Why can’t you divide by zero?

Basic Mathematical Operations Read more from
Chapter Math Basics

Dividing by zero is like the old saying, “You can’t get something from nothing.” Mathematically speaking, it’s the same way: You can’t “divide by nothing.” In fact, when something is divided by zero, the answer is always undefined.

Here are a few ways of looking at this: There is a rule in arithmetic that a(b/a) = b. So if we say that 1/0 = 5, then 0(1/0) = 0 × 5 = 0. In other words, if you could divide by 0, this rule would not work. Another way to look at the “no to 0 as a divisor” problem is through multiplication: if 10/2 = 5, we know that 5 × 2 = 10; the same for 5/1 = 5, thus we know that 5 × 1 = 5. But if you take 5/0, that would mean that the answer times 0 would equal 5, but anything times 0 is equal to zero. Because there is no answer to this dilemma, mathematicians say you can’t divide by zero.


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