If the numbers 17/24, 1/2, 3/8, 3/4, and 9/16 were ordered from greate

Yes, that's true when everything is positive -- the idea is, if you add a to the numerator and b to the denominator of a fraction, its overall value moves towards a/b. That can be a great way to compare fractions quickly when other techniques (common denominator, benchmarking, converting to decimal, etc) would be awkward. Here, I'd use that principle, but only once -- we can almost immediately see here that 3/8 < 1/2 < 9/16 < 3/4, whether by comparing each fraction to 1/2, getting a common denominator of 16, or using knowledge of decimal conversions. To find which number is the median, the only question is whether 17/24 is less than or greater than 9/16. And going from 9/16 to 17/24, we're adding 8 to the numerator and 8 to the denominator, so the value of the fraction would move towards 8/8 = 1, and therefore must get bigger since we're starting with a fraction less than 1, and 9/16 < 17/24 must be true. So 9/16 is in the middle.

For your second question, again assuming everything is positive, subtraction will work in the opposite way as addition (e.g. subtracting 8 on the top and on the bottom, as you were doing, will move you away from 8/8 = 1). But there's never any reason to think about subtraction, because you can always think only about addition in situations like this. So rather than start, in this question, from 17/24, and notice you subtract 8 from the top and bottom to get to 9/16, you can instead start from the fraction with the smaller numbers, 9/16, and notice you add 8 to the top and bottom to get to 17/24. Then you're in a situation that is easier to think about, conceptually.