- Maurice OReilly
This app allows you to compare fractions between 0 and 1 on the number line. At the left and right, you see and , each represented by a vertical line, 1 unit tall. is in the middle, a unit tall. and are each of a unit tall. Find and . How tall are the lines representing these fractions? is already represented by . How many fractions do you see that are of a unit tall? Note the symmetry. Note that there are 9 distinct fractions between 0 and 1 with denominators 2, 3, 4 or 5. Now move the slider. What are the distinct proper fractions with denominators from 2 up to 9? How many are there? Can you arrange them in order of size? Use the slider to explore further ... There are 277 distinct proper fractions with denominators from 2 up to 30. For details relating to this diagram, see The Farey Sequence by Ainsworth, Dawson, Pianta & Warwick (2012).