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