Talk:Fraction/Archive 1

Irrational Fraction

“An irrational fraction is, none of

all fractions must be capable of being good at vulgar fraction.”

Removed this contribution. It’s a non-concept that seems to have been concocted to make the page more ‘interesting’.
—Herbee 14:19, 12 Dec 2004 (UTC)

I disagree. One often hears talk of irrational fractions even sometimes amongst mathematicians. To be able to search for that term here at the encyclopaedia is benficial. Paul Beardsell 21:36, 13 Dec 2004 (UTC)

I moved it into a section "counter examples", but it should be, at least, explained what it means to those who use it.MFH 18:10, 7 Apr 2005 (UTC)

latest edit

Concerning Revolvers last edit, I think it was a good idea to distinguish clearly between numerical fractions (which are just complicated ways of writing a simple number) and the other quite different objects: rational functions, partial fractions.

Secondly,

The term partial fraction is used in algebra, when decomposing rational functions. However, a partial fraction is an expression of a particular decomposition, and so is more than just an element of a quotient field.

seems not clear to me. Even if not well precised on partial fraction, this term has a well posed definition, and the decomposition into partial fractions is not the same thing than *one* partial fraction (which is a fraction).

I better liked the old version. Any comments? — MFH: Talk 18:03, 26 May 2005 (UTC)

The point is that partial fraction is not really an object so much as an expression, a technique. It has much less to do with numerical fractions that rational functions do. Rational functions are very similar to numerical fractions, in that you can think of them as elements of some quotient field. "Partial fractions" can't be interpreted this way...a partial fraction is a formal expression, so maybe there's some way to express that, but there's no way to interpret the definition of "partial fraction" as an element of an appropriately chosen quotient field. So, I don't see the point in grouping partial fraction and rational function together, the only way they are similar is not being numerical, whereas one is very similar to numerical fractions, the other is not. Revolver 02:31, 28 May 2005 (UTC)

What do you mean by "one partial fraction". A partial fraction is just a formal expression of a partial fraction decomposition: otherwise, you're just talking about elements of a quotient field. (E.g. a rational function is always equal to its partial fraction decomposition, when considering each as an element of a quotient field, but they are NOT the same as partial fractions...a rational function does not even qualify normally, whatever specific definition you come up with (btw, the article on partial fractions has no formal definition, all I'm saying is, I don't know what the exact definition is, but whatever it is, it's not interpretable as being equivalent to the element of some quotient field.)) Revolver 02:45, 28 May 2005 (UTC)

External links

Can you guys move the external links to the appropriate pages? I'm sure none of them talk about fractions in general; I'm betting they all talk about vulgar fractions. But, I'm no math-talking-guy. Josh Parris ✉ 30 June 2005 00:54 (UTC)

Merge (with Vulgar Fraction)

Obviously it's not clear that this page is a disambiguation page, given that User:TakuyaMurata thinks Vulgar fraction should be merged into this article. Someone want to clear the article up? Josh Parris ✉ 10:10, 31 July 2005 (UTC)

There is already disambig page Fraction (disambiguation). -- Taku 10:23, July 31, 2005 (UTC)

Fraction (disambiguation) complies with the Wikipedia:Manual of Style (disambiguation pages); Fraction (mathematics) doesn't. The disabiguation here is a specialized version, because of the subtle distinctions between fraction variations. Josh Parris ✉ 04:14, 1 August 2005 (UTC)

I am not sure about your position on the merger. What I see here is that the basic notion of a fraction (vulgar fractions) is not discussed but some specialized cases are. So I proposed the merger. -- Taku 23:24, August 1, 2005 (UTC)

I vote to merge Vulgar fraction into Fraction (mathematics). I don't see a need for a Vf article; no beginning math student is likely to be searching for such an underused phrase, and those who are far enough along in math that they've encountered non-vulgar fractions will probably have no problem finding what they need if Vf is just a redirect to F (especially F#terminology or some such). However, either way, I think the "arithmetic of fractions material" is expanding to the point where it deserves its own article -- or, better still, a Wikibook (see my comment below). --Jay (Histrion) (talk • contribs) 17:56, 15 December 2005 (UTC)

I agree with Histrion that Vulger fractions should merge here. The term is now archaic. Rick Norwood 23:58, 21 December 2005 (UTC)

I agree that vulgar fractions should be merged in here AdamSmithee 13:09, 5 January 2006 (UTC)

All right, so now we need someone to carry out the merge? I'll do it when I have a chance. —Keenan Pepper 06:13, 1 June 2006 (UTC)

Proper fraction

The definitions of proper and improper fractions do not correspond to common usage. Specifically, a fraction equal to one is considered improper. Ref http://mathworld.wolfram.com/ProperFraction.html, for example. Frank Adams-Watters 27-Oct-2005.

The mathworld remarks on this issue contradict each other. At one point they say a fraction p/q is "improper" when p/q > 1 (we'll just ignore the problem of negatives here ;-) ), then later they say that since a fraction is "proper" when p/q < 1, the p=q cases are considered improper -- implying that the definition of "improper" isn't "p/q > 1" but rather "any fraction that's not proper." I'm reluctant to rely on them as an authoritative source if they can't tell the difference. I'm going to revert until we can find some other source. --Jay (Histrion) (talk • contribs) 20:35, 27 December 2005 (UTC) **EDIT: Er, scratch that. Other sources are saying the same thing. Still, I think a comment regarding either negatives or absolute values is called for. --Jay (Histrion) (talk • contribs) 20:40, 27 December 2005 (UTC)

Wikibook?

In the past few months a lot of "fraction arithmetic for beginners" material has been added to this article. As a math tutor, I'm glad to see it, but I can't help wondering if it's more suited to the Wikibooks area than here. In fact, I'm looking at the Wikibooks material on fractions right now, and a lot of it could stand a rewrite. (Some of it's just plain wrong.) Would anyone like to discuss the ramifications of transferring some of the newer material? --Jay (Histrion) (talk • contribs) 20:49, 14 December 2005 (UTC)

I've done a lot of work on the wikibook on elementary mathematics and would welcome some help. Rick Norwood 23:27, 27 December 2005 (UTC)

BTW, good work on your recent rewrite of this article. Rick Norwood 23:29, 27 December 2005 (UTC)

Template

I like the way you folks did in-text fractions using <sup>, <sub> and the Unicode slash, but I found it tough to edit. Plus, I wanted to use that format in other articles.

So I created the {{Fraction}} template. To use it, you just enter {{Fraction|1|2}} to get 1⁄2. Of course, it will work for any textual fraction. The <math> stuff is nice too, but it isn't so nice when it's in-text. Markkawika 07:22, 3 January 2006 (UTC)

Bullet points

Re the recent history section -- I'm told that bullet points are unencyclopedic and should be reworked into paragraph form. Rick Norwood 14:31, 7 February 2006 (UTC)

Fine by me, its largly a cut a past job from Timeline of mathematics, first step in a reasonable history section. --Salix alba (talk) 15:06, 7 February 2006 (UTC)

I disagree, bulletpoints are just as encyclopedic as periods and commas. The point of these articles is to get across information with the greatest efficiency, with or without bulletpoints.

I looked at the edit in the history, and find that the bullet points make it much easier to read. Bullet points are used in hundreds and maybe thousands of pages on wikipedia, and are in no way against policy or common usage. Why would wikimedia program in bulletpoints if we're not supposed to use them? Fresheneesz 03:15, 26 May 2006 (UTC)

Terminology

Is there a name for the slash or horizontal line when used between the numerator and the denominator? I remember discussing this in a high school math class some years ago, but I don't remember if anyone ever determined it's name, if indeed it has one. Stubblyhead 00:07, 11 February 2006 (UTC)

If the line is horizontal it is a "vinculum", if slanting a "solidus". Good question. Rick Norwood 00:18, 11 February 2006 (UTC)

"fraction" meaning decimal

I've seen the usage of the word "fraction" to mean "a value less than one" (which includes decimal values). For example, at talk:significand theres much talk about a "fraction part" of a logarithm, which is the decimal part of the log of a number. For example the "fraction part" of log (base 10) of 120 is about .079181 (log.10[120] = 2.079181). I would have put this in the intro, but I figured itd be better to discuss it first. Fresheneesz 03:11, 26 May 2006 (UTC)

Historically, what we today call "decimals" were originally called "decimal fractions", and they represented not necessarily a decimal less than one, but any number, such as 1.5, that was not a whole number. As for the "fraction part" of a logarithm, this is baby talk for what is more properly called the ordinate. log(50) = 1.69897... . In this case 1 is the mantissa and .69897... is the ordinate. This vocabulary is becoming obsolete, as calculators have replaced slide rules. In using a slide rule, the user found the mantissa by estimation and only used the slide rule to find the first few decimal places of the ordinate. Rick Norwood 19:45, 26 May 2006 (UTC)

Elongation and shortening?

In the article, it says:

==Equivalent fractions==

Multiplying the numerator and denominator of a fraction by the same (non-zero) number...

In Danish, thisproces has a name - not so in English? A rough translation of the Danish terminology: Converting 1/2 into 3/6 is called "elongation by 3"; the opposite process is "shortening by 3". In this case, "shortening" could be called "reduction". In case we rewrite (1/3) / (5/3) as 1/5, "elongation" by 3 could be called "reduction". I'm native Danish but teach math in English; I often miss these precise terms in cases where the purpose is not simply a reduction. E.g., in order to put 2/3 + 4/5 on a common fractional line, I "elongate" the first fraction by 5 and the second by 3.

Does anyone know an equivalent terminology in English?--Niels Ø 13:52, 2 December 2006 (UTC)

An then, silence... Does that mean that there is no such terminology in English?--Niels Ø (noe) 17:02, 22 December 2006 (UTC)

"Multiply through" and "divide through"; to put 2/3 + 4/5 in a form with a common denominator, I multiply through the first fraction by 5 and the second by 3. The terminology is used in equations as well. Not sure if there's a Latinate equivalent; it wouldn't surprise me. –EdC 02:21, 24 December 2006 (UTC)

I've heard “reduce” used, but there is not a specific word, in the US anyway, that is used as elongation is used above. Typically, each instructor, if necessary, will introduce a term that will be used in his/her classroom for that purpose, but there is no consensus or common terminology. Clifsportland (talk) 21:28, 10 January 2011 (UTC)

typing

anyone know how to type fraction in microsoft word? Ragnaroknike 09:14, 5 December 2006 (UTC)

Either use some of the exotic characters in exotic fonts, or use Equation Editor, an optional Office component - see [1], click the "How?" link. Equation Editor is a "light" version of a separate proram called MathType.--Niels Ø (noe) 11:21, 27 January 2007 (UTC)

Picture

I think the picture of the cake would be much better if the cake were divided into three quarters instead of into one quarter and one half, but I have no idea how to edit a picture. Can anyone help? Rick Norwood 13:07, 20 April 2007 (UTC)

You need to download the image (look for the link just below the picture on Image:Cake_fractions.svg, edit it in Inkscape (Free vector graphics editor, multiple platforms available), and re-upload it. Alternatively you could talk to User:Acdx, who created it. –EdC 15:20, 21 April 2007 (UTC)

I agree "only quarters" would be better; if someone needs an illustration, they need a simple one at first. I've put in a new version with quarters. I moved the old version to the adding section might be helpful since fraction addition can give people trouble. -R. S. Shaw 04:14, 2 July 2007 (UTC)

Types of fraction

"A decimal fraction is a vulgar fraction where the denominator is a power of 10". Is this true? The only definition of "decimal fraction" in the Concise Oxford Dictionary, and the only definition I've ever heard, is a fraction expressed with a decimal point, e.g. the 51 in "3.51".

"A vulgar fraction (or common fraction) is a rational number written as one integer (the numerator) divided by a non-zero integer (the denominator), for example, 4⁄3 as opposed to 11⁄3.[1]" This might not be a good definition, since most vulgar fractions are things like 3/4 rather than 4/3. Anyway, the purpose of the term "vulgar fraction" is to contrast these fractions with decimal fractions (indeed, this is clearly stated in the link referenced by the [1]), not with proper fractions (which, as the next paragraph says, contrast with improper ones). -86.136.194.22 07:16, 4 July 2007 (UTC)

Good call. I've removed that unreferenced "definition" from the article. Rick Norwood 14:51, 4 July 2007 (UTC)

curious...

What is the name of the line that separates the numerator and the denominator? Kingturtle (talk) 14:09, 15 January 2008 (UTC)

Commonly, it is just called a "fraction line". If it is horizontal, the technical name is vinculum, and it is both an operation (division) and a symbol of grouping. If it is slanting, the technical name is a solidus, also called a "forward slash". Rick Norwood (talk) 14:36, 7 February 2008 (UTC)

Pedagogical Tools

This section is a one-sided presentation of issues belonging to the reformed vs. traditional mathematics debate, in the guise of warning parents against reformers (and thereby taking a position). It might be appropriate in an article such as "Math Wars" or "Reform Mathematics," but is out of place here. It is also largely an American issue, but is not labeled as such. Finally, it contains several factual errors. CMP does treat division of fractions. "Fraction strips" are merely pictorial representations of fractions, a tradition that goes back to the early 19th century and is hardly "unknown" to parents or mathematicians. They are widely used by even traditional math teachers. This section contributes nothing to the world's understanding of fractions and should be deleted or rewritten.70.114.139.142 (talk) 03:12, 7 October 2008 (UTC)

The point made above is basically correct. This section should be cleaned up.128.62.136.12 (talk) 18:26, 7 October 2008 (UTC)

Numerator? Denominator?

This post needs the terminology section improving. It does nothing to help someone who does not know what a numerator is. —Preceding unsigned comment added by 144.82.242.13 (talk) 09:50, 13 February 2009 (UTC)

Removed incorrect part

The article had this:

Combining both this method and the first method to compare ${\tfrac {5}{18}}$ and ${\tfrac {4}{17}}$, first note that ${\tfrac {5}{18}}$ > ${\tfrac {5}{17}}$, because the first fraction has a smaller denominator.

Then note that ${\tfrac {5}{17}}$ > ${\tfrac {4}{17}}$, because the first fraction has a smaller numerator.

Therefore, by the transitive property of inequality, ${\tfrac {5}{18}}$ > ${\tfrac {4}{17}}$. Note that there are pairs of fractions for which this trick does not work, for example 2/3 and 3/4.

The first inequality is wrong: ${\tfrac {5}{18}}$ < ${\tfrac {5}{17}}$, because the last fraction has a smaller denominator. This is therefore a bad example.--EdgeNavidad (talk) 07:56, 19 February 2009 (UTC)

Quarter vs fourth

I've only the time to write this, as opposed to actually going through and fixing the article, but the word "quarter" is used through out the article as if it's the equivalent to saying "one fourth." "Quarter" as simple and common a word as it may be, is a type of lingo, and it seems as if the article makes it a given that quarter = 1/4 without it ever really being defined. On the side of consistency and professionalism, the article should probably say one fourth in the same fashion it says one third or one hundredth in stead of taking advantage of the common lingo word "quarter." —Preceding unsigned comment added by 24.111.116.220 (talk) 23:36, 21 April 2009 (UTC)

So I would assume you think all instaces of the word "half" should be replaced by "one second"? 1/4 = a quater. 217.39.171.201 (talk) 15:23, 16 March 2010 (UTC)

Reducing a fraction

This article could use a section describing how one reduces a fraction. A fraction is reduced in the section about division, but it is not explained in the article. People that knows nothing about frations probably doesn't know what it means to reduce a fraction. --mgarde (talk) 22:27, 20 June 2009 (UTC)

There is a basic explanation of reducing fractions in the section on Equivalent fractions.--seberle (talk) 12:47, 22 June 2009 (UTC)

Vulgar fractions

Which of the following are NOT vulgar fractions?

• 11/3 ? --an improper common fraction
• 3/11 ? --a proper common fraction
• 3½ ? not --a mixed number.
• 0/2 ? - not, according to a few --a proper common fraction
• 2/0 ? not, acc to many --undefined
• 0.11 ? not, acc to probably all -yet, it can be converted to one --a decimal (in older usage, a decimal fraction)
• 0.111111... ? not, acc to probably all - yet, it can be converted to one --a repeating decimal
• 1½ /7 not, acc to p. all - --ambiguous notation which should be avoided (does it mean one plus the quotient of one half and seven, or does it mean one and a half divided by seven)
• 3:7 ? possibly vulgar - just diff notation --a ratio
• 3½ : 7 ? not - not an expression relating two integers --a ratio
• 3 div 7 ? possibly vulgar - just diff notation --an arithmetic expression
• 3 (ANY symbol for divided by) 7 ? possibly vulgar - just diff notation --a natural number
• (1.5)/7 ? not, acc to probably all --a compound fraction not a common fraction
• 1/(3.1) ? not, acc to p. all --a compound fraction
• 1/pi ? not, acc to all - CANNOT be converted --the reciprocal of pi
• (1.4)/(3.1) ? not, acc to p. all --a compound fraction
  • http://www.worldwidewords.org/qa/qa-vul1.htm
  • http:// www.easycalculation.com/what-is-fraction.php

Are vulgar fractions to be defined as "an expression of a part-whole relationship using two integers" or as "a specific notation using an integer numerator, an integer denominator and a 'fraction line' "? --JimWae (talk) 00:46, 13 January 2009 (UTC)

A few defs seem to exclude zero from both numerator and denominator, but the rest just from denominator. This seems to be a convention more than anything else --JimWae (talk) 07:35, 13 January 2009 (UTC)

A vulgar or common fraction is one particular method of expressing parts in relation to wholes. In other words, "common fraction" describes a notation, not a kind of number. Common fractions are rational numbers, but rational numbers can be written using other notations. Because they are "common" (that is, in general use -- as in the phrase "common ground") we should restrict them to the most common notation: an integer numerator, a bar of some kind, and a natural number denominator. The other things have other names, which I've added after a dash and in italics to the list above. Rick Norwood (talk) 15:49, 13 January 2009 (UTC)

There are several good books on the history of mathematical notation. Unit fractions did precede vulgar fractions by many centuries -- the notation for unit fractions did not look anything at all like our notation for vulgar fractions. Rick Norwood (talk) 16:00, 13 January 2009 (UTC)

- The best source I can find on wikipedia is Egyptian fractions - from which it appears they used fractions other than reciprocals quite early. While their notations for 1/2, 2/3 & 3/4 do not qualify as even a ratio of 2 numbers, they did USE more than unit fractions. I think any reader would construe the present lede as indicating otherwise. I have to ask again if there is near-universal agreement that if archeologists found 3 ¡ 7 (where by ¡ I mean any symbol at all [and the 3 & 7 are meant to represent those numbers expressed in any numeral system] ) was used the same way we use 3/7, that this would not count as a vulgar fraction merely because the fraction sign was different? --JimWae (talk) 19:06, 13 January 2009 (UTC)

A finding of an ancient 3 ' 7 meaning 3/7 would be very interesting. In most ancient cultures, 3/7 would be indicated by a much more complicated notation. If you can find an example of anything like "3 ' 7" in the literature, please let me know. Rick Norwood (talk) 13:42, 14 January 2009 (UTC)

I am disturbed by the fact that wikipedia continues to use the term “vulgar fraction.” Until today I never heard the term, and am surprised to see it so vigorously defended except in a history section. I have a masters degree in mathematics and live in the United States. Is it just the states that have stopped using this term? Just my state? Is this term still used or is it a term referenced from the 1940s? Clifsportland (talk) 21:18, 10 January 2011 (UTC)

Is the continued use of Vulgar Fraction simply a remnant of the merge of the vulgar fraction article and this one? If so, We should work to change definitions from their "vulgar" base and mention "vulgar" as an archaic term.Clifsportland (talk) 21:31, 14 January 2011 (UTC)

It's nice to know there are only two countries...

[...] to the right of a mark (a period in the United States, a comma in France). It's a period in the United States, and a comma in France. Nice. But how about Brazil? Germany? ... I guess it should read: "a period in most English-speaking countries, and a comma in most other countries". Correct me if I'm wrong. —Preceding unsigned comment added by 81.240.14.217 (talk) 14:36, 19 June 2009 (UTC)

I wish I knew. Anybody have an authoritative source? Rick Norwood (talk) 13:36, 20 June 2009 (UTC)

The page decimal also needs this information. Clifsportland (talk) 21:04, 10 January 2011 (UTC)

Problems in Reference section.

The reference section is inconsistent, and has dead links. Further, some of the references are blogs, not really a good source for mathematical information. Anyone with time?134.29.231.11 (talk) 18:40, 31 January 2011 (UTC)

Removed information - need source

The earliest known use of fractions is ca. 2800 BC as Ancient Indus Valley units of measurement.

I've removed the above line, tag intact, from the article. It has been unsourced since February 2007. I think it should remain here until sourced. Cliff (talk) 15:53, 21 March 2011 (UTC)

Related to the definition

Related to the discussion in the Definition section above, the following sentence in the article's introduction is wrong:

In mathematics, the set of all (vulgar) fractions is called the set of rational numbers, and is represented by the symbol Q.

No matter what the definition, this should clearly be:

In mathematics, the set of all numbers which can be expressed as a fraction is called the set of rational numbers, and is represented by the symbol Q.

But I'll wait until the opening sentence is settled to make the correction. --seberle (talk) 03:12, 22 March 2011 (UTC)

I would be sure to say, "the set of all numbers which can be expressed as a fraction of two integers is called..." 1/pi is not a rational number, but it can be expressed as a fraction. Cliff (talk) 05:38, 22 March 2011 (UTC)

Good point. --seberle (talk) 18:25, 22 March 2011 (UTC)

I'm not sure in what sense the first sentence is "wrong". The adjective "vulgar" is just to distinguish between what are now called fractions and what are now called decimals but were once called decimal fractions. Originally, a 'fraction' was a part, and a vulgar fraction was a ratio of whole numbers. Rick Norwood (talk) 20:07, 22 March 2011 (UTC)

Well, I suppose whether the current is sentence is wrong depends on one's definition of "fraction", which is not well-defined in mathematics. That is why I was hesitating to correct it until the opening sentence is settled. If fraction is a notation, it makes no sense to say rationals are a set of those notations unless you mean for 4/4 and 2/2 to be included as separate elements in that set. You have potentially the same problem if fraction is defined as a ratio. Are 4/4 and 2/2 distinct elements? If a fraction is a part of a whole, then whole numbers are possibly excluded. In any case, the standard definition of rational number in any textbook, and even on Wikipedia, is the definition given by Cliff. --seberle (talk) 23:40, 22 March 2011 (UTC)

But your definition, and Cliff's, both use the word "fraction". Maybe in place of "(vulger) fraction" we could say "fraction in which the numerator and denominator are integers and the denominator is not zero". Or maybe just "fraction". Rick Norwood (talk) 12:05, 23 March 2011 (UTC)

Yes, usually the word "quotient" is used instead of "fraction", but I think "fraction" is acceptable for this article as long as it is acceptably defined. Using the word "vulgar" is not the problem; in fact maybe "vulgar" should be included? The problem is equating "rational number" with "fraction" (or "vulgar fraction"). If "fraction" gets defined as "a part of a whole" (which is sort of what it seems to be saying now), then "fraction" won't work because whole numbers are rational too. If "fraction" is defined as a notation, then the current definition won't work because the set of rational numbers is a set of numbers, not a set of notations.

The point Cliff and I are making is that the set of rational numbers is not the set of fractions (no matter how "fraction" is defined), but rather the set of all numbers which can be expressed as a fraction (of integers). This distinction is important and is always included in the definition. The number π/2 is a fraction, but it is not rational because it cannot be expressed as a fraction of integers no matter how hard you try. The number 1 is rational (even though it is not a fraction) because it can be expressed as a fraction. --seberle (talk) 14:12, 23 March 2011 (UTC)

I understand the term "vulgar" and its historic use and etymology. However, I think that its prominent use in this article is inappropriate. Never once in my educational career did I hear this term used, it was here at WP that I first encountered the term. It seems also that there is some debate about what it actually means. I think the term should be introduced in a terminology or history section and then abandoned for something less archaic. Cliff (talk) 17:05, 23 March 2011 (UTC)

Cliff, I am glad to hear you say this. I am also quite ignorant of the term "vulgar fraction", having only heard it here. If "vulgar fraction" is largely unknown to others as well, I definitely think it should be moved out of the introduction. --seberle (talk) 19:49, 23 March 2011 (UTC)

How about this? In mathematics, the set of all numbers which can be expressed as a fraction m/n, where m and n are integers and n is not zero, is called the set of rational numbers. This set is represented by the symbol Q. Rick Norwood (talk) 19:03, 23 March 2011 (UTC)

Rick, your definition sounds great to me. It is almost identical to the current Wikipedia definition, but with "fraction" in place of "quotient". The only thing is, why include the expression "and n is not zero"? We are only talking about numbers that can be expressed as.... Because no number can be expressed as a fraction with a zero denominator, is that caveat really necessary? I always prefer the simplest possible definition. --seberle (talk) 19:49, 23 March 2011 (UTC)

I think ruling out division by zero is necessary. It is obvious to you and me, but I know grade school teachers who teach their students that any number divided by zero is zero! People come to Wikipedia for information on topics they know nothing about.Rick Norwood (talk) 12:31, 24 March 2011 (UTC)

Ok, I'll trust your judgment on this, Rick. I definitely would like to see this article friendly to children, parents, and teachers. We still need to fix that opening sentence. Either reword it so it doesn't sound like a definition, or fix the definition. As it is, the opening sentence could be describing numbers like π - 3 and omitting notations like 3/3. I like the last proposal in the section above by JimWae: "fractions are numbers expressed as the ratio of 2 numbers, and are used primarily to express a relationship between parts and a whole". Can we go with this? --seberle (talk) 17:56, 24 March 2011 (UTC)

arithmetic with fractions

It is particularly important to get arithmetic with fractions right. In the current issue of the Notices of the American Mathematical Society, a letter reports strong efforts in New Jersey to eliminate any requirement that grade school teachers take math courses to preparte them to teach, with the result that some teachers teach addition of fractions as: add numerators, add denominators. Students who see how illogical this is may, we can hope, turn to Wikipedia for correct information.

As they stood, the sections I've just edited assumed the reader knew how to multiply fractions before the section on how to multiply fractions, assumed the reader knew how to divide fractions before the section on how to divide fractions, gave misleading examples, and confused left and right. I've done some work, and fixed a few typos. More probably needs to be done.

Rick Norwood (talk) 13:19, 4 August 2011 (UTC)

Definition

The opening definition "A fraction is a number that can represent part of a whole" is not very satisfactory. It is at odds with most dictionary definitions and would seem to exclude fractions greater than or equal to one. The term fraction usually refers to the fact that it is a number expressed as a quotient. --seberle (talk) 23:59, 20 March 2011 (UTC)

I think that fractions were invented and are still primarily used to represent a part of a whole rather than division. The use of the word "improper" to describe a fraction that represents more than a whole suggests this. As it stands, the sentence says a fraction "can" represent a part of a whole, not that it "must" represent "only" a part of a whole. Still, I think that sentence can be improved on. Any ideas? Rick Norwood (talk) 15:38, 21 March 2011 (UTC)

I agree with your point, Rick. If we eliminate the part starting with "that can", the opening sentence is rather vacuous ("A fraction is a number."), so that part must remain. And yet the sentence misleads by reading as a definition. In any case, my point is not that the fraction represents a division, but that a fraction is a written notation. You are right that no reference need be made in the opening sentence to a fraction being a division, though it could. I suppose it depends on the audience. Are we trying to include children who might be confused to know a fraction is a quotient? If so, let's avoid division. If not, this fact might be helpful in the definition.

The problem, as I see it, is that the first sentence reads as a definition and as a definition it does not work well. I suspect part of the problem is that "fraction" is not a term mathematicians tend to use and is therefore perhaps not well-defined in mathematics, probably because "fraction" refers to the written form of the number more than the quantity itself. Ideas:

1. If we want to make the opening sentence a valid definition, I think we simply need to make it clear that "fraction" is a written notation, as most dictionaries do. E.g. my Random House College Dictionary begins their definition of fraction as "a number usually expressed in the form a/b ...". Wolfram Mathematics defines a fraction as "A rational number expressed in the form a/b." I think most dictionaries do the same. Preliminary suggestion: "A fraction is a number written (at least implicitly) in the form a/b, where a and b are usually integers." This could be followed by descriptions of what the numerator and denominator stand for. Or we could avoid that by saying "in the form of a division a/b".
2. If we want to remain at the level of a historical description or popular idea of the word, then the sentence just needs to be changed so that it doesn't sound like a definition. In particular, we should avoid the expression "A fraction is" and make it clear that "fraction" is referring to the written expression of the number rather than the number itself. Preliminary suggestion: "The word fraction is used to describe parts of a whole using the notation a/b."

Other suggestions? --seberle (talk) 20:27, 21 March 2011 (UTC)

The word fraction is used to describe numbers that may include parts of a whole. Cliff (talk) 00:02, 22 March 2011 (UTC)

Fractions are fractions no matter how they are written - how they are written cannot form the entire definition. Fractions are the ratios of 2 whole numbers, used primarily to express a relationship between parts and a whole. --JimWae (talk) 00:12, 22 March 2011 (UTC)

JimWae, I'm struggling with your statement because it sounds really good. But is it true that "Fractions are fractions no matter how they are written"? Is 4/4 a fraction? The article implies it is. What if I write this same number as 1? Is it still a fraction? I think the way it is written is important to the definition. There is no question that 4/4 or 1 is a rational number (a mathematically well-defined term) no matter how it is written, but a fraction is not merely a rational number. Again, part of the problem IMHO is that "fraction" is not a well-defined mathematical term. (I have heard mathematicians argue inconclusively over its definition.) Dictionaries embrace both a notational definition (usually their first definition, as I quoted above) as well as other definitions describing fraction as merely a part of a whole (as in "I have seen only a fraction of your work."). I don't think this article is addressing the latter definition, but I think that definition is creeping into the opening sentence, possibly because it is closer to the historical and popular notion of a fraction.

Nevertheless, I really like your proposed opening sentence, JimWae, "Fractions are ratios of 2 whole numbers, used primarily to express a relationship between parts and a whole." I think this might work. --seberle (talk) 03:02, 22 March 2011 (UTC)

If we introduce the term fraction in that way, "Fractions are ratios of two whole numbers, used primarily to express a relationship between parts and a whole." we may encounter two problems.

1. For those who don't understand how "whole" is understood two different ways, that sentence can be mighty confusing.
2. This does not allow for the term fraction to be applied to other concepts. We can use the word fraction to describe these things which may or may not be rational functions. And fractions can involve irrational numbers, not only whole numbers. So again we have the issue of the opening sentence being too limiting, and sounding like a definition when that is only one way fractions are used.

We might be able to get away with introducing a qualifier like "most commonly" or something, but that sounds iffy and might need a source that would be hard to find. Cliff (talk) 05:35, 22 March 2011 (UTC)

OK π/2 (though not rational) is a fraction too; so is 0.15, and also 27%. So fractions are numbers expressed as the ratio of 2 numbers, and are used primarily to express a relationship between parts and a whole.--JimWae (talk) 08:27, 22 March 2011 (UTC)

I like that better, but we still lose the ability to talk about rational expressions, unless you make the confusing jump of talking about algebraic expressions as numbers. Cliff (talk) 15:08, 22 March 2011 (UTC)

Any number CAN be expressed as a fraction (by putting it over 1). 7 is not a fraction, 7/1 is. pi-3 is a fraction when expressed as 0.14159..., but not when expressed as pi-3 (though it can be evaluated as a fraction). 7.0000 expresses (at least part of) the number it represents as a fractional expression, as does 700%. "7" does not express the number 7 as the ratio of any part(s) to any whole.--JimWae (talk) 19:13, 23 March 2011 (UTC)

I think we should follow the common convention in most references and restrict the definition of a fraction to rational numbers, although the numerator and the denominator do not have to be integers. The example π/2, though written on fraction form, does not result from a parts-to-whole calculation but from the ratio of arc length to radius (see radian for the definition). On the other hand, if the arc length of a quarter circle is related to the arc length of the complete circle, the result is a fraction, ${\frac {\pi /2}{2\pi }}$, which of course is equal to 1/4. So my suggestion is as follows: Restrict the definition of fraction to rational numbers and use fraction form consistently for any expression that is not a rational number. Isheden (talk) 09:50, 25 September 2011 (UTC)

Non-breaking spaces

Would you people stop adding & nbsp; and/or & #160; between every pair of words your posts? I'm tempted to just remove all non-breaking spaces from this talk page for readability. If you must use non-breaking spaces, please use the {{nowrap}} template. — Arthur Rubin (talk) 14:52, 25 September 2011 (UTC)

Perhaps it is not deliberate, and the choice if editor they are using? --Iantresman (talk) 20:35, 25 September 2011 (UTC)

In that case, I should clearly remove the non-breaking spaces, as they make it virtually impossible to read the comments in edit mode. — Arthur Rubin (talk) 20:57, 25 September 2011 (UTC)

How to satisfy everybody? For example, some people need a big font-size to display text, and don’t like see the last word of a sentence at the beginning of the next line. For example, here I code  ³/₄  with one non-breaking space after '4' (one again before the last '4').
Aughost (talk) 07:15, 26 September 2011 (UTC)

Fixed, so I can read the comments; SOME non-breaking spaces retained, within non-Wikilinked short quotes. Also removing nonstandard spaces within fractions, and after punctuation. 17:22, 26 September 2011 (UTC)

Holy cow! Over 1500 characters of unnecessary garbage. I knew it was bad, not that bad. Aughost, perhaps you should abandon html coding here. It's really not necessary. Cliff (talk) 21:24, 26 September 2011 (UTC)

I left some, within quoted strings which were not linked. (I also changed a 10-7 to 10^-7, although it should be 10⁻⁷.) — Arthur Rubin (talk) 00:25, 27 September 2011 (UTC)

In order to define correctly the word "fraction"

A entire page may be absurd because of differences in interpretations of words. In this stage of the article, the words “ratio” and “fraction” are interchangeable, and that is false.  In Wiktionary, the word “fraction” is correctly defined:  “a ratio of two integers, the numerator and the denominator, usually written one above the other and separated by a vinculum (horizontal bar).  Consequently, a given ratio is not always a fraction — what I said to explain my modifications —.  We read also this definition in this article:  “a fraction is a division expression where both dividend and divisor are integers”.
Aughost (talk) 08:59, 20 September 2011 (UTC)

Regardless of what Wiktionary might say, I think almost all mathematicians would describe an expression such as 1/√2 as a fraction. Not to mention algebraic expressions such as ${\frac {x}{x^{2}+1}}$. We can't rely on English language dictionaries to define mathematical terms correctly. Jowa fan (talk) 09:24, 20 September 2011 (UTC)

The distinction pointed out by User:Aughost is supported by other references as well. For example, MathWorld defines fraction as a rational number with integer numerator and denominator (see Weisstein, Eric W. "Fraction". MathWorld.), whereas a ratio is defined as a quotient between two arbitrary numbers (see Weisstein, Eric W. "Ratio". MathWorld.). Judging from the term rationalization you would also expect that the result is a ratio and not a fraction. I'm further not convinced that numbers expressed using exponential notation can be considered as fractions. In any case, the articles Fraction (mathematics) and Ratio should be clearly distinguished based on solid references. Finally, using the template {{frac}} is discouraged in mathematical articles, see WP:MOSMATH. Isheden (talk) 10:50, 20 September 2011 (UTC)

By the way, the expression ${\frac {x}{x^{2}+1}}$ is most accurately called a rational function (or rational expression), defined as the ratio of two polynomial functions. Isheden (talk) 12:49, 20 September 2011 (UTC)

Yes, I've heard of rational functions, thank you. You'll find that the rational function page uses the word fraction more than once. Note especially the references to partial fractions and field of fractions. You might find some sources that define fraction in a narrow sense, but there are also many sources that use the word in a much broader context. Jowa fan (talk) 13:17, 20 September 2011 (UTC)

Partly for historical reasons, there are a number of mathematical concepts that have fraction in the name although ratio might have been more accurate. One example is fractional programming, for which a more accurate name would be ratio optimization. However, the terms fractional programming and linear-fractional programming persist as there are hundreds of papers in the literature that use them. Isheden (talk) 14:39, 20 September 2011 (UTC)

Some more words to be quite clear, I hope. The article under discussion is entitled "Fraction (mathematics)". What is a “fraction” in mathematics?  Wiktionary gives the definition.  My modifications of the article were explained, and in my explanation there was a link to that definition in Wiktionary. Here, I have already quoted a sentence from the article "Elementary arithmetic", and that sentence is consistent with the definition in Wiktionary. I regret that the title "Rational fraction" redirects to "Fraction (mathematics)", because someone which types "Rational fraction" probably thinks to "rational function". Of course two integers are not two polynomials. The numerator and denominator of a fraction are two integers.
Aughost (talk) 17:03, 20 September 2011 (UTC)

The numerator and denominator of a rational number are integers. A fraction can be defined more broadly. A rational function is a fraction where the numerator and the denominator are functions in their own right. This is the reason that my merge request was denied. That said, this page deals almost entirely with expressions involving rational numbers rather than any broader meanings of the term "fraction". Cliff (talk) 18:51, 20 September 2011 (UTC)

Typically, a rational function is defined as the ratio of two polynomial functions. It also makes sence because the quotient does not necessarily express parts (numerator) of a whole (denominator). Which merge request of yours was rejected? Isheden (talk) 12:03, 21 September 2011 (UTC)

Unimportant, I agree that the merge should not happen. fraction (mathematics) and rational number.Cliff (talk) 17:10, 21 September 2011 (UTC)

---

None of the sources at wiktionary

• http://dictionary.reference.com/browse/fraction
• http://wordnetweb.princeton.edu/perl/webwn?s=fraction

give "a ratio of two integers". The closest to that is "the quotient of two rational numbers" which is just ONE of several definitions. We call irrational numbers such as the non-repeating decimal number 0.010010001000010000010000001... fractions because the part following the decimal expresses a part of a number that is not a whole number. (However, "the part of a number that is not a whole number" does not suffice as a complete definition because 9⁄1 is also a fraction. Look here for more defs.) It seems is is the wiktionary entry that needs revision.--JimWae (talk) 18:56, 20 September 2011 (UTC)

A fraction in which both numerator and denominator are integers is called a common fraction.[2] --JimWae (talk) 19:07, 20 September 2011 (UTC)

Yes, and the other example can also be expressed as a common fraction, for example 12/40, although in the form 1.2/4 it is not. This example does not suggest, however, that the basic definition of fraction should include irrational numbers. Isheden (talk) 11:44, 21 September 2011 (UTC)

If 10^-7 is treated as number, it is a fraction. If it is treated as a numeral (simply an expression of a number), it is more problematic (but not impossible) to treat it as a fraction. In practice, we accept both usages (thus including 0⁄1 as a fraction too). I do not know of any source that could authoritatively decide neither is a fraction, and it seems the article must not exclude them. --JimWae (talk) 00:22, 21 September 2011 (UTC)

Yes, $10^{-7}$ is a rational number that can be expressed as $1/10^{7}$, which is a (common) fraction. I think it is a matter of taste if $10^{-7}$ can be considered a fraction although not written on fraction form. However, although a number expressed using scientific notation such as $5.3\times 10^{-7}$ can be written as the common fraction $53/10^{6}$, it is not clear that the number in scientific notation should be considered as a fraction (although it is doubtlessly a rational number). At some point, the definition gets too broad to be understandable to the typical reader. I suggest the basic definition should be mentioned in the beginning of the article and broader definitions included later, preferably after a number of examples to illustrate the basic definition (i.e. the common fraction). Isheden (talk) 11:44, 21 September 2011 (UTC)

Again, this is a matter of number v numeral. The meaning and usage of of "fraction" covers both. Perhaps we need to present the def per each: A fraction can be either 1> a number, or part of a number, that is between 0 and 1, or 2> the symbolic expression of a number in terms of a ratio of numerical quantities --JimWae (talk) 21:03, 21 September 2011 (UTC)

---

By the way, Wiktionary is not considered a reliable source: see Wikipedia:Reliable_sources/Noticeboard/Archive_7#Wiktionary_a_source? and Wikipedia:Reliable_source_examples#Are_wikis_reliable_sources? Jowa fan (talk) 03:00, 21 September 2011 (UTC)

First problem:  choose a terminology. Second problem: be understood. Whatever the word or phrase chosen to denote our object, perhaps “simple fraction” might be appropriate, perhaps the adjective “simple” would be implied, we have to be consistent. Would you explain me how do you get a more simple writing by dividing by a non-zero number a dividend that is not an integer, π for example? How do you understand the following two sentences, drawn out of this article.  “Dividing the numerator and denominator of a fraction by the same non-zero number will also yield an equivalent fraction. This is called reducing or simplifying the fraction.” That is written below the title “#Equivalent_fractions”  of  Fraction_(mathematics).
Aughost (talk) 04:52, 21 September 2011 (UTC)

Actually, π is a good example because it does not result from calculating a part of a whole (which would be a fraction), but from the ratio of the circumference to the diameter of a circle. Moreover, it cannot be expressed as a common fraction. Isheden (talk) 11:53, 21 September 2011 (UTC)

There really is a reason why this article should not be edited hastily. I remember reading a long discussion (in the Notices?) on how badly most mathematicians fail in their attempts to define "fraction". Now we have the following in the article:

"A fraction ... is a number that can be expressed as the ratio of two numbers ... . Other uses for fractions are to represent ratios ... ."

Often the simplest concepts require the most thought. Please slow down, discuss here, and do not make major changes without consensus. Rick Norwood (talk) 21:10, 21 September 2011 (UTC)

It would be great if you could find a reference to that "Notices" article. Jowa fan (talk) 01:32, 22 September 2011 (UTC)

First question
In this stage of the introduction, the words “ratio” and “fraction” are interchangeable, and that is false.  Everybody agree?
Aughost (talk) 05:21, 22 September 2011 (UTC)

Disagree. A rational number is one of the ways of writing a ratio. In many contexts the words fraction and ratio are, in my opinion, synonymous. Of course if you can find reliable sources stating the contrary, then it's reasonable to represent the other point of view in some way. Jowa fan (talk) 05:44, 22 September 2011 (UTC)

Bad answer. A rational number is not a writing. A fraction is a way to write a rational number.
Aughost (talk) 09:11, 22 September 2011 (UTC)

Okay, I expressed myself a little carelessly: I should have said represent rather than write. I still disagree. But it's not constructive for either of us to state unsupported opinions. Can you provide some references regarding the use of the word ratio? Jowa fan (talk) 09:17, 22 September 2011 (UTC)

Good, “fractions” and “ratios” are ways to write numbers. You agree, I think. But when I say that the words “fractions” and “ratios” are interchangeable in this stage  of the introduction, you disagree. Therefore, the two words are not synonyms in your mind — in any reference, a definition will be written with words —. Would you tell us, please, in what place of this introduction  we see that these words are not synonyms.
Aughost (talk) 13:28, 22 September 2011 (UTC)

Does anyone want to assert that when I speak the words "one-tenth" I am not talking about a fraction? We properly use the word fraction for far more than JUST "a way we write numbers". There's the "numeral meaning" and the "number meaning".--JimWae (talk) 23:51, 22 September 2011 (UTC)

The ratio 1/10 is a fraction, because the numerator and denominator are two integers.  As any decimal number, one-tenth is not a fraction, because we distinguish between mathematical objects that are decimal numbers, and the ways to write these objects.  Do you approve?
Aughost (talk) 08:55, 23 September 2011 (UTC)

The problem with describing a fraction as a ratio in the first paragraph, is that it assumes that the audience will understand (a) what a ratio is, (b) how ratios can be used to describe fractions. I think we should describe fractions in non-mathematical language in the introduction, and later, include a section on the comparison between ratios and fractions. An understanding of ratios should not be necessary to understand fractions. --Iantresman (talk) 10:57, 23 September 2011 (UTC)

The words “ratio” and “fraction” either are synonyms or are not, what do you think about that?
Aughost (talk) 15:31, 23 September 2011 (UTC)

Second question
Think about the first sentence:  “a fraction (from Latin: fractus, "broken") is a number…”  That beginning is wrong, because we have to distinguish between a given number and the ways to write it.  For example,  9.000  is an integer that is written with a decimal mark.  The first sentence of this lead section  is wrong.  Everybody agree?
Aughost (talk) 09:04, 23 September 2011 (UTC)

I would argue that a fraction is a number, in that it represents a quantity. It may be different to an integer, decimal, etc, in which case it is a special kind of number, written in a different way to integers and decimals. --Iantresman (talk) 10:51, 23 September 2011 (UTC)

You can't say that a number represents a number. First an introduction exposes what is a fraction. And this example might follow, to help understand the general meaning:  ³/ ₄  and  ⁷⁵/ ₁₀₀  are two writings that represent the same number.  What do you think about this definition,  and about this other one?  Thank you if you answer this first question, or if you answer this second question, the two questions perhaps, it would be nice.
Aughost (talk) 15:31, 23 September 2011 (UTC)

The first definition you gave here is better because it does not use the term "a writing". Cliff (talk) 05:43, 24 September 2011 (UTC)

I don't know how to understand the word “here”.  On the other hand, I know very well what I wrote in the article.  I suggest that we discuss in this new section about the best formulation.
Aughost (talk) 08:51, 24 September 2011 (UTC)

Yesterday perhaps, someone thought about the words "fraction" and "number"
that an expression never had been pronounced: “the numerator of a number”.
Hence this statement: to be accurate,
a fraction is not a numeral object.

— Aughost (talk) 01:47, 24 September 2011 (UTC)

"fraction" - different meanings

The word "fraction" probably has slightly different meanings, depending on who is describing it. A mathematician may have a more rigorous definition than a ley-person. Unfortunately, the mathematical definition is probably more difficult to understand. In my opinion, we should be offering as simple an explanation as possible in the introduction, and provide more rigorous definitions later on.

I fully understand that a fraction is "the ratio of two numbers", but I think it is too technical for most people (ask people). That's not to say that we don't describe a fraction as such, but I wouldn't do so in the introductory sentence. --Iantresman (talk) 11:22, 22 September 2011 (UTC)

A ratio is not the same as a fraction. For example, if the odds of winning a game of chance are three to two (3:2) that is not the same as the fraction 3/2. The idea that a ratio is the same as a fraction is due to the oversimplification in modern US math education, where the ideas are often conflated. There was a time when, to check the ratio 3:2 = 6:4, every student learned "the product of the means equals the product of the extremes". Now they learn: "cross multiply" the fractions. Of course, we could do away with the concept of a ratio. In many US schools this has already happened. But when ratio and proportion were taught correctly, it was a lot easier for students to grasp the idea of quantities being directly proportional or inversely proportional. Students today are not taught this, and if you ask them a question such as "If a car goes 600 miles in 10 hours, how far does it go in 20 hours at the same speed," they answer, "Huh?"

Lets keep this article honest. A fraction is a way of expressing parts of a whole. Common fractions can be extended to express quantities equal to any rational number, but parts of a whole is the most fundamental use. A fraction is a single number. This can be contrasted to ratios, which express a relationship between two or more numbers. Note that the ratio of the dimensions of a 7 inch long two by four, 2:4:7, cannot be expressed as a fraction.

Rick Norwood (talk) 15:43, 22 September 2011 (UTC)

I'm not sure that introducing the "product of the means equals the product of the extremes" leads to better learning, or understanding. and that's not the point anyway. What is our definition of fraction, "a way of expressing parts of a whole"? That seems lacking. Are we defining "common fraction", "vulgar fraction", "proper fraction" or simply "fraction" in the intro? Cliff (talk) 21:21, 22 September 2011 (UTC)

I agree, a ratio is not the same as a fraction (although one can be converted into the other). But I would still have a very simple, non-mathematically description in the introduction. How about something along the lines of my description of "Fraction" in Simple Wikipedia? --Iantresman (talk) 23:25, 22 September 2011 (UTC)

Simple Wikipedia says "A fraction is a number that shows how many equal parts there are." That is not nearly enough and it should say, at the least, "numeral", not number. There are also plenty more ways to write fractions than the one way the rest of that paragraph gives. This article does not say a fraction IS a ratio, it says "a fraction... can be expressed as the ratio" --JimWae (talk) 23:36, 22 September 2011 (UTC)

I disagree that the intro should use the term "numeral". This article is designed for a different level of readership than that for which numeral is appropriate. I assume that numeral would be wikilinked. Then people who are trying to learn about fractions would have to try and figure out how a number is different from a numeral... That's inappropriate. Cliff (talk) 05:09, 23 September 2011 (UTC)

I agree, "numeral" is a little harder to understand than "number". Using "number" will help non-technical people understand the description better. We can always use "numeral", and other more rigorous vocabulary, later on. We can of course expand on the Simple Wiki description. I've always like the idea of giving an early example, so people can visual the description. Something to do with cakes cut into equal pieces I think is good, it's something that nearly everyone is familiar with. How about:

A fraction is a number that shows how many equal parts there are. For example, if a cake cut into four equal parts, we can described each equal part as the fraction "a quarter". If two pieces of the cake are missing, then we are left with two quarters, the same as half the cake. (Then we can go on to how to write fractions). --Iantresman (talk) 07:57, 23 September 2011 (UTC)

This illustrates how difficult it is to define the word. I add my voice to those who want to avoid "numeral" as needlessly pedantic. "A fraction is a number that shows how many equal parts there are." No, the numerator of a common fraction does that, not the whole fraction. In two thirds, we have two equal parts, not two thirds equal parts. The more complicated we make the lead, the worse it gets. It wasn't bad when the current spate of discussion began. It wasn't bad the last time I looked. But fiddling with it will probably make it worse. Rick Norwood (talk) 13:53, 23 September 2011 (UTC)

The meaning of a writing depends on the context, OK.  For example, the product of a given quantity G and the number  3/4  equals a fraction of G.  In that example, we can say that the ratio 3/4 represents a number.
Aughost (talk) 15:58, 23 September 2011 (UTC)

This inserted warning to tell you: be careful.  JimWae should not insert a message between two answers.
Aughost (talk) 23:38, 24 September 2011 (UTC)

I was not advocating we use "numeral", just that technically the simple wikipedia entry was wrong as it stands - for several reasons - and using "numeral" would at least correct it a bit. Numbers do not show anything.--JimWae (talk) 09:51, 24 September 2011 (UTC)

It is done all the time to respond to a particular comment after the topic has changed a bit - as I am doing now - and then & now I put the extra indent there to indicate it was not in sequence. Stop warning me about perverting things, please--JimWae (talk) 01:24, 25 September 2011 (UTC)

And what I meant to say is that I was not advocating that simplewiki use "numeral" and everything would be OK with that entry. WP is expected to be written at the reading level of high-school students. Even those high-school students who cannot articulate the difference between a number and a numeral have had enough exposure to the concepts that they are aware there is something different about them. High-school students also have had exposure to "ratio", but I can see that such wording may presume a bit too much. If so, I think we may have to define fraction in terms of both number and numeral, and will present something soon--JimWae (talk) 02:11, 25 September 2011 (UTC)

I have made an attempt to define fractions based on various sources here: User:Isheden/sandbox I would be interested in your comments. Isheden (talk) 10:42, 24 September 2011 (UTC)

What words in the upcoming beginning

Please, would you describe quite accurately the merits and faults of the following formulations of the first paragraph.

Suggestion 1

A fraction (from Latin: fractus, "broken") is a writing of a quotient of two integers, as a ratio.  For example,  ³/ ₄  and  ⁷⁵/ ₁₀₀  are two fractions that represent the same number:  0.75.  A given fraction of a given quantity G is the product of G and the given number.  For example, three quarters of G may be written:  0.75 × G.

---

— Aughost (talk) 07:25, 24 September 2011 (UTC)

Nice try, but I think it is too complicated:

• How fractions are written is important, but I don't think it defines the concept. eg. the word "half" is a fraction, spoken or written.
• "quotient, integer and ratio" mean little to most people, though I think they are important later on
• I think the algebraic description using G, is also too complicated at this stage.

I would suggest that you ask someone who does not have a mathematical or scientific background, (your mother, your son, sister?) and see whether the description explains it for them. --Iantresman (talk) 08:20, 24 September 2011 (UTC)

With your word "half", do you mean that the fraction 1/2 is a better example? The image shows three quarters of a cake…
Aughost (talk) 08:38, 24 September 2011 (UTC)

I meant that "A fraction is a writing of a quotient...", is too speific, and that while a fraction can be written as a numerator and a denominator, it can also be written in words, and exists as a concept too without writing it. In maths we think of fractions as 1/2, 1/4 etc, but half a cake is an equally valid representation. My point is that we can define fractions without using the mathematical notation, and without using mathematical terminology, and should do in order to make it understood by non-technical people. Later we should be more rigorous, but not in the introduction. --Iantresman (talk) 09:15, 24 September 2011 (UTC)

This definition is unsatisfactory because it relies on the related concepts of quotient and ratio, from which a distinction should be made. I am working on a proper treatment of fraction in my user sandbox, see User:Isheden/sandbox. I would be happy for comments and modifications, but please use proper references. Isheden (talk) 10:35, 24 September 2011 (UTC)

Your first sentence reads "A fraction is a rational number expressed in the form a/b", which while it is accurate, I think also suffers from the use of mathematical terminology. I don't think that non-technical person would understand "rational number", nor what is meant by the "form a/b". I would prefer that the initial description was non-technical and non-mathematical, otherwise we lose most of the readership. I think the first couple of sentences of the explanation should be understandable by a child, eg.

A fraction, is a part of a number, often referring to a small part (eg. a fraction of a second), or more generally, a proportion of a certain quantity (eg. a large fraction of scientists use mathematics.). A fraction can be more specific, such as a "half", "third" or "quarter", and mathematics writes these amounts as 1/2, 1/3, 1/4, where the bottom number tells us how many possible parts there are, and the top number, how many parts we actually have. For example, a cake cut into quarters has four parts. If we remove one quarter, then we are left with three quarters, written as 3/4. In mathematics, the top number which tells us the number of parts we have, is called the numerator, and the bottom number which denotes the size of each part, is called the denominator. Usually, the numbers used to write fractions are whole numbers (ie. integers), but in mathematics, fractions can use nearly any kind of number (see Forms of Fraction) --Iantresman (talk) 11:05, 24 September 2011 (UTC)

We need to make the lead simpler, not more complicated. We should not say that a fraction is a ratio. A fraction represents a number; a ratio compares two or more numbers. Further, 'ratio' is a less common word than 'fraction', and we should not define a simpler idea in terms of a more complicated idea,

A fraction represents a part of a whole. Both common fractions and decimal fractions are also used to represent any number that is the quotient of two whole numbers. In mathematics, the word fraction is sometimes used to describe symobls that do not represent the quotient of two whole numbers, but have the form and properties of common fractions, for example pi/2 and 1/x.

Rick Norwood (talk) 12:47, 24 September 2011 (UTC)

Rick has a very good point. We should be sure to discuss common usage of the term "fraction" rather than sticking only to the rational number idea. Cliff (talk) 03:44, 25 September 2011 (UTC)

I propose a rule to discuss

I insist. About the word "fraction" and its different meanings, I had replied to Rick Norwood.  I had suggested him that we had (and we have still) to distinguish two contexts of use. Later, JimWae has inserted its message before my answer.  At the end,  it seems that I reply to Isheden, and my answer is meaningless, of course.

In order to evaluate different stages of the first paragraph:  the suggestion 2, suggestion 3, and so on, I propose the following rule of discussion. The evaluations should be numbered in chronological order with anchors "s_2", "s_3", and so on, because of this HTML element before each evaluation: <br id="s_x"/>

About the successive stages of the first paragraph, it would be nice to distinguish the merits and faults of each version. So, for the clarity of a given evaluation, each participant should use the anchors "s_x_m_1", "s_x_m_2", and so on, while the faults should be coded "s_x_f_1", "s_x_f_2", and so on.

Do you wish the clarity?  Would you like the respect of the chronological order?  Do you aim the consensus?  What do you think about that rule of discussion?
Aughost (talk) 08:08, 25 September 2011 (UTC)

A million apologies I don't quite understand how this works. Could we not just quote specific sentences and phrases? --Iantresman (talk) 10:27, 25 September 2011 (UTC)

Proposed introductory paragraph

Based on the previous discussions, I would like to propose the following introductory paragraph. It is non-technical and non-mathematics. It mentions different usage, ways to represent fractions in writing, and introduces the idea that the are more rigorous definitions:

A fraction, is a part of a number, often referring to a small part (eg. a fraction of a second), or more generally, a proportion of a certain quantity (eg. a large fraction of scientists use mathematics.). A fraction can be more specific, such as a "half", "third" or "quarter", and mathematics writes these amounts as 1/2, 1/3, 1/4, where the bottom number tells us how many possible parts there are, and the top number, how many parts we actually have. For example, a cake cut into quarters has four parts. If we remove one quarter, then we are left with three quarters, written as 3/4. In mathematics, the top number which tells us the number of parts we have, is called the numerator, and the bottom number which denotes the size of each part, is called the denominator. Usually, the numbers used to write fractions are whole numbers (ie. integers), but in mathematics, fractions can use nearly any kind of number (see Forms of Fraction)

--Iantresman (talk) 10:27, 25 September 2011 (UTC)

There are several problems with this, beginning with a comma error (don't separate subject and verb with a comma). A fraction represents part of a whole, not part of a "number". We hardly need to tell anyone that "half" is 1/2, certainly not in the lead. "Mathematics" doesn't write anything, mathematicians do, but they are not the only ones who write 1/2 and 1/2 is not the only way they write a half. The bottom number does not tell how many parts are "possible". Any number of parts is "possible". I could go on, but you really need to think for a long time about this subject before you try to write about it. Rick Norwood (talk) 13:43, 25 September 2011 (UTC)

The title of the article is "Fraction (mathematics)", so we have to speak about games with mathematical writings. It is true that a teacher speaks with the pupils in a classroom, but everybody also writes when the lesson deals with mathematics. And nobody in the classroom likes read the blackboard when it is overloaded with many sentences. Sometimes you read recommendations of Wikipedia, I am sure. Now I quote:  “while consideration should be given to creating interest in reading more of the article, the lead should nevertheless not "tease" the reader…” And in #First_sentence:  “the article should begin with a declarative sentence telling the nonspecialist reader what (or who) is the subject.” What is “a part of a number”?
Aughost (talk) 15:15, 25 September 2011 (UTC)

I was under the impression that "Fraction (mathematics)" is to differentiate the word from the other fraction disambiguation meanings, and that consequently, the subject does not limit us to the mathematical treatment of the word, only that we are dealing with the general numeric meaning of the word, ie, it is anything to do with quantities. When I talk of a "fraction of a second", I am still using the word in its mathematical sense, and I still think that my introduction is relevant.

I'm glad that you highlighted "the nonspecialist reader", and also note that "a part of a number" is not clear. Perhaps:

• A fraction is a quantity that consists of one or more equal parts of an whole number. --Iantresman (talk) 20:48, 25 September 2011 (UTC)

What is the numerator of a quantity?
Aughost (talk) 04:27, 26 September 2011 (UTC)

Of course a "quantity" does necessarily have a numerator, unless you decide to express such a quantity (a) as a fraction, AND (b) write the fraction in a certain way. The concept of a "half" is without doubt a fraction, and does not require numerators and denominators to express it. --Iantresman (talk) 11:50, 26 September 2011 (UTC)

Three quarters of the area of ABC  equals the area of  ACH.

A fraction OF a quantity is a quantity, it is not a writing. So, we have to distinguish between “a fraction” and “a fraction of” a given quantity. For example,  if  r( S )  denotes the area of a given surface S,  with the figure of the image we can write:

^{r( ACH )}/ _{r( ABC )}  =  ³/₄.

In my opinion, whatever the choice of the area unit, the first ratio is not a fraction. For example, I distinguish between  3 m² and  3.  But it is not for the whole audience of Wikipedia, it is a secret.
Aughost (talk) 15:49, 26 September 2011 (UTC)

"A fraction OF a quantity is a quantity" - Sure. Though I would say that fractions are dimensionless?

"So, we have to distinguish between “a fraction” and “a fraction of” a given quantity." - Indeed. I believe that the latter is more descriptive, and does not require a knowledge of mathematical terminology, so I would describe that latter first, and described fractions (numerators and denominators, etc) later.

The diagram could well be useful, but certainly not part of the introduction, which I think should be aimed at all audiences. --Iantresman (talk) 16:20, 26 September 2011 (UTC)

This diagram is not useful for this article. We are attempting to introduce fraction to students and readers. Trigonometry and square roots are not appropriate. Cliff (talk) 21:27, 26 September 2011 (UTC)

Suggestion 2
A fraction is a mathematical writing:  a ratio of two integers that represents their quotient.  For example, the fraction  ³ / ₄  equals  0.750.  The line that separates the integers is often horizontal:  a vinculum.  The two integers are called the numerator and denominator of the fraction.

Remark
The title of this section is “Proposed introductory paragraph”, and this page is not the article.

Remark
“Reduce a fraction” would be meaningless if the expression “two numbers” replaces “two integers” in the definition of “a fraction”.
Aughost (talk) 02:11, 27 September 2011 (UTC)

My main criticisms is "ratio", "integer" and "quotient" are mathematical terminology, hence this introductory definition is not aimed at all audiences. I think it is fine to mention all of these in subsequent paragraphs, but not in the introduction. I have a science background, and I don't understand "quotient", and would have to look-up the definition, before working out what the definition means.

As a test, I read out the definition to several people, excluding "A fraction is a mathematical writing", and unfortunately, none of the could work out what was meant. I don't think we should use technical terminology to explain terminology in an introduction. --Iantresman (talk) 10:39, 27 September 2011 (UTC)

You understand me when I say that, but maybe for you the expression is bad. How do you call “a mathematical writing”?  Remember the title of the article:  "Fraction (mathematics)".
Aughost (talk) 17:01, 27 September 2011 (UTC)

As I mentioned before, I don't think that "Fraction (mathematics)" implies that we deal with fractions only as they are expressed rigorously in mathematics. I believe that "mathematics" differentiates the word "fraction" from all of its other meanings, and that in this case, the "mathematics" means that we are dealing with the word in a generally numerical context.

I've also mentioned that I think that the numeric meaning of "fraction" also refers the concept of fractions, and would also include the meaning where we might speak of "a fraction of second".

I believe that the writing of fractions mathematically, (1/2 etc) is very very important, but it would be premature to talk of a writing system for a concept that we haven't yet explained.

I think perhaps we need to get more input from other editors as to whether we should be describing the subject non-technically and non-mathematically first. --Iantresman (talk) 18:28, 27 September 2011 (UTC)

"A fraction of second", again a fraction of a given quantity!  I repeat that we have to distinguish between “a fraction” and “a fraction of…”  Already in "Suggestion 1" I said that.  Please, would you read again "Suggestion 1"?
Aughost (talk) 18:52, 27 September 2011 (UTC)

Suggestion 1

A fraction (from Latin: fractus, "broken") is a writing of a quotient of two integers, as a ratio. For example, ³/ ₄ and ⁷⁵/ ₁₀₀ are two fractions that represent the same number: 0.75. A given fraction of a given quantity G is the product of G and the given number. For example, three quarters of G may be written: 0.75 × G.

My criticisms of your suggestion (above), are as follows:

(a) The suggestion begins with how to write fractions, when we haven't said what a fraction is (in general terms). (b) In describing how we write fractions, it uses technical mathematical terminology "quotient", "interger" and "ratio". Non-technical people will not understand the words. Please, read out "what is the writing of a quotient of two integers, as a ratio" to a non-technical person: your son/daugher, mother/father, spouse/partner, and ask them if they can guess what we are describing. (c) We continue with calculating the fraction of a quantity, and use decimal notation. In my opinion, we have not yet described what a fraction means.

I am quite happy with your description in a section on how to write fractions, but I believe it is too technical for an introduction. I think perhaps we need to get more input from other editors as to whether we should be describing the subject non-technically and non-mathematically first. --Iantresman (talk) 19:13, 27 September 2011 (UTC)

Can I also suggest reading "Wikipedia manual of style for mathematics: Introduction". It suggests that:

• "A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds."
• "The lead should as far as possible be accessible to a general reader, so specialized terminology and symbols should be avoided as much as possible"

(My bold) --Iantresman (talk) 19:24, 27 September 2011 (UTC)

Aughost, Iantransman said that he thinks we should discuss "a fraction of" before "a fraction" because it is easier to introduce the concept in that way without using technical language. Please read again his response to you in  "Suggestion 1"? Cliff (talk) 19:22, 27 September 2011 (UTC)

I agree with Iantrensman, I think that Aughost should also. Aughost said: "in #First_sentence:  'the article should begin with a declarative sentence telling the nonspecialist reader what (or who) is the subject.'" In order to tell a nonspecialist about fractions, we should avoid the use of other terms that would need to be defined. At least as much as feasibly possible. Cliff (talk) 19:22, 27 September 2011 (UTC)

Rationalizing the denominator of fractions

Evidence that fractions are commonly accepted to include non-rational components is provided by the common usage of "rationalizing fractions" and/or "rationalizing the denominator of a fraction" [3]. It is totally unneccesary, goes against common usage, AND is not comprehensive to have the article say such expressions are not fractions. It is also common to accept 2√3⁄3√12 and pi⁄2⁄ pi as fractions --JimWae (talk) 20:47, 29 September 2011 (UTC)

I realized recently that I am approaching this discussion using only my concept of what fraction is. My apologies for this. I intend, soon, to run some journal searches to determine the mathematical community's consensus about the term fraction. I will return with this information as soon as it is acquired and digested. Cliff (talk) 13:53, 30 September 2011 (UTC)

More and more incoherent

Never in my life I heard the locution "vulgar fraction" or "common fraction".  Never I had read such an expression. When I wrote the beginning of the new section 'In_order_to_define…',  I gave notice to everybody that I had been satisfied before the Wiktionary, where a fraction was a ratio of two integers.  Now, I read in the Wiktionary that both numerator and denominator are integers in the so-called vulgar  fractions, or common  fractions, but not in all the fractions.  However, the page entitled Common_fractions  in Wikipedia redirects to Fraction_(mathematics).  That is inconsistent with “common fraction” in the Wiktionary, since a fraction represents any real number in the mind of JimWae, for example.  Maybe tomorrow it will be different.  Being more and more incoherent is always possible.  But it is never too late to think seriously…
Aughost (talk) 14:09, 28 September 2011 (UTC)

You sound angry. Maybe you should take a deep breath and calm down. Cliff (talk) 18:37, 28 September 2011 (UTC)

What do you mean?
Aughost (talk) 01:55, 29 September 2011 (UTC)

I agree. You do sound angry. I also recommend a time out to calm down. There are probably lots of words you've never heard of -- certainly there are lots of words I never heard of -- but when I read an unfamiliar phrase I am always glad to learn something new. Be glad you now know the difference between a vulgar fraction and a decimal fraction. They are two different ways to express a part of a whole. Rick Norwood (talk) 15:36, 29 September 2011 (UTC)

How someone's anger could be a (valid) argument in a reasoning?  How one meaning of “common fractions” could be an argument favourable or unfavourable to one definition of a “fraction”, or another definition?

Assume that a “common fraction” is a ratio of two integers, as JimWae says in the Wiktionary.  The current content of "Common_fractions" in Wikipedia is only a link to "Fraction_(mathematics)".  And the current introduction of "Fraction_(mathematics)" says (badly says) that a fraction is a ratio of two (real) numbers. What do you think about that?
Aughost (talk) 07:43, 30 September 2011 (UTC)

The reason that two people, now, have commented on your apparent anger is that anger seems the best explanation for your incoherence. You could actually read the article, and you would learn that a common fraction has a numerator and a denominator, that the numerator gives the number of equal parts, and the denominator gives the number of those equal parts that make up a whole. Fractions represent numbers; ratios compare two or more numbers. The current lead mixes the two. I plan to fix it when the controversy has cooled a bit. Rick Norwood (talk) 13:37, 30 September 2011 (UTC)

That sounds like a good proposal. The term "common fraction" is used in many online North American textbooks, and the term "vulgar fraction" is occasionally, though less and less frequently, used in Britain and Ireland. --Hroðulf (or Hrothulf) (Talk) 14:46, 30 September 2011 (UTC)

I repeat that the current page "Common_fractions"  in Wikipedia redirects to the current page "Fraction_(mathematics)":  precisely the top of the page, where we read that a fraction is a ratio of (real) numbers. So, we understand that the numerator and denominator of a “common fraction” are any real numbers.
— Aughost (talk) 03:57, 1 October 2011 (UTC)

It's easy enough to change the redirect to Fraction (mathematics)#Vulgar, proper, and improper fractions if that is important enough to you. That's where Vulgar fraction goes. --JimWae (talk) 04:21, 1 October 2011 (UTC)

Well, I tried. But the version that says a fraction is a ratio and another use for fractions is to express a ratio is back. If anyone prefers my version, please restore it. If everyone prefers this version, so be it. Rick Norwood (talk) 14:56, 1 October 2011 (UTC)

I agree with your changes, but I think it is pointless to start an edit war. My understanding of the discussion here is that we need a lead that captures not only the arithmetic concept of a fraction representing part of a whole (leading to rational numbers) but also for example algebraic fraction as synonym for a rational expression. Still, I think the lead should start simple, i.e. explaining what a common fraction is, what a proper fraction is, and so on. Isheden (talk) 09:34, 2 October 2011 (UTC)

I agree that the current lead isn't ideal. But the alternative "A fraction (from Latin: fractus, "broken") represents a part of a whole or, more generally, any number of equal parts" is confusing. The current article is about numbers that are fractions, and so I think the first sentence really needs to include the word number. We should start by saying what a fraction is (if we can ever agree on an approximate description), and only later pass to what it represents. Jowa fan (talk) 09:50, 2 October 2011 (UTC)

I also am trying to avoid an edit war, but if the current lead isn't good, it shouldn't be preserved just to avoid an edit war. It can be improved in stages.

I avoided the use of "number" because I didn't want to open the can of worms about the difference between a number and a numeral. I have no objection the use of number, but at least one person did.

Jowa fan: Would you accept "A fraction is a number that represents a part of a whole or, more generally, any mathematical expression with a numerator and a denominator."

Rick Norwood (talk) 13:19, 2 October 2011 (UTC)

That's better, but still not quite right. There are three problems to my mind. First, "part of a whole" suggests that fractions can only be between 0 and 1. Second, the sentence as written is ambiguous: it could be read as meaning a fraction is ... any mathematical expression; or a fraction represents ... any mathematical expression. Third, I'm not sure it's good to have the words numerator and denominator in the lead sentence. I think it's OK for the lead sentence to only refer to the meaning of fraction as a rational number (or equivalent); if it's appropriate to mention algebraic fractions or other things, this can be done later. Right now I can't think of a good alternative lead, but I'll let you know if inspiration strikes. Sorry not to be any more constructive at this moment. Jowa fan (talk) 12:59, 3 October 2011 (UTC)

Aughost's concerns

A few comments on the points Aughost raises.

Clearly not every phrase with the word "fraction" in it is a kind of fraction. "Equivalent fractions" are fractions that are equivalent, but "algebraic fractions" not fractions that are algebraic, they are algebraic expressions that resemble fractions in form.

I can't recall hearing the phrase "irrational fraction". What I have heard is "irrational expression".

It may be that rational functions and partial fractions should not be in this article proper, but just listed in the "see also" section at the end, with links to the subject pages.

3/3 is an improper fraction. If the article says otherwise, it needs to be fixed.

Vulgar fraction should merge here.

I think the new first sentence now addresses both uses of fraction, sometimes to mean only proper fractions (a part of a whole) but sometimes to include improper fractions (any number of equal parts).

The absence of an adjective before the noun in the title is commonplace in Wikipedia, where the plain word is given its most common meaning, and other meanings are supplied in a reference to a disambiguation page. So calling this article "fraction" does not suggest discussing the chemical process, for example.

Aughost remains convinced that a fraction is a ratio. It isn't, and I don't think anyone else in this discussion thinks it is. A fraction represents a number of equal parts. A ratio compares two or more numbers.

Aughost suggests "a fraction is a way to write a rational number". Since the definition of a rational number is "a number which can be written as a fraction, with an integer numerator and a non-zero integer denominator" that attempt at a definiton is circular, and also defines a simple concept in terms of a less familiar concept.

Rick Norwood (talk) 15:44, 5 October 2011 (UTC)

Reading this section is it a good way to get ideas about Rick Norwood?  Add unnecessary text below an ongoing discussion is a way to increase the difficulty to read and understand the page.
— Aughost (talk) 17:11, 24 October 2011 (UTC)

JimWae's edit.

Excellent edit, JimWae. Rick Norwood (talk) 22:48, 11 October 2011 (UTC)

Technical terms in the introduction: Request for input

There is no doubt that the article should use technical (mathematical) terms, but should this include the start of the introduction? I've put in a request for some more input from other editors, regarding the use of technical terms used in the introduction to this article. Guidelines:

• "Manual_of_Style/Lead_section"
• "Wikipedia:Manual of Style/Mathematics:Article Introduction" --Iantresman (talk) 12:56, 23 October 2011 (UTC)

There are a few technical terms in the lead, but these are mostly explained in everyday language. I'm more concerned with the lack of connection between the lead and the contents of the article. Decimal fractions, percentages, and negative exponents don't appear to have any coverage in the article, yet half the lead discusses these peripheral topics. I know the article isn't very good, and maybe it should mention these things later on, but the lead seems like the last place to discuss topics of peripheral relevance. Sławomir Biały (talk) 15:00, 23 October 2011 (UTC)

Technical terms are terms that are used by professionals and advanced students in a discipline and unknown to most people outside that discipline OR used in a different way. Terms that are taught in the first 6 years of school are not technical terms that one should avoid in the lede. Additionally, it is simply impossible to define EVERY term with simpler terms. Wikipedia articles are generally written to be understood by high-school students, not 9-yr-olds. The first paragraph, besides being somewhat vague, is presently an oversimplification in that it treats fractions only as numerals and never as numbers. WP:JARGON need not apply to this article, because the terms used here are used in the same way in the general population. --JimWae (talk) 19:52, 23 October 2011 (UTC)

+1--Kmhkmh (talk) 16:19, 30 October 2011 (UTC)

You'll get no debate from me, but have you considered maybe cutting the stuff from the lead that isn't addressed in the article as a whole (percentages, decimal fractions, negative exponents)? To me these seem like peripheral topics that don't belong in the lead. Sławomir Biały (talk) 16:06, 30 October 2011 (UTC)

I think they are important. And of course they are linked to the appropriate article. Maybe they should be discussed, briefly, in the body of this article. Rick Norwood (talk) 13:21, 31 October 2011 (UTC)

I agree that some mathematical terms cannot be considered techincal terms. How do we propose to determine which terms are those that have been taught in the first 6 years of school? I was not taught the word Quotient in the first 6 years. I'm not sure about ratio, but am leaning toward not. Are we then going to define fraction as implied division? Cliff (talk) 18:10, 31 October 2011 (UTC)

If you were not taught the word "quotient" in your first six years of schooling, sue your school system. We are not going to define fractions as applied division because that is not the definition of a fraction. A fraction is a number, not an arithmatic problem. Rick Norwood (talk) 18:20, 31 October 2011 (UTC)

Don't confuse my argument against the "by the 6th grade" measure as an argument for defining fraction as implied division. I'm also not sure that "fraction" is used only in the number context. Cliff (talk) 20:46, 31 October 2011 (UTC)

The numeral "5" refers to the number 5. The numerals/symbols "1/5" also refer to a number - a fractional number - a fraction that has a value of 0.2. "1/5" and "0.2" both refer to the same number - the same fraction of a whole. "1/5" refers to a number that IS a fraction. "5/1" refers to a number that is not fraction, but the symbol "5/1" writes that number AS a fraction (and people have agreed to call "5/1" [and 10/2, and 85/17] a fraction). "Fraction" has a meaning in terms of numbers and a meaning in terms of numerals. In terms of numbers, all fractions are between -1 and 1, excluding 0 (and -1 and 1, as already stated by "between"). [Also all numbers between -1 and 1, except for zero, are fractions.] Non-integer numbers above 1, and below -1, have fractional parts. --JimWae (talk) 21:01, 31 October 2011 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Fraction/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

General expansion as per Addition. Salix alba (talk) 19:14, 29 September 2006 (UTC) History needs expanding, Addition is a good example of where to aim

Last edited at 18:28, 16 April 2007 (UTC). Substituted at 20:35, 2 May 2016 (UTC)