The division into 0 raises a lot of questions among those people who were engaged in mathematics and had contact with her only at the stage of school education. At the time when the child begins to study in general the operations of multiplication and division, the matter is also suitable for dividing by zero. At this point the teacher says, more often than not, that you can not divide by zero and ... everything.
The explanations at this stage are over. You can not, and even though you're cracking
Before the pupil there is a dilemma - to trust teachers on a word and simply to write, that there is no answer in an example where such operation floats, or to try to understand this question. But most parents who graduated from school a long time ago and were safely thrown into the dump of the brain all the knowledge that they were hammered into during school hours (except those that were somehow useful to them in life), too, can not really help in this matter . And the output is relatively simple. Well, if the teacher approaches the question, why can not you divide by zero, from the creative side. To do this, it will be sufficient to perform normal operations with a visual demonstration of the process. What are we talking about?
Demonstration of different division operations with the help of actions understandable to any person
You can take a few apples, say, six pieces, and explain that 6 is the number that you want to share, that is, according to the studied mathematical terms, is divisible. The teacher stands near the board, and 6 apples lie on the table in front of him. Then he calls two people from the class and divides these apples equally between them. That is, two people in this case stand for the divisor-the number to which the dividend should be divided. To each student the teacher hands over three apples. That is, the process of division occurs precisely when the teacher passed the apples to the hands of the disciples. And three apples in the hands of each child - this is the private of the division.
Zero-to-number division - demonstrating the origin of the process
The question of why you cannot divide by zero, occurs on the reverse of the situation – why it is possible to divide zero by the number? It is now we are smart and we know that any number can be divided by another, and it will be divided evenly, or you will be shot, or even a negative sign, root or PI, anything is possible. But with zero mystery and all.
What happens when you divide zero by a number?
In order to explain that it is impossible to divide by zero, first we will understand what happens when 0 is divided by a certain number. The same teacher stands near the board, and he has nothing on the table. Before him, emptiness, zero. When students approach him and stretch out their hands to get their private, the teacher shares this with nothing, just by touching their palms. That is, he had one big nothing, and he gave it to two disciples. Thus, it becomes clear that the division of zero into any number takes place, because the transfer process took place. With the only difference is that with zero result.
Case of the third
Similar, the third situation is needed already in order to show why it is impossible to divide by zero. The teacher in the hands or on the table in front of him again those six apples, as in the first situation. But we divide by zero, because to him for apples no one is perfect.
That is, those two students who came up earlier in the first situation were number 2. To represent the number 0, it turns out that no one should come. As we remember, it is the transfer from the hands of the teacher of apples to the hands of the disciples is the process of division. But now there are no students, and the process of division does not happen to anyone. From this, it turns out that it is impossible to divide by zero. For children at the level of school education, this is an elementary explanation.
Simple and easy to explain. And after let the same teachers of the Institute do the same
After the higher education institution and study the concept of boundaries, for example, removed the question of why you cannot divide by zero, because you find that it can be done. Dividing something by zero, we get infinity, uncertainty. The infinite dimensionality of such a result is not yet fully defined, and a person who does not have a special mathematical education is not able to understand why this is needed, what goals were pursued in solving this operation, and what this generally gives. But for schoolchildren of the above described explanation is quite enough to satisfy their desire to understand why it is still impossible to divide by zero - do not just say it and put the children before the fact, but give them an interesting and entertaining explanation.