Is $1/(1/0)$ undefined, or does it equal zero?

Question

Is $1/(1/0)$ undefined, or does it equal zero? By one way of thinking, you could say $1/(1/0)=1*0/1=0$ (taking the reciprocal) and thus equals $0$. But by another, the original expression simply cannot be evaluated because there is division by zero. I think it's undefined (with the reciprocal in fraction division merely being a shortcut to calculate the number of times one fraction can go into the other), but many other sources seem to disagree (with others agreeing). Which is correct?