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Math Help - Fractions problem

  1. #1
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    Fractions problem

    How can I show that  \frac {3}{10} is  \frac {1}{7} of the way from  \frac {1}{4} to \frac {3}{5} ?
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  2. #2
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    Quote Originally Posted by sarahh View Post
    How can I show that  3/10 is  1/7 of the way from  1/4 to  3/5 ?
    First you need to find out the length of "the whole way" from \frac{1}{4} to \frac{3}{5}, which you do by subtraction:

    \frac{3}{5} - \frac{1}{4} = \frac{12}{20} - \frac{5}{20} = \frac{7}{20}.

    So what's 1/7 of 7/20? 1/20. So now the question becomes, is \frac{3}{10} a distance of \frac{1}{20} from \frac{1}{4}?

    \frac{3}{10} - \frac{1}{4} = \frac{6}{20} - \frac{5}{20} = \frac{1}{20}

    and the answer is yes.
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  3. #3
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    But how would you prove it without using 3/10 to show it? If you didn't know it was 3/10?
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  4. #4
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    Quote Originally Posted by sarahh View Post
    But how would you prove it without using 3/10 to show it? If you didn't know it was 3/10?
    We figured out that \frac{3}{5} and \frac{1}{4} are \frac{7}{20} apart. So a number which is \frac{1}{7} of the way from \frac{1}{4} to \frac{3}{5} is going to be a distance of \frac{1}{20} from \frac{1}{4}. Therefore, the desired answer is \frac{1}{4} + \frac{1}{20} = \frac{5}{20} + \frac{1}{20} = \frac{6}{20} = \frac{3}{10}.
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  5. #5
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    Ahhh that makes sense. Thanks so much iceman!
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