Which of these continued fractions is bigger and why?

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

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?

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.

Can you find the value of this function involving algebraic fractions for x=2000?

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

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?

Here is a chance to play a fractions version of the classic Countdown Game.

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?

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

Which dilutions can you make using only 10ml pipettes?

What does the empirical formula of this mixture of iron oxides tell you about its consituents?