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)
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,
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)
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)
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)
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 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)
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.
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 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)
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)
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)
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)
In the article, it says:
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)
anyone know how to type fraction in microsoft word? Ragnaroknike 09:14, 5 December 2006 (UTC)
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)
"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)
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)
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)
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)
The article had this:
Combining both this method and the first method to compare and , first note that > , because the first fraction has a smaller denominator.
Then note that > , because the first fraction has a smaller numerator.
Therefore, by the transitive property of inequality, > . 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: < , because the last fraction has a smaller denominator. This is therefore a bad example.-- EdgeNavidad ( talk) 07:56, 19 February 2009 (UTC)
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)
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)
Which of the following are NOT vulgar fractions?
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)
[...] 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)
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)
The earliest known use of fractions is ca. 2800 BC as Ancient Indus Valley units of measurement. citation needed
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 discussion in the Definition section above, the following sentence in the article's introduction is wrong:
No matter what the definition, this should clearly be:
But I'll wait until the opening sentence is settled to make the correction. -- seberle ( talk) 03:12, 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)
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)
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)
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)
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)
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)
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)
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)
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)
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 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)
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)
None of the sources at wiktionary
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)
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)
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)
"A fraction ... is a number that can be expressed as the ratio of two numbers ... . Other uses for fractions are to represent ratios ... ."
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)
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)
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)
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)
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)
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)
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)
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)
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:
-- 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)
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:
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)
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)
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)
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)
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)
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 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)
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)
Excellent edit, JimWae. Rick Norwood ( talk) 22:48, 11 October 2011 (UTC)
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:
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)
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)
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)
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)
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,
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)
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)
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)
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 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)
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.
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 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)
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)
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)
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)
In the article, it says:
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)
anyone know how to type fraction in microsoft word? Ragnaroknike 09:14, 5 December 2006 (UTC)
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)
"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)
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)
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)
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)
The article had this:
Combining both this method and the first method to compare and , first note that > , because the first fraction has a smaller denominator.
Then note that > , because the first fraction has a smaller numerator.
Therefore, by the transitive property of inequality, > . 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: < , because the last fraction has a smaller denominator. This is therefore a bad example.-- EdgeNavidad ( talk) 07:56, 19 February 2009 (UTC)
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)
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)
Which of the following are NOT vulgar fractions?
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)
[...] 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)
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)
The earliest known use of fractions is ca. 2800 BC as Ancient Indus Valley units of measurement. citation needed
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 discussion in the Definition section above, the following sentence in the article's introduction is wrong:
No matter what the definition, this should clearly be:
But I'll wait until the opening sentence is settled to make the correction. -- seberle ( talk) 03:12, 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)
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)
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)
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)
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)
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)
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)
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)
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)
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 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)
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)
None of the sources at wiktionary
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)
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)
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)
"A fraction ... is a number that can be expressed as the ratio of two numbers ... . Other uses for fractions are to represent ratios ... ."
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)
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)
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)
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)
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)
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)
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)
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)
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:
-- 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)
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:
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)
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)
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)
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)
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)
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 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)
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)
Excellent edit, JimWae. Rick Norwood ( talk) 22:48, 11 October 2011 (UTC)
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:
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)
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)
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)