The easy challenge in this applet asks the user to decompose a fraction
into the sum or difference of two fractions that have the same denominator.
A harder challenge is to decompose a fraction into the sum or difference of
two fractions with different denominators.
Harder still is the challenge to decompose a fraction into two fractions
neither of whose denominators is the same as that of the original fraction.
What questions could/would you put to your students based on this applet?