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Math Help - Simplfying fractions and deciding what is the correct answer?

  1. #1
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    Simplfying fractions and deciding what is the correct answer?

    I am getting a little confused with different answers to my fractions, any advice welcome. I have,

    3/5 + 1/6 - 2/3 = ?

    My understanding is to do the addition first, but change the demonitors so,

    3/5 + 1/6 = (3/5 x 6/6) + (1/6 x 5/5) = 18/30 + 5/30 = 23/30 - 2/3 = 21/27 = 7/9

    My problem is that the calculator gives an answer of 1/10 in its simplest form which is not equivalent to 7/9.

    I can't see where I am going wrong?

    Any help greatly appreciated
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  2. #2
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    e^(i*pi)'s Avatar
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    You haven't converted your 2/3 into 30ths
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    Quote Originally Posted by David Green View Post
    18/30 + 5/30 = 23/30 - 2/3
    This one is more or less a pet peeve of mine, but I think a somewhat valuable one. If you notice the line I quoted is incorrect. The -2/3 comes out of nowhere.

    Now everyone here knows what is happening, but there are a number of circumstances that this might be confusing. You especially don't want to do this kind of thing on an exam, where confusion on the part of the grader could lose you points. My advice is to put the 2/3 in there the whole way through, or separate the problem into two lines like:
    18/30 + 5/30 = 23/30

    then 23/30 - 2/3 = ...

    -Dan
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  4. #4
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    Hello, David Green!

    \displaystyle\text{Simplify: }\;\frac{3}{5} + \frac{1}{6} - \frac{2}{3}

    Why make two problems out of it
    . . and double your chances to make errors?


    We have: . \displaystyle \frac{3}{5} + \frac{1}{6} - \frac{2}{3}

    Determine the least common denominator: 30.


    Convert the fractions to the LCD.

    . . \displaystyle \frac{3}{5}\cdot{\bf \frac{6}{6}} \;+\; \frac{1}{6}\cdot{\bf\frac{5}{5}} \;-\; \frac{2}{3}\cdot{\bf\frac{10}{10}} \;=\;\frac{18}{30} + \frac{5}{30} - \frac{20}{30}


    . . \displaystyle =\;\frac{18 + 5 - 20}{30} \;=\;\frac{3}{30} \;=\;\frac{1}{10}

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  5. #5
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    Thanks to all who have given advice. I carried on working through the problem and I came up with this;

    3 + 1 – 2 = [3 • 6] = 18 + 5 = 23 = [2 • 1] = 2 = 1
    5 6 3 [5 6] 30 30 30 [3 10] 30 10

    I further confused myself with the above when I decided that (23/30) was simplifed, but then could simplify more by saying 1 into 23 and 10 into 30?

    Then I had the added delema that I was originally subtracting 2/3 from 23/30, but then multiplied then and then simplifed again to get 1/10?

    I can see some differences in my method with comparison to the last thread, but is my version mathematically correct, or can there not be more than one method to find a solution?
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  6. #6
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    Quote Originally Posted by Soroban View Post
    Hello, David Green!


    Why make two problems out of it
    . . and double your chances to make errors?


    We have: . \displaystyle \frac{3}{5} + \frac{1}{6} - \frac{2}{3}

    Determine the least common denominator: 30.


    Convert the fractions to the LCD.

    . . \displaystyle \frac{3}{5}\cdot{\bf \frac{6}{6}} \;+\; \frac{1}{6}\cdot{\bf\frac{5}{5}} \;-\; \frac{2}{3}\cdot{\bf\frac{10}{10}} \;=\;\frac{18}{30} + \frac{5}{30} - \frac{20}{30}


    . . \displaystyle =\;\frac{18 + 5 - 20}{30} \;=\;\frac{3}{30} \;=\;\frac{1}{10}

    Very much appreciated that you put the effort in to give such a clear example. I spent some time working through what you have done and learned a lot from it, thank you very much.

    David
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