Why can't ratios be derived from algebraic expressions? 100 cents is worth 1 dollar, so if I wanted to express it in algebra I will write something like this: $100C=1D$, which checks out when I try to calculate for some other D.
For eg: how many cents in 2 dollars. Then, $2D=200C$, in essence, expression was multiplied by 2 on both sides.
Now, if I wanted to check what's the ratio of dollar(D) to cents, it will be $D:C=1:100$. This makes sense since in a dollar there will be more cents than the dollar as cents is a lower denomination.
The above ratio can also be written as $D/C=1/100$.
But, if I try to write $D/C$ from the algebraic expression it gives me: $D/C=100/1$
That's the opposite of what I got from my ratio $D:C=1:100$. So, what's happening here? I mean it feels intuitive when we are given 14 daks = 1 jin to write $DAK/J=1/14$ as ratio but it's wrong. For the purpose of solving questions I can just memorize it but what if someone asks me to explain it?

You have to be careful about what the symbols $C$ and $D$ mean. Is it the value of a cent and a dollar (which gives $D/C=100$), or is it the number of cents and dollars needed to pay for a particular thing (which gives $D/C=1/100$)? You seem to swap between the two without noticing.
