#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 "|))#