How can Cross Multiplication be intuited or pictured? average(average(a,b),c) vs. average(a,average(b,c)).
Why were my two questions closed? Moderator Peter Taylor's comments feel dissimulating.
But another user r~~ understood my question.
If the question is "Why does dividing two equal things by the same thing give two equal things" then I'm not sure why that isn't intuitive already. Separately, the first image gives a false statement (because you always need to be wary of the special case of division by zero), and I'm not sure what the second image is about..
Peter Taylor understands my question faultlessly, but the hitch is that he doesn't know how to intuit this? This is the same question as https://math.stackexchange.com/a/2667399, but I'm seeking a better explanation than cakes and pieces of cake.
I'm seeking intuition like these questions. Intuitively, why $pt = qr \iff p/q = r/t$?