Talk:Fraction (mathematics)

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Mathematics grading:	B Class	Top Importance	Field: Basics
A vital article
History needs expanding, Addition is a good example of where to aim

Contents 1 Irrational Fraction 2 latest edit 3 External links 4 Merge (with Vulgar Fraction) 5 Proper fraction 6 Wikibook? 7 Template 8 Bullet points 9 Terminology 10 "fraction" meaning decimal 11 Elongation and shortening? 12 typing 13 Thanx!

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] "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)

[edit] 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)

[edit] 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)

[edit] Thanx!

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