My knowledge of Excel is all self-taught just by playing around. I've done it before, but I am drawing a complete blank. I've got two separate numbers representing different categories in the same cell (three examples, (1/1) or (56/198) or (78/0)). In my case referring to cuts from a customer order as (chargeable/non-chargeable). Can I set a particular cell to display the sum in the same format (from above (134/199))?
What you're asking is certainly possible. You've made it trickier than it could be--because the "numbers" in your figures are actually text (they'd have to be; otherwise Excel would resolve those numerators and denominators as 1, 0.28282828, and 78)
So to create what you're asking requires first figuring out the value of each numerator, each denominator, adding those, and then converting back to text. Easily done (I've attached a spreadsheet that does that, to illustrate). But presumably these three examples are just that, examples. You may, in the real world, have longer sets of such items.
This could even be done in a single formula (a rather elaborate one), but again, how many such instances of this kind of cell are you wanting to sum up?
My suggestion would be to rethink how you store the raw data in the first place. Specifically, have a column for Chargeable and another for Non-Chargeable for each order, and then plain ol' addition at the bottom would take care of those sums.