#color(blue)("Preamble about percentages")#
Basically percentage is just a fraction. It is a special one in that the bottom number (denominator) is fixed at 100.
The symbol % is a sort of unit of measurement but one that is worth #1/100#
So as an example: #20% " "->" "20xx%" "->" "20xx1/100" "->" "20/100#
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#color(blue)("Answering your question")#
In mathematics the word 'of' in 90% of 95.6 is the same as multiply. So we have:
#90%" of "95.6" " ->" "90%xx95.6#
But 90% is the same as #90/100# so we have:
#90/100xx95.6#
#" "color(green)(ul(bar(|color(white)(2/2)"Using a calculator I get 86.04 "|))#
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#color(blue)("Additional teaching")#
#color(brown)("Suppose you do not have a calculator to hand. let me show you a")##color(brown)("sort of cheat method to make the manual calculations easier.")#
#color(purple)("Doing the preparation")#
Once used to this you would do it in 1 line
Consider the #90/100 -=(90-:10)/(100-:10)=9/10=9xx1/10#
So we can write #90/100xx95.6" "# as #" "1/10xx9xx95.6#
Do not like decimals so lets get rid of them in 95.6
#95.6" is the same as "956xx1/10#
So putting all this together we have:
#1/10xx9xx956xx1/10#
#1/100xx9xx956#
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#color(purple)("Doing the calculation")#
#956#
#ul(color(white)(95)9) larr" Multiply"#
#8604#
Now we deal with the #1/100#
#1/100xx8604 = 86.04#
#" "color(green)(ul(bar(|color(white)(2/2)"Calculating manually I get 86.04 "|))#
