# What is 6 of 20?

May 14, 2017

6 of 20 is the same as $\frac{3}{10}$ which is also 30%

#### Explanation:

It all depends on the format you are after.

$\textcolor{b l u e}{\text{As a fraction:}}$

All of the sample is 20 and you have 6 of that sample $\to \frac{6}{20}$

But this can be simplified. Notice that both 6 and 20 are even numbers so 2 is a 'common factor'

$\frac{6 \div 2}{20 \div 2} = \textcolor{b l u e}{\frac{3}{10}}$

3 is a prime number so you have to stop there.
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$\textcolor{b l u e}{\text{As a percentage:}}$

Percentage is just another fraction. It is however, a special fraction in that the bottom number (denominator) is always fixed at 100

The percentage symbol % is a bit like a unit of measurement but one that is worth $\frac{1}{100}$

Using the example of 30% we can write:

30%" "->" "30xx%" "->" "30xx1/100" "->" "30/100

$\textcolor{b r o w n}{\text{Back to your question:}}$

We have the fraction $\frac{3}{10}$

So we need to change the 10 into 100

$\textcolor{g r e e n}{\left[\frac{3}{10} \textcolor{red}{\times 1}\right] \text{ "->" "[3/10color(red)(xx10/10)]" "=" }} \textcolor{b l u e}{\frac{30}{100}}$

Write as $30 \times \frac{1}{100}$

but $\frac{1}{100}$ is the same as % giving: color(blue)(30%)