Adding Ratios

In the first half of a basketball game, Shaundra made 2 of 6 free throws. In the second half, she made 7 of 8. Overall, what was her success rate for free throws in this game?

Suppose a middle school student responded to the above problem by writing:

Evaluate the student’s answer.

Is the addition of ratios and fractions comparable?
Do the ratios 1:3 and 7:8 add to yield a success rate equivalent to that of 2:6 plus 7:8? Why or why not?

Extension:
Can you find any non-zero real numbers that would produce this type of equivalent relationship for fractions? That is, does:

for some case of a, b, c, and d? Explain