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Math Help - This kind of scenario (DIVISION help).

  1. #1
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    This kind of scenario (DIVISION help).

    I need your insight on this matter again.
    Can you explain why 2/5/2 cancels out the 2 and only leaves 1/5. I mean, if you write it down it would look like
    2
    __
    5
    __
    2

    You cancel out the twos and get left with 1over 5.
    I don't really get this unless the following is the explanation:
    2 .....1
    __ x __
    5 ..... 2

    And that's how 2 and 2 cancel out because they are both divisible by themselves and they become 1.
    But shouldn't it be something like
    2 ..... 2
    __ x __ ?
    1...... 5

    But then how would you get the answer of .20 if it was solved in this manner? So this is definitely wrong but isn't this supposed to be how it looks like?

    Now I don't know whether that is right or wrong but I'd appreciate it if you could explain on that.
    ~
    Another one like the above. The inverse of csc, sec, and cot is just one over sin, cos, and tan respectively.
    This might be a very elementary question, but I need the answer to it if you do know; since I don't know the answer.
    So cot = 1/tan
    In turn that means 1/sin/cos
    or
    1
    __
    sin
    __
    cos
    .
    Now look back at the case of 2/5/2. This is where I'm confused. And I'm already past this law. I'm just reviewing. But suddenly seeing the 2/5/2 pop up, I actually became really confused.

    Can you explain to me why
    1
    __
    sin
    __
    cos

    is not equal to

    1 ...... 1
    __ x ___
    sin .. .cos

    so to get the cancellation if ever that 1 was a cosine to actually simulate the 2/5/2 expression?
    Thanks to anyone who's willing to help and reply.

    This is the proper forum I believe since the latter still boils down to the concept of the former and I need to understand the former before the latter would make sense.
    Last edited by RandomInquirer; August 6th 2013 at 04:18 AM. Reason: The dots are just there for the spaces. I could have made us of Math Type but I thought this wouldn't really need it.
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  2. #2
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    Re: This kind of scenario (DIVISION help).

    Quote Originally Posted by RandomInquirer View Post
    I need your insight on this matter again.
    Can you explain why 2/5/2 cancels out the 2 and only leaves 1/5. I mean, if you write it down it would look like
    2
    __
    5
    __
    2

    ...
    Hello,

    the confusion is caused by the writing of the fraction:

    2/5/2 could be (2/5)/2
    or
    2/5/2 could be 2/(5/2)

    In both cases: You divide by multiplying with the reciprocal. That means:

    (2/5)/2 = (2/5) * (1/2) = 1/5

    or

    2/(5/2) = (2/1) * (2/5) = 4/5

    You wrote:
    So cot = 1/tan
    In turn that means 1/sin/cos


    Set paranthese
    1/(sin(x)/cos(x)) and multiply with the reciprocal:

    (1/1) * (cos(x)/sin(x)) = 1 * cot(x)
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