It's just a naming convention for the scale length. The numbers don't actually equate to anything. See the quote below:


  Smaller scale instruments are used extensively to teach younger
  players. The size of these is described by a "conventional" fraction
  that has no mathematical significance. For example, a 7/8 violin has a
  scale of about 317 mm, a 3/4-size instrument a scale of 307 mm, a
  half-size one 287 mm, and a quarter-size one 267 mm. 1/8, 1/10, 1/16
  and 1/32 and even 1/64 violins also exist, becoming progressively
  smaller, but again in no proportional relationship. (A full-size
  instrument is described as 4/4.) - Wikipedia 


While it doesn't have a math reason, it is more practical remember simple a fraction over a seemingly random number. 

Why are 1/2 (or 3/4, etc) violins called that way if they are not 1/2 size?
What is it?

How is it performed?

May one perform it?

And, if so, when may it be used?
