Doesn't mean much unless you are solving a separable differential equation. You can always use the rules of algebra to put them together whether you divide or multiple them across.
I know that dy/dx is the notation for the derivative of a function and i also know that dy is the infinitely small difference between two y values and dx is the infinitely small difference between two x values.
The part that confuses me is when i see the dy and dx seperated from eachother on both sides of an equation. I don't know what that means.
If you treat as a simple fraction, you can "multiply" in a sense by and rearrange to get.
, and integrate both sides with respect to the respective variables.
As dwsmith said this is used when solving separable differential equations.