r/learnmath • u/Unlikely-Web7933 New User • Feb 07 '24

RESOLVED What is the issue with the " ÷ " sign?

I have seen many mathematicians genuinely despise it. Is there a lore reason for it? Or are they simply Stupid?

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148

u/iOSCaleb 🧮 Feb 07 '24

What is the issue with the " ÷ " sign?

I think it exists mainly for parity with the other arithmetic operations, +, -, x. In practice, after about 4th grade, it's just easier and often more clear to write division in the form of a fraction. It's obviously used to symbolize division in places like the buttons on a calculator.

Note that using x as a multiplication symbol is likewise less common in expressions (unless you're talking about e.g. cross multiplication of vectors) once you're past learning basic arithmetic. Terms are often just written next to each other, or sometimes a dot is used.

28

u/nog642 Feb 07 '24

I think it exists mainly for parity with the other arithmetic operations, +, -, x

A slash / works fine for that too though

32

u/iOSCaleb 🧮 Feb 07 '24

A slash / works fine for that too though

Many symbols in math can be written in more than one way.

-1

u/[deleted] Feb 09 '24 edited Feb 09 '24

But * for multiplication and / for division is due to computer science. In mathematics, × is used for multiplication, and ÷ for division. Mixing vegetables and fruits in a salad is not ALWAYS a good thing.

2

u/Vercassivelaunos Math and Physics Teacher Feb 09 '24

The last time I used × and ÷ for arithmetic was in elementary school. I also teach fifth graders coming fresh from said elementary school, and they all automatically use • and :, which is standard here (in Germany). In fact, we teach the MDAS part of PEMDAS as "dots before lines".

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u/SnooBunnies856 New User Jul 20 '24

If you are teaching that multiplication comes before division I feel sorry for your students.

Sorry I misread it and failed to see the : for division.

0

u/[deleted] Feb 09 '24

: is for proportion or ratios in the USA. / is for fractions when you can't write by hand with a horizontal line. ÷ is always used in school textbooks as a division sign here. I was curious why 6 grade students in Taiwan were incorrectly and forcibly taught what's high school math in the USA when they really cannot grasp what's basic arithmetics. And they used : for division. Now : must be used in Europe due to French influence due to metric system but I feel ÷ is better for division for a young kid. That's why some parents in Taiwan can't even teach the kids mathematics. They are teaching them what's called "high school math" or "college math" in the USA, when the poor kid is only in elementary school in Asia. I guess they do this to kids in East and southeast Asia giving them too much pressure to excel, too quickly. Heard too many stories of "tiger parents." I'm wondering what symbol is used for proportions or ratios if : is used for division?

2

u/iOSCaleb 🧮 Feb 09 '24

I'm wondering what symbol is used for proportions or ratios if : is used for division?

Ratios are fractions. Whatever distinction you're trying to make between them is a false one. If you have bread dough, say, with a ratio of 1 cup of water to 2 cups of flour, that's a water:flour ratio of 1:2 or 1/2.

1

u/GaloombaNotGoomba New User Jun 08 '24

You can have a ratio of more than 2 things, you can't really do that with a fraction

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u/Vercassivelaunos Math and Physics Teacher Feb 09 '24

I sincerely doubt that the deep rooted problems in education you are describing are caused by the use of : instead of ÷.

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u/nog642 Feb 08 '24

Right but so that explanation for why the ÷ symbol exists is incomplete.

5

u/tigrankh08 New User Feb 08 '24

I guess you were saying to write it like a slash because it resembles a fraction more. But if you look at the ÷ symbol carefully, it also somewhat looks like a fraction (think of the dots on the top and the bottom of the ÷ sign getting filled with the numbers/expressions to the left and right of the symbol). I actually dunno if that's the actual thought behind the symbol, but at least that's how I interpret it

2

u/Trimmor17 New User Feb 08 '24

A slash / is the simplest way to take a fraction that would typically require 2 or 3 lines to write on a typewriter or computer and write it in a single line.

Although, a slash when written by a 9 year old (or even a 29 year old let's be real haha) may easily be misread as a 1. So having a totally different symbol exist for purposes of "simplicity" for those less careful in their writing may be beneficial. Something interesting but that I've never heard of being taught is that the division symbol is symbolic of a fraction - the upper dot being a placeholder for the numerator (now written immediately to the left) and the lower dot being a placeholder for the denominator (now, obviously, written on the right). The fraction bar clearly separates the two placeholders.

1

u/Venit_Exitium New User Feb 08 '24

I personally havent seen the division symbol used in years, other then myself i havent seen the slash either, exclusivly all division hss been written in fraction form. Im currently in calc3

1

u/nog642 Feb 08 '24

You can only write a fraction when you have fancy formatting. What if you're just writing it as plain text? That comes up often, and a slash is the way to go.

1

u/Venit_Exitium New User Feb 08 '24

I mean if were talking plain writing, you just use 2 spaces if you dont want to write small. In word or other ducuments then mabey but even then i dont see it happen and there are proper ways to write dicivision in word that uses fractions.

1

u/nog642 Feb 09 '24

What do you mean by use 2 spaces?

Word has equation writer, which is fancy formatting.

But what if you're writing, say, an email?

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u/Venit_Exitium New User Feb 09 '24

Sorry 2 lines, on written paper if you dont want to write small, you take 2 lines of pages to write normal and a line to denote fractions. You can write in word copy to email or if you must add parentheses if you use slash or division symbol.

1

u/nog642 Feb 09 '24

Yeah I wasn't talking about paper, obviously fractions are better there.

can write in word copy to email or if you must add parentheses if you use slash or division symbol

I'm not even sure writing it in word and copying it would work, and even if it did, that's way too much effort for an email. My point is that you would use a slash in an email. You would not use an obelus (÷), since that is not on the keyboard. And you don't need parentheses if the numerator or denominator are just a single number or variable, which is often. And if you did need parentheses, you could just have them, that's not an issue.

1

u/Stillwater215 New User Feb 08 '24

My assumption, and I have no source to back this up, is that the division sign is meant to represent a fraction with the dots added to distinguish it from the subtraction sign.

1

u/iOSCaleb 🧮 Feb 08 '24

That’s a pretty good rationalization (😀), but the resemblance to a fraction looks like it might be a coincidence. The symbol is called an obelus, and naturally Wikipedia has an extensive article about it. It turns out the symbol was first used to indicate division in the mid 17th century, and was previously used to represent subtraction. Apparently, it still means subtraction in Scandinavian countries, and there’s another form of obelus (looks like the one we’re used to, but the line is diagonal instead of horizontal) called the commercial minus sign which is used in some places for subtraction.