#

Separately adding numerators and denominators of two fractions gives their mediant, also known as the Farey mean. In this Demonstration, fractions are represented as vectors, and the mediant is seen to be the vector sum. The mediant vector is always between the original vectors and is closer to the target slope than at least one of them.

You can drag the endpoint of either of the two vectors to different points in the plane (or click shortcut buttons) to change the vectors and the numerical values above the graph.

Numerators are plotted on the vertical axis and denominators are plotted on the horizontal axis. Therefore the slope of the vector equals the fraction it represents and nearly parallel vectors represent nearly equal fractions. You can select and display various targets (shown by a dotted red line) for comparison to fractions.

Checkboxes and toggle buttons show, hide or adjust target, grid and vector labels.