Results 1 to 5 of 5

Math Help - [SOLVED] Z18 Calculation

  1. #1
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175

    [SOLVED] Z18 Calculation




    \frac{2}{7}+\frac{7}{13}=\frac{[2]X[13]+[7]X[7]}{[7]X[13]}

    Im not sure how to multiply this out please show steps on how to do this. Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by ronaldo_07 View Post



    \frac{2}{7}+\frac{7}{13}=\frac{[2]X[13]+[7]X[7]}{[7]X[13]}

    Im not sure how to multiply this out please show steps on how to do this. Thanks
    From the Euclidean algorithm (or trial and error)

    7^{-1}=13 \mod(18) and

    13^{-1}=7 \mod(18)

    so we end up with
    13 \cdot 2 +7\cdot 7 =26+49=75 \equiv 3 \mod(18)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175
    How did you get from 75 to 3mod(17)?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2009
    Posts
    35

    Smile

    Hi as you mentioned it's not 3 mod 17, actually it is 3 mod 18.

    take 75 and when you try to divide 75 by 18, you will get 3 as a remainder and hence 3 mod 18. is it helpful...?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Here is another way. To find inverse of 7 you need to solve 7x\equiv 1(\bmod 18).
    This is equivalent to 7x\equiv 1 - 2\cdot 18(\bmod 18)\implies 7x\equiv -35(\bmod 18) \implies x\equiv -5(\bmod 18)\implies x\equiv 13(\bmod 18).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with calculation...
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 7th 2011, 03:55 AM
  2. GDP calculation
    Posted in the Business Math Forum
    Replies: 0
    Last Post: December 1st 2010, 09:33 AM
  3. SST Calculation
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: October 21st 2010, 12:58 PM
  4. [SOLVED] Compound Interest Calculation
    Posted in the Business Math Forum
    Replies: 7
    Last Post: November 24th 2009, 05:07 PM
  5. pKa and pKb calculation
    Posted in the Math Topics Forum
    Replies: 17
    Last Post: February 5th 2008, 02:58 PM

Search Tags


/mathhelpforum @mathhelpforum