23 Jun 20% Very detailed answer. Shows 2 methods and also explains
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##
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