Can ratios really be manipulated as fractions?
In high-school Maths, we were taught that it was possible to manipulate ratios as fractions. For example,
My question relates to the second line of working, where we represent as . As I understand it, s better represented as one part of 8 total parts, i.e. My question, then, is this:
Is there a simple way of showing (or better still, a rigorous proof!) that a ratio-equation of the form can in all cases be rewritten as ?