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Thread: reduce fraction

  1. #1
    Sep 2008

    reduce fraction

    could somebody please help these maths problems:

    Reduce the following fraction to its simplest form 1319977/1884823


    Find all the pairs of integers m and n such that 89m + 53n = 1

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  2. #2
    MHF Contributor Matt Westwood's Avatar
    Jul 2008
    Reading, UK
    "reducing a fraction to its simplest form" means "cancel out any common factors of the numbers on the top and the bottom".

    For example, $\displaystyle \frac 4 6$ has a common factor of $\displaystyle 2$ as $\displaystyle \frac 4 6 = \frac {2 \times 2} {2 \times 3} = \frac 2 3$.

    In the example given, I presume you're supposed to use the Eclidean algorithm to get the highest common factor of the two numbers given. You can then cancel out (i.e. divide both top and bottom) by that factor.

    From the form of the second part of the question, I assume you're studying basic number theory, in which case you ought to have covered these aspects in your course work.
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