Question

What is 6 of 20?

Answer 1

6 of 20 is the same as `3/10` which is also `30%`

Explanation:

It all depends on the format you are after.

`color(blue)("As a fraction:")`

All of the sample is 20 and you have 6 of that sample `->6/20`

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

`(6-:2)/(20-:2)=color(blue)(3/10)`

3 is a prime number so you have to stop there.
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`color(blue)("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 `1/100`

Using the example of 30% we can write:

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

`color(brown)("Back to your question:")`

We have the fraction `3/10`

So we need to change the 10 into 100

`color(green)([3/10color(red)(xx1)]" "->" "[3/10color(red)(xx10/10)]" "=" ")color(blue)(30/100)`

Write as `30xx1/100`

but `1/100` is the same as % giving: `color(blue)(30%)`