure not simply the results - where do the various start fractions go to and why?

An article that examines this problem in more depth can be found here.