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Thread: Denominator 1 With A Decimal Numerator: Is "0.5/1" a mathematically valid stmt?

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    Denominator 1 With A Decimal Numerator: Is "0.5/1" a mathematically valid stmt?

    Is it mathematically correct to have a decimal as a numerator and one (1) as a denominator as in 0.5/1?

    I think that it is correct because of complex fractions. For example, (1/2)/(2/3) uses fractions as both numerator and denominator. I assume that 0.5/1 is correct since it can be expressed as a complex fraction (1/2)/1.
    Likewise 0.5/(6/2) will equal 0.5/3 or (1/2)/3. If 3 is changed to 1, the fraction becomes (1/6)/1.

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    Quote Originally Posted by KWF View Post
    Is it mathematically correct to have a decimal as a numerator and one (1) as a denominator as in 0.5/1?

    I think that it is correct because of complex fractions. For example, (1/2)/(2/3) uses fractions as both numerator and denominator. I assume that 0.5/1 is correct since it can be expressed as a complex fraction (1/2)/1.
    Likewise 0.5/(6/2) will equal 0.5/3 or (1/2)/3. If 3 is changed to 1, the fraction becomes (1/6)/1.
    Certainly there's nothing invalid about it; you can obviously calculate its value, if that's all that matters.

    The question is, why are you doing it? What question are you answering with it, and what format is appropriate to that question? Sometimes a specific form of answer is required, sometimes it doesn't matter.

    Can you tell us the context of your question? Why are you asking this?

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    Quote Originally Posted by KWF View Post
    Is it mathematically correct to have a decimal as a numerator and one (1) as a denominator as in 0.5/1?

    I think that it is correct because of complex fractions. For example, (1/2)/(2/3) uses fractions as both numerator and denominator. I assume that 0.5/1 is correct since it can be expressed as a complex fraction (1/2)/1.
    Likewise 0.5/(6/2) will equal 0.5/3 or (1/2)/3. If 3 is changed to 1, the fraction becomes (1/6)/1.
    To be a little more precise, 0.5:1 is a reasonable format in which to state a ratio (of certain types); and [tex]\dfrac{0.5}{1}[/tex] is a valid expression to write in the course of your work; but if you are asked to give an answer as a decimal, it would be 0.5 by itself, and if you are asked to give it as a simplified fraction, it would be [tex]\frac{1}{2}[/tex], and so on. We don't generally give complex fractions as answers, because they are too ... well ... complex! Answers should be readable, and commonly in a standard form so that everyone will write it the same way. (That's partly for the teacher's benefit, and also so you can compare your answer with the back of the book.)

    So there is nothing mathematically wrong with any sort of expression, as long as it is valid; but it may be inappropriate in a particular context. That's why I want to know where you are using 0.5/1.

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    Quote Originally Posted by Dr.Peterson View Post
    To be a little more precise, 0.5:1 is a reasonable format in which to state a ratio (of certain types); and [tex]\dfrac{0.5}{1}[/tex] is a valid expression to write in the course of your work; but if you are asked to give an answer as a decimal, it would be 0.5 by itself, and if you are asked to give it as a simplified fraction, it would be [tex]\frac{1}{2}[/tex], and so on. We don't generally give complex fractions as answers, because they are too ... well ... complex! Answers should be readable, and commonly in a standard form so that everyone will write it the same way. (That's partly for the teacher's benefit, and also so you can compare your answer with the back of the book.)

    So there is nothing mathematically wrong with any sort of expression, as long as it is valid; but it may be inappropriate in a particular context. That's why I want to know where you are using 0.5/1.


    I want to thank you for the reply! There is no particular reason or context for my using 0.5/1. I am just curious to know whether or not it is correct to use decimals with whole number denominators, especially "1". I seldom see this except with scale model ratios. I saw a ratio expressed as 1/16:1 on a model kit box. I suppose that this can be expressed as (1/16)/1. I have not ever seen a ratio like this (1/16)/1 or any other model kit ratio expressed as a decimal such as 0.0625:1 or 0.0625/1.

    Thanks again for your assistance!

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    Quote Originally Posted by KWF View Post
    I want to thank you for the reply! There is no particular reason or context for my using 0.5/1. I am just curious to know whether or not it is correct to use decimals with whole number denominators, especially "1". I seldom see this except with scale model ratios. I saw a ratio expressed as 1/16:1 on a model kit box. I suppose that this can be expressed as (1/16)/1. I have not ever seen a ratio like this (1/16)/1 or any other model kit ratio expressed as a decimal such as 0.0625:1 or 0.0625/1.

    Thanks again for your assistance!
    The important thing is that what you are asking about is not just a usage within your own work, but how things are expressed in communicating with others. As I suggested, this is not a mathematical issue, but one of convention in particular contexts. You would never (well, rarely) express a number in general as a fraction "???/1" in such a situation, but it is quite common with ratios such as you are asking about (whether represented with a colon or slash). It seems odd to me to write 1/16:1 rather than 1:16, but where the convention is to always expect ":1", it makes sense, and it makes it easy to compare them.

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    Quote Originally Posted by Dr.Peterson View Post
    The important thing is that what you are asking about is not just a usage within your own work, but how things are expressed in communicating with others. As I suggested, this is not a mathematical issue, but one of convention in particular contexts. You would never (well, rarely) express a number in general as a fraction "???/1" in such a situation, but it is quite common with ratios such as you are asking about (whether represented with a colon or slash). It seems odd to me to write 1/16:1 rather than 1:16, but where the convention is to always expect ":1", it makes sense, and it makes it easy to compare them.
    In the following context or example, I think it makes good sense to use "1" as a denominator. For example, express a decimal rate of 0.0625 as a dollar rate per $100. One solution would be as follows:
    0.0625/1 X $100/$100 = $6.25/$100.

    I think this example make good sense.

    Thanks again for your help and assistance!

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    Quote Originally Posted by KWF View Post
    In the following context or example, I think it makes good sense to use "1" as a denominator. For example, express a decimal rate of 0.0625 as a dollar rate per $100. One solution would be as follows:
    0.0625/1 X $100/$100 = $6.25/$100.

    I think this example make good sense.

    Thanks again for your help and assistance!
    As I said previously, your 0.0625/1 is a usage within your work, not a final answer or a communication. That's different from the last thing I had said; yes, it is entirely reasonable (especially as a way of explaining your result to people who are not thoroughly familiar with fractions).

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    Quote Originally Posted by Denis View Post
    per $100 = percent = %
    How does $100.00 equal percent? I have not ever seen $%!

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    Quote Originally Posted by KWF View Post
    Is it mathematically correct to have a decimal as a numerator and one (1) as a denominator as in 0.5/1?
    It is confusion about what is being measured by those numbers, and will likely cause thinking problems. Adding unit of measure can help:

    1/2 car/passenger; 1 car per 2 passengers
    1/2 mile/hour; 1 mile per 2 hours
    1/2 milk/recipe; 1 milk per 2 recipes

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