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Math Help - Reporting a ratio

  1. #1
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    Reporting a ratio

    Im doing some online tests and seem to keep getting my ratio expressions wrong,

    Example:

    QUESTION
    What is the ratio of the number of tornados in 2008 to those in 2005?

    A) 1.36:1 B) 1:1.28 C) 0.78:1 D)1.26:1

    Answer:

    Jets in 2008 = 297
    Jets in 2005 = 380

    279:380 = 1:1.28

    However correct answer is 0.78:1 - why?

    Why does it matter whether you express it as "one to..." or "...to one"?

    Arent both expressions the same?

    If someone could clarify this for me id appreciate it, thanks.
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  2. #2
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    e^(i*pi)'s Avatar
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    Each expression is the reciprocal of other so the order does matter.

    If you're asked to find the ratio of A to B then you work out \dfrac{A}{B}

    In this question you want \dfrac{n_{2008}}{n_{2005}}
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  3. #3
    Junior Member RHandford's Avatar
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    Hi

    297:380 or 297/380=0.78

    It is 0.78 to 1 as in 2008 you only have 0.78 times the events of 2005, if expressed the other way (1:0.78) you would have less events then in the past. Hope that makes sense but it's hard for me to describe in words - sorry
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  4. #4
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    Thanks, that explains the above question, which makes sense - but what about here, that method above doesnt seem to apply:




    What is the ratio of women to men working in Audit In 2005?

    A) 1:1.12 B) 1.18:1 C) 1:1.31 D) 1.15:1

    By your method

    women working = 26758
    men working = 31500

    women:men = 26758:31500 = 26758/31500 = 0.849 - not a given answer

    Im sure im being thick, but I simply dont see it!
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  5. #5
    Junior Member RHandford's Avatar
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    Hi

    As mentioned above you need the reciprocal to give the answer shown so:

    either 26758/31500 = 0.849 then 1/0.849 = 1.18 (b)
    or 31500/26758 = 1.18 (b)

    As the result is 1.18:1 you can see that you would anticipate that the number of males is more than females as is shown in the table.
    Last edited by RHandford; September 12th 2010 at 11:11 AM. Reason: Typo
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  6. #6
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    e^(i*pi)'s Avatar
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    The Ratio of A to B is essentially how many of B is there for every 1 of A.


    In your example it is asking how many men are there for each woman. To this end we can divide both sides by the number of women

    \dfrac{26758}{26758} : \dfrac{31500}{26758} which is 1:1.18.

    I believe the question is incorrectly worded though as this is not the same as 1.18:1 - after all the ratios given imply that there are more women than men which is clearly not the case
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  7. #7
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    Notice the order in the question.

    First question: "number of tornados in 2008 to those in 2005"
    So the ratio is "number of tornados in 2008": " number of tornados in 2005" or 297: 380 which is the same as 1: 380/297= 1.28.
    You could have divided the other way: 297/380= 0.78: 1 but- (1) it is more common to write a proportion as 1 and a number greater than 1. (2) (More importantly) None of the given answers say "0.78: 1".

    Second question: " ratio of women to men working in Audit In 2005" so the order is "women": "men" or 26758: 31500. Since 26758 is the smaller number, this is 1: 31500/26758= 1.18: 1. You could have written it as 1: 26758/31500= 0.81 but that is not a given answer.

    Just make sure you undestand the difference between 1: 0.81 which is correct but not one of the given answers and 0.81: 1 which is NOT correct. 0.81: 1 would be "men": "women", not "men": "women".
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  8. #8
    Junior Member RHandford's Avatar
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    Hi

    Sorry to be pedantic but:

    None of the given answers say "0.78: 1".
    however from the original post

    QUESTION
    What is the ratio of the number of tornados in 2008 to those in 2005?

    A) 1.36:1 B) 1:1.28 C) 0.78:1 D)1.26:1
    Last edited by RHandford; September 12th 2010 at 01:18 PM.
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  9. #9
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    Hi, thanks for all the replies.

    Just to clarify, my question was never "is 1:0.78 the same as 0.78:1" - i know full well these are two different things.

    My confusion came from the first question having 1:1.28 and 0.78:1 as possible answers and not know which was right.

    The above two posts seem to highlight my point!
    Last edited by jack2010; September 12th 2010 at 01:33 PM. Reason: clarity of mind
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