
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?

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?

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.

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

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!
The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.

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?

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

Which dilutions can you make using only 10ml pipettes?

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?

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