I'm not sure if you're familiar with this visual way of multiplying numbers together, it has nothing to do with fractions, but I just thought about it. I think it's called vedic multiplication sometimes, or just the sticks method.
I'm using a thicker line here to represent 4 to save me some time, so intersections with the thicker line are worth 4, two thick intersecting lines would be worth 16.
@neauoire it reminds me a little technique i had found somewhere (but i don't remember where) when i was at school, to multiply 2 polynomials. You put the coefficients on lines and columns of a table, you multiply them in each cell, and you add the diagonals to obtain the result. It looks like we can do it with your technique too, except you have to invent a way to deal with negative numbers ☺️