Why can't we divide by zero?

Question

We say that division by zero or a fraction with a denominator of zero is "undefined" or "not a Real number." Why is this? Isn't anything divided by zero, zero?

Answer 1

The statement "n divided by d is q" is equivalent to another statement: "d times q is n."

For instance, when we assert that 12 divided by 4 is 3, we are correct because 3 times 4 is12. To say that 12 divided by 0 is some number, however, would imply that some number times times 0 is 12. Since any number times zero is zero, there is no number that can be multiplied by zero to make 12. Therefore no number is 12 divide by zero; it is an impossible operaton.

The same argument holds for every number you might try to divide by zero -- every number except zero itself. The statement 0 divided by 0 is some number is not so much impossible as ambiguous because it implies that 0 times some number is 0. Since 0 times ANY number is 0, the statement has infinite possible solutions and therefore is not meaningful.

Hence, division by zero is undefined.

Answer 2

Hey there!

Great question—dividing by zero is one of those things in math that seems like it should make sense, but actually causes a lot of problems. The simplest way to think about it is that division is just asking, "How many times does this number fit into that number?" If you divide 10 by 2, you get 5 because 2 fits into 10 exactly five times. But if you divide by zero, you're asking, "How many times does nothing fit into something?" That doesn’t really work—zero times anything is still zero, so there’s no number that makes the equation hold up.

Another way to see the issue is with multiplication. If we say 10 ÷ 0 = X, then that means X × 0 should equal 10. But anything multiplied by 0 is always 0—never 10! That’s why division by zero is undefined; it just doesn’t play by the normal rules of math.

Hope that helps! Let me know if you have any follow-up questions—I’d be happy to explain further.

Answer 3

Hi, this is a good question. The number zero is neither positive nor negative or even nor odd making it a completely neutral number. Since the number can’t really go into any other number a certain amount of times ( as we would think of as 8 going into 16 twice) it can’t really be justified that zero can divide a number

Answer 4

Anything divided by zero is infinity or undefined.

Answer 5

Try dividing any number by a small number. Say, 1 divided by 2. The result is 0.5, as a decimal fraction, or 1/2, as a ratio fraction.Then take half of 2 to get 1. Divide again, and you get 1. Divide the divisor by 2 and you get 1/2, and 2 divided by 1/2 is 4.

The closer your divisor get to zero, the bigger the quotient is. As your divisor gets closer and closer to 0, your quotient gets closer to closer to infinity. You can't stop this process of approaching infinity as you divide by smaller and smaller numbers. Infinity cannot be defined by a single number, and hence it is undefined.

Similarly, a number divided by zero is undefined. Does this make sense now?