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You can prove (a/b)/(c/d)=ad/bc, by showing that bc/ad is the multiplicative inverse of (a/b)/(c/d) duh, but need to use the identity (a/b)(p/q)=ap/bq, I am too lazy to write it all, I have no practical example for this, like that with the circle, let me see if I can think of someting
