Comparing fractions
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).