If you were drawing a map and were using the ratio 1cm:20km how many cm would 22km be? 1.1? —The preceding unsigned comment was added by 81.178.228.183 (talk • contribs) .
someone added the word 'chicken' to the start of the page. it wasn't in context and i assume it was a mistake so i removed it. if you're terribly fond of chickens and find this edit to be offensive, i apologize.
I'm sorry. I don't edit and don't know what the standards are involved. I just wanted to point out something I think needs correction:
Under: Ratios and fractions
"a) If you have three apples for every four oranges then you have a 3:4 ratio b) If you want to determine what fraction of the total fruit will be apples or oranges then you add the parts of the ratio to determine the total fruit, in this case: 3+4=7 c) The total fruit becomes the common denominator and the parts of the ratio become the numerators, in this case: 3/7 of the fruit are apples and 1/7 are oranges d) The fractions implied in a ratio will always total one whole (or 100% of the fruit), in this case: 3/7 + 4/7 = 7/7 = 1"
Specifically
"c) The total fruit becomes the common denominator and the parts of the ratio become the numerators, in this case: 3/7 of the fruit are apples and 1/7 are oranges"
I believe the "1/7 are oranges" should read "4/7 are oranges"
A ratio is an ordered finite set of quantities provided two sets are equivalent when their correspondent elements are proportional. For example, <a, b c, d,…> = <A, B, C, D,…> if A=ka, B=kb, C=kc, … for some k≠0. The equality sign is usually used in this case to designate equivalence of the two sets.
The quantities may or may not have units of measurement. Colon is usually used as separator, for example, a:b:c:d:… or A:B:C:D…
Main property of ratios: For any two pairs of corresponding elements, say b, d and B, D, the following equality is held: bD=dB.
Example: An ordered set <5 dogs, 2 houses, 3 apples, 4 oranges> is a ratio if it represents a structure, so that <5 dogs, 2 houses, 3 apples, 4 oranges> = <10 dogs, 4 houses, 6 apples, 8 oranges> = <15 dogs, 6 houses, 9 apples, 12 oranges> = …, where k=2, 3,…, respectively.
Using a colon notation, we get 5 dogs : 2 houses : 3 apples : 4 oranges = 10 dogs : 4 houses : 6 apples : 8 oranges = 15 dogs : 6 houses : 9 apples : 12 oranges = …
The chain of equalities may be continued further using arbitrary values of k≠0.
In this example the main property of ratios leads to the following equalities:
2 houses • 6 apples = 4 houses • 3 apples = 12 apple-houses,
6 apples • 12 oranges = 8 oranges • 12 apples = 72 apple-oranges etc.
Recipes provide good examples of ratios. Thus, a recipe that reads "For serving two persons take 2 pound rabbit, ½ cup flour, 1 tablespoon butter, and 1cup red wine", may be written as the ratio 2 persons : 2 lb : ½ cup : 1 tablespoon : 1 cup. This ratio tells us that depending on the number of persons served, the amounts of each product should be increased or decreased proportionally.
Two-element ratio related to direct variation of two quantities is called a rate.
For example, <126 miles, 3 gallons> =126 miles : 3 gallons is a rate of gasoline consumption.
A rate with the second element equals to one is called a unit rate. Thus, this example may be written as 126 miles : 3 gallons = 42 miles : 1 gallon, with the latter rate being the unit rate.
Rates and other two-element ratios without units of measurement possess the following property of fractions: they do not change their meaning if their elements are multiplied or divided by any non-zero number. In particular, they may be expressed in lower terms. For example, the following ratios are equivalent: 126:3 = 42:1.
Nevertheless, rates or two-element ratios are not fractions, because they do not possess all of the fractions' properties. For instance, ratios cannot be added or subtracted; if we formally add or subtract them as fractions, the result may or may not make sense as a ratio. —Preceding unsigned comment added by Hostosv (talk • contribs) 01:01, 5 November 2007 (UTC)[reply]
Current definition is very bad. It mentions the word proportional which leads to circular definition. Somebody provided a better one above:
The ratio of two numbers of is value of one number in terms of the other, and is expressed as the quotient of their measures. A ratio is a general means of comparing any two numbers in a multiplicative sense.
"The VNR Concise Encyclopedia of Mathematics", by W. Gellert and H. Kuestner and M. Hellwich, and H. Kaestner, published in 1977, ISBN9780442205904.
I believe this one also has an issue, as it defines "ratio of numbers" and isn't it supposed to be a "ratio of quantities" per discussion above? By the way Rate also seems to have a broken lead section, it contradicts this article. Could someone comment or correct? I'm not feeling "bold" enough because of my poor English. --Kubanczyk15:25, 11 October 2007 (UTC)[reply]
I think the confusion in the article reflects widespread confusion in the use of the terms. As a result, I see the definitions themselves keep going around in circles over time! I agree the current definition is not good, but also agree that the proposed definition above is problematic. Another concern is to make the article encyclopedic rather than just definitions with examples.
Ratio is used in three related but distinct senses. There are ratios of two quantities of the same kind (e.g. 2 cm/1 cm), which are real numbers. There are ratios of numbers, which are themselves also real numbers. Rates are written using the same notation as ratios, but they are clearly not real numbers. For example, 3 cm/ sec is a rate and 3 cm/ 1 cm is a ratio. Most uses of ratio imply that a ratio is a number, whereas a rate clearly is not a number. I think rate is more clearly defined as the change in the magnitude of one quantity with respect to change in another kind of quantity. Nevertheless, it is not unusual for definitions of rate to refer to ratio so it clearly needs to be noted.
My preference based on these considerations is to clarify the different usages of the terms with respect to the key concepts, with examples, rather than to have rather confusing (to me) and potentially contradictory (depending on definition) usages. This should be done, preferably, with reference to some good sources. Sources should include, but most certainly not be limited to mathematical ones such as the dictionary cited above; for example physics sources and sources relating to historical usage are very much relevant. I will try to find some time to do this, but it probably won't be soon.
On other points, unitless is a term I don't find particularly helpful: if there are no units, it is a number pure and simple. Again, it's commonly used so it is reasonable to note the usage but this does not mean the term should feature prominently in the opening lines as is currently the case. An acid test for me is to ask: what does it add to the reader's understanding? In addition, I find the use of quantity in the article potentially quite confusing. Quantity in the definition refers to numbers, whereas quantity more often refers to those such as 1 cm, 2 ohm, 2 sec etc., which are clearly not numbers. Nevertheless, quantity is used very often in mathematics to refer to (pure) numbers, particularly when relationships between more than one variable are described, so this needs to be noted.
Ratios often do have units and sometimes those differ. Consider the ratio of boys to girls in a student body. This may be 7 boys to 13 girls == 7 boys : 13 girls == 7 boys / 13 girls. That ratio is not a rate as we have no rule to establish an influential relationship between the two measurements. A change in number of girls in the group would not imply or necessitate a change in the number of boys. To stretch the example a bit if there were a requirement for at least 1 teaching assistant per 10 students, then we have a rate. Adding one more students and another teaching assistant is added as well to maintain the relationship.
Rate is a special case of ratio that establishes a relationship. The contradiction on the ratio and rate entries comes from assertion on ratio entry that rate is per unit of time. Per example above of "3 cm/ sec", that is a rate, but also a ratio. (Technically just stating "3 cm/ sec" is not enough information to be certain it is a rate. But we humans have trouble seperating anything with time as non-relational. What if "3 cm" is length of wood block and "1 sec" is amount of time a second hand was observed to move? There is a comparison of two unrelated measurements and therefore is not a rate, though it still qualifies as a ratio.)
The article had gotten quite long considering there were no references cited. I've added some older sources on the assumption that there haven't been a lot of changes to the subject in the last hundred years. It will take some time to go through the article section by section to see what needs to be further referenced, what should be deleted as OR, what should be expanded based on the material in the sources, and what is OK as is. I'm leaving the references needed tag until this is all sorted out.--RDBury (talk) 21:45, 4 November 2009 (UTC)[reply]
The problem being, of course, that referenced material can be rubbish. Now, I cannot speak for the quality or otherwise of the Penny Encylopledia in general, but I would like to in this particular. The PE (of which I do not have a copy, so I am taking this on trust) is referenced and, perhaps, *interpreted* to say that the ratio n:m is the fraction n/m. No it is not. The ratio n:m is the fraction n/(n+m). The Penny Encyclopedia is wrong, you get what you pay for! Paul Beardsell (talk) 10:23, 26 December 2009 (UTC)[reply]
An example to illustrate. The ratio 1:1 is not 1/1 but 1/2. If an equal amount of butter is added to sugar by weight what is the weight of the butter in ratio to that of the sugar? 1:1. What is the weight of the butter as a proportion of the total? 1/2 Paul Beardsell (talk) 10:23, 26 December 2009 (UTC)[reply]
Firstly, you don't need a copy of the Penny Cylopledia, there is a link to it online at the bottom of the page. Second, the Penny Cyclopedia isn't the only source on this; Fundamentals of practical mathematics (also available online through a link at the bottom of the page) uses the same definition. I could probably find more but the statement is already referenced. If you don't agree with the statement then the burden is on you to find a reference supporting your claim, not on me to keep finding more and more references until you're satisfied.
In your butter and sugar example, the ratio of butter to sugar is still 1 to 1, however the ratio of butter to the total is 1 to 2. This is normally called the proportion of butter, to the proportion of butter in your example is 1/2; maybe that's what you're thinking of.--RDBury (talk) 19:32, 26 December 2009 (UTC)[reply]
The article is right, if you think it's wrong then give a reference. Engaging in pointless arguments on a talk page is a waste of time for both of us.--RDBury (talk) 00:39, 28 December 2009 (UTC)[reply]
Stating that proportions often is taken with respect to the total is not the same as stating that "n:m corresponds to n/(n+m)". Actually, n/m often is defined as an equivalence class of ratios, including n:m. (Two ratios a:b and c:d then are considered as equivalent, if there are non-zero or otherwise restricted elements e and f, such that ae = cf and be = df; cf. localization of a ring, where the ratios are identified with certain pairs (r,s).) JoergenB (talk) 19:17, 11 January 2010 (UTC)[reply]
If you think of a negative number as being directional, then that is what you are doing to get a negative ratio. I'm not really comfortable with that, and haven't seen any definition that would accommodate it. To me, what you really have is a ratio of 2:3, where the units are apples owed to surplus oranges. Trishm05:02, 18 June 2007 (UTC)[reply]
Classically, the theory of ratios was developed in antiquity, long before the Western philosophers and mathematicians had learned about negative numbers. (There were some sorts of theory of negative numbers very early in China and India, but these ideas did not reach Europe until much later.) Therefore, of course the ratios considered by the ancients were all positive.
This article needs much work. I've fiddled around with it a bit whilst watching TV, but it needs restructuring. I suggest a brief lead, followed by the simple examples for those who come here wondering what the word means, or how to use the concept, with the technical definitions and philosophy of rationality at the end. What does anyone else think? Thanks to 24.51.192.180 for removing the bit I didn't like but wasn't brave enough to remove, and to Anonymous Dissident for improving my wording.Dbfirs23:16, 25 January 2010 (UTC)[reply]
Thanks to RDBury for improving the article, including removing my heading that turned out to be OR (though I thought when I used it that I could find someone else who called it "Normal Form"). I've restored the content of the paragraph because it can be found in most elementary texts on ratio. Dbfirs23:24, 23 February 2010 (UTC)[reply]
Right now (19:27, 11 January 2010 (UTC)), the article completely seems to lack creferences to commensurability issues. This is a pity; at least, the historical relation between ratios of commensurable entities and rational numbers ought to be explained. IMHO, the explanation of the term "rational" is clearly of encyclopedial interest. JoergenB (talk) 19:26, 11 January 2010 (UTC)[reply]
Yes, already Eudoxus developed a theory for more general ratios or "proportions". However, these are not in general commensurable. Indeed, the main reason for the Eudoxus's rather abstract treatment of proportions is the trouble with noncommensurability - or "irrationality", to use the modern term. JoergenB (talk) 17:24, 6 February 2010 (UTC)[reply]
Perhaps we should have a separate article on ratios of commensurable entities? I don't think a long discussion on the history of commensurability and rationality belongs here. Dbfirs20:57, 15 July 2010 (UTC)[reply]
I find the opening sentences to be somewhat confusing, particularly to a person who is looking for a basic understanding of ratio. The first sentence definition makes sense and serves as an adequate definition of ratio: "In mathematics, a ratio expresses the magnitude of quantities relative to each other." That's clear.
But, the opening goes on: "Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second..." What does that mean? Right now, the graphic example given next to the opening paragraph is a "4:3" ratio. A reader would presumably look over at that example and try to puzzle out the opening. Using the second sentence definition, that means "the ratio of 4 to 3 indicates how many times 4 is contained in 3." What?? The Penny Encyclopedia is cited for this, but I looked at the entry linked at the bottom of the page, and I don't see this idea mentioned prominently. It's a long article, so it might be buried in there somewhere, but in general the source seems to go more with the definition of the first sentence, i.e., a ratio compares the relative magnitude of two things, which means 4:3 is the same as 3:4, it's just the order of the things expressed (width:height vs. height:width) has changed -- so why the focus on which quantity is "contained" in which other quantity?
The opening continues: "and may be expressed algebraically as their quotient." (I don't disagree with this, but it seems to focus on only two-term ratios that represent fractional relationships, which is only one class of ratio -- is that appropriate for a general opening?) And then "Example: For every Spoon of sugar, you need 2 spoons of flour ( 1:2 )" This isn't a very good example for what was just stated (quotient relationships), since expressing this ratio as 1/2 is potentially misleading. In terms of "spoons," there is 1/2 as much sugar as flour, but -- as is clear from some confusion expressed in earlier Talk Page discussion -- this is not the only possible fractional relationship to be derived from such a ratio. If the ratio clearly represented a part-to-whole relationship (as many ratios do, such as "3 students compared to the entire class of 12 students," or 3:12), it would make sense to represent it as a quotient (3/12, or 1/4). In the case of the example provided, however, the application of a quotient as mentioned in the previous sentence is ambiguous.140.247.240.127 (talk) 22:08, 19 July 2010 (UTC)[reply]
By the way, here's a possible draft suggestion to replace the opening. I'm not going to edit the article myself (I long ago stopped participating in edit wars on Wikipedia), but this might serve to push the discussion forward for improvement:
"In mathematics, a ratio expresses the magnitude of quantities relative to each other. Although ratios can represent the relative size of any number of quantities, ratios are most commonly used to compare two quantities. Such a relationship can compare relative amounts or sizes of two things. For example, if a lake is 3 miles long and 2 miles wide, the length and width create a 3:2 ratio with each other. Ratios can be expressed in many ways; a recipe that states "for every spoon of sugar, you need 2 spoons of flour" implies a 1:2 ratio of sugar to flour. In some circumstances, a ratio represents a part-to-whole relationship (similar to a fraction), and in that case the ratio may be expressed algebraically as a quotient. For example, if there are 5 blond students in a class of 17 students, the ratio of blond students to the entire class would be 5:17, or, equivalently, 5/17." 140.247.240.127 (talk) 22:40, 19 July 2010 (UTC)[reply]
Please clarify the first sentence under Number of Terms to say something like,
"In general, when comparing the quantities of a two-quantity ratio, this can be expressed as a fraction derived from the ratio. For example, in a ratio of 2:3, the amount/size/volume/number of the first quantity will be 2/3 that of the second quantity. This pattern also holds in ratios with more than two terms; however, a ratio with more than two terms cannot be converted into a single fraction, where a single fraction can represent only one part of the ratio."
I'm requesting this clarification because I often find that my students think that ratios are the same thing as fractions. While this is clearly demonstrated in the Fraction and Proportion subheadings, the Number of Terms text muddies and confuses this important distinction.
Ok done. Thank you for this contribution. I made a bit of a change to the final clause of your edit request, as I found it a bit unclear. Feel free to let me know if I've ruined everything by doing this. Also, why don't you make an account and stay for a while. That way you'll be able to make edits like these by yourself without needing to submit a request first. Zachlipton (talk) 03:01, 1 January 2011 (UTC)[reply]
What of ratios of quantities of different measures?
This "w/v" expression is often used in science, and is not what mathematicians would call a pure ratio, but it is a ratio of mg of substance to ml of water. Have you any suggestions on how to improve the article? Should we have a separate paragraph on w.v ratios? Dbfirs08:07, 23 June 2011 (UTC)[reply]
In antiquity writers such as Vitruvus went back as far as the historian Herodotus checking for ratios between the unit fractions used up until medieval times for calculation and unit measures and discovered that the body measures which were the basis for Egyptian inscription grids were expanded to the agricultural measures used for Egyptian and Mesopotamian fields, and further expanded into architectural proportions based on structural loads and spans and distance measures such as the surveyed length of a days march or sail.
The proportion of foot to remen can be either 4:5 making it the hypotenuse or 3:4 making it the side of a right triangle. If the remen is the hypotenuse of a 3:4:5 triangle then the foot is one side and the quarter another so the proportions are 3:4 quarter to foot, 4:5 foot to remen and 3:5 quarter to Remen. The quarter is 1/4 yard. The foot is 1/3 yard. The remen is
The remen may also be the side of a square whose diagonal is a cubit
The proportion of remen to cubit is 4:5
The proportion of palm to remen is 1:5
The proportion of hand to remen is 1:4
The proportion of palm to foot is 1:4
The proportion of hand to foot is 1:3
The table below demonstrates a harmonious system of proportion much like the musical scales, with fourths and fifths, and other scales based on geometric divisions, diameters, circumferences, diagonals, powers, and series coordinated with the canons of architectural proportion, Pi, phi and other constants..
In Mesopotamia and Egypt the Remen could be divided into different proportions as a similar triangle with sides as fingers, palms, or hands. The Egyptians thought of the Remen as proportionate to the cubit or mh foot and palm.
They used it as the diagonal of a unit rise or run like a modern framing square. Their relatedseked gives a slope. Its convenient to think of remen as intermediate to both large and small scale elements.
Even before the Greeks like Solon, Herodotus, Pythagorus, Plato, Ptolomy, Aristotle, Eratosthenes,
and the Romans like Vitruvius, there seems to be a concept that all things should be related to one another proportionally.
Its not certain whether the ideas of proportionality begin with studies of the elements of the body as they relate to scaling architecture to the needs of humans, or the divisions of urban planning laying out cities and fields to the needs of surveyors.
In all cultures the canons of proportion are proportional to reproducable standards.
In ancient cultures the standards are divisions of a degree of the earths circumference into mia chillioi, mille passus, and stadia.
Stadia, are used to lay out city blocks, roads, large public buildings and fields
Fields are divided into acres using as their sides, furlongs, perches, cords, rods, fathoms, paces, yards, cubits, and remen which are proportional to miles and stadia
Buildings are divided into feet, hands, palms and fingers, which are also systematized to the sides of agricultural units.
Inside buildings the elements of the architectural design follow the canons of proportion of the the inscription grids based on body measures and the orders of architectural components.
In manufacturing the same unit fraction proportions are systematized to the length and width of boards, cloth and manufactured goods.
The unit fractions used are generally the best sexigesimal factors, three quarters, halves, 3rds, fourths, fifths, sixths, sevenths, eighths, tenths, unidecimals, sixteenths and their inverses used as a doubling system
Greek Remen generally have long, median and short forms with their sides related geometrically as arithmetric or geometric series based on hands and feet.
The Egyptian bd is 300 mm and its remen is 375 mm. the proportion is 1:1.25
The Ionian pous and Roman pes are a short foot measuring 296 mm their remen is 370 mm
the Old English foot is 3 hands (15 digits of 20.32 mm) = 304.8 mm and its remen is 381 mm
The Modern English foot is 12 inches of 25.4 mm = 304.8 mm and its remen is 381 mm (15")
The Attic pous measures 308.4 mm its remen is 385.5
The Athenian pous measures 316 mm and is considered of median length its remen is 395 mm
Long pous are actually Remen (4 hands) and pygons
See cubit for the discussion of the choice of division into hands or palms
See the table below for proportions relative to other ancient Mediterranean units
Roman Remen generally have long, and short forms with their sides related geometrically as arithmetric or geometric series based on fingers palms and feet.
By Roman times the Remen is standardized as the diagonal of a 3:4:5 triangle with one side a palmus and another a pes. The Remen and similar forms of sacred geometry formed the basis of the later system of Roman architectural proportions as described by Vitruvius.
Generally the sexagesimal (base-six) or decimal (base-ten) multiples have Mesopotamian origins while the septenary (base-seven) multiples have Egyptian origins.
= 2 stadia, only used for the Olympic footrace introduced in 724 BC
1 dolikhos
= 6 or 12 diauloi. Only used for the Olympic foot race introduced in 720 BC
1 parasanges
= 30 stadia ≈ 5.5 km. Persian measure used by Xenophon, for instance
1 skhoinos (pl. skhoinoi, lit. "reefs")
= 60 stadia ≈ 11.1 km (usually), based on Egyptian river measureiter or atur, for variants see there
1 stathmos
≈ 25 km, one day's journey. May have been variable, dependent on terrain
For variant, the stadion at Olympia measures 192.3 m. With a widespread use throughout antiquity, there were many variants of a stadion, from as short as 157.5 m up to 222 m, but it is usually stated as 185 m.
The Greek root stadios means 'to have standing'. Stadions are used to measure the sides of fields.
In the time of Herodotus, the standard Attic stadion used for distance measure is 600 pous of 308.4 mm equal to 185 m. so that 600 stadia equal one degree and are combined at 8 to a mia chilioi or thousand which measures the boustredon or path of yoked oxen as a distance of a thousand orguia, taken as one orguia wide which defines an aroura or thousand of land and at 10 agros or chains equal to one nautical mile of 1850 m.
Several centuries later, Marinus and Ptolemy used 500 stadia to a degree, but their stadia were composed of 600 Remen of 370 mm and measured 222 m, so the measuRement of the degree was the same.
The same is also true for Eratosthenes, who used 700 stadia of 157.5 m or 300 Egyptian royal cubits to a degree, and for Aristotle, Posidonius, and Archimedes, whose stadia likewise measured the same degree.
Another question. So a ratio can never be expressed as a percentage? —The preceding unsigned comment was added by 202.4.4.48 (talk • contribs) .
If the ratio of apples to oranges is 2 to 1, then the number of apples is 200% (twice) the number of oranges, and the number of oranges is 50% (half) the number of apples. - dcljr (talk) 08:28, 13 April 2006 (UTC)[reply]
I think that a ratio is always 100% of everything you are talking about. For example, if you have a 2:1 ratio of apples to oranges then two thirds or approximately 67% of your fruit are apples and one third or 33% are oranges, for a total of 100% or three thirds.--Dwetherow05:18, 23 February 2007 (UTC)[reply]
I think I'd go with User:Dcljr's definition. The whole thing doesn't have to be 100%. Rather, you can fix one to be 100% and see what the other one is. Isn't that what you do with fractions, which are essentially the same as ratios? --116.14.34.220 (talk) 13:10, 16 June 2009 (UTC)[reply]
Maps present another interesting example. A map ratio of 1:100 sensibly presented as a percentage would be 1%. Meaning a distance on the map is 1% of the distance in the real world.
It makes no sense to add the distance on the map to the distance in the real world, and use this combined 'real' and 'virtual' distance in any calculation. —Preceding unsigned comment added by 89.242.145.251 (talk) 17:43, 14 February 2010 (UTC)[reply]
a ratio can be both a proportion and a percentage. Suppose for example we were to compare the ratio of pennies (100:1) in a dollar to nickles (20:1) or quarters (4:1)in a dollar. You might count a random dollars worth of change and determine the proportion of nickles to pennies, dimes, quarters or half dollars then compare the percentage of each.142.0.102.93 (talk) 18:47, 23 May 2014 (UTC)[reply]
The article begins by declaring a ratio to be a linear relationship. What about, say, the ratio of a square's perimeter to its area? That's nonlinear; is it a ratio? --VP 38.113.17.321:41, 17 April 2006 (UTC)[reply]
Yes, I'd like to hear the reasoning for stating that ratios are linear relationships. This implies to me a relationship across the range of magnitudes of a quantity, which is not a (necessary) feature of a ratio. A ratio between two continuous quantities of the same kind is a real number. Ratios between different quantities are not numbers at all. For example 1cm/1g is not a number. However, it is possible to form a ratio between the numbers arising from measurements. You might say that there is a 1:1 correspondence between the volume, say in , and mass, in grams, required to store some material. Then, the ratio is between numbers which are measurements, not between quantities. Holon01:08, 12 May 2006 (UTC)[reply]
1 cm / 1 g is a number, but it is not dimensionless (ie it has units of cm/g). A ratio between, say, the area of two different shapes would give a dimensionless real number (ie no units). --72.140.146.24619:10, 3 June 2006 (UTC)[reply]
1cm/1g is not a number. Take a simpler example; 1g. One gram is not a number: it is a quantity; an amount of mass. The 1 in 1 g is a measure of quantity of mass, and to know its dimension is to know its unit. Quantities themselves are not numbers. Measures of quantities are numbers. Holon02:16, 4 June 2006 (UTC)[reply]
you can easily compare ratios of measures of length, area, or volume by making a linear measure the side of a square or a cube.
in which case they become non linear since they are exponential. Further you can change the rate of increase at an increasing rate over time introducing a fourth dimension. The ancient problems of squaring a circle, doubling a cube and trisecting an angle were solvable so long as you didn't add constraints such as limiting their construction to ruler and compass.142.0.102.93 (talk) 19:04, 23 May 2014 (UTC)[reply]
Comensurability allows you to take two different scales and put them in harmony. For example a Mesopotamian foot was three hands of 100 mm each, an ordinary cubit was 5 hands or 1/2 meter and a great cubit was 6 hands, 2 feet or 600 mm. To make that sexigesimal division commensurable with a septenary Egyptian ruler which used palms of 75 mm rather than hands of 100 mm you used a ration of 4 palms to 3 hands to make one foot. The Egyptian ruler would have an ordinary cubit of 5 palms or 450 mm and a royal cubit of 525 mm. Its ell of 8 palms would be two feet (1 nibw) which was the same as a Mesopotamian Great cubit. The use of different scales used to be a feature of slide rules which could be used for logarithmic computation.142.0.102.93 (talk) 19:04, 23 May 2014 (UTC)[reply]
I have some confusion over ratios and fractions - In the opening statement, the example 2:3 is used and is described as a whole consisting of 5 parts. In the first example, the ratio 1:4 refers to four parts in the whole. Which is the correct description of a ratio? This has always confused me. Stating the question in other terms - if I have a solution consisting of 1 part X and 3 parts Y, do I describe the ratio as 1:3 or 1:4? —Preceding unsigned comment added by 67.161.203.22 (talk • contribs)
The example was incorrect. To answer your question, the ratio of X to Y would be 1:3 (1 to 3), not 1:4. The proportion of the whole that is X would be 1/4 (one out of 4). I've completely rewritten the article to try to clarify the situation. - dcljr (talk) 19:05, 14 August 2006 (UTC)[reply]
I've changed the edits because the concept of ratio is fundamental to the very definition of measurement throughout the physical sciences, and arguably all science. I'm open to debate on how to present the two subtly different usages of the term. Let me know if you have qualms, I'm always open to suggestions Holon11:07, 16 August 2006 (UTC)[reply]
I'm a HS teacher, and have always taught that fractions are synonymous with ratios; that the ratio 2:3, for example, is the quotient of 2 divided by 3 or 2/3. Under this interpretation, a ratio would be "a fraction turned on its side." This is in many textbooks, for example Dolciani "Algebra-Structure and Method." I'd be interested in seeing a reference with an alternative interpretation, making 1/2 not equal to 1:2. While on the subject: Dolciani defines a proportion as "an equation that states that two ratios are equal." So, 2:3 = 4:6 would be a proportion. Splendiff23:42, 6 June 2007 (UTC)[reply]
Dude! You're freaking me out! I'm in my first year of teaching - Grade 6 - and don't understand a ratio to be a fraction-on-its-side at all. I think you're right in that 2:3 is equivalent to 4:6, but I don't think 2:3 is two thirds. Take this set for example: [xxyyy] - 2/5 are x's, three fifths are y's, and the ratio of x to y is 2:3 (no '5' present in the ratio). A fraction represents a part of a whole - a ratio compares parts of a whole (usually all the parts). Another example [1 apple and 2 bananas] - one third is apple, two thirds are banana and the ratio of apple to banana is 1:2 (for every apple there are two bananas; for every banana there's half an apple). Add an orange and you have a ratio of 1:2:1, which shows the proportion of parts of the whole rather than representing one part of the whole (such as 1/4 being oranges). Neither specify how big the whole is. Arcrawfo (talk) 11:47, 14 June 2008 (UTC)[reply]
OK, Arcrawfo again. I've been thinking about the fraction thing. Splendiff; I think I may get what you might mean... Back to the fruit bowl example: 8 apples, 12 oranges; the apples to oranges ratio is 3:4. This means that for every 3 apples there are four oranges. It also means that however many oranges there are, there will be 3/4 the amount of apples. For 6 apples and 9 oranges - 2:3 - however many oranges there are, there will be two thirds the apples. And this is how the ratio is used as a fraction. Si?Arcrawfo (talk) 01:17, 15 June 2008 (UTC)[reply]
Try "The VNR Concise Encyclopedia of Mathematics", by W. Gellert and H. Kuestner and M. Hellwich, and H. Kaestner, published in 1977, ISBN9780442205904.
The ratio of two numbers of is value of one number in terms of the other, and is expressed as the quotient of their measures. A ratio is a general means of comparing any two numbers in a multiplicative sense.
Rather than thinking of a ratio as a special case of a fraction, think of the ratio as the way numbers were compared in a multiplicative sense, before fractions assumed their full power.Ratios are more flexible than fractions, because they can be used to compare part to part, such as often used in chemistry or maths (like a 3:4:5 triangle), or part to whole, as in a fraction. The techniques for manipulating fractions are much more powerful though (I don't think I've ever tried to add dissimilar ratios), so we use fractions most of the time now.
Trishm04:53, 18 June 2007 (UTC)[reply]
The example given under concentration not only makes no sense, it's incorrect. 1:5 means 1 part TO 5 parts (i.e. 1 part of X added to 5 parts Y) and should not be confused with 1 in 5 (which means 1 part in 5 parts TOTAL). The same is true for smaller ratios such as 1:100 which is not the same as 1% but actually, in terms of concentration, refers to 1 part added to 100 parts which equates to 0.91%. An easy way to understand it is to look at a 1:1 mixture. Using Splendiff's explanation above, this would be equivalent to 1/1 or 100%. When in fact it represents a 50% mixture of one component in the other or 1/2. I'm not sure how they teach these concepts in high school, but I teach it this way to our pharmacy students - and we're pretty picky with life-threatening concentration calculations. PharmaG (talk) 14:03, 15 July 2010 (UTC)[reply]
The problem is in the imprecise way in which we state ratios. We should always specify clearly whether we are stating the ratio of one component to another or the ratio of one component to the total. Both are used in real science. In high school, questions are usually set with precision and clarity, as with your examples to pharmacy students. Unfortunately, industrial chemists and biologists seem not always to specify which ratio they are stating. I've moved this confusing example nearer to the end, and mentioned that dilution factors are not normally used in pharmacy (though I suspect that they are in homeopathy?) Dbfirs20:07, 15 July 2010 (UTC)[reply]
In ancient times people used to use unit fractions computationally. 2/3 and 3/4 were special cases, but lets suppose I'm an architect and I want to instruct a carpenter or a mason how to build a circular arch using unit fractions. This problem actually was solved at Saqarra c 3000 BC. http://en.wikipedia.org/wiki/File:Egyptian_circle.png The architect created a grid of vertical lines 1 ordinary cubit apart and then marked a height on each vertical through which the workmen bent a stick to get a fair line. This method is still used today in lofting boats where each frame of the boat has a different curve. 142.0.102.93 (talk) 19:12, 23 May 2014 (UTC)[reply]
I am confused the following line in the article
"There is often confusion between dilution ratio (1:n meaning 1 part solute to n parts solvent) and dilution factor (1:n+1) where the second number (n+1) represents the total volume of solute + solvent. "
I thought n was already solute + solvent as the example (1mL+4mL water = 5 has shown). That line just adds more confusion. About the difference between dilution ratio and dilution factor; here is what I know. When in biology, we are ask to prepare a 1:100 dilution - I assume that this is the Dilution Ratio
The Dilution Factor - for me, it is the 100 above. So if I write 1:a dilution ratio, then a is the dilution factor. For example, a 7.56 M of acid following a 1:100 dilution ratio, the answer would be .0756M which is easily obtained by having 7.56/100 where the denominator is the dilution factor. Of course one may argue that the same result can be obtain by having the stock concentration * Dilution ratio. Essentially, we are adding 1mL of acid + 99 mL of water to dilute the acid.
This sort of a problem comes up when studying climate change and rising sea levels. Ice loads the poles as a solid, melts into the sea as fresh water diluting salt water. The coefficients of expansion of the fresh and salt water are influenced by temperature and pressure. Warm salt water sinks to the bottom where there is more pressure but cold fresh water stays at the top for a while, then becoming warmer and more saline begins to sink. As the ice on the land melts and flows into the sea it relieves the load on the land while adding to the load on the thinner ocean plates so that there is isostatic rebound reflecting the changed loading.
::Now the acidity of the oceans may be affected by the levels of atmospheric carbon in the greenhouse gas emissions so that's another factor to take into account, also winds tend to pile the seas up in the direction of the prevailing wind and relieve them in the opposite direction but weather events such as el Nino can reverse the prevailing winds affecting sea levels. Also surface water near land is attracted more strongly gravitationally than surface water over great depths. The dilution ratio thus has to take into account state, relative frozen or liquid height when floating, temperature, pressure,gravitational attraction, acidity, lateral loading from wind and all of these factors become variables in your dilution ratio equation. Given a body of water the size of the earths oceans its probably also necessary to consider the relative humidity of that portion of the water which is in suspension in the atmosphere, and perhaps also tidal forces.Your formula will eventually have as many or more variables than the computation of seismic forces caused by the changed loading on the mantle.Metaphysical Engineering (talk) 19:17, 26 May 2014 (UTC)[reply]
When I researched this, I found that different disciplines use differing conventions, with some applications using "ratio" when they mean "factor" or "ratio to the combined amount", hence the mention of "confusion". The statement is made from a mathematical viewpoint, rather than from any particular practical application. How can we make things clearer? Dbfirs07:06, 6 June 2014 (UTC)[reply]
Yes, the section "Number of terms" gives an example using four terms in the percentage part. You can certainly say that the ratio of lengths of sides in the simplest Pythagoras triangle is 3:4:5. Ratio numbers do not have to be integers. Perhaps we should have a mention in the article that the ratio of circumference to diameter in any circle is :1 and that the ratio of side length to diagonal length in a regular pentagon is 1:Dbfirs06:58, 6 June 2014 (UTC)[reply]
One way to use ratios is with a sequence of heights/widths/depths per unit time
that essentially invokes a fourth dimension of time to create an arc which can be either two dimensional or three dimensional
and in practice is a lot like lofting the hull of a boat; theoretically if the line has a shape you could get nurbs and splines.
Pythagorus studied Egyptian unit fractions and their use by Egyptian architects to define curves as for example.
About 5000 years ago an Egyptian architect at Saqarra came up with a method for describing the arc of a circle at least well enough that his contractor could use it to construct an arch. I know that the Egyptian Rhind papyrus of 1800BC gives the area of a circle as , where is the diameter of the circle, but thats much later.
17. Somers Clarke and R. EnglebachAncient Egyptian Construction and Architecture. Dover. 1990. ISBN0486264858.
A text found at Saquara dating to c 3000 BC or 5000 years BP has a picture of a curve and under the curve the dimensions given in fingers to the right of the circle as reconstructed to the right. It was presumed the horizontal spacing was based on a royal cubit but the results if based on an ordinary cubit are different. It appears the value for PI being used is 3 '8 '64 '1024. which at 3.141601563 is slightly better than the Rhind value.
The circumference of the circle is 1200 fingers and the diameter of the circle is 191 x 2 = 382
3 '8 '64 '1024 x 382 ~= 1200.0
The side of the square is 12 royal cubits and its area is 434 square feet.
The area of the circle is 191^2 x 3.141601563.
The algorithm suggests working with coordinates and numerical analysis to define a curve.
"The quotient of two numbers (or quantities); the relative sizes of two numbers (or quantities)", "The Mathematics Dictionary" [1]
"'Velocity' can be defined as the ratio... 'Population density' is the ratio... 'Gasoline consumption' is measure as the ratio...", "Ratio and Proportion: Research and Teaching in Mathematics Teachers" [2]
Another quote: "Ratio as a Rate. The first type [of ratio] defined by Freudenthal, above, is known as rate, and illustrates a comparison between two variables with difference units. (...) A ratio of this sort produces a unique, new concept with its own entity, and this new concept is usually not considered a ratio, per se, but a rate or density.", "Ratio and Proportion: Research and Teaching in Mathematics Teachers" [3]. Fgnievinski (talk) 05:48, 22 July 2015 (UTC)[reply]
So ratios are not necessarily dimensionless; non-dimensionless ratios are called rates; and dimensionless ratios are... proportions/scales? Fgnievinski (talk) 06:06, 22 July 2015 (UTC)[reply]
The problem would be more easily solved by removing the text "of the same kind (e.g., objects, persons, students, spoonfuls, units of whatever identical dimension)". The rest of the article does not seem to be restricted to dimensionless units, and in fact the first example given is in units of oranges per lemon.--Wikimedes (talk) 14:51, 22 July 2015 (UTC)[reply]
The problem is that the word means different things to different people and the meaning has evolved in the last hundred to mean something different. In the context of geometry the words "of the same kind" are necessary since you can talk about the ratio of the circumference of a circle to its diameter (two lengths) but not about the ratio of the area of a circle to its diameter (area vs. length). In modern usage, especially outside mathematics, this distinction has disappeared and the word "ratio" has become synonymous with "quotient". We already have an article for Quotient and another for Division (mathematics), so I don't see the need to create another article. Some effort might be put into resorting the material so everything is in the right article. Wikipedia is not a dictionary, so articles should be about things/concepts, not words. I'm thinking the article Ratio should be about the, perhaps anachronistic, concept used in geometry and people looking for information on ratio meaning quotient or ratio meaning rate should be pointed to the corresponding articles. --RDBury (talk) 19:21, 22 July 2015 (UTC)[reply]
Yes, I would not support removing or distorting the basic concept that is taught to all schoolchildren (and the first example is a plain ratio of two categories of fruit, not a "rate"). We might mention that the word ratio is often used informally to mean "rate", and point the reader to appropriate articles. Dbfirs19:29, 22 July 2015 (UTC)[reply]
The basic concept seems to have now been distorted. I agree that the word is commonly misused. What does anyone else think? Dbfirs07:05, 24 July 2015 (UTC)[reply]
We live in an ever-changing world of vocabulary. Examples:
random
secular
gay
liberal (a.k.a., classical liberal)
denier
gentleman
bitch
marriage
None of those words are used the same as they were 100 years ago. I think it good that the Wikipedia uses the classical or traditional definitions for these words and topics, but popular usage is difficult to deny. I think it would be best to point out both uses, traditional or strict ratios and the less rigidly defined kind of ratio. Educated people now are quite a bit less educated than people were 100 years ago, so the strict definitions slip. I like to saw logs! (talk) 05:25, 25 July 2015 (UTC)[reply]
Hmmm .... is this an argument for "dumbing down" Wikipedia. I agree with you that modern usage should be included, but should we not make a clear distinction between this and the classical definition taught in schools, rather than conflate the two? Dbfirs07:15, 25 July 2015 (UTC)[reply]
The classical concept of ratio is far wider than just geometry. How would your new broad-concept article differ from Rate (mathematics)? I'd prefer to keep most of this article in its previous form, with a mention that the word is often used instead of "rate", a summary of this informal usage, and a link to the already existing and more precisely named article. Dbfirs12:29, 27 July 2015 (UTC)[reply]
::::::Ratio should remain a broad concept article, but I have no objection to having sections within the article addressing things like geometry, numerical analysis, arithmetic and geometric sequences, dimensionality where for example we might discuss a rate that changes over time, or whose properties change at some nano scale Metaphysical Engineering (talk) 00:54, 28 July 2015 (UTC)[reply]
I partially agree, though trying to impose engineering usage on the article is not appropriate either. Perhaps we should have separate sections on ratio in mathematics and ratio in engineering. The Oxford English Dictionary Third Edition seems to give only the mathematical (traditional) sense, so I think this should be given priority, but a section on usage in sciences seems appropriate. Dbfirs13:35, 28 July 2015 (UTC)[reply]
While the statements made in a recent edit concerning expressing ratios as decimal fractions are certainly mathematically correct, I question whether this is actually done in practice (for instance, you never see the aspect ratio of a TV screen expressed as 1.3333...). It is possible that this is a cultural difference and that such expressions are more common in different parts of the world. If this is the case, it should be brought up on this talk page so that we can decide how best to put that information in the article. I reverted the edit so that a discussion of its intent could take place here. Bill Cherowitzo (talk) 04:40, 27 September 2015 (UTC)[reply]
Have you looked at the back of your DVDs or Blu-ray Discs - how is that for cultural reference? Have you tried searching at all before removing my edits? Here are just a few links from the first couple of page after searching on Google:
I feel like the 4:3 image at the top of the page is unclear. Which of the rectangles in that image is 4:3? The inner one or the outer one? Margalob (talk) 22:21, 5 June 2016 (UTC)[reply]
