Definition of Ratio
Date: 08/21/2003 at 13:59:03 From: Suzanne Subject: The correct definition of "ratio" I am a copy editor for a public-relations firm that works with clients in high technology. Recently, I lost a battle with other editors on the staff who insisted that a construction such as "eight out of ten" is a ratio. I said I didn't think it met the mathematical criteria for ratio, but since I don't know precisely how "ratio" is defined by mathematicians, I was unable to argue persuasively - and don't know for a fact that my co-editors aren't right, that "eight out of ten" (or 8 out of 10) IS a ratio. Can you help? Thank you.
Date: 08/21/2003 at 17:07:19 From: Doctor Peterson Subject: Re: The correct definition of "ratio" Hi, Suzanne. This is as much an English language question as a math question, and that makes it very confusing. Words like this are not used as consistently as you might expect, even among math teachers or mathematicians. (That's partly because mathematicians today don't tend to pay much attention to ratios, and therefore don't have to define them carefully.) My first impression is that we TEND to think of ratios as comparisons of, say, the number of boys to the number of girls, rather than of a part to a whole, but that the term "ratio" does not necessarily exclude the latter. So it might not be technically wrong to use it that way, but depending on the context there might be clearer ways to phrase what you want to say, so as to avoid suggesting that the comparison is part to part. Then I did a little searching. For word questions, I like to see what a dictionary says, since lexicographers know how to make distinctions between words (though they often don't understand the mathematical distinctions). Merriam- Webster (m-w.com) says ratio 1 a : the indicated quotient of two mathematical expressions b : the relationship in quantity, amount, or size between two or more things : PROPORTION This agrees with my general sense of the word: any quotient can be called a ratio, but in particular it tends to compare two distinct things. But, of course, we make a distinction between ratio and proportion, and they call them synonymous. How do they define the latter? proportion 3 : the relation of one part to another or to the whole with respect to magnitude, quantity, or degree : RATIO 4 : SIZE, DIMENSION 5 : a statement of equality between two ratios in which the first of the four terms divided by the second equals the third divided by the fourth (as in 4/2=10/5) Their definition 5 is the one we use technically, in distinction to ratio. But look at their definition 3: when they consider this synonymous with ratio, they specifically include relations of part to whole as well as part to part. That would say that your example IS a ratio. How about math sites? Mathematicians, as I said, don't deal with this much, but math teachers do. Here is one reference I found: Ratio. Fraction. What's the Difference? https://web.archive.org/web/20080915000000/
Date: 08/21/2003 at 17:26:19 From: Suzanne Subject: Thank you (The correct definition of "ratio") Wow, thank you for the incredibly thorough explanation you so quickly provided. I admit to be being math-phobic, but I found your examples illuminating. Thanks again, and I'll quit arguing with my co-workers. Or find something else to argue about, more likely.
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