The logic your student used seems rather obvious. 2/3 -1 = 2/3 - 1/1 so therefore, the answer is (2-1)/(3-1) or 1/2. :lol: I love playing with math. 
In my freshman year of chemistry, I bought the text and the paperbacked problem syllabus. The text author was an obnoxious, pompous old instructor at UC Berkeley who started his preface by insulting all the readers. I got pissed and even now, 65 years later have never opened that stupid book beyond the preface. However, the syllabus was loaded with humdreds of chem based math problems. We were assigned two or three of them for each chapter, but I loved doing them so I would go through and do all fifty or so for each chapter. Using what I learned there and listening to the lectures, I was in a three way tie for first place out of 340 students by the end of the semester. In other words, understanding the mathematical basis in science courses is far more important than the minor stress put on it in classes.
Occam