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Rationals Between...

What fractions can you find between the square roots of 65 and 67?

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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
What is the routine for calculating the result when the fraction is less than or equal to a half ?

What is the routine when the fraction is greater than a half?

Can you express that in algebra?

If $x$ is the fraction value what is the result in terms of $x$ for the two cases above?

For each denominator (bottom number of the fraction) which fractions are equivalent to other fractions with a smaller denominator?

Which fractions form a loop?

Which fractions do not belong to the loop but track into it?