Ratios as Fractions I’m having trouble understanding how fractions relate to ratios. A ratio like 3:5 isn’t directly related to the fraction 3/5, is it? I see how that ratio could be expressed in terms of the two fractions 3/8 and 5/8, but 3/5 doesn’t seem to relate (or be useful) when considering a ratio of 3:5.
Many textbooks I’ve seen, when introducing the topic of ratios, say something along the lines of “3:5 can be expressed in many ways, it can be expressed directly in words as ‘3 parts to 5 parts’, or it can be expressed as a fraction 3/5, or it can be…” and so on. Some textbooks will clarify that 3/5, when used this way, isn’t “really” a fraction, its just representing a ratio. This makes absolutely no sense to me. Why express 3:5 as 3/5 at all?

"Why express 3:5 as 3/5 at all?" 
There is a way 3/5 can be a useful representation of the ratio 3:5, as described in this excerpt from wikipedia (I added the boldface):
"If there are 2 oranges and 3 apples, the ratio of oranges to apples is 2:3, and the ratio of oranges to the total number of pieces of fruit is 2:5. These ratios can also be expressed in fraction form: there are 2/3 as many oranges as apples, and 2/5 of the pieces of fruit are oranges. If orange juice concentrate is to be diluted with water in the ratio 1:4, then one part of concentrate is mixed with four parts of water, giving five parts total; the amount of orange juice concentrate is 1/4 the amount of water, while the amount of orange juice concentrate is 1/5 of the total liquid. In both ratios and fractions, it is important to be clear what is being compared to what, and beginners often make mistakes for this reason."
I think I've fallen into that beginner mistake category. As long as it is clear what is being compared to what, representing a ratio of 3:5 as a fraction (3/5), can make sense and be useful. I was jumping to the conclusion that a fraction is always comparing "number of parts" to "total number of parts that make a whole". You can also have a fraction which directly compares "number of parts of type A" to "number of parts of type B".
So for example, say you are told there are 12 apples in a bin (this bin contains both apples and oranges). You are also told that the ratio of oranges to apples is 1:6. You are asked, "how many oranges must be in this bin?" You can find the answer by turning the ratio into a fraction, 1/6. You can understand this fraction as, "there are 1/6 as many oranges in this bin as there are apples." So doing the math, 12 * 1/6 = 2. There must be 2 oranges in the bin.
