I've been tutoring 1 on 1 middle school kids (at the 8th grade level) in underprivileged areas and what I find is that they have little understanding for what fractions are/represent at all. For example, I asked a student what the decimal value of 1/2 was (I had explained what decimal values were beforehand) and she didnt know. I was shocked (maybe its because we're cs people we have a special affinity for 2s). As a further test I gave her a piece of paper and asked fold the paper in half and she knew it instantly. I then asked where on the paper the 1/4 mark was. Again, she didnt know. This came from a further problem of not understanding that (1/2)/2 is 1/4. After playing with the paper folding it in so many ways she started to internalize what these fractions meant.