Talk:Fraction

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'Fourth' vs 'quarter'

The illustration of a cake cut into 3/4 describes it as 'three fourths'. Is this correct as opposed to 'three quarters'?

I may be wrong, but isn't it only North America that uses 'fourth' as opposed to 'quarter'? groovygower (talk) 08:07, 14 June 2014 (UTC)

As a Maths teacher in Australia, I'll agree that "three quarters" is far more common, but I do point out to my students that it means exactly the same things as "three fourths". HiLo48 (talk) 08:16, 14 June 2014 (UTC)

I was originally the one who specified the "three-fourths" for that pie. In my classes (known locally as math and not maths) we would often say "fourths" in context of numeric discussion. But nary a soul would even bother to lodge a complaint with "quarters" for most fractions less than 5/4. We have a unit of currency known widely as the "quarter" (dollar) that makes this use obvious. But if I would have to guess, the usage might be split unevenly toward the "quarter" in everyday speech, and unevenly toward the "fourth" in math class. A typical pie or pizza or inch would be quartered, while a measuring cup or a bare fraction is often in fourths. Larger improper fractions (e.g. 11/4) is almost always in fourths. I like to saw logs! (talk) 19:49, 14 June 2014 (UTC)

I wasn't complaining, if I was I would have edited it - just curious. I'm guessing it's an American English thing. As most of the English spoken in the world is American English, I guess it makes more sense to keep it. groovygower (talk) 17:30, 18 July 2014 (UTC)

Most of the English spoken in the world is American English? Checked out India lately? HiLo48 (talk) 07:53, 19 July 2014 (UTC)

I also think that non-native English speakers will understand "fourths" easier at first blush than "quarters." I like to saw logs! (talk) 07:34, 10 February 2015 (UTC)

Basic fraction conversion

Every student should know how to change between fractions, decimals, and percents. Some of these changes are so common that they are worth memorizing, such as 1/2 = 0.5. But the long list in the article obscures which conversions are most important, and which of the infinitely many other conversions should be carried out as needed. I propose to shorten the list, but wanted to discuss that here first. Rick Norwood (talk) 13:01, 6 February 2015 (UTC)

I do not refer exactly to the mentioned above matter, but to the headline of this section in your version

A fraction can be converted into other forms which have the same numerical value, including decimals, percents, and other fractions.

Considering the conversion of "1/3" to "0.333..." I conceive a broad hint to reinsert the concept of representing a number instead of having a numerical value. Taking into account that the same number represented by 1/3(decimal) might be converted to say 0:1 in a positional numbering system with base 3(decimal), the ":" representing the ternary point these perception gets even stronger. In a strict math sense already a rational number is an infinite equivalence class of objects, usually represented by some proxy. I will not take care of this anyhow.

Strictly on topic, I'm with Arthur Rubin (talk · contribs) to delete rather more than less of these lines (see reverted edits for not interesting). Purgy (talk) 09:59, 7 February 2015 (UTC)

I think the entire section should be removed. Wikipedia is not a place to present tables of numeric values or a thing to substitute for a calculator. This section does not explain conversion, just presents a table of some particular values -- pointless cluttering of the article. --R. S. Shaw (talk) 01:34, 10 February 2015 (UTC)

Apoorva Goel version

I agree that Cluebot was wrong to revert Apoorva Goel's rewrite. But Apoorva Goel was wrong to call the version which has been fairly stable for many years "rubbish". I think the earlier version better. They are compared below, line by line, with a minus on the earlier version and a plus on the Apoorva Goel version. I've indented my comments.

− A fraction (from Template:Lang-la, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

+ A fraction (from Template:Lang-la, "broken") represents equal parts of a whole number. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, four-eighths, three-quarters.

>>>>>"equal parts of a whole" is better than "equal parts of a whole number" because a fraction can represent equal parts of a pie, it is not limited to equal parts of a number. "eight-fifths" is better than four_eighths" because it is an "improper" fraction. I would have no objection to both.

- A common, vulgar, or simple fraction (examples: ${\tfrac {1}{2}}$ and 17/3) consists of an integer numerator, displayed above a line (or before a slash), and a non-zero integer denominator, displayed below (or after) that line.

+ A simple fraction (examples: ${\tfrac {1}{2}}$ and 17/3) consists of a numerator, displayed above a line or before a slash and a denominator, displayed below that line or after that slash.

>>>>>All three words are standard; "vulgar" is somewhat obsolete but is found in older books and there is no harm in including it. That the numerator and denominator of a simple fraction are integers is essential, it is what makes the difference between a simple fraction and a complex fraction.

- Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

+ Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

>>>>>No major difference here, but I slightly prefer to italicize the important word.

− Fractional numbers can also be written without using explicit numerators or denominators, by using decimals, percent signs, or negative exponents (as in 0.01, 1%, and 10⁻² respectively, all of which are equivalent to 1/100). An integer such as the number 7 can be thought of as having an implicit denominator of one: 7 equals 7/1.

+ Fractional numbers can also be written without using numerators or denominators, by using decimals or percent signs.

>>>>>The change removes an important concept, that of the "understood" denominator. The word "denominator" does not just mean "the bottom of a fraction", rather it is the name of the number of parts that make up a whole. Thus a percent has an understood denominator of 100.

- Other uses for fractions are to represent ratios and to represent division. Thus the fraction 3/4 is also used to represent the ratio 3:4 (the ratio of the part to the whole) and the division 3 ÷ 4 (three divided by four).

+ Other uses for fractions are to represent ratios. Thus the fraction 3/4 is also used to represent the ratio 3:4 (the ratio of the part to the whole) and the division 3 ÷ 4 (three divided by four).

>>>>>The use of fractions to represent division is widespread, and to remove the word "division" while keeping the example is inconsistent.

Rick Norwood (talk) 14:51, 26 June 2015 (UTC)

From the reasons given above any person capable of comprehending reading can derive, why this version has been stable for many years.

Congrats to Wikipedia for its night-watchmen, detecting each fire before it's burning hot. Purgy (talk) 17:10, 26 June 2015 (UTC)

Anomalocaris's edit

Thanks for an excellent edit. Rick Norwood (talk) 17:58, 24 February 2016 (UTC)

Placement of history section

Raguks has attempted to put the history section at the top of the page and has now been reverted at least twice. His argument seems to be that there are some pages that have the history section placed there, so this one should be! The tone of one of his edit summaries indicates to me that there is something else motivating him, but I shall not speculate on that. While it is true that there are some math pages that have a history section placed high in the article, this is certainly not universal nor any type of requirement. There are many reasons for placing sections where they are, but in my mind the most important has to do with the nature of the article and who the intended audience is. In articles dealing with elementary topics the readers are looking for clear and simple explanations of what the objects are and how they are to be manipulated. How these things are used is of vital importance. An interest in the history comes in as a low priority because it does not help with the fundamental issues that bring readers to the page. In different areas this may not be the case. For a more abstract topic, such as Algebra, the historical perspective helps to understand how and why the abstraction was necessary, and so, should come early in the article. There is no "one size fits all" rule for section placement and one must judge each article on its own merits. I stand by my revert and wish that this section be placed back where it belongs. --Bill Cherowitzo (talk) 05:39, 3 April 2017 (UTC)

Shall we see what is motivating you to write a lengthy explanation about placement? I won't speculate on that either! But I am quite sure it is something else! Why is "how and why the abstraction was necessary" for fraction isn't important? Or do you claim there was no "abstraction" necessary to invent fractions? I do not have time for this. But should be enough to lead to that "something else". I will let you decide what size fits this one. Be happy.

~rAGU (talk)

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order of operations ambiguity in complex fractions

The article points out that notation such as x/y/z/w is ambiguous, or even "improperly formed". This obviously goes just as well for complex fractions such as ${\frac {\frac {x}{y}}{\frac {z}{w}}}$, but not ${\frac {{\frac {x}{y}}+1}{{\frac {z}{w}}-1}}$. I would like to stress that the possible excuse that the middle fraction line is a bit longer and/or thicker is not good: there is no way to guarantee or even hope for this in clients, especially given all the math display options users have. I propose we replace complex fractions such as

${\frac {\frac {x}{y}}{\frac {z}{w}}}$

with unambiguous representations such as

${\frac {\left({\frac {x}{y}}\right)}{\left({\frac {z}{w}}\right)}}$ or ${\frac {x}{y}}\div {\frac {z}{w}}$

melikamp (talk) 19:25, 11 August 2017 (UTC)