Dividing by Nothing

It is well known that you cannot divide a number by zero. Math teachers write, for example, 24 ÷ 0 = undefined. They use analogies to convince students that it is impossible and meaningless, that “you cannot divide something by nothing.” Yet we also learn that we can multiply by zero, add zero, and subtract zero. And some teachers explain that zero is not really nothing, that it is just a number with definite and distinct properties. So, why not divide by zero? In the past, many mathematicians did.