Fractions

problem
Favourite

Harmonic Triangle

Age

14 to 16

Challenge level

Can you see how to build a harmonic triangle? Can you work out the next two rows?
problem

Investigating the Dilution Series

Age

14 to 16

Challenge level

Which dilutions can you make using only 10ml pipettes?
problem

Not Continued Fractions

Age

14 to 18

Challenge level

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

All Tangled Up

Age

14 to 18

Challenge level

Can you tangle yourself up and reach any fraction?
article
The Harmonic Triangle and Pascal's Triangle

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

Look Before You Leap

Age

16 to 18

Challenge level

Relate these algebraic expressions to geometrical diagrams.
problem

A Swiss Sum

Age

16 to 18

Challenge level

Can you use the given image to say something about the sum of an infinite series?