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Math Help - [SOLVED] Laws of Numbers

  1. #1
    Member ronaldo_07's Avatar
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    [SOLVED] Laws of Numbers

    Use the definition of addition for rational numbers to verify that it satisfies the
    commutative and associative laws.

    Use the definition of multiplication for complex numbers to verify that it satisfies the commutative and associative laws.

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    For the first part I did this: is this correct?

    \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}

    \frac{c}{d}+\frac{a}{b}=\frac{cb+da}{db}

    \frac{ad+bc}{bd}=\frac{cb+da}{db}

    EDF
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  2. #2
    MHF Contributor
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    Quote Originally Posted by ronaldo_07 View Post
    For the first part I did this: is this correct?

    \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}

    \frac{c}{d}+\frac{a}{b}=\frac{cb+da}{db}

    \frac{ad+bc}{bd}=\frac{cb+da}{db}

    EDF
    Hi

    I think it is correct.
    Of course you need to suppose that multiplication and addition are commutative for integers.

    a and d being integers : ad=da
    b and c being integers : bc=cb
    ad and bc being integers : ad+bc=bc+ad
    Therefore ad+bc=bc+ad=cb+da

    b and d being integers : bd=db

    Therefore the conclusion
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