In my work, when covering the topic of fractions in the 6th grade, I suggest that children write an essay on the topic “Man is a fraction.” The students are surprised. How? Write an essay on mathematics. At the same time, I give this task to high school students. I read these mini-essays with pleasure.
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Man is a fraction
The work was completed by: Umyarova R.A., mathematics teacher MBOU-Starokulatkinskaya Secondary School No. 1 r.p. Staraya Kulatka Ulyanovsk region
Goals To educate children positive traits; The desire for self-improvement, self-affirmation, self-education; Ability to balance abilities and capabilities
For several years, in my work, I have been asking children to write an essay on the topic “Man is a fraction” based on the statement of L.N. Tolstoy Students are surprised: how? Can I write an essay in mathematics? But many guys write their thoughts so well that adults wouldn’t write them like that. Moreover, I give this task to students of different ages, i.e. 5-7 grades and 11th grade. While re-reading the essay, I decided to make a presentation.
Already in the early days of his work, Tolstoy came to the idea that a living human character is a complex combination of various, often contradictory, traits and qualities. And, observing the multiplicity of such combinations, Tolstoy tried to find a “formula” to designate them. Living human character seemed to him to be a fraction, in the numerator of which the writer put the advantages and virtues of a person (his “advantages”), and in the denominator - his shortcomings, the main one of which he considered conceit. The larger the denominator, the smaller the fraction, naturally, and vice versa: with a smaller denominator, the fraction expressing the actual “cost” of a person, his moral value, increases. A person is like a fraction: the denominator is what he thinks about himself, the numerator is what he really is. The larger the denominator, the smaller the fraction. (L.N. Tolstoy) Success Self-esteem = ------ Claims
L.N. Tolstoy said: “A person is a fraction whose numerator is what a person is, and the denominator is what he thinks about himself.” I think that the more correctly and adequately you evaluate yourself, the closer the numerator and denominator are, that is, you strive for the whole, with the world around you, with society. Bulkhin Rafael 6th grade
Who you imagine yourself to be in life and who you are in life do not always coincide. In most cases, the fraction is incorrect, since a person is not characterized by self-criticism and he most often overestimates his capabilities, increasing the denominator of the fraction, and the small numerator is explained by external factors and coincidence of circumstances: “Yes, I am so handsome, hardworking, but I am underestimated, there are enemies all around ill-wishers." An ideal indicator would be a unit, that is, the coincidence of self-image and reality, or a fraction, an equal numerator and denominator, but this is not typical for humans. Ismail Maryam 7th grade
Each person has his own character and his own self-esteem. Some people have high self-esteem, which is not a good character trait. In this case, the true face of a person is lost. According to the rules of mathematics, the larger the denominator and the difference between the numbers in the fraction of the numerator and denominator, the smaller the final number. For example: which is greater than 2/3 or 2/7? Of course, 2/3 is greater than 2/7. Returning to the statement of L.N. Tolstoy, if a person thinks about himself and has the same conceit as his character, people will appreciate him. For example: one of my friends sometimes wants to seem smarter than she really is, and then it turns out that she is a braggart. This poor quality person. You must try to think about yourself, too, what you are. You shouldn’t praise yourself in front of others; it’s better to let others appreciate your character and praise you. Safarova Aisylu 7th grade
According to Tolstoy, a person is a fraction. If the numerator is greater than the denominator in this fraction, then the person is good, active, smart, kind, but thinks to himself that he is stupid, evil, passive. This person has low self-esteem, he will oppress himself with this. If the denominator is greater than the numerator, this person will praise himself without representing anything. This person has high self-esteem, and he thinks good things about himself, for example, the donkey from Krylov’s fable “The Donkey and the Nightingale.” I would choose as a friend the person whose numerator and denominator are equal, that is, a person who represents what he thinks about himself. Ablyazova Regina 7th grade
“A person is a fraction in which the numerator is what a person is, and the denominator is what he thinks about himself.” This is how I understand this statement. For example, it happens that a person thinks of himself better than he represents. It also happens that he has a less high opinion of himself, but he himself is much better. They say about such people: a person with low self-esteem, although his capabilities and merits are high. This is bad. One day, one of my friends boasted that he could easily beat any two guys in football, and when we decided to check, it turned out that my friend had overestimated himself and lost. Therefore, I came to the conclusion that there are few fractions with the same numerators and denominators. Bashirov Lenar 7th grade
The great Russian writer L.N. Tolstoy said: “A person is a fraction, the numerator of which is what a person is, and the denominator is what he thinks about himself.” Thus, we can say that Tolstoy derived a “formula” to indicate human character. From mathematics we know that if the denominator is equal to the numerator, then there will be one. But we also know that the denominator should not be zero, since the entire fraction will not make sense. And also, the larger the denominator, the smaller the fraction. From here you can conduct your reasoning. It is a very rare occurrence when the “denominator” is equal to the “numerator,” that is, the opinion of others does not always coincide with one’s self-esteem. From childhood, our parents taught us that loving ourselves is bad, that a decent person should think first about others, then about himself. You have to be selfless and benefit people. Yes, all this is of course correct, but... I believe that everyone should love and respect themselves. This is simply necessary to maintain self-esteem. But you need to love yourself in moderation. If a person thinks only about himself, then he is an egoist. A person should love himself, but think about the feelings of others. There is such a thing as self-esteem. Self-esteem is an individual’s assessment of himself, his capabilities, qualities and place among other people; it, of course, refers to the basic qualities of a person. It is this that largely determines relationships with others, criticality, self-demandingness, and attitudes toward success and failure. A person, of course, should have moderate self-esteem. That is, you shouldn’t elevate yourself above others, but you shouldn’t underestimate yourself either. A person must be strong, which means confident, and to be confident, you should never think about what others think about you. Shafieva Elmira 11th grade
“A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” Immediately after reading this aphorism, you think, what does a fraction have to do with a person? But if you delve into the statement, if you think about it, so many thoughts come to mind that it is difficult to get out of them. So, a fraction is a decomposed number, the modulus of which is written in the form m / n, where m, n are natural numbers, and m is called the numerator of the fraction, and n is the denominator. A fraction can be proper - an ordinary fraction whose numerator less than the denominator. Consequently, there are people who are “little” but think of themselves as “many.” But for some reason they are classified as a proper fraction. This means that a person always thinks well of himself. I think Tolstoy “when he wrote this statement, knew a lot about fractions. A fraction can also be irregular. This means that their numerator is greater than the denominator, that is, it represents more than he thinks about himself. If the numerator and denominator in a fraction are equal, then it is no longer a fraction, but a whole number. This means that there cannot be a person whose qualities are all equal. Another property of a fraction: the denominator should not be equal to zero! Thus, we come to the conclusion that there are no people who do not think about themselves, who do not have self-esteem. You can not do it this way! This shouldn't happen! I think that a person himself has the right to choose which “fraction” he wants to use as “right” or “incorrect”. But the point is that the difference between the numerator and denominator should not be large. If the “numerator” is equal to zero, then the “fraction” will have no meaning. A person must represent something. And he can think whatever he wants about himself, but! You can't be arrogant. Abdyukova A.R., 11th grade
In mathematics, a fraction is a part of something. It consists of a numerator and a denominator. And even great people respected this mathematical expression. So L.N. Tolstoy wrote: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” The larger the denominator, the smaller the fraction. In fact, we often overestimate ourselves in front of others. But true - only if you take into account the opinions of others about yourself. Mathematics is an exact science, so people should strive to increase the numerator, and this will increase the fraction as a whole. Uzbekova A. 6th grade
Billions of people live on planet Earth. I think, on the one hand, a person is one whole, without fractions. For example, there are people whose character is even, calm, and balanced. He is hardworking, fair, lives honestly. He is respected and appreciated. I think this one has the same numerator and denominator. It's a whole. On the other hand, L.N. Tolstoy correctly noted that: “A person is a fraction, the numerator of which is what a person is, and the denominator is what he thinks about himself.” Because people are never the same. Each person has his own character, which consists of a numerator and a denominator. Some have a very high opinion of themselves, but people judge them low by their deeds and actions. Others are the opposite. Based on this, I think a person is a fraction. Rakhmatullina L., 7th grade
A person is a fraction in which the numerator is what the person is, and the denominator is what he thinks about himself. I completely agree with the statement of L.N. Tolstoy. The numerator of a person is his virtues, skills, abilities and in general everything about what he can do. The numerator is a comparison with others, a person’s dignity; the denominator is a person’s assessment of himself. It is not in the power of man to increase his numerator - his merits, but anyone can reduce his denominator - his opinion about himself, and by this decrease he will approach perfection. But complete perfection never happens anywhere, so you can only get closer to this until the end of your days. This can (and even should) set an example for the younger generation, so that they also strive to improve their abilities and virtues. When the denominator coincides with the numerator, then the fraction becomes whole, the person becomes a full-fledged person. The main thing is not to be arrogant. Don’t say that you can do it well and that you are better than others or that you know more than others. The more you talk about yourself, the larger your denominator becomes and the person is closer not to perfection, but to zero. He becomes a proud, arrogant zero who does not improve himself, while those who silently and constantly say about themselves “This is not enough, I know little and can’t do well” become masters of their craft. Over time, others notice this, begin to praise the master, and recognize him as a master. And he, in turn, lives quietly and peacefully, increasing his skill every day. Tolstoy is a brilliant man. He described the person so accurately, there are no words. I have nothing more to add to this statement. Yagudin I. 11th grade
A living human character is a complex combination of various, often contradictory, traits and qualities. And, observing the multiplicity of such combinations, the writer Lev Nikolaevich Tolstoy tries to find a “formula” to designate them. Living human character seemed to him like a fraction, in the numerator of which the writer put the merits and advantages of a person, and in the denominator - his shortcomings, the main one of which he considered conceit. The larger the denominator, the smaller the fraction, naturally, and, conversely: with a smaller denominator, the fraction expressing the actual “cost” of a person, his moral value, increases. In my statement, L.N. Tolstoy touched upon the mathematical definition. Mathematics - exact science. She teaches logical thinking, analysis and giving an accurate definition. After all, a person is a whole, personal, rational being. There are so many thoughts and dreams about himself in his head that no one will ever know. In life, he will not be able to achieve everything that he thinks about himself. Many years ago, the American psychologist Williams James also derived a formula according to which a person’s self-esteem can be represented as a fraction, the numerator of which is his real achievements, and the denominator is his ambitions and claims. In other words, the most reliable way to increase self-esteem is, on the one hand, not to complete your aspirations, on the other, to add real tangible success. "... Best person- it's not only significant person, but also with good self-esteem. These are the people who usually succeed. Self-esteem gives self-belief, and what he represents propels that person even further. It's like a steam locomotive moving forward. And he gets to his goal!” I believe that you should always make sure that in your own and other people’s eyes you have a fraction equal to one. But fractions are different, and what does it mean that there are many in the world? different people. Mukminova A. 11th grade
The great Russian writer Lev Nikolaevich Tolstoy wrote: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” I realized that the numerator is what people around him see in a person, then there is his upbringing. And the denominator is a person’s assessment of himself. This amazing comparison of a person with a fraction makes one think about what a person should be like. The larger the denominator, the smaller the fraction. We know this from mathematics. But I think the numerator and denominator should be the same. You always need to make sure that you are the same in both your own and other people’s eyes. Recently in a math lesson we covered the topic “Fractions”. There we studied proper and improper fractions. We can conclude that the improper fraction is a person for whom the opinions of others are more important than he thinks about himself, and the correct fraction is a person who overestimates himself. Kurmasheva Elnara, 7th grade
The great Russian writer Lev Nikolaevich Tolstoy said: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” I believe that he is right and I will try to prove it... If a person is more than he thinks about himself, that is, he underestimates (in the best sense of the word) himself, then a person is able to improve and achieve something completely great. Let's do the same with mathematics. In the case considered, the numerator is greater than the denominator, the fraction will be greater than one. (We will not consider fractions with a negative value, since the value must be greater than or equal to zero) If a person is less than he thinks about himself, that is, he is arrogant, then, accordingly, the value of the fraction will be less than one. Let's consider another case when someone represents nothing in total, that is, the numerator is zero. Then, no matter what he thinks about himself, no matter who he considers himself to be, he will still remain nothing, exactly like the value of a fraction whose numerator is zero. There is another type of people who think that they have achieved nothing in this life (the exception is midlife crisis), that is, they are zeros in the denominator of the fraction. In this case, you cannot divide by zero and the value of the fraction does not exist, just as the person as an individual does not exist. From the above we can conclude... It is necessary that the fraction be greater than or equal to one. And a fraction is equal to one if and only if its numerator and denominator are equal, that is, when a person thinks about himself what he is. For me, it is more acceptable when the denominator of the fraction is greater than one, because it is in this case that a person is able to improve more. As Socrates said: “I only know that I know nothing” Timushev I.
“A person is a fraction whose numerator is what a person is, and the denominator is what he thinks about himself” I completely agree with this statement. Man is a fraction. But sometimes either the numerator is greater than the denominator, or vice versa. It happens that they are the same. Of course, every person is something. Sometimes you walk, look at passers-by, and think that each of them is a separate person, an individual, and each of them does not think the same about himself. Everyone represents what is inside them. Nowadays, many people look at a person’s appearance, at his connections, and not at his inner world. This is the mistake; first of all, you need to get to know the person better, without opening up at the first meeting. It is necessary to study his character, his view on certain things, if possible, against him in some situations. It’s not for nothing that they say: “Trust, but verify.” Opinion about yourself is completely different. People, as a rule, have a good opinion of themselves. Some people have high self-esteem, others have the opposite. I believe that every person is what he thinks about himself. In a period of time called life, everything awaits us: joys and sorrows, difficulties and successes, love and breakups, victories and defeats... Everyone lives their life according to their own concepts. In any situation, first of all, self-confidence and a person’s self-esteem are important. A person is a fraction, and I think both the numerator and denominator should be the same. Khabibullina A. 11th grade
We live in a society among individuals. Each of us is diverse in our own way. And whether you become an individual or some kind of “Mr. from San Francisco,” the hero of Bunin’s work, depends on you. The futurist Igor Severyanin had a high self-evaluation, he called himself a genius, although he was a simple writer, he deeply understood the surrounding society, the indifference of some people towards others. Not every talented person, a statesman, may have a high opinion of himself. They strive to gain even more skills and knowledge. There are many types of fractions in mathematics, and so do people all over the globe. Each person chooses his own path to development and subsequent presence in society. Some people listen to the opinions of others and their advice. As they climb the career ladder, they don’t forget old friends. In contrast to them, there is a second type of people. These are self-confident people who do not take into account the opinions of others, considering many to be of secondary importance. Conclusion: they represent more than their own self-esteem. This fraction can be represented as a whole number. That is, these people have a core, they are more friendly towards people. The second type of person is a proper fraction. They consider themselves correct, although they are not. For example, 5/11. These are more selfish creatures. They put themselves first. But in fact, in society, they represent a “loner”, not sociable, proud, narcissistic person. Abdryashitova Z.Z. Grade 11
I agree with the statement of L.N. Tolstoy, because we are all different and that means the numerators too, we think differently and that means the denominators are also different. If you judge me, then I consider myself as one whole, because I am the same as I think about myself. Some people inflate my numerator, and some do the opposite. But I think that people should think better of me rather than worse. Arslanov Lenar, 6th grade
Most likely, a person is a product: The first factor = the amount of what he can do. The second multiplier = the amount of what works how much. If something is equal to zero, then consider there is no person. I mostly agree with them, but how do we understand the phrase “The larger the denominator, the smaller the fraction”? What did the author want to say? I think that the higher he puts himself, inflates his own self-esteem (denominator), the lower he actually is, and what if both the numerator and the denominator are equal. This means that the person is ideal. Unfortunately, such people are hard to find. Adelshin A, 6th grade.
Literature http://bse.sci-lib.com/particle028237.html http://www.omg-mozg.ru/tolstoy.htm http://www.artvek.ru/kramskoy.html
Description of the presentation by individual slides:
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The work was completed by: Umyarova R.A., mathematics teacher MBOU-Starokulatkinskaya Secondary School No. 1 r.p. Staraya Kulatka, Ulyanovsk region
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Goals To develop positive qualities in children; The desire for self-improvement, self-affirmation, self-education; Ability to balance abilities and capabilities
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For several years, in my work, I have been asking children to write an essay on the topic “Man is a fraction” based on the statement of L.N. Tolstoy Students are surprised: how? Can I write an essay in mathematics? But many guys write their thoughts so well that adults wouldn’t write them like that. Moreover, I give this task to students of different ages, i.e. 5-7 grades and 11th grade. While re-reading the essay, I decided to make a presentation.
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Already in the early days of his work, Tolstoy came to the idea that a living human character is a complex combination of various, often contradictory, traits and qualities. And, observing the multiplicity of such combinations, Tolstoy tried to find a “formula” to designate them. Living human character seemed to him to be a fraction, in the numerator of which the writer put the advantages and virtues of a person (his “advantages”), and in the denominator - his shortcomings, the main one of which he considered conceit. The larger the denominator, the smaller the fraction, naturally, and vice versa: with a smaller denominator, the fraction expressing the actual “cost” of a person, his moral value, increases. A person is like a fraction: the denominator is what he thinks about himself, the numerator is what he really is. The larger the denominator, the smaller the fraction. (L.N. Tolstoy) Success Self-esteem = ------ Claims
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L.N. Tolstoy said: “A person is a fraction whose numerator is what a person is, and the denominator is what he thinks about himself.” I think that the more correctly and adequately you evaluate yourself, the closer the numerator and denominator are, that is, you strive for the whole, with the world around you, with society. Bulkhin Rafael 6th grade
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Who you imagine yourself to be in life and who you are in life do not always coincide. In most cases, the fraction is incorrect, since a person is not characterized by self-criticism and he most often overestimates his capabilities, increasing the denominator of the fraction, and the small numerator is explained by external factors and coincidence of circumstances: “Yes, I am so handsome, hardworking, but I am underestimated, there are enemies all around ill-wishers." An ideal indicator would be a unit, that is, the coincidence of self-image and reality, or a fraction, an equal numerator and denominator, but this is not typical for humans. Ismail Maryam 7th grade
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Each person has his own character and his own self-esteem. Some people have high self-esteem, which is not a good character trait. In this case, the true face of a person is lost. According to the rules of mathematics, the larger the denominator and the difference between the numbers in the fraction of the numerator and denominator, the smaller the final number. For example: which is greater than 2/3 or 2/7? Of course, 2/3 is greater than 2/7. Returning to the statement of L.N. Tolstoy, if a person thinks about himself and has the same conceit as his character, people will appreciate him. For example: one of my friends sometimes wants to seem smarter than she really is, and then it turns out that she is a braggart. This is a bad quality of a person. You must try to think about yourself, too, what you are. You shouldn’t praise yourself in front of others; it’s better to let others appreciate your character and praise you. Safarova Aisylu 7th grade
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According to Tolstoy, a person is a fraction. If the numerator is greater than the denominator in this fraction, then the person is good, active, smart, kind, but thinks to himself that he is stupid, evil, passive. This person has low self-esteem, he will oppress himself with this. If the denominator is greater than the numerator, this person will praise himself without representing anything. This person has high self-esteem, and he thinks good things about himself, for example, the donkey from Krylov’s fable “The Donkey and the Nightingale.” I would choose as a friend the person whose numerator and denominator are equal, that is, a person who represents what he thinks about himself. Ablyazova Regina 7th grade
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“A person is a fraction in which the numerator is what a person is, and the denominator is what he thinks about himself.” This is how I understand this statement. For example, it happens that a person thinks of himself better than he represents. It also happens that he has a less high opinion of himself, but he himself is much better. They say about such people: a person with low self-esteem, although his capabilities and merits are high. This is bad. One day, one of my friends boasted that he could easily beat any two guys in football, and when we decided to check, it turned out that my friend had overestimated himself and lost. Therefore, I came to the conclusion that there are few fractions with the same numerators and denominators. Bashirov Lenar 7th grade
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The great Russian writer L.N. Tolstoy said: “A person is a fraction, the numerator of which is what a person is, and the denominator is what he thinks about himself.” Thus, we can say that Tolstoy derived a “formula” to indicate human character. From mathematics we know that if the denominator is equal to the numerator, then there will be one. But we also know that the denominator should not be zero, since the entire fraction will not make sense. And also, the larger the denominator, the smaller the fraction. From here you can conduct your reasoning. It is a very rare occurrence when the “denominator” is equal to the “numerator,” that is, the opinion of others does not always coincide with one’s self-esteem. From childhood, our parents taught us that loving ourselves is bad, that a decent person should think first about others, then about himself. You have to be selfless and benefit people. Yes, all this is of course correct, but... I believe that everyone should love and respect themselves. This is simply necessary to maintain self-esteem. But you need to love yourself in moderation. If a person thinks only about himself, then he is an egoist. A person should love himself, but think about the feelings of others. There is such a thing as self-esteem. Self-esteem is an individual’s assessment of himself, his capabilities, qualities and place among other people; it, of course, refers to the basic qualities of a person. It is this that largely determines relationships with others, criticality, self-demandingness, and attitudes toward success and failure. A person, of course, should have moderate self-esteem. That is, you shouldn’t elevate yourself above others, but you shouldn’t underestimate yourself either. A person must be strong, which means confident, and to be confident, you should never think about what others think about you. Shafieva Elmira 11th grade
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“A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” Immediately after reading this aphorism, you think, what does a fraction have to do with a person? But if you delve into the statement, if you think about it, so many thoughts come to mind that it is difficult to get out of them. So, a fraction is a decomposed number, the modulus of which is written in the form m/n, where m,n natural numbers, with m called the numerator of the fraction, and n the denominator. A fraction can be proper - an ordinary fraction in which the numerator is less than the denominator. Consequently, there are people who are “little” but think of themselves as “many.” But for some reason they are classified as a proper fraction. This means that a person always thinks well of himself. I think Tolstoy “when he wrote this statement, knew a lot about fractions. A fraction can also be irregular. This means that their numerator is greater than the denominator, that is, it represents more than he thinks about himself. If the numerator and denominator in a fraction are equal, then it is no longer a fraction, but a whole number. This means that there cannot be a person whose qualities are all equal. Another property of a fraction: the denominator should not be equal to zero! Thus, we come to the conclusion that there are no people who do not think about themselves, who do not have self-esteem. You can not do it this way! This shouldn't happen! I think that a person himself has the right to choose which “fraction” he wants to use as “right” or “incorrect”. But the point is that the difference between the numerator and denominator should not be large. If the “numerator” is equal to zero, then the “fraction” will have no meaning. A person must represent something. And he can think whatever he wants about himself, but! You can't be arrogant. Abdyukova A.R., 11th grade
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In mathematics, a fraction is a part of something. It consists of a numerator and a denominator. And even great people respected this mathematical expression. So L.N. Tolstoy wrote: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” The larger the denominator, the smaller the fraction. In fact, we often overestimate ourselves in front of others. But true - only if you take into account the opinions of others about yourself. Mathematics is an exact science, so people should strive to increase the numerator, and this will increase the fraction as a whole. Uzbekova A. 6th grade
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Billions of people live on planet Earth. I think, on the one hand, a person is one whole, without fractions. For example, there are people whose character is even, calm, and balanced. He is hardworking, fair, lives honestly. He is respected and appreciated. I think this one has the same numerator and denominator. It's a whole. On the other hand, L.N. Tolstoy correctly noted that: “A person is a fraction, the numerator of which is what a person is, and the denominator is what he thinks about himself.” Because people are never the same. Each person has his own character, which consists of a numerator and a denominator. Some have a very high opinion of themselves, but people judge them low by their deeds and actions. Others are the opposite. Based on this, I think a person is a fraction. Rakhmatullina L., 7th grade
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A person is a fraction in which the numerator is what the person is, and the denominator is what he thinks about himself. I completely agree with the statement of L.N. Tolstoy. The numerator of a person is his virtues, skills, abilities and in general everything about what he can do. The numerator is a comparison with others, a person’s dignity; the denominator is a person’s assessment of himself. It is not in the power of man to increase his numerator - his merits, but anyone can reduce his denominator - his opinion about himself, and by this decrease he will approach perfection. But complete perfection never happens anywhere, so you can only get closer to this until the end of your days. This can (and even should) set an example for the younger generation, so that they also strive to improve their abilities and virtues. When the denominator coincides with the numerator, then the fraction becomes whole, the person becomes a full-fledged person. The main thing is not to be arrogant. Don’t say that you can do it well and that you are better than others or that you know more than others. The more you talk about yourself, the larger your denominator becomes and the person is closer not to perfection, but to zero. He becomes a proud, arrogant zero who does not improve himself, while those who silently and constantly say about themselves “This is not enough, I know little and can’t do well” become masters of their craft. Over time, others notice this, begin to praise the master, and recognize him as a master. And he, in turn, lives quietly and peacefully, increasing his skill every day. Tolstoy is a brilliant man. He described the person so accurately, there are no words. I have nothing more to add to this statement. 11th grade Yagudin I. 11th grade
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A living human character is a complex combination of various, often contradictory, traits and qualities. And, observing the multiplicity of such combinations, the writer Lev Nikolaevich Tolstoy tries to find a “formula” to designate them. Living human character seemed to him like a fraction, in the numerator of which the writer put the merits and advantages of a person, and in the denominator - his shortcomings, the main one of which he considered conceit. The larger the denominator, the smaller the fraction, naturally, and, conversely: with a smaller denominator, the fraction expressing the actual “cost” of a person, his moral value, increases. In my statement, L.N. Tolstoy touched upon the mathematical definition. Mathematics is an exact science. She teaches logical thinking, analysis and giving an accurate definition. After all, a person is a whole, personal, rational being. There are so many thoughts and dreams about himself in his head that no one will ever know. In life, he will not be able to achieve everything that he thinks about himself. Many years ago, the American psychologist Williams James also derived a formula according to which a person’s self-esteem can be represented as a fraction, the numerator of which is his real achievements, and the denominator is his ambitions and claims. In other words, the most reliable way to increase self-esteem is, on the one hand, not to complete your aspirations, on the other, to add real tangible success. “...The best person is not only a significant person, but also one with good self-esteem. These are the people who usually succeed. Self-esteem gives self-belief, and what he represents propels that person even further. It's like a steam locomotive moving forward. And he gets to his goal!” I believe that you should always make sure that in your own and other people’s eyes you have a fraction equal to one. But there are different fractions, and that means that there are many different people in the world. Mukminova A. 11th grade
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The great Russian writer Lev Nikolaevich Tolstoy wrote: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” I realized that the numerator is what people around him see in a person, then there is his upbringing. And the denominator is a person’s assessment of himself. This amazing comparison of a person with a fraction makes one think about what a person should be like. The larger the denominator, the smaller the fraction. We know this from mathematics. But I think the numerator and denominator should be the same. You always need to make sure that you are the same in both your own and other people’s eyes. Recently in a math lesson we covered the topic “Fractions”. There we studied proper and improper fractions. We can conclude that the improper fraction is a person for whom the opinions of others are more important than he thinks about himself, and the correct fraction is a person who overestimates himself. Kurmasheva Elnara, 7th grade
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The great Russian writer Lev Nikolaevich Tolstoy said: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” I believe that he is right and I will try to prove it... If a person is more than he thinks about himself, that is, he underestimates (in the best sense of the word) himself, then a person is able to improve and achieve something completely great. Let's do the same with mathematics. In the case considered, the numerator is greater than the denominator, the fraction will be greater than one. (We will not consider fractions with a negative value, since the value must be greater than or equal to zero) If a person is less than he thinks about himself, that is, he is arrogant, then, accordingly, the value of the fraction will be less than one. Let's consider another case when someone represents nothing in total, that is, the numerator is zero. Then, no matter what he thinks about himself, no matter who he considers himself to be, he will still remain nothing, exactly like the value of a fraction whose numerator is zero. There is another type of people who think that they have achieved nothing in this life (the exception is midlife crisis), that is, they are zeros in the denominator of the fraction. In this case, you cannot divide by zero and the value of the fraction does not exist, just as the person as an individual does not exist. From the above we can conclude... It is necessary that the fraction be greater than or equal to one. And a fraction is equal to one if and only if its numerator and denominator are equal, that is, when a person thinks about himself what he is. For me, it is more acceptable when the denominator of the fraction is greater than one, because it is in this case that a person is able to improve more. As Socrates said: “I only know that I know nothing” Timushev I.
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“A person is a fraction whose numerator is what a person is, and the denominator is what he thinks about himself” I completely agree with this statement. Man is a fraction. But sometimes either the numerator is greater than the denominator, or vice versa. It happens that they are the same. Of course, every person is something. Sometimes you walk, look at passers-by, and think that each of them is a separate person, an individual, and each of them does not think the same about himself. Everyone represents what is inside them. Nowadays, many people look at a person’s appearance, at his connections, and not at his inner world. This is the mistake; first of all, you need to get to know the person better, without opening up at the first meeting. It is necessary to study his character, his view on certain things, if possible, against him in some situations. It’s not for nothing that they say: “Trust, but verify.” Opinion about yourself is completely different. People, as a rule, have a good opinion of themselves. Some people have high self-esteem, others have the opposite. I believe that every person is what he thinks about himself. In a period of time called life, everything awaits us: joys and sorrows, difficulties and successes, love and breakups, victories and defeats... Everyone lives their life according to their own concepts. In any situation, first of all, self-confidence and a person’s self-esteem are important. A person is a fraction, and I think both the numerator and denominator should be the same. Khabibullina A. 11th grade
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We live in a society among individuals. Each of us is diverse in our own way. And whether you become an individual or some kind of “Mr. from San Francisco,” the hero of Bunin’s work, depends on you. The futurist Igor Severyanin had high self-esteem, he called himself a genius, although he was a simple writer, he deeply understood the surrounding society, the indifference of some people towards others. Not every talented person, statesman, can have a high opinion of himself. They strive to gain even more skills and knowledge. There are many types of fractions in mathematics, and so do people all over the globe. Each person chooses his own path to development and subsequent presence in society. Some people listen to the opinions of others and their advice. As they climb the career ladder, they don’t forget old friends. In contrast to them, there is a second type of people. These are self-confident people who do not take into account the opinions of others, considering many to be of secondary importance. Conclusion: they represent more than their own self-esteem. This fraction can be represented as a whole number. That is, these people have a core, they are more friendly towards people. The second type of person is a proper fraction. They consider themselves correct, although they are not. For example, 5/11. These are more selfish creatures. They put themselves first. But in fact, in society, they represent a “loner”, not sociable, proud, narcissistic person. Abdryashitova Z.Z. Grade 11
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Literature http://bse.sci-lib.com/particle028237.html http://www.omg-mozg.ru/tolstoy.htm http://www.artvek.ru/kramskoy.html
A person is like a fraction, as follows from the statement: “A person is a fraction, the numerator of which is what he thinks about himself, and the denominator is what others think of him.” What are fractions and how are they related to a person’s personality.
A fraction is a part of something, a number made up of one or more parts of a unit, just like a person who is part of a society. In mathematics, we often take a unit as a whole, and society can be considered a unit, which consists of shares (people who have different coefficients (shares) of importance in society, different parts of the unit). The numerator is the dividend, how many shares of the whole were taken. The denominator is the divisor, the number of equal parts the whole is divided into. If the numerator is the opinion about oneself, and the denominator is the opinion of others about the person, then we can conclude that the importance of a person in society is equal to the ratio of the person’s opinion about himself to the opinion of others about this person. If we assume that the opinion of others will be objective, then the value of the denominator will increase in direct proportion to the negativity of the opinion. So the larger the denominator, the smaller the value of the fraction, the less the importance of a person in a single society. If the denominator is zero, then the fraction does not make sense, and the same with a person, if the opinion of others is equal to zero, then the person’s importance in society will not make sense. It is very rare when the denominator is equal to the numerator, because, however, if the opinion about oneself coincides with the opinion of others, then there will be balance in society, but this is extremely rare, there is asymmetry in life, people commit crimes, therefore, ideal people No.
Fractions are common and decimal. In turn, there are ordinary ones: regular, incorrect and mixed. It’s the same with people, they are also different - with different characters, lifestyles, morals, ethics. Then you can “draw a parallel” between the types of fractions and human personality types.
A proper fraction is a fraction in which the modulus of the numerator is less than the modulus of the denominator. An example of a “correct fraction” personality would be a person who has low self-esteem, but who does a lot for society, is polite and kind, and those around him have a good opinion of him. An improper fraction is the opposite of a proper fraction. An example of an “improper fraction” personality would be a selfish person with high self-esteem.
Mixed fractions. A fraction written as a whole number and a proper fraction. I think that an example of such a person can be a person who is always polite and kind to everyone, his self-esteem is normal, and he is an example for those around him.
“A person is like a fraction, the numerator of which is what a person is, and the denominator is what he thinks of himself. How bigger man opinions about oneself, the larger the denominator, and therefore the smaller the fraction” L. N. Tolstoy
Let's do it orally 2. Name common fractions as. decimal: : a) ; b) ; V) ; d) 3. Calculate: a) + 0.15 b) 0.3 4. Express meters in centimeters: a) m = ... cm b) m = ... cm
Let's do it orally 5. Replace the sum with the product. . a) 2+2+2+2 b) + + c) a+ a + a 6. Replace the product with a sum. a) 6 ∙ 2 b) ∙ 5 c) b ∙ 3
Problem 1. A turtle crawls 1 m in 1 minute. What distance will it cover in 4 minutes? ?
The study of fractions has always been considered difficult. The Germans have a proverb: “GET INTO FRACTIONS.” What do you think it means? Find yourself in a difficult, difficult situation.
2 A turtle crawls m in 1 minute. 9 What distance will it cover in 4 minutes? 1 m 2 9 4= 2 9 + 2 9 4= = 2+2+2+2 9 2 4 9 = 8 9
To multiply a fraction by natural number, you need to multiply its numerator by this number, and leave the denominator the same. a b m= a m b
Find the product 1) ∙ 3; ∙ 6; ∙ 5; 2) 5 ∙ ; 1 ∙ ; 0 ∙ ; 3) ∙ 36; 12∙ ; 12∙
Question. Isn’t it possible to shorten it first and then write down the answer? 7 12. 36 = 7 ∙ 36 12 1 3 = 21
Find the error 1. Find the product: 1. A) ; B) ; IN) . 2. Find the product: A) ; B) ; IN) .
Mathematical dictation Test yourself: option 1 1. 2 3 17 2. 2 3 3. 3 8 4. 2 53 5. 3 13 5 4 8 2 = 6 17 = 10 3 = 3 2 = 16 53 = 6 13 2 option 1. =3 1 3 =1 1 2 3 4 13 2. 2 5 3. 5 3 12 4. 2 41 9 5. 3 7 2 7 = 12 13 = 14 5 = 5 4 = 18 41 = 6 7 =2 4 5 =1 1 4
An essay based on a statement by Leo Tolstoy and received the best answer
Answer from Valentin Aquarius[guru]
1) The great Russian writer L.N. Tolstoy said: “A person is a fraction whose numerator is what a person is, and the denominator is what he thinks about himself.” Thus, we can say that Tolstoy derived a “formula” to indicate human character.
ka with a fraction forces himself to think about what a person should be like.
The larger the denominator, the smaller the fraction. We know this from mathematics. But I think the numerator and denominator should be the same. ,
Answer from Grigory Moiseenkov[active]
Idk
Answer from Murat Rimbaev[newbie]
He's right
Answer from Yunzala Musaeva[newbie]
Don't know
Answer from Old Man of Your Mothers[newbie]
From mathematics we know that if the denominator is equal to the numerator, then there will be one. But we also know that the denominator should not be zero, since the entire fraction will not make sense. And also, the larger the denominator, the smaller the fraction. From here you can conduct your reasoning.
It is a very rare occurrence when the “denominator” is equal to the “numerator,” that is, the opinion of others does not always coincide with one’s self-esteem.
From childhood, our parents taught us that loving ourselves is bad, that a decent person should think first about others, then about himself. You have to be selfless and benefit people. Yes, all this is of course correct, but... I believe that everyone should love and respect themselves. This is simply necessary to maintain self-esteem. But you need to love yourself in moderation. If a person thinks only about himself, then he is an egoist. A person should love himself, but think about the feelings of others.
There is such a thing as self-esteem. Self-esteem is an individual’s assessment of himself, his capabilities, qualities and place among other people; it, of course, refers to the basic qualities of a person. It is this that largely determines relationships with others, criticality, self-demandingness, and attitudes toward success and failure. A person, of course, should have moderate self-esteem. That is, you shouldn’t elevate yourself above others, but you shouldn’t underestimate yourself either.
A person must be strong, which means confident, and to be confident, you should never think about what others think about you.
2) A person is a fraction in which the numerator is what the person is, and the denominator is what he thinks about himself.
I completely agree with the statement of L.N. Tolstoy. The numerator of a person is his virtues, skills, abilities and in general everything about what he can do. The numerator is a comparison with others, a person’s dignity; the denominator is a person’s assessment of himself. It is not in the power of man to increase his numerator - his merits, but anyone can reduce his denominator - his opinion about himself, and by this decrease he will approach perfection. But complete perfection never happens anywhere, so you can only get closer to this until the end of your days. This can (and even should) set an example for the younger generation, so that they also strive to improve their abilities and virtues. When the denominator coincides with the numerator, then the fraction becomes whole, the person becomes a full-fledged person. The main thing is not to be arrogant. Don’t say that you can do it well and that you are better than others or that you know more than others. The more you talk about yourself, the larger your denominator becomes and the person is closer not to perfection, but to zero. He becomes a proud, arrogant zero who does not improve himself, while those who silently and constantly say about themselves “This is not enough, I know little and can’t do well” become masters of their craft. Over time, others notice this, begin to praise the master, and recognize him as a master. And he, in turn, lives quietly and peacefully, increasing his skill every day. Tolstoy is a brilliant man. He described the person so accurately, there are no words. I have nothing more to add to this statement.
3) The great Russian writer Lev Nikolaevich Tolstoy wrote: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.”
I realized that the numerator is what people around them see in a person, that is, his upbringing. And the denominator is a person’s assessment of himself. This is an amazing comparison
Answer from Alena Anikeeva[newbie]
1) The great Russian writer L.N. Tolstoy said: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.” Thus, we can say that Tolstoy derived a “formula” to indicate human character.
From mathematics we know that if the denominator is equal to the numerator, then there will be one. But we also know that the denominator should not be zero, since the entire fraction will not make sense. And also, the larger the denominator, the smaller the fraction. From here you can conduct your reasoning.
It is a very rare occurrence when the “denominator” is equal to the “numerator,” that is, the opinion of others does not always coincide with one’s self-esteem.
From childhood, our parents taught us that loving ourselves is bad, that a decent person should think first about others, then about himself. You have to be selfless and benefit people. Yes, all this is of course correct, but... I believe that everyone should love and respect themselves. This is simply necessary to maintain self-esteem. But you need to love yourself in moderation. If a person thinks only about himself, then he is an egoist. A person should love himself, but think about the feelings of others.
There is such a thing as self-esteem. Self-esteem is an individual’s assessment of himself, his capabilities, qualities and place among other people; it, of course, refers to the basic qualities of a person. It is this that largely determines relationships with others, criticality, self-demandingness, and attitudes toward success and failure. A person, of course, should have moderate self-esteem. That is, you shouldn’t elevate yourself above others, but you shouldn’t underestimate yourself either.
A person must be strong, which means confident, and to be confident, you should never think about what others think about you.
2) A person is a fraction in which the numerator is what the person is, and the denominator is what he thinks about himself.
I completely agree with the statement of L.N. Tolstoy. The numerator of a person is his virtues, skills, abilities and in general everything about what he can do. The numerator is a comparison with others, a person’s dignity; the denominator is a person’s assessment of himself. It is not in the power of man to increase his numerator - his merits, but anyone can reduce his denominator - his opinion about himself, and by this decrease he will approach perfection. But complete perfection never happens anywhere, so you can only get closer to this until the end of your days. This can (and even should) set an example for the younger generation, so that they also strive to improve their abilities and virtues. When the denominator coincides with the numerator, then the fraction becomes whole, the person becomes a full-fledged person. The main thing is not to be arrogant. Don’t say that you can do it well and that you are better than others or that you know more than others. The more you talk about yourself, the larger your denominator becomes and the person is closer not to perfection, but to zero. He becomes a proud, arrogant zero who does not improve himself, while those who silently and constantly say about themselves “This is not enough, I know little and can’t do well” become masters of their craft. Over time, others notice this, begin to praise the master, and recognize him as a master. And he, in turn, lives quietly and peacefully, increasing his skill every day. Tolstoy is a brilliant man. He described the person so accurately, there are no words. I have nothing more to add to this statement.
3) The great Russian writer Lev Nikolaevich Tolstoy wrote: “A person is a fraction, whose numerator is what a person is, and the denominator is what he thinks about himself.”
I realized that the numerator is what people around them see in a person, that is, his upbringing. And the denominator is a person’s assessment of himself. This is an amazing comparison
