Disclaimer - I only work off of knowledge that I have; the knowledge thus far is very elementary compared to calculus as I am still in algebra 1, but my knowledge is very scattered. This is just something I have noticed about fractions. We all know fractions are equivalents right? Well that is true, but to an extent. What I have found is that fractions are only equivalent ratios or rates. 1/2 = 2/4 is a ratio because they both give 0.5 as the answer, however, you could say you have any quantity of something over a number. Say you have 1/2 apples in a basket. You could express this as 1/4, 1/400, or 1/4000000. This is not a ratio to anything, it is a quantity. 1/2 apples is not the same as 2/4 apples, because you now have two apples instead of one. Your basket can hold an invariable amount of apples so it doesn't matter what the denominator is (you can stack the apples). So saying your basket has 1/2 apples or 1/9000 apples does not change the number of apples you have. When you say you have 1/0 apples, you are saying you have an apple that does not fit into your basket. Honestly, you could compare 1/2 and 2/4 and notice that 2/4 is a scale of 2 from 1/2, and so the ratio here is that one of your apples is the volume of two apples you could say. And so on down the line. You can also say vice versa: The volume of two apples is equal to one. This also applies for fractions with decimals like (0.5)/(1.5). If you multiply by 10 you get 5/15 and that is not equal to having half of an apple. I'm not saying that if you divide 2 by 4 or 1 by 2 that you don't get 0.5, I'm just saying they are only equivalent ratios or rates, not quantities.
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