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Math Help - Having trouble figuring out why a certain equation works, any ideas?

  1. #1
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    Having trouble figuring out why a certain equation works, any ideas?

    Hi All

    Given the following numbers

    a=2, b=19, c= 3

    using the equation:

    b/c - (a-1) / c

    yields the result of how many numbers between a and b are divisible by c - I have tested this and it seems to work - but I am stumped if I know why?!

    b/c gives the amount of times C divides into B using 0 as a base starting point, but what stumps me is the significance of (a-1)/c?

    Can anyone give me the break down of it because for reason I just can't get it right in my head!!

    Many thanks
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  2. #2
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    Re: Having trouble figuring out why a certain equation works, any ideas?

    The number of multiples of c less than or equal to b is equal to \lfloor \frac{b}{c} \rfloor ( \lfloor x \rfloor is the floor value function). We want to subtract the multiples of c that are strictly less than a, which is just \lfloor \frac{a-1}{c} \rfloor.


    Therefore the number of multiples of c between a and b, inclusive, is \lfloor \frac{b}{c} \rfloor - \lfloor \frac{a-1}{c} \rfloor.
    Last edited by richard1234; July 30th 2012 at 04:27 PM.
    Thanks from GariBaldi
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  3. #3
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    Re: Having trouble figuring out why a certain equation works, any ideas?

    Thank you Richard - much appreciated
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