When learning to add fractions, many students naively think that:
This can be stated more generally as:
This isn’t correct, of course, the sum is correctly written as
, for three fractions:
and in general:
What I find particularly interesting is how this expression looks very similar to a generalization of the product rule from introductory calculus.
I feel like there is a connection here that I am not seeing. I’ve tried looking this up and have found no reference to these general forms. I’d love to see how other people can run with this.