Fractions

problem
Archimedes and numerical roots

Age

14 to 16

Challenge level

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?
problem
Tiny nines

Age

14 to 16

Challenge level

What do you notice about these families of recurring decimals?
problem
Repetitiously

Age

14 to 16

Challenge level

Can you express every recurring decimal as a fraction?
problem
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
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?
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?