Talk:Ratio

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Ratios between more than two quantities

I've written an example under the section on ratios and fractions that addresses this issue, I hope.--Dwetherow 05:18, 23 February 2007 (UTC)

Hmmm. I thought you could have ratios between more than two quantities. E.g. If my fruit bowl has apples, pears and bananas in the ratio 1:3:4 and there are 2 apples in there then there are 6 pears and 8 bananas.

So, why does the article limit rations to being between only two quantities? —The preceding unsigned comment was added by 217.22.155.67 (talk • contribs) .

Why wouldn't you just put 2:6:8 ? —The preceding unsigned comment was added by 81.4.160.194 (talk • contribs) .

Usually you try to express ratios in lowest terms. - dcljr (talk) 08:28, 13 April 2006 (UTC)

What you are defining are relative proportions, not a ratio. —The preceding unsigned comment was added by 192.124.26.250 (talk • contribs) .

really —The preceding unsigned comment was added by 71.96.145.159 (talk • contribs) .

Well... it is true that if the fruits are in the "ratio" of 1:3:4 (I have seen this wording in textbooks before), as described above, then the ratio of apples to pears is 1:3, pears to bananas 3:4, and apples to bananas 1:4, so there's nothing wrong with applying the concept of "ratio" to this situation, you just have to think about it two things at a time. Strictly speaking, the word "ratio" refers to a relationship between two quantities only, but proportions (or "proportional" things) can involve any number of quantities (for example, the corresponding sides of any two similar figures are proportional, regardless of how many sides they have). Finally, any ratio can be explained in terms of proportions, as well: if the ratio of pears to bananas is 3:4, then the proportions of pears and bananas, respectively, are 3/7 and 4/7 of the total number of fruits. (And in the previous example, the proportions of apples, pears and bananas are 1/8, 2/8 = 1/4, and 4/8 = 1/2 of the total.) - dcljr (talk) 08:28, 13 April 2006 (UTC)

Therefore a ratio between more than two quantities is a shorthand for expressing several ratios? --72.140.146.246 13:35, 3 June 2006 (UTC)

Yes. --116.14.34.220 (talk) 13:08, 16 June 2009 (UTC)

Ratios as percentages

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)

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.--Dwetherow 05:18, 23 February 2007 (UTC)

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)

Comparing ratios

So if you have two ratios, 1:2000 and 1:4000, which one is "higher"? —The preceding unsigned comment was added by 69.157.57.16 (talk • contribs) .

Well, you divide 1 by 2000, get a number. Then, divide 1 by 4000, get another number. See which one of the two obtained numbers is bigger. Oleg Alexandrov 20:36, 27 September 2005 (UTC)

Scale map

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) .

Yes. 1 is to 20 as 1.1 is to 22. Or: (1/20)=(x/22) → x=1.1. - dcljr (talk) 06:36, 13 April 2006 (UTC)

Are ratios necessarily linear?

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 38.113.17.3 21:41, 17 April 2006 (UTC)

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 $cm^{3}$, and mass, in grams, required to store some material. Then, the ratio is between numbers which are measurements, not between quantities. Holon 01:08, 12 May 2006 (UTC)

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). --72.140.146.246 19:10, 3 June 2006 (UTC)

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. Holon 02:16, 4 June 2006 (UTC)

Can Ratios Be Negative?

Lets say I'm dealing in apples and oranges, and I am in debt apples but have a surplus of oranges.

I may have a ratio of (-2 apples / 3 oranges), and a ratio of (-3 apples / 2 oranges). Which is the larger ratio of apples to oranges?

If thought about as a fraction then -2/3 = -.666, and -3/2 = -1.5.

Therefore, -2/3 is a bigger ratio of apples to oranges because it is 'less negative' compared with -1.5.

However, if thought about in absolute terms, there are more apples to oranges in the -3/2 ratio.

Can ratios work with one (or more) parts of the ratio being negative? Or are ratios strictly absolute?

71.142.81.237 08:11, 22 February 2007 (UTC)Dave A

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. Trishm 05:02, 18 June 2007 (UTC)

Correctly stating a ratio

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)

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 Holon 11:07, 16 August 2006 (UTC)

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. Splendiff 23:42, 6 June 2007 (UTC)

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)

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)

Try "The VNR Concise Encyclopedia of Mathematics", by W. Gellert and H. Kuestner and M. Hellwich, and H. Kaestner, published in 1977, ISBN 9780442205904.

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. Trishm 04:53, 18 June 2007 (UTC)

no chickens!

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.

gba 05:11, 12 February 2007 (UTC)

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"

24.61.93.51 15:30, 17 March 2007 (UTC)peter

Poorly defined in the lead section

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, ISBN 9780442205904.

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. --Kubanczyk 15:25, 11 October 2007 (UTC)

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.

Thoughts? Holon 10:39, 13 October 2007 (UTC) (updated to clarify the main points Holon 12:22, 15 October 2007 (UTC))

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.)

-Geek Jason (talk) 16:21, 12 May 2009 (UTC)

Ratio, definitions and examples

RATIO

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)

ų —Preceding unsigned comment added by 41.242.171.21 (talk) 11:38, 17 August 2008 (UTC)