Ian's discovery to get any number in Pascal's Triangle

I always found this interesting... A 12-year old student, when presented with an incomplete Pascal Triangle and told to complete it; found a different way of completing it (because they weren't told how, they were expected to figure it out)...

Instead of adding the two parents from above, they took the row as an entity in an of itself, without relation to previous rows... This was done using fractions....

Here's a brief example (click the title above for the full document) :















Note: The previous links/images became invalid. I found another copy of it online and have changed the links.