Question

What percent of 20 is 4?

Answer 1

`color(green)(20%)`

Explanation:

Suppose `x%` of `20` is `4`

That is
`color(white)("XXX")x/100 xx 20 = 4`
or
`color(white)("XXX")x/5=4`

`rarrcolor(white)("XXX")x=4xx5 = 20`

So `20%` of `20` is `4`

Answer 2

20%

Very detailed answer. Shows 2 methods and also explains the difference between fraction and ratio

Explanation:

Using the shortcut method
If I were to be answering this for my self it would look like this

`4/20xx100=20%`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Out of the 20 you have 4. So, as a fraction this is expressed as:

`" "4/20`

To change this to a percentage you multiply it by 100 giving

`" "4/20xx100`

which is the same as
`" "4xx100/20`

But `100-:20 = 5` giving

`" "4xx5 = 20`

This needs to be expressed as a percentage so we write the 20 as:

`" 20 %"`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("A different approach")`

`color(brown)("% is a unit of measurement that is worth "1/100)`

The question means: 4 parts `color(red)(ul("in"))` every 20 parts.

`=>4/20=("some value")/100 = x/100`

`color(green)([ 4/20color(red)(xx1)] =x/100 )`

But `5/5=1` giving:

`color(green)([ 4/20color(red)(xx5/5)] = [20/100]=x/100 )`

`20xx1/100" " =" " x xx1/100`

But `1/100` is the same as %

`20%" "=x%`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(magenta)("Very important note about difference between fraction and ratio")`

Fraction:

`20/100 ->" "color(red)(ul("within"))" the 100 you are looking at 20 parts"`

So the total count of parts is 100. Thus as a fraction of the whole you have `20/100` as previously written.

In words this is: some count of parts `ul(color(red)("in"))` every 100 parts.
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