Fractions

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

Can you find the pairs that represent the same amount of money?

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

It would be nice to have a strategy for disentangling any tangled ropes...

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

What do you notice about these families of recurring decimals?

Can you express every recurring decimal as a fraction?

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

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.