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?

In general I would not compare ratios with fractions, because they are different things. As rschwieb mentioned in the comments: when you have apples, lemmons and oranges, you can say that the ratio is $3:4:5$. The only "link" you can make to fractions is that you can now say that this the same as saying the ratio is $\frac35:\frac45:1$. From which you can very easily see that there are $\frac35$ as much apples as there are oranges. You see, the fraction is used to express a relation between two "elements" of your whole whatever. 
The key thing is this: when you have a bowl with $3$ oranges and $5$ apples, the ratio $3:5$ gives you the relation between the amount of oranges and the amount of apples. And so does the number $\frac35$ within this context. Confusion arrises from the fact that we are trained to immedately conclude that a fraction, alway gives you a relation between the whole of someting and a part of the whole. This is not always the case though as you can see from the ratio story.

N.B. I would like to add that I personally feel that someone or some method that is teaching mathematics should avoid the comparrison of ratios with fractions, because it generally leads to confusion as it did for the OP. Someone in the process of learning ratios is very likely not ready to be confronted with such a subtle, yet major difference in the application of fractions.  
