### Rationals Between

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

### 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?

### Weekly Problem 4 - 2012

What fraction of the volume of this can is filled with lemonade?

# Stretching Fractions

##### Stage: 4 Challenge Level:
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?