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# Why can’t you divide by zero?

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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