# Comparing fractions

- Author:
- Maurice OReilly

- Topic:
- Arithmetic, Fractions, Line Segment, Symmetry

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).