Fractions

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

A jigsaw where pieces only go together if the fractions are equivalent.

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

If three brothers will get £20 more if they do not share their money with their sister, how much money is there?

In a certain community two thirds of the adult men are married to three quarters of the adult women. How many adults would there be in the smallest community of this type?

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

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