Little question for you

[Proud_Dad]

As an aside, I sometimes wonder why primary school children are ever taught the '÷' sign in the first place? I know that when my own DS first started learning about fractions he simply thought of 1/2 as a 'half' as in half a piece of cake and it took quite a while to appreciate that it was one divided by two.

If they were taught that the symbol for divide was '/' from the beginning then I think understanding fractions would come more naturally. I guess there must be a reason for using the '÷' sign though. Maybe Guest55 has an explanation?

Fractions can only have integer numerators and denominators - a division can involve any numbers. It would be confusing to write, for example, 12.45/30.57 ...

I have to say I was shocked at some CPD I attended that a group of teachers from one well-known Bucks GS argued with the presenter about 2/5 meaning 2 divided by 5; they were saying it had nothing to do with division.

This is why I worry about how fractions are taught ... children meeting them formally earlier and earlier will not help. They need LOTS of practical play in KS1.

12.45/30.57 just means "12.45 divided by 30.57". Not sure why that would be confusing? A "fraction" is just a special divide where both dividend and divisor are whole integers (or numerator and denominator if your prefer, but again why confuse with 2 different naming systems for the same thing?).

Are you seriously saying that a maths teacher did not know that the symbol '/' or a horizontal line in an equation or mathematical expression means divide?!

That's the standard symbol for divide in all of science! If for example they saw written "speed = distance / time" would they not have known what that meant?!

[Guest55]

I disagree - fractions are written in a specific way - numerator over/upon a denominator - division calculations are written horizontally. If there are several decmal points it could be misread.

Yes - I am saying that - the rest of the room of maths teachers just could not believe their ears! I felt sorry for the presenter who was gobsmacked as they could not accept they were wrong ... I don't think they had ever thought about a fraction as 'division'.

[mystery]

Hadn't done maths beyond 16 at school then perhaps? Can't imagine you could get through A level without clicking that a/b means a divided by b. And in my old day, you couldn't have got through O level either.

[Proud_Dad]

I disagree - fractions are written in a specific way - numerator over/upon a denominator - division calculations are written horizontally. If there are several decmal points it could be misread.

Yes - I am saying that - the rest of the room of maths teachers just could not believe their ears! I felt sorry for the presenter who was gobsmacked as they could not accept they were wrong ... I don't think they had ever thought about a fraction as 'division'.

Division calculations are certainly not always written horizontally, particularly in science.

e.g. Newton's law of gravitation is usually written as:

GMm = F
r^2

rather than

GMm / r^2 = F

or GMm ÷ r^2 = F

(well normally the F would be on the left but I couldn't get the pesky formatting on this site of the first one to work that way round! )

BTW, my computer keyboard doesn't even HAVE a '÷' symbol on it! I had to copy it from another post. The only way I can type divide on my keyboard is '/'. I truly am shocked that anyone with any normal level of education had never come across '/' used for divide before let alone a grammar school maths teacher!!

[Guest55]

A formula is always written in 'fraction' form - it is easier to typeset.

It was a shocking statement wherever they taught - teaching at a GS does not mean they are 'better' teachers - far from it sometimes.

[yoyo123]

Our children know by year 4 (or earlier if I have taught them) that the line means divide, makes it so much easier to understand fractions and then percentages.

[Proud_Dad]

A formula is always written in 'fraction' form - it is easier to typeset.

Not on this forum it ain't coz all leading spaces get cut out and mess it up!

Surely though the whole point is that a horizontal line in a formula or fraction, a diagonal slash '/' or the '÷' symbol all mean exactly the same thing. Just as 1/2, "1 ÷ 2" and 0.5 all mean the same thing. Furthermore the reason we write "a half" as 1/2 is exactly because it is 1 divided by 2. If I have one pizza and DIVIDE it equally between 2 people each gets half a pizza!

It was a shocking statement wherever they taught - teaching at a GS does not mean they are 'better' teachers - far from it sometimes.

Yes agreed, I certainly didn't mean to imply GS teachers were any better. Obviously any maths teacher, or any teacher of any subject for that matter, ought to know what '/' means!

[PurpleDuck]

A formula is always written in 'fraction' form - it is easier to typeset.

I am surprised it would be easier to typeset, don't quite see how that would work. Whenever I have to write a formula in a typed document, it is always a struggle to lay it out properly in a fraction format, especially when it is incorporated within a paragraph of text. Most of the time I end up typing it up as a string instead.

Out of curiosity, I've just looked up images of Isaac Newton's own hand-written notes (on University of Cambridge Digital Library website) and it looks like he used fraction format for his formulae and calculations, even some very long-winded ones. Was he doing that for the sake of ease of potential future typesetting or because using a fraction format was a convention in his times? Just wondering...
http://cudl.lib.cam.ac.uk/view/MS-ADD-04004/41" onclick="window.open(this.href);return false;

[Guest55]

If you don't write a formula in a 'fraction' form there is often confusion about which letters are the denominator.

If you use WORD you need to insert 'object' then equation - or use a special format like LaTeX.

https://www.latex-project.org/" onclick="window.open(this.href);return false;

Newton wrote for academics not children learning to use formulae; if he were wrtiting now he'd use a PC and use something like LaTeX.

[PurpleDuck]

If you don't write a formula in a 'fraction' form there is often confusion about which letters are the denominator.

If you use WORD you need to insert 'object' then equation - or use a special format like LaTeX.

https://www.latex-project.org/" onclick="window.open(this.href);return false;

Newton wrote for academics not children learning to use formulae; if he were writing now he'd use a PC and use something like LaTeX.

Thank you for the tip for typing up equations properly - it will make things easier.

I am not arguing against presenting formulae in a fraction format - quite the contrary. I always write them like that (if by hand) simply because it makes sense to me; I was only surprised that such presentation could be due to typesetting.

I'm not suggesting Newton was writing for children, but even if he did, he could have happily carried on presenting formulae in his fraction format (which, if I interpret your post correctly, is the way you say it should be done, so we agree on this one).

There is an interesting website with information on how mathematical symbols and fractions evolved over time: http://jeff560.tripod.com/fractions.html" onclick="window.open(this.href);return false;. I'm sure this is no news to you, but for me it was a very interesting read. I'm copying a few bits below for the benefit of other un-initiated souls like me...

FRACTIONS NOTATION
Ordinary fractions without the horizontal bar.
According to Smith (vol. 2, page 215), it is probable that our method of writing common fractions is due essentially to the Hindus, although they did not use the bar. Brahmagupta (c. 628) and Bhaskara (c. 1150) wrote fractions as we do today but without the bar.

Fractions with the horizontal bar.
The horizontal fraction bar was introduced by the Arabs. "The Arabs at first copied the Hindu notation, but later improved on it by inserting a horizontal bar between the two numbers" (Burton). Several sources attribute the horizontal fraction bar to al-Hassar around 1200.

When Rabbi ben Ezra (c. 1140) adopted the Moorish forms he generally omitted the bar.

Fibonacci (c.1175-1250) was the first European mathematician to use the fraction bar as it is used today. He followed the Arab practice of placing the fraction to the left of the integer (Cajori vol. 1, page 311).

According to the DSB, Abu Abdallah Yaish ibn Ibrahim ibn Yusuf ibn Simak al-Umawi (14th or 15th century) insisted that the horizontal fraction bar be used, whereas easterners continued to write it without the bar.

The bar is generally found in Latin manuscripts of the late Middle Ages, but when printing was introduced it was frequently omitted, doubtless owing to typographical difficulties.This inference is confirmed by such books as Rudolff's Kunstliche rechnung (1526), where the bar is omitted in all ordinary fractions but is inserted in fractions printed in larger type and those having large numbers (Smith vol. 2, page 216).

Michael Closs points out that if we define a horizontal fraction bar to be a horizontal line that separates the numerator from the denominator and demarcates them as such, then this type of notation was used with exactly that purpose more than a millennium before al-Hassar. In Demotic Mathematical Papyri, (Brown University Press, London, 1972, pages 8-9) Richard A. Parker writes that in three papyri dating from the third century B. C. to the Roman period, "the numerator is written first, and the denominator follows on the same line. In problems 2, 3, 10, and 13 (the Cairo papyrus) the numerator is underlined. In problems 51 and 72 the denominator is underlined."

Some writers use the term vinculum for the horizontal fraction bar. This term originally applied to the mark when used as a grouping symbol. Fibonacci used the Latin word virga for the horizontal fraction bar.

Diagonal fraction bar
The diagonal fraction bar (also called a solidus or virgule) was introduced because the horizontal fraction bar was difficult typographically, requiring three terraces of type.

An early handwritten document with forward slashes in lieu of fraction bars is Thomas Twining's Ledger of 1718, where quantities of tea and coffee transactions are listed, e.g. 1/4 pound green tea

The things I learn from Google...