Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you
notice when successive terms are taken? What happens to the terms
if the fraction goes on indefinitely?
Which rational numbers cannot be written in the form x + 1/(y +
1/z) where x, y and z are integers?
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
Mixing Lemonade investigates the strengths of different solutions informally and may provide a useful starting point.