color(blue)("The teaching bit - explaining percentage")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