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Math Help - The Division Algorithm

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    The Division Algorithm

    The Division Algorithm states: Let a,b belong to Z, b does not equal zero. Then there exist unique integers q and r, with 0 is less than or equal to r and less then the absolute value of b, such that a = qb+r

    I have a question here that asks: Find q and r as defined in the Division Algorithm in each of the following cases:

    i) a = 5286; b = 19
    ii) a = -5286; b = 19
    iii) a = 5286; b = -19
    iv) a = 19; b = 5286

    Any help with any of these would be greatly appreciated. Thanks a lot guys.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by GreenDay14 View Post
    The Division Algorithm states: Let a,b belong to Z, b does not equal zero. Then there exist unique integers q and r, with 0 is less than or equal to r and less then the absolute value of b, such that a = qb+r

    I have a question here that asks: Find q and r as defined in the Division Algorithm in each of the following cases:

    i) a = 5286; b = 19
    ii) a = -5286; b = 19
    iii) a = 5286; b = -19
    iv) a = 19; b = 5286

    Any help with any of these would be greatly appreciated. Thanks a lot guys.
    There are many ways to find this. Merely note that q=\left\lfloor\frac{a}{b}\right\rfloor where \left\lfloor .\right\rfloor is the floor function. and r is just a\text{ mod }b. Or if your aren't familiar with that notation, let {x} be the "fracional part" of x. Then r=b\cdot\left\{\frac{a}{b}\right\}
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