Yes, there was a need for fractions.  Now they bury these things in the symbols menu.  I use the ASCII code for ½ most of the time.  I use fractions when describing one of the cameras that I use.  It is called whole plate and the dimensions of whole plate are 6½ x 8½ inches.

They were most likely used to fill out forms when those forms required a description of some sort, maybe lumber lengths.  Possibly on invoices.  There weren't always digital scales that gave everything in decimal places.

And a question about fractions: why do English typewriters or typewriters intended for the British market have such an overwhelming number of fractions compared to other keyboard layouts?

All I know is that one of my SM9s has a 1/3, 2/3 key, but types 1/4, 1/2! It's not a replacement key, according to the guy I bought it from, who got it new.

I still think they're a waste of key space, since you can type any fraction you want using the / key.

Re: British typewriter keyboards and fractions, my British keyboard Lettera 22 has 1/4, 1/2, 3/8, 3/4. For what purpose, I've asked myself? I've thought perhaps when describing weight measurements in the older stone units, but a quick glance at Wikipedia dispels that thought, as I didn't see mention made of fractional values of stone units.

Then I took a look at the older Pound Sterling units of pounds, shillings and pence. I didn't see much reference to fractional values being represented there either, since prior to the decimalization of the pound in around 1971 it was more common to use terminology such as £1 12s 6d, but after it would be represented as £1.62 1⁄2, for example. However, this was well after my Lettera 22 was built (in the late 1950s), so there's still some reason I'm missing.

Perhaps one of our British members can enlighten us, as I'd be curious to know.

~Joe