#color(blue)("The teaching bit - explaining percentage")#
Percentage is in fact #ul("just a fraction")#. However it is a special fraction in that the bottom number (denominator) is fixed at 100.
Example: 60 percent is #60/100#
In fact this is 60 lots of #1/100# or #60xx1/100#
You also see the symbol % used for example #60%#
This is EXACTLY the same thing as #60/100->60xx1/100#
If they are the same thing then there is a direct comparison between the two
#60xx1/100#
#60 color(white)("dd")% larr" Direct comparison" #
So this has to mean that #xx1/100# is EXACTLY the same thing as #%#
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#color(blue)("Answering the question")#
Given: #1/2#
#color(brown)("Changing this to a percentage")#
Let the unknown value be represented by #x#
So we need:
#1/2=x/100#
Multiply both sides by 100
#color(green)(1/2=x/100 color(white)("dddd")->color(white)("dddd")1/2color(red)(xx100)=x/100color(red)(xx100))#
#color(green)(color(white)("dddddddddddd")->color(white)("dddd")color(red)(100)/2 = x xxcolor(red)(100)/100)#
#color(green)(color(white)("dddddddddddd")->color(white)("ddddd")50 color(white)(".")= x xxcolor(white)("d")1)#
So #x=50#
#color(magenta)("Remember that this is the "ul("top number")" of "x/100)#
so we have #x xx1/100 = 50xx ubrace(1/100) = 50/100#
#color(white)("ddddddddddddddddddddddd")darr#
#color(white)("ddddddddddddddddddd")50 color(white)("dd")% =50%#
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#color(brown)("Changing this to a decimal")#
We have: #50/100# and to change this to a decimal we need to change the 100 into 1.
For multiply or divide on a fraction what we do to the bottom we also do to the top.
#50/100 = (50-:100)/(100-:100) =0.5/1=0.5#
