Suppose you are trying to approximate some number

xand you’ve got it sandwiched between two rational numbers:

a/b<x<c/d.Now you’d like a better approximation. What would you do?

The obvious approach would be to take the average of

a/bandc/d. That’s fine, except it could be a fair amount of work if you’re doing this in your head.

Read on for a separate approach taking the mediant (not median) of the two fractions.