I think: “÷” can be replaced by “——”, and “÷” is prone to ambiguity
In addition, after elementary school, any mathematics book, physics book can not see “÷”, so why not abolish it?

Because it is very friendly to elementary school students. It is also convenient for the teacher to speak. Mathematics education needs to explain various concepts clearly and clearly. In the beginning, “÷” was an operation that represented the inverse operation of multiplication. Then everyone will learn the nature of division. Then, because integers are not always divisible, decimals and fractions are introduced. The score is a number, and the line of the score is just a symbol. The beginning of the score is also a better understanding of the real score. Then began to learn false marks and mixed marks. These are numbers, and we use symbols like horizontal lines to represent them. After learning these, we must start the four arithmetic calculations of credits. There are a lot of things to learn in this part, and elementary school students also need to spend a certain amount of time to understand these things. Mathematical formulas like “2÷3=2/3” are to be learned during this period. This formula is not trivial in elementary school mathematics. This formula expresses a number “2”, divided by another number “3”, is equal to a number “2/3”. If the division is directly expressed in the form of fractions, on the one hand, it is difficult for the teacher to clearly explain what this thing is at once, and the primary school students will be directly confused after listening: Is this a division or a fraction? What is the relationship between division and fraction? On the one hand, +, -, and × are originally in the form of binary operators. If you suddenly use fractions to express division, it is estimated that elementary school students will find it difficult to accept. Even if you accept it, it will be difficult for you to talk about scores later. In mathematics above elementary school,’÷’ is really not very useful. I answered anonymously at first, just wanting to make complaints. As a result, I didn’t expect to resonate with so many people. Then I will spit out seriously now. Some other answers interpreted this question from the algebraic aspect. To be honest, I was thinking about algebra at the beginning. What I wanted to answer at the beginning was: “The division sign can indicate the inverse operation of the multiplication sign, and it can appear in the division ring. The fraction sign is a symbol used to represent the elements in the fraction ring. Any whole ring can define a fraction. Type ring.” What’s interesting is that the statement I thought at the beginning is different from the high praise answer next door. The division ring is not necessarily the Euclidean ring, and the Euclidean ring is not necessarily the division ring. The whole ring is not necessarily an Abelian group in terms of multiplication. The general Abel group is not a complete ring. It’s not me. When I was learning abstraction, my teacher would indeed use fractions to express the elements in the fractional ring. The general integral ring is really not an Abelian group in terms of multiplication. The a/b written by our teacher can neither be written ab^{-1} nor b^{-1}a. So these are just questions of symbols. I personally think that arguing about how many ways to write “divide by” has no practical mathematical meaning. Therefore, in my answer, the reason for the existence of “÷” is attributed to the early education of mathematics. Of course, there may be some problems left over from history.

zhiwo

By zhiwo

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helpmekim
8 months ago

The notation that produces ambiguity should be the ellipsis notation used when the elementary school teaches the division with remainder. But that has nothing to do with the ÷ sign…
I think the design of this symbol is pretty good. The usage of f(·) and (·,·) often appears in mathematics books after college. Here, the division sign is probably a similar consideration.

heloword
8 months ago

Repeal is a very slow process. If it is not a thorough investigation, it will generally be considered only when there is a problem. And ÷ is basically forgotten. I guess the person who made the symbol does not remember that there is ÷, so there will be no abolition for this. As for some people say that the division with remainder, in fact, the division with remainder generally uses the form of multiplication: a=bq+r, if it is the minimum non-negative residue, then 0<=r<|b|, and the absolute minimum residue is r<= |b|/2. The division sign is not needed at all.

helpyme
8 months ago

The teaching of the lower grades should start from the “concrete perception” as much as possible, combined with the understanding of “life experience”, and then “concrete to abstract” to obtain the concept of “division” is the process of averaging. Moreover, the understanding of division is more difficult than addition, subtraction and multiplication. From the division sign alone, everyone has many opinions. The division also involves “average score, inclusion score, division, division, removal” and so on, so this division symbol is still reserved for elementary school students. It’s already difficult. Of course, this is also the symbol left by the predecessors. At present, it is regarded as the optimal solution used in the learning of division at the elementary school level. As for the meaning of / etc. to express the meaning of division, it has an impact on the learning of “fractions” by the subsequent elementary school students. So for us adults, it seems that the existence of the division sign is of little significance, but for a primary school student to understand division, it is of great significance. Keep it, wait for a mathematician to think of a better solution, then change it~

sina156
8 months ago

Because the meanings of the two are different, the scope of application is also different. The division sign is used to indicate the division operation and the relationship between the divisor and the dividend. The scope of application is the Euclidean ring. Specifically, let it be an entire ring. If there is one Function makes: For all and non-zero, there is makes, and or, then we call it an Euclidean whole ring, and the function is Euclidean assignment function (assignment for short). The equation is the so-called division operation, It is pronounced “a divided by b equals q remainder r”, which is recorded as the dividend, is the divisor, is the quotient, and is the remainder. For example, a rational coefficient polynomial is an Euclidean ring, and its assignment is the degree of the polynomial. This means that we can perform division operations on polynomials. Examples: Divide by, can be obtained by long division, so it can be written as Note that the number of the remainder is less than the divisor. On the other hand, it is different from the division sign that represents an operation. It represents an element and the scope of application is Specifically, the Abelian group is a group. If: for all, then we call it an Abelian group. Why do we need an Abelian group? If we want to have a good definition, what are the conditions? First is the inverse of to exist, which requires a group to be followed by to, otherwise, is it representative or is it? The mathematical structure that satisfies the above two conditions is the Abelian group. For example, the unit circle on the complex plane is an Abelian group. For the convenience of calculation, we can express the elements in polar coordinates: In this way, we need to calculate two The result of dividing the elements is easy

yahoo898
8 months ago

Indeed, as the subject said, most of the divisions encountered in daily life can be expressed without barriers in the form of fractions. But there is a division that cannot be written as a component, and that is the case with a remainder. 10÷3=3…1 is written in the form of one up and down with -, which can only express the ratio of two numbers. In this case, no remainder is allowed. The remainder is a very important concept in the study of number theory, so even if no other circumstances are considered, the division sign cannot be abolished.

leexin
8 months ago

In fact, what the subject said-substitution is not enough. Because this symbol is difficult to recognize. But whether the symbols you provide are appropriate, this is actually not the point. The point is that no matter what the modification is, it is difficult to implement. In fact, programmers have long replaced the division sign with / and the multiplication sign with *. Why has there been no problem for years? I think it is because programmers have been using * for multiplication and / for division since the birth of programming languages. So there is no difficulty. And mathematics was born for many years. The use of symbols is deeply ingrained, and there are enough historical documents to be relatively difficult to change. If a new mathematics subject is born in the future, it is possible to completely modify the symbol, but it is difficult to change the existing subject. Personally, if you really want to change it, it is appropriate to change the multiplication sign to * and the division sign to /. In addition, the colon used in the scale: is also completely equivalent to the division symbol. But there is no way to become a division sign, it is probably a historical habit established by convention.

greatword
8 months ago

Even the Chinese pinyin ü, the tone symbol, did not adapt to the keyboard because of the high input cost. Things that are declining in a specific stage, industry, and region are not all instrumental in terms of their existence alone. Everyone’s value is also. In addition to tradition, culture and habits must be respected. There is no need to move textbooks, and Today’s integration will also be divided into tomorrow. The annexation will also carry the hat of strong bullying and weak chauvinism. Vocabulary, dialects, and writing are commonplace. We cannot solve everything from instrumentality and practicability. What about American English conversion? The set of gadgets that the U.S. Emperor insists on is rare in the world. Copy from Wanwei Encyclopedia: obelus as a horizontal line with a dot above and a dot below, ÷, was first used as a symbol for division by the Swiss mathematician Johann Rahn in his book Teutsche Algebra in 1659. This gave rise to the modern mathematical symbol ÷, used in anglophone countries as a division sign.[16][17] This usage, though widespread in Anglophone countries, is neither universal nor recommended: the ISO 80000-2 standard for mathematical notation recommends only the solidus / or fraction bar for division, or the colon: for ratios; it says that ÷ “should not be used” for division.[18]This form of the obelus was also occasionally used as a mathematical symbol for subtraction in Northern Europe; such usage continued in some parts of Europe (including Norway and, until fairly recently, Denmark).[19] In Italy, Poland and Russia, this notation is sometimes used in engineering to denote a range of values.[20]In some commercial and financial documents, especially in Germany and Scandinavia, another for m of the obelus – the commercial minus sign – is used to signify a negative remainder of a division operation.[21][14]

loveyou
8 months ago

If you are deeply exposed to the concept of set to group and then to ring, you know that the status of division as an arithmetic symbol is not low. As for this symbol, the reason is that it will cause the formula to be too long compared to the fractional form. Let the formula develop in a vertical direction. It does seem that there are fewer divisions in physical formulas than multiplications, mainly the commutative law of multiplication of one-dimensional arrays. Formally, it can use more multiplication forms. For example, ab is a/b not interchangeable, and the variables under the score are all multiplications. abcd/efgh becomes efgh/abcd. a becomes/a posted 22 hours ago

strongman
8 months ago

In fact, the division sign can be replaced by /, and in fact it is basically replaced by /. Of course, it can also be represented by other symbols. There is no question that cannot be abolished. As for the difference between division and fraction. In fact, the score is represented by another symbol, a horizontal horizontal line. According to the definition, this number can also be divided/represented. Due to the input method, it is more convenient to multiply and divide. In fact, you can use / to denote multiplication and division from the beginning.

stockin
8 months ago

Let’s abolish the multiplier and the multiplicand first. The only thing that elementary school teachers are good at has been abolished. How can people survive? Don’t you want to lose face? Compared with the writing of a symbol, the dividing line is more unreasonable for me. Really tangled units do dimensional analysis like physics. Yesterday, I taught the commutative law of multiplication. Today, I was judged wrong because the order of the multiplier and the multiplicand was wrong. The previous question is still asking. There are several ways of writing the word “fennel” which satirizes what the next question is. There is a false word in this article, what is the word and what is it? Double standards, changes in the days and evenings, and chaotic logic are issues that many people hate. In fact, they have been written in our textbooks since childhood and passed on from generation to generation.

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