What is 0 divided by 0?

Most of us learn basic math in school, and it is commonly said and even widely accepted that any number divided by zero has the result undefined.This means that the answer to the question "What is 0 divided by 0?" is that the answer is undefined. What this means is that there is no real answer to this question since one cannot typically divide a number by zero.

Understanding the Concept

Earlier, many mathematicians have tried to come up with a definitive answer to this question by looking at the behaviour of fractions when divided by zero. To understand "what it is to divide 0 by 0", we must first look at how the numerator is divided by the denominator in the fraction and then examine the behaviour of fractions when divided by zero.

When dividing fractions, we usually want to make the denominator (the number on the bottom) of the fraction equal to one. We typically try to simplify the fraction as much as possible, making its numerator and denominator co-prime or without common factors except 1. To do this, we divide both the numerator (the number on the top) and the denominator by the common factor number. This is called "cancelling out" since whatever number we are dividing, both the numerator and denominator will cancel each other out.

For example, if we are dividing the fraction 8/24, we would divide both the numerator (8) and the denominator (24) by the common factor number 8. This would give us the fraction 1/3, since 8/8 = 1 and 24/8 = 3. In other words, we have cancelled out the number 8 from both the numerator and denominator, leaving us with a common factor number of 1. The fraction 1/3 is in the simplest form because the numbers 1 and 3 do not have any common factor except 1.

Now, what happens when we try to divide a fraction by zero? We typically make the denominator (the number on the bottom) of the fraction equal to zero, not one. This is not even a defined fraction form anymore. Since we can't divide any number by zero, it is generally accepted that the answer is undefined. This is the same answer that we get when we ask, "What is 0 divided by 0?" because we can't divide zero by zero either.

However, some mathematicians argue that if we take the same concept of "cancelling out" and apply it to a fraction divided by zero, then the answer would be "1". This is because if you divide both the numerator and denominator of a fraction by zero, then both numbers will effectively be "cancelled out", and the resulting fraction would be 1/0, which can be simplified to just 1. However, there is no specific concept to prove this mathematically.

That is why, this theory is still debated among mathematicians, and there is no single accepted answer to the question, "What is 0 divided by 0?". Some mathematicians argue that the answer is undefined, while others argue that the answer is 1. Ultimately, it seems that this is a question that has no definitive answer and can only be answered with a philosophical debate.

The Bottom Line

Either way, it is important to remember that you cannot divide a number by zero and that the answer to the question "What is 0 divided by 0?" is undefined. This is a fundamental rule of mathematics, and it is important to remember when dealing with fractions and other mathematical concepts.