# Thread: Multiplying a fraction by 100

1. ## 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

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

2. Originally Posted by p.numminen
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

3. Originally Posted by CaptainBlack
$\displaystyle x\%$ 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%.

4. Originally Posted by p.numminen
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

5. Originally Posted by CaptainBlack
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.