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Thread: Multiplying a fraction by 100

  1. #1
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    Angry Multiplying a fraction by 100

    In this message, I will be talking about real numbers only. I also presume that every reader understands that for any real number $\displaystyle a$, $\displaystyle 1a = a$ and that $\displaystyle 100\% = 1$.

    Why is it, that converting a fraction to a percentage, the fraction should be "multiplied by 100%"? Here are some examples:

    http://www.cimt.plymouth.ac.uk/proje...gcse/bkb11.pdf

    What sense does it make to multiply a fraction by 100%, which equals 1?

    But here is what is far worse:

    Many business books in my country actually suggest that, for example

    $\displaystyle \frac{1}{2} \cdot 100 = 50\%$! Yes, multiplied by 100, not 100%.

    Am I incorrect if I state that

    $\displaystyle \frac{1}{2} \cdot 100 = 50 = 5000\%$ and that

    $\displaystyle \frac{1}{2} = 0.5 = 50\%$?

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  2. #2
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    Quote Originally Posted by p.numminen View Post
    In this message, I will be talking about real numbers only. I also presume that every reader understands that for any real number $\displaystyle a$, $\displaystyle 1a = a$ and that $\displaystyle 100\% = 1$.

    Why is it, that converting a fraction to a percentage, the fraction should be "multiplied by 100%"? Here are some examples:

    http://www.cimt.plymouth.ac.uk/proje...gcse/bkb11.pdf

    What sense does it make to multiply a fraction by 100%, which equals 1?

    But here is what is far worse:

    Many business books in my country actually suggest that, for example

    $\displaystyle \frac{1}{2} \cdot 100 = 50\%$! Yes, multiplied by 100, not 100%.

    Am I incorrect if I state that

    $\displaystyle \frac{1}{2} \cdot 100 = 50 = 5000\%$ and that

    $\displaystyle \frac{1}{2} = 0.5 = 50\%$?

    $\displaystyle x\%$ is shorthand for $\displaystyle x/100$.

    Now if $\displaystyle u$ is a real number $\displaystyle u=\frac{u \times 100}{100}=(100 \times u) \%=100 \times (u\%)=u \times (100\%)$


    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    $\displaystyle x\%$ is shorthand for $\displaystyle x/100$.

    Now if $\displaystyle u$ is a real number $\displaystyle u=\frac{u \times 100}{100}=(100 \times u) \%=100 \times (u\%)=u \times (100\%)$
    Yes, $\displaystyle 100\% = 1$. But what sense does it make to tell students to multiply $\displaystyle \frac{1}{2}$ by 100% to obtain 50%, when 100% is not necessary?



    Multiplying by 100, not 100%:
    How do you obtain

    $\displaystyle \frac{3.25 \cdot 100}{25} = 13\%$

    like they have done here:

    Contribution margin - an example

    I got 1300%.
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  4. #4
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    Quote Originally Posted by p.numminen View Post
    Yes, $\displaystyle 100\% = 1$. But what sense does it make to tell students to multiply $\displaystyle \frac{1}{2}$ by 100% to obtain 50%, when 100% is not necessary?



    Multiplying by 100, not 100%:
    How do you obtain

    $\displaystyle \frac{3.25 \cdot 100}{25} = 13\%$

    like they have done here:

    Contribution margin - an example

    I got 1300%.
    There is really nothing to get excited about here $\displaystyle 100\%=1$ as it is short hand for $\displaystyle 100/100$. So nothing changes when you multiply by $\displaystyle 100\%$ which is as it should be.

    If you multiply by $\displaystyle 100$ things do change $\displaystyle 0.5 \times 100=50 \ne 50\%=50/100=0.5$.

    Since multiplying by $\displaystyle 100\%$ does nothing there is never any harm done, all you have is a computational aide for those who really do not understand what is going on.

    Multiplying by $\displaystyle 100$ and then appending a $\displaystyle \%$ at the end of the calculation is a slight abuse of notation but if you know what you are doing then it does not matter.

    CB
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    If you multiply by $\displaystyle 100$ things do change $\displaystyle 0.5 \times 100=50 \ne 50\%=50/100=0.5$.
    So, in other words,

    $\displaystyle \frac{3.25 \cdot 100}{25} = 13\%$

    is wrong.

    I don't wonder why some people are confused by mathematics when students are taught notation like this.
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