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.

Template: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.

Template: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 (deprecated template usage) 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)

Implied adjectives

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 not a natural 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 ^1⁄₂⁄₂. If ^a⁄_b 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 ²⁄₁ and ⁰⁄₁ 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 ^pi⁄₄ 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 ^pi⁄₂⁄_pi --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√3⁄_3√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)