Talk:Ratio

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Contents 1 Ratios between more than two quantities 2 Ratios as percentages 3 Comparing ratios 4 Scale map 5 Are ratios necessarily linear? 6 Correctly stating a ratio

[edit] Ratios between more than two quantities

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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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 cm³, 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)

[edit] 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? —The preceding unsigned comment was 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)