Replace the 3 by some other positive integer , and the problem works out the same way. Here's a fantastic video by Numberphile explaining what goes on behind the scenes when you divide by 0, have 00, and have We know that division is the same as repeated subtraction.
Dividing by 0 would be repeatedly subtracting 0 from a number. This would go on forever and we would never reach an answer. Let's think about fractions for one second. If two fractions have the same denominator , the one with the bigger numerator is bigger. The process we described means that every single fraction with a denominator has the same value.
This is impossible as we know that the fraction with the higher numerator in this case should be the bigger number. Pre-Algebra Dividing Integers. Explanations 4 Alex Federspiel. Video Division Properties by mathman Here's a video by mathman that goes over some properties of division. A Number Divided by 0 Finally, probably the most important rule is: a0 is undefined You cannot divide a number by zero!
Related Lessons. View All Related Lessons. Caroline K. Dividing by 0. Image by Caroline Kulczycky. We could argue that it's 1, or 2, and again we have a contradiction since 1 does not equal 2. But perhaps there is a number z satisfying 2 that's somehow special and we just have not identified it? So here is a slightly more subtle approach. Division is a continuous process. Suppose b and c are both non-zero.
Then, in a sense that can be made precise. A similar statement applies to the numerator of a ratio except that it may be zero. There are many ways in which we can choose a and b and let them become smaller. For example, we might pick. But we could just as well pick. So that means that 6 divided by 2 does equal 3.
And we can also say that this is "defined" because it satisfies the whole definition of division. Likewise, if it only satisfies one part of the definition, it would mean that it is "undefined. So let me clear this, and let's start with zero divided by 1. I am going to say that this equals zero because 1 times zero equals zero.
It satisfies this second part of the definition. And this first part, if you were to plug in, say, a 1, a 2, or any other number, then it wouldn't equal that so we can actually say that "c" is unique. So it satisfies that this is actually the only number that you can put there to actually equal zero. We can say that zero divided by 1 equals zero and we can also say that this is "defined" as well.
Our next example is going to be 1 divided by zero. And a lot of people like to guess that it would be zero. So, let's try that out. We take our "b" which is zero and multiply it by our "c" which is zero. We don't get what "a" is because of course, zero times zero does not equal 1. Since it doesn't satisfy at least one part of that definition, then that means that it is considered "undefined. Well, I think all of us can agree that we can obviously put in a zero there and the second part will be defined.
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