I see this as an arcane question. I don't fault anyone for failing to notice that 3/5 is 12/20, and hence the largest. Math rules.
This is not a particularly difficult question. I put it more in a "general education" category than a hard math question. Every teacher above kindergarten should be able to answer it without blinking an eye.
If you think this is "arcane" what happens when the kids get to algebra? Or, a little bit of trigonometry anyone?
It's hardly arcane. This is from a qualifying test for teachers. This the sort of problem teachers need to decipher for students along about fifth or sixth grade. They can't explain it if they can't handle it themselves.
I don’t know. If you ask me, the question is aimed at the lowest common denominator.
One quick glance can see that 3/5 is the only one greater than 1/2. You don’t need to know exactly how much greater to answer the question.
Most common sense people will think of pieces of a pie and immediately see 3/5 as the biggest piece of the pie.
Teachers (at least at ISU, Normal) are trained to avoid common sense and live in a world of semantic fantasy.
But that's not even necessary to arrive at the correct answer. Only one of the fractions is greater than 1/2.
Ability to convert fractions to decimals is pretty basic stuff. I wouldn’t consider it arcane at all.