# Why is the “÷” not abolished in mathematics?

#### Byzhiwo

Apr 4, 2021

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.

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