The division by 0 raises many questions for those people who were engaged in mathematics and had contact with it only at the stage of school education. At the time when the child begins to study the operations of multiplication and division as a whole, it also comes down to division by zero. At this moment, the teacher says, most often, that it is impossible to divide by zero and ... that's all.
The explanations at this stage are over. You can not, and even you burst
There is a dilemma in front of the student - take the word for the teachers and just write that there is no answer in the example where such an operation pops up, or try to sort out this question. But the majority of parents who had graduated from school long ago and safely threw all the knowledge that they hammered into during school time (except for those who were somehow useful to them in life) safely didn’t help much in this matter. . And the output is relatively simple. Well, if the teacher comes to the question, why can not be divided by zero, from the creative side. To do this, it will be enough to perform the usual operations with a clear demonstration of the process. What is it about?
Demonstration of various division operations using actions that any person can understand
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 blackboard, and in front of him on the table are 6 apples. 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 into which the dividend should be divided. A teacher gives three apples to each student. That is, the process of division occurs precisely when the teacher handed the apples into the hands of the students. And three apples in the hands of each child - this is the quotient of the division.
Dividing zero by number - 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, let us first understand what happens when 0 is divided by a certain number. The same teacher stands near the blackboard, and he has nothing on the table. Before him is emptiness, zero. When students come to him and stretch their hands to get their private, the teacher shares this with him with nothing, just touching their palms. That is, he had one big nothing, and he gave it nothing to two students. Thus, it becomes clear that the division of zero by any number takes place, because the transfer process took place. With the only difference that with zero result.
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 the number 2. To represent the number 0, it turns out that no one should go. As we remember, the transfer from the hands of the teacher of apples to the hands of the students is the process of division. But now there are no students, and the process of sharing does not happen with anyone. From this it turns out that it is impossible to divide by zero. For children at the school level, this is an elementary explanation.
Simple and easy to explain. And then let the 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 dimension 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 it gives. But for school-age pupils, the explanation described above is quite enough to satisfy their desire to understand why it’s still impossible to divide by zero — not just say this and put the children before the fact, but give them an interesting and entertaining explanation.