# Talk:fraction

Is definition 4 a mistake? It says "part of a particular society or group." but it seems to me this is a faction. I don't have a paper dictionary to hand at the moment. Visctrix 10:08, 26 August 2005 (UTC)

In one of your definitions you used the word "ratio" and "integer" to help define a fraction. Ratio usually is defined and worked with in the fifth grade and integer is a sixth grade subject, while fraction is defined and worked with in the third and fourth grades in most elementary school mathematics textbooks. It has been that way for at least 30 years. You may want to check that out in k-12math.info [1] . Jim Kelly

## missing definitions.

A rational function can be thought of as a fraction where the numerator and denominator are functions in their own right. More than, "thought of", this usage is common in classrooms. The arithmetic term described is actually the definition of a rational number. Fraction has a broader sense, for instance. 1.2/3 is a fraction, though it does not meet the definition as currently stated. 134.29.231.11 18:56, 20 September 2011 (UTC)

## Correct definition with "integer"

With a non-integer numerator or a non-integer denominator, simplify a fraction would be meaningless. So the following definition is wrong.

(arithmetic) A ratio of two numbers, the numerator and the denominator, usually written one above the other and separated by a vinculum (horizontal bar)

With the word "integers" instead of "numbers", the following definition is correct.

(arithmetic) A ratio of two integers, the numerator and the denominator, usually written one above the other and separated by a vinculum (horizontal bar)

Ceciliia 08:16, 24 September 2011 (UTC)

No source says integer. A fraction with integers is a special type of fraction - a common (or vulgar) fraction. pi/4 is a fraction, as is sqrt(2)/2, 1.5/2 and 1 1/2 /2. This was pointed out in the edit summary AND even in the previous section here --JimWae 09:45, 24 September 2011 (UTC)

A fraction is a particular ratio, where both numerator and denominator are integers. See below.
Ceciliia 08:27, 28 September 2011 (UTC)
WRONG - what you are describing is a common fraction. SemperBlotto 08:34, 28 September 2011 (UTC)

Affirm is not sufficient to convince.  The definition deals with `arithmetic`.  Had you read below my explanation before canceling  my changes?  Had you read this code at the entry “fraction”:

```<!-- A fraction is a way to write a rational number:
as a digit and a number are two different things,
a fraction and a number are two different things -->
```

What is the meaning of “simplify” or “reduce” a fraction, in your opinion?
Ceciliia 09:29, 28 September 2011 (UTC)

A correct definition of “fraction” was already justified in the previous section. Since we had again to correct the expression “two numbers”, I thought that the sentence would be better without comma. Now, there are four sentences. In the second sentence, an example enlightens about the general meaning. The topic of the third sentence is the line that separates the integers. The last sentence defines the words “numerator” and “denominator”.

No source justifies the wrong JimWae’s definition.  Maybe a source is upcoming.

How to find a source that says what we might write before a noun in a given context, without changing the meaning?  Before the noun “fraction”, we can add an adjective like “common”, or “ordinary”, or “simple”, or “vulgar”, to denote the same thing: a fraction. Create an entry “vulgar fraction” is a very bad idea, because readers will believe that such an adjective is necessary to denote a particular fraction. The two expressions “vulgar fraction” and “fraction” have the same (ordinary) meaning, an adjective like “vulgar” is implied.

When some definitions are together in a book or website, the set of definitions is coherent or incoherent. Nobody will find a source that says they are consistent or inconsistent. The words “ratio” and “fraction” would be two synonyms, if the numerator or denominator of a fraction may represent any number. Fortunately, there is no list of synonyms neither in the entry “fraction”,  nor in the entry “ratio”.  A fraction is a particular ratio, where both numerator and denominator are integers.

The following statements are in (elementary) `arithmetic`.  For example,  2.50  is notnatural number, so the ratio  1 / 2.50  is not a fraction.  However,  1 / 2.50 = 40 / 100   and  40 / 100  is a fraction. The GCD  of  40  and  100  is  20,  so we get the reduced fraction  2 / 5  equal to  0.40  by dividing  40  and  100  by this same common divisor:  20.
Ceciliia 08:27, 28 September 2011 (UTC)

Simplify  1 / 2.50  is meaningles with the last definition.
Ceciliia 09:50, 28 September 2011 (UTC)

• No source has been supplied which says fractions must be written with integer numerator and integer denominator. "Half" is a fraction, so is 0.1, so is 40%, so is 122. If ab is a way to expresses a fraction, no citation has been found to support saying it is so only when a and b are both integers - it is even unnecessarily dogmatically restrictive to say it only expresses a fraction when both a and b are rational numbers. Fraction has 2 meanings - one as a number (or non integer part of a number) that is between zero and one. A second meaning is as the expression of a number (thus qualifying 21 and 01 as fractions).
• No source has been supplied that common fraction and fraction mean the same thing - indeed many sources can be found to the contrary, specifying integers for common fractions and not so specifying for "fraction".
• Also note what are called compound or complex fractions - fractions in which numerator and/or denominator are fractions
• Whether pi4 is a fraction is a separate matter - but there is no immediate reason to rule it out - especially if someone has not yet determined that pi is irrational. It is written in the form of a fraction, and it is certainly a part of a whole - an incommensurate part. We could indeed write fractions containing irrationals that evaluate to rational numbers - such as pi2pi --JimWae 20:23, 29 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 [2]--JimWae 20:42, 29 September 2011 (UTC)
• 2√33√12 is also commonly accepted as a fraction - AND it makes sense to ask a person to simplify it.--JimWae 21:14, 29 September 2011 (UTC)

In that definition of “fraction”,  the first word is between brackets:  “`arithmetic`”.  The word  “arithmetic”  does it have the same meaning for you and me,  I am unsure.  For example, the number  √2  is irrational, and  √2  is not an arithmetical writing.  In my opinion, both numerator and denominator of a fraction  `are integers`.
Ceciliia 05:12, 4 October 2011 (UTC)
Well, we could simply change "arithmetic" to "mathematics", but there's no need. I have not argued that we must say fractions do not have to be rational numbers. You have not addressed the other points I made, such as 122, nor have you provided a single source for what you acknowledge is your "opinion".--JimWae 01:30, 7 October 2011 (UTC)
I disagree, the ordinary context of the word “fraction” in mathematics is not the entire domain of mathematics, that is too wide.  The ordinary context is indicated between brackets:  arithmetic.
Why not a comment about your writing:  1  2  2,  that is not a ratio of two integers,  but that represents a rational number.  The writing  1  4  is one way among the infinite number of ways to write  0.25  as a fraction — as a ratio of two integers —.
Ceciliia 09:57, 7 October 2011 (UTC)
You have been arguing - without providing a single reference - that fractions are the ratio of integers. 1  2  2 is not a ratio of integers - or at least is not written as such, even though it evaluates to such - yet it is still accepted as a fraction - even in grade school arithmetic. Your argument goes against common usage and is unsourced. What more needs to be said?--JimWae 20:42, 7 October 2011 (UTC)
Please, let’s be clear.  First, your writing  1  2  2  is a ratio.  Then, the numerator of your ratio represents a conceptual object called numerical object.  That number equals  0.500,  it is not integer.  Therefore your ratio is not a fraction.  But the number that is represented by your ratio is rational:  the conceptual object is rational, that we can write  0.250  for example.  In other words, at least one fraction exists — one ratio of two integers exists — that represents your numerical object.  There are an infinite number of fractions that are equal to  0.250  — that represent the number  0.250 —.
Many abuses of language are unavoidable in the current language.  For example, I will say that I write a number, and everybody will understand me.  However I have written something that represents a number.  Here we are discussing about a definition in arithmetic, so we have to be accurate.  For example, when you write above “at least is not written as such”, so you no longer talk about your writing, you are talking about the object represented by the writing.  For example, you wrote above that "half" is a fraction, and I disagree, sorry.  Without any context we cannot understand the word "half", and a given word will never be an arithmetical writing.  For example, there is no numerator in three quarters of some cake.  In other words, a quantity of cake is not an arithmetical writing.  We don’t need reference to affirm that.
Ceciliia 03:47, 8 October 2011 (UTC)
Please see my previous post--JimWae 18:35, 8 October 2011 (UTC)
I had quoted several passages of JimWae’s messages, to indicate several mistakes.  And JimWae’s answer is:  “please see my previous post.”  Quite unconvincing.

“WRONG - what you are describing is a common fraction”, wrote SemperBlotto above.  But we cannot deduce anything from a definition of “common fraction”, that is an outdated phrase.  Moreover, "Common_fractions"  in Wikipedia redirects to the top of "Fraction_(mathematics)",  so “common fraction” and “fraction” have the same meaning in the current pages of Wikipedia.

In "Talk:Fraction_(mathematics)" of Wikipedia, the meaning of the title word is forcefully discussed, notably by JimWae.  According to his last messages,  it seems that a fraction would be “a part of a whole”, that is obviously not mathematical.  Very surprising.  JimWae is locked in contradictions.

Ceciliia 09:24, 23 October 2011 (UTC)
If it helps, we go by usage, so whatever English speakers call a fraction is a fraction. 'Accuracy' according to a prescriptive source isn't too important. Mglovesfun (talk) 09:32, 23 October 2011 (UTC)
Moreover, contradiction of implications isn't necessarily a fatal objection to a definition. Also, it is normal for a definition to be about one sentence long, with very few clauses. The challenge is in inferring meaning from actual usage. The art is in coming up with a small number of terse definitions that together span the range of usage. DCDuring TALK 12:49, 23 October 2011 (UTC)
The above comments are off the point.  Here JimWae does not reply, but often he has written in Wikipedia, notably in Talk:Fraction_(mathematics).  A fraction would represent a “part of a whole”, according to the current beginning  of "Fraction_(mathematics)" in Wikipedia.  That definition is not mathematical.
Ceciliia 05:30, 12 November 2011 (UTC)
I am not responsible for that definition at wikipedia, and when the right time comes I will discuss it there. You have been arguing - without providing a single reference or receiving any support from other editors - that fractions are the ratio of integers. What's any of this got to do with your unsupported conflation of common fractions with fractions in general? --JimWae 20:06, 12 November 2011 (UTC)
When you replaced “integers” with “numbers”,  you wrote:  “no source below (or elsewhere) says integer”.  We don't need source, because the simple reason to say “integer” is context: arithmetic.  And you are off the point when you add an adjective like “common” or “vulgar”.
Ceciliia 08:34, 13 November 2011 (UTC)
So you are saying there's a different definition for "fraction" in arithmetic from the one in mathematics? Do you have a source for that? In fact, it is routine to treat (3/4)/4 as a fraction even in elementary school arithmetic. Even if there were different definitions, that would not justify keeping "integer" there for this entry - as the entry ought to be comprehensive -- for all of mathematics, not just arithmetic. Probably we should change "arithmetic" to "mathematics" -- AND, as I point out above, even in arithmetic there can be non-integers in fractions, AND thus the definition is the same regardless. What else needs to be said? I will not repeat this again, and will ignore any responses that do not consider this. --JimWae 21:25, 13 November 2011 (UTC)

Your first contradiction is more and more flagrant:  affirm without source is a fault for other people, not for you.
Ceciliia 09:20, 14 November 2011 (UTC)