Vector View of the Mediant
Separately adding numerators and denominators of two fractions gives their mediant, also known as the Farey mean. In this interactive 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.
R. Lewis Caviness and Kenneth E. Caviness, "Vector View of the Mediant", from Wolfram Demonstrations Project, http://demonstrations.wolfram.com/VectorViewOfTheMediant/, June 16, 2020.