Talk:Fraction

Semi-protected edit request on 26 April 2024

Please change 'number' to 'real number' in the fourth paragraph of the introduction section Fraction. Details: It says "In mathematics the set of all numbers that can be expressed in the form a/b, where a and b are integers and b is not zero, is called the set of rational numbers " Change 'numbers' to 'real numbers' possibly with a blue hyperlink. I mean what kind of number is being referred to by the word 'number'? Complex numbers? integers? rational numbers? Hyper-real numbers? Of course it would be circular, or a tautology, to say the rational numbers are the set of all rational numbers. But we can define rational numbers using real numbers as the superset. 207.244.169.9 (talk) 19:57, 26 April 2024 (UTC)

The rational numbers can certainly not be defined using the real numbers, since the real numbers are defined using the rational numbers, and this would be a circular definition. The phrase "all numbers that can be expressed in the form a/b, where a and b are integers and b is not zero" does not imply thaat there are other numbers. It simply means that an expression a/b represents a number that is called a rational number. However, the sentence can be simplify and clarified, and I'll do it. D.Lazard (talk) 20:22, 26 April 2024 (UTC)

Understanding fraction operations visually

Visual representations play a pivotal role in elucidating the concept of fractions, providing learners with intuitive tools to grasp abstract mathematical ideas.

Visual Representations of Fractions:

Pie Charts: Fractional parts of a whole are often depicted using pie charts, where each sector represents a fraction of the entire circle. This visualization allows learners to visualize fractions as proportions of a whole and understand relationships between different fractions.

Bar Models: Bar models represent fractions using segmented bars, with each segment corresponding to a fraction of the whole bar. This visual tool aids in comparing fractions, understanding equivalent fractions, and performing arithmetic operations.

Number Lines: Fractions can be represented on number lines, where each point corresponds to a fraction between 0 and 1. Number lines provide a linear representation of fractions, facilitating comparisons, addition, subtraction, and identifying fractional positions.

Area Models: Area models partition geometric shapes, such as rectangles or circles, into equal parts to represent fractions visually. This method helps learners visualize fractions as areas or regions, fostering a deeper understanding of fraction values and operations.

A tool like https://www.visualfractioncalculator.com/ can help understand fraction addition, subtraction, multiplication and division. Swapsshah (talk) 09:26, 14 May 2024 (UTC)

Compound and complex fractions

Hi, the present section on compound and complex fractions seems outdated and/or incorrect:

• It explains a distinction between the two terms in > 200 words, only to then state that both terms can be considered outdated. The two works cited for the distinction are from 1814 and 1853, respectively! And the one from 1814, by Peter Barlow, even says that these distinctions "are certainly improper".
• The source used to back up the claim that both terms can be considered outdated, an archived version of the online Collins Dictionary, does in fact not make any such claim. It says just what the current version of this dictionary says: that complex fractions are fractions where the numerator and/or the denominator are fractions themselves, and that they are also called compound fractions.
• The source used to back up the claim that the terms are also used to denote mixed numerals is an archived version of an online mathematics course called "S.O.S. Math", which is not active any more.

I suggest a complete rewrite by a native speaker, just stating that both terms are used synonymously for what is presently described as complex fractions here, using the Collins source, and getting rid of everything else. Biologos (talk) 17:44, 8 November 2024 (UTC)

Note that this is explicitly in a section about "historical notions".

The term compound fraction meaning several fractions composed by multiplication, often written as "a/b of c/d of e/f" or the like, was certainly commonly taught in the 18th–19th century (here's another example from 1870, JSTOR 44859615), and the concept is still in use today though it is no longer necessarily named or given prominence in educational materials (I think today it would more likely just be called a "product of fractions" or similar). From what I can tell the term compound fraction is not too widely used today, and a few examples I found in a quick literature search were inconsistent and somewhat unclear. I did find somewhat more recent examples of compound ratio and compound proportion used to mean the same thing. The term complex fraction is still in currency, used in elementary education, with the meaning described here; we could definitely include better sources though. The distinction made between these two concepts seems accurate (here's another source comparing the two, from 1856, JSTOR 44364747), though as with any subject so common there is always some inconsistency between regions and individual authors.

Dictionaries are unfortunately usually poor sources for this kind of thing, typically unreflective of real-world use. However, Barlow accurately describes the meaning of those two terms as found in early 19th century arithmetic instruction. His comment that this is "improper" is about his own interpretation of what "compound" and "complex" mean: he is complaining that whoever turned these names into technical jargon made a poor choice conflicting with the plain-language meaning of the individual words. I'm not sure I agree; "complex" comes from Latin for "braid together" whereas "compound" comes from Latin for "put together". These words are both used in a wide range of technical jargon across several fields, without tremendously strong consistency. The use of "compound" to mean multiplication by some scaling factor is also found e.g. in compound interest.

I think this section is more or less fine in general content, though the text could be clearer and the sourcing could be improved. The main purpose is to give a target for the wikilinks compound fraction and complex fraction so someone encountering these terms and looking them up in Wikipedia can figure out what they mean. Giving examples seems helpful, so I wouldn't significantly reduce the length of this section. –jacobolus (t) 21:04, 8 November 2024 (UTC)

Thank you for your prompt and comprehensive reply! Indeed, I had not noticed the Historical notions section heading, because I found the subsection by searching for the term complex fraction in the article and jumping directly to its location. Since you are saying that the main purpose is to give a target for the wikilinks naming the two terms, the Historical notions heading might be overlooked frequently. To guide the reader, could the first sentences in the subsections for the terms again state that the terms were used to describe what is described then? And then, the last paragraph could be shortened and updated somewhere along the following lines: "The terms "complex fraction" and "compound fraction" are now used in no well-defined manner, partly even taken synonymously for each other[25]."? Biologos (talk) 07:50, 11 November 2024 (UTC)

5/90 to 1/18

5/90 is equal to 1/18 so the 5/90 should be changed to 1/18. Max Dalton69142 (talk) 20:42, 1 November 2025 (UTC)

@Max Dalton69142: Why? — LlywelynII 22:21, 20 March 2026 (UTC)

Vocabulary

Following some hopefully uncontroversial cleanup of the Latin formatting, this section currently reads

In a fraction, the number of equal parts being described is the numerator (numerātor being Latin for a "counter" or "numberer") and the type or variety of the parts is the denominator (dēnōminātor being Latin for a "namer" or "designator").[1][2] As an example, the fraction ⁠8/5⁠ amounts to eight parts, each of which is of the type named fifth. In terms of division, the numerator corresponds to the dividend and the denominator corresponds to the divisor.

1) The boldface here is being protected by a comment <!--both boldface per WP:R#PLA-->. The reason the protection is needed is that the terms already show up bolded in the lead section, so of course they don't need to be bolded again... and shouldn't be. The policy being linked is related to helpful redirects but the relevant redirects are pointing at the lead section, not the Vocabulary one.

The lead is currently a labrador puppyish mess that would be much more helpful to our wp:readers (and AI overlords) if it were consistently using the single most common fraction ⁠1/2⁠ or the slightly more normal fraction ⁠1/3⁠ only while the idea is being explained and whatever is trying to happen in those last three paragraphs were shunted to the end of the article (or possibly the surface of the sun. Variables are potential numbers and the language is not only off-putting to young students trying to learn about fractions but apparently entirely off-topic for the article lead.) I'm very happy if the lead section were just rewritten. Part of that could be deitalicizing and debolding the vocabulary words there and leaving them bolded in the appropriate following sections. In that case, the redirects need to be changed to actually point to the Vocabulary section.

Alternatively, if we're leaving the lead and redirects alone, there is no policy that is being upheld (and some are being violated) by needlessly bolding them again in a place that the redirects aren't using. The comment should be removed and the terms debolded.

2) The treatment by D.E. Smith in his History of Mathematics quoted in Archive 3 is far superior to what we've got. First, it explains why we're using these needlessly opaque terms for the top and bottom numbers. Second, it lays out what they mean clearly. The current phrasing that we're using—number of equal parts—instantly makes readers think of the denominator instead. It is the equal parts that are being counted up by the numerator. (You don't need to reply with what was intended by the current version. I get it. It's just much too awkwardly expressed and does not come across clearly.)

This article is being used by middle schoolers. You don't need to write everything for their level—we don't need to fill the vocabulary section with diagrams of pizzas—but we shouldn't be actively disdainful of them either. Use the words top and bottom in this paragraph and make it clear that the denominator is the number of equal parts composing the whole, counted by the numerator, and with no "type" or "variety" of anything involved. (Yeah, I could wp:bebold like the fixes I already did but the exact phrasing here seems more contentious among the page's usual editors and I'm not interested in fighting over each detail, just pointing out that this bit needs reworking when you have time.) — LlywelynII 22:21, 20 March 2026 (UTC)