# Talk:Fraction (mathematics)

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## Negative fraction

Would "-34" be spoken as "minus three-quarters", "negative three-quarters", or either? I have always used "minus", and have never noticed anyone to use anything different. It's difficult to remember such an unmemorable point, but I think this has mostly come up as an exponent in my personal experience, e.g., "x to the minus two-thirds". I've reverted a change; it's "minus" again, not "negative", but would like a consensus, I may be wrong. Pol098 (talk) 00:13, 19 June 2013 (UTC)

I'm going to restore Jim Wae's version. "Minus" is a binary operation, meaning subtraction. You read 7 - 2 as "seven minus two". But "negative" means "less than zero". Since -3/2 is less than zero, but does not involve subtraction, Jim Wae is correct. Rick Norwood (talk) 00:51, 19 June 2013 (UTC)
OK, let's leave the article with "negative". But I remain curious for myself; regardless of what is considered as formally correct language, among people who use mathematics (e.g., theoretical physicists, rather than teachers), do most speak of "minus three-quarters", "negative three-quarters"? Have I been misspeaking all these years? Pol098 (talk) 09:43, 19 June 2013 (UTC)
While I’m not a native speaker, I’m a mathematician, and this is the first time I’ve heard of this distinction. I’ve consulted several dictionaries, and all of them include the usage of “minus” for negation, even giving explicit examples like “minus five degrees” or “subtract ten from seven and the answer is minus three”.—Emil J. 11:06, 19 June 2013 (UTC)
The symbol is called minus sign and in this case it is used to mean a negative number. So I'd say if you're referring to the sign in front of the number, it's called minus, whereas if you're referring to the number as such, it's "negative". The minus sign is used both as binary operator for subtraction and as unary operator for negation. Isheden (talk) 11:15, 19 June 2013 (UTC)
So, if I understand right what you are saying: the correct usage is “the negative number minus three quarters”, whereas “negative three quarters” is a contradictio in adiecto as 3/4 is in fact positive.—Emil J. 13:03, 19 June 2013 (UTC)
I guess neither is wrong. It boils down to whether you view - as the mathematical symbol "minus" or as the unary operator "negative". "Negative" might be considered more specific since it rules out the operation of subtraction. Isheden (talk) 13:47, 19 June 2013 (UTC)
This whole discussion has become about what is "correct" n some sense. It's highly relevant to note what is actually used; if you go to a conference or lecture involving people working with applied mathematics (in physics, for example), what will you actually hear? Ultimately that's highly relevant for an encyclopaedia that's recording what happens, not laying down the law. Pol098 (talk) 23:23, 24 June 2013 (UTC)

I hear both. My own preference would be to call -3/4 the opposite of three fourths, but that ain't gonna happen. Rick Norwood (talk) 14:23, 19 June 2013 (UTC)

Isn't $\tfrac{-8}{5}$ usually written $-\tfrac{8}{5}$? Bo Jacoby (talk) 14:19, 22 June 2013 (UTC).

Yes, unless the point is to emphasize that the fraction is used to mean -8 divided by 5. Rick Norwood (talk) 15:33, 22 June 2013 (UTC)

Then I will remove the example from the lead. Bo Jacoby (talk) 17:13, 22 June 2013 (UTC).

## Redundant sections

The Naming section & the Pronunciation and spelling section are somewhat redundant, though both are also somewhat incomplete. Neither has sourcing, though there is little to be challenged -- except the minus/negative terminology.--JimWae (talk) 20:18, 20 June 2013 (UTC)

Agree. They have little to do with mathematics, the topic of the article. Since this kind of common sense is not discussed in mathematics textbooks, it will be difficult to provide sources. I suggest moving it to fraction and move the disambiguation part of the present article fraction to fraction (disambiguation). Isheden (talk) 09:03, 21 June 2013 (UTC)

Most science and math articles say something about how words are used. I don't see how it does any harm, and some people may find it useful. Rick Norwood (talk) 11:38, 21 June 2013 (UTC)

OK, but a few sentences in the subsection on common fractions should be enough to clarify this. It is disproportionate in a mathematics article to have two full sections dedicated to "Naming" and "Pronunciation and spelling". Isheden (talk) 12:08, 21 June 2013 (UTC)
I think the sub-subsection "Writing simple fractions" is also a bit out of place at least in the beginning of the article. Perhaps all topics that are not clearly related to mathematics could be moved to a separate section towards the end of the article? Isheden (talk) 12:24, 21 June 2013 (UTC)

From the Wikipedia Manuel of Style (Mathematics): "The articles should be accessible, as much as possible, to readers not already familiar with the subject matter. Notations that are not entirely standard should be properly introduced and explained." Rick Norwood (talk) 14:12, 21 June 2013 (UTC)

Do notes on how fractions are used in typography and how they are printed in scientific literature really make the article more accessible to the typical reader of this article? Isheden (talk) 11:46, 22 June 2013 (UTC)
Poets are people who think seriously about death and commas. Mathematicians think seriously about commas. All kidding aside, I'm fascinated by the nicities of mathematical typography and nomenclature. I suspect I'm not alone. In discussions such as this one, I usually come down on the side of more information rather than less. Rick Norwood (talk) 11:51, 22 June 2013 (UTC)
I restructured the article somewhat while keeping all information in it, just presenting the stuff in slightly different order. Feel free to change it further as you see fit. Perhaps the sentences from "Naming" should rather be moved to the lead section? Isheden (talk) 12:37, 22 June 2013 (UTC)

Good edit, Isheden.Rick Norwood (talk) 14:18, 22 June 2013 (UTC)

I moved some stuff around too. There was quite a bit in common fractions that was not specific to that topic. I also added to the section on common/simple fractions. Much of what is still in Pronunciation and spelling section has now been copied to a new Vocabulary section (for want of a better term). I think it makes sense to have this (vocabulary) presented fairly early-on (since it is so elementary), but the text in the Pronunciation and spelling section is much more complete & I would prefer to move more of it up higher & thus also remove some redundancy.--JimWae (talk) 23:03, 22 June 2013 (UTC)
I agree with you. I've merged the two sections. Isheden (talk) 16:50, 23 June 2013 (UTC)

## Policy

Please note, I don't necessarily agree with the United States' CCSSM definition of fraction. However, that's what it is. And it is what United States schools will be teaching to students.

• fractions cannot be negative
• fractions are strictly "expressible" in a/b form where a is a whole number and b is a positive whole number.

Under the CCSSM definition: 0.3 is a fraction but -0.3 is not a fraction. Both are rational numbers.

The policy document uses $\tfrac{\sqrt{2}}{2}$ and $\tfrac{\pi}{2}$, but these are called "expressions." They are never called "fractions" or "fractional forms" in the policy document.

Again, I wouldn't change the body of this article. I just think the nuances of educational policy need to be noted somewhere. Thelema418 (talk) 07:03, 14 October 2013 (UTC)

The CCSSM does not say that fractions cannot be negative. In fact, the quote in the article explicitly states that a fraction can be expressed in the form a/b where a is a whole number and b is a positive whole number. This allows fractions to be negative or zero. If they had intended fractions to always be positive, they would have said "a and b are positive whole numbers". The parenthetical remark has nothing to do with what fractions "are". It has to do with the kinds of fractions they talk about in their document, positive fractions, which pedagogically usually come before negative numbers. In other words, it is a pedagogical statement, and one that only refers to the document in question, not a mathematical statement. Rick Norwood (talk) 12:09, 14 October 2013 (UTC)
Please note, the CCSSM glossary states whole numbers are non-negative. This is a definition in a major policy document, supported by mathematicians like H. Wu (who is cited in the present article). This definition, and others like it, need to appear in a section about pedagogy of fractions because it is a different realm than mathematical research. Thelema418 (talk) 06:35, 17 October 2013 (UTC)
If it is "policy" (which there is no indication it is) it is so only for a number of states in the US, and is part-of-US-specific. The glossary indeed speaks of positive fractions and negative fractions, so at the very least is inconsistent if it indeed (needlessly) claims that all fractions are positive. The entry has little relevance to the article except as a supposed dispute over definition. An "initiative" is not an mathematical paper & has no authority to redefine what a fraction is, especially not an initiative that is self-contradictory. Mostly, the entry is not international & mostly irrelevant to the article. Additionally, as pointed out above, whole numbers can include negative integers, though the term whole number is quite imprecise and does not serve to clarify anything. As a retired educator, I have several times encountered terms in educational documents that are simplistically defined in their glossaries only for the purposes of the document (it says "The word fraction in these standards always refers to a non-negative number") or only to establish guidelines for sequencing in teaching. Also, glossaries are often last edited by someone with a POV to push - such as that s/he is more erudite than others. All rational numbers are expressible as a simple fraction, but compound fractions & decimal fractions are also expressible as simple fractions, and it is often overlooked that not all fractions need be (expressible as) simple fractions (ie rational). To say that pi/4 is not a fraction is a needless, artificial distinction that only needlessly complicates pedagogy. I can find nowhere in the document where teachers are directed to ever touch in class on the definition of a fraction - which is, fortunately, just as well. How would students be getting better prepared for anything by being made to distinguish solving sqrt(12)/5 * sqrt (3)/7 from solving 12/5 * 3/7 ? --JimWae (talk) 20:43, 14 October 2013 (UTC)

Note that the CCSSM has clear definitions for whole number in the document. It clearly states that fractions are not negative; this is not my interpretation, that is verbatim. Today I looked at a textbook series that was recently published for alignment to the CCSSM: it uses the "fractions are not negative" definition in the resource book. Again, this is a definition that educational policymakers intend to have used in the classrooms.

It seems rather odd that the article has pedagogical tools listed, but not a single remark about the definitions of fractions that teachers are expected to use. Thelema418 (talk) 06:02, 17 October 2013 (UTC)

Also, if you do not like the word policy, you can change it to another term. Thelema418 (talk) 06:35, 17 October 2013 (UTC)

Please see WP:BRD. It is up to you to find support for your additions. So far there are 2 against your addition, none but you for it. Repeatedly inserting it without support is edit warring. It is not up to me to "fix" this mostly irrelevant & less than US-centric addition. If you don't understand why that is an objection, consider that wikipedia is an international encyclopedia, not a US one. Additionally, their idiosyncratic, wayward "definitions" have no impact on what happens in the classroom & thus have no pedagogical impact. The terms are defined only for the document itself. There is nothing in it about teaching any definitions to kids. Besides that, the document is self-contradictory.--JimWae (talk) 18:58, 17 October 2013 (UTC)

I think the way Thelema418 has stated it in the most recent version, in a parenthetical remark that makes it clear the subject is how this government document uses the word, not how mathematicians use the word, is ok. Rick Norwood (talk) 20:07, 17 October 2013 (UTC)

That is an improvement, but on what grounds does such a silly definition, contradicted by other text in the document, merit inclusion in the article - except as a point of embarrassment for anyone involved in its production? The definitions given just seem to be the result of oversimplification & "dumbing down" so that teachers with little mathematical background can find a way to "relate" to the material.--JimWae (talk) 22:53, 17 October 2013 (UTC)

Have you been following the "math wars"? Essentially, people with math ed degrees demand to be treated as the equal of those with degrees in mathematics, only many of them are very weak both in math and in education. Still, the document exists, it says what it says, and it is apt to be very influential for years to come. There was an article I read somewhere (Notices of the AMS?) written by one of the mathematicians who worked on the standards, which said that he fought the good fight, that compromise was necessary, and that we have to accept the document as is. Rick Norwood (talk) 17:29, 18 October 2013 (UTC)

## Easy way to teach Fractions to Young Children using Lego Bricks

This idea was suggested on Reddit: • SbmeirowTalk • 17:31, 16 November 2013 (UTC)