This app allows you to compare fractions between 0 and 1 on the number line.[br]At the left and right, you see [math]0=\frac{0}{1}[/math] and [math]1=\frac{1}{1}[/math], each represented by a vertical line, 1 unit tall.[br][br][math]\frac{1}{2}[/math] is in the middle, [math]\frac{1}{2}[/math] a unit tall. [math]\frac{1}{3}[/math] and [math]\frac{2}{3}[/math] are each [math]\frac{1}{3}[/math] of a unit tall.[br][br]Find [math]\frac{1}{4}[/math] and [math]\frac{3}{4}[/math]. How tall are the lines representing these fractions? [math]\frac{2}{4}[/math] is already represented by [math]\frac{1}{2}[/math].[br][br]How many fractions do you see that are [math]\frac{1}{5}[/math] of a unit tall? Note the [b]symmetry[/b].[br]Note that there are 9 [b]distinct[/b] fractions between 0 and 1 with denominators 2, 3, 4 or 5.[br]Now move the slider. What are the distinct [b]proper[/b] fractions with denominators from 2 up to 9?[br]How many are there? Can you arrange them in order of size?[br]Use the slider to explore further ... [br]There are 277 distinct proper fractions with denominators from 2 up to 30.[br]For details relating to this diagram, see [i][url=https://www.maths.ed.ac.uk/~v1ranick/fareyproject.pdf]The Farey Sequence[/url][/i] by Ainsworth, Dawson, Pianta & Warwick (2012).