Eric,
I'm not very good at this, but I will take a stab at it. You are trying to use Tex notation in one place, where it is okay, and in another place, where it is not. In other words, you can use Tex notation to show pretty math formulas in the question, but, in the calculated answers you have to use the notation used for the calculated question type (also for calculated multichoice type). Check this doc page: http://docs.moodle.org/24/en/Calculated_question_type#Page_2._Choose_dataset_properties
Instead of your answer: {=$\frac{{{a}+{x}}}{{{b}+{y}}}$}
It should be something like {a+x}/{b+y} to get a fraction answer or {={a+x}/{b+y}} will give a decimal point answer.
Hope this helps,
AL