37.5% the word percent can be split into 2 parts The part per means ‘for each of’ and the part cent refers to 100. Think of centaury or centimetre. So this fraction is 3 per 8. We need some as yet unknown count per 100. ‘~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##color(blue)(Shortcut method)## ##(3 -: 8) xx 100 alternative notation 3/8 xx 100## giving ##37 1/2 %## ‘~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##color(blue)(From first principles)## We have ##3/8## To keep proportionality of fractions you need to apply the rule: what you do to the bottom number (denominator) you also do to the top number (numerator) We need to change the bottom number into 100 ##(color(red)(3xx100/8))/(cancel(8)xx100/cancel(8)) = (37.5)/100## ##color(brown)(Look at the red top bit. It is exactly the same as the shortcut!)## ##color(blue)(So writing 37.5% means 37.5/100##

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