What percent of 20 is 4?

20%

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

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. .........................................................................................................

Ratio in fractional format:

##20/100 ->" "color(red)(ul("in addition"))## to 100 parts you are looking at the related ##" "##20 parts.

So the total count of parts is ##100+20 = 120##

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

To change this to a fraction of the whole you would have: ## 20/120##