Talk:Fraction

Irrational Fraction

“An irrational fraction is, if 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)

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)

Thanx!

Thank you for making this page!!!!!! ^.^

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)

Wikipedia's Math Help

Wikipedia is a great source to find answers to questions in Math, best yet I've found. —Preceding unsigned comment added by 76.27.28.131 (talk) 23:42, 9 January 2008 (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)

math

i like math because it is a fun and learning process that you need to know —Preceding unsigned comment added by 66.250.190.118 (talk) 17:46, 9 September 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)

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)

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)

Fractions

fractions are good for learning and knowing the answer and thinking of the answer in your head and in your brain and when you think of more you can say it in you head in know it with out having to say it out loud so every body can hear you. when your doing a test remember to think of some answers what you already know —Preceding unsigned comment added by 98.70.129.214 (talk) 20:11, 15 June 2009 (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)

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)