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Math Help - Proper definition of the ratio a:b:c

  1. #1
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    Proper definition of the ratio a:b:c

    If am given a ratio 2:5:6 I understand that we make that 2x:5x:6x
    (so I guess I could write 2:5:6 <--> 2x:5x:6x)

    I understand how we can prove when we just have two numbers that a:b <--> ax:bx because you can write a:b = \frac{a}{b},= ax:bx and the x's just cancel. However after playing with it for a little while I realized we cannot write a:b:c = \frac{\frac{a}{b}}{c}

    Is the proper definition the following: X,Y,Z are in the ratio a:b:c <--> \frac{X}{Y} = \frac{a}{b}, \frac{Y}{Z} = \frac{b}{c}

    from which it would follow as a theorem that \frac{X}{Z} = \frac{a}{c} ?
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  2. #2
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    Re: Proper definition of the ratio a:b:c

    Strictly speaking a "ratio" is a fraction so only a:b, which is the same a/b makes sense. However, a:b:c is often used as shorthand for the two ratios a:b and b:c. Saying "a:b:c= 1:2:3 means a/b= 1/2 and b/c= 2/3.
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  3. #3
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    Re: Proper definition of the ratio a:b:c

    Quote Originally Posted by HallsofIvy View Post
    Strictly speaking a "ratio" is a fraction so only a:b, which is the same a/b makes sense. However, a:b:c is often used as shorthand for the two ratios a:b and b:c. Saying "a:b:c= 1:2:3 means a/b= 1/2 and b/c= 2/3.
    Thanks a lot, for some reason I still haven't been able to find this after searching through a bunch of textbooks or a quick google search.
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