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?
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 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?
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.
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
Can you see how to build a harmonic triangle? Can you work out the next two rows?
The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.
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?