What percent of 15,000 is 18,000?

#x%" of "15000=18000#

#=>x/(1cancel(00))times150cancel(00)=18000#

#=>150x=18000#

Dividing both sides by 150,

#=>(cancel(150)x)/color(red)((cancel(150)))=18000/color(red)(150#

#=>x = 1800/15 = 120#

Therefore, #120%# of #15000# is #18000#.

Percentage is basically just a fraction. It is however a special fraction in that the denominator is always fixed at 100.

Thing is; there is a convention to use the symbol %.
This may be considered a #ul("bit"color(red)(" like"))# units of measurement but one that is worth #1/100#

This is similar ( just using 3 as it happened to come to mind)

#3 " centimetres"#

centi is #1/100color(white)()^("th")# so 3 cm #-> 3xx 1/100xx1" metre"#

#color(white)("dddddddddd")#Thus 3% #->3xx1/100xx"Something"#
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#color(white)("dddddddddddd")color(blue)(ul(bar(|color(white)(2/2)"Quick solution "|)#

The wording 'percent of' make the 15000 the basis for comparison. So if we express this as a fraction we have:

#18000/15000#

#(18cancel(000))/(15cancel(000)#

#color(brown)("Shortcut method")#

#color(white)("d")18/15xx100 # and stick a % on the end# ->120%#

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#color(brown)(" Why do we stick a % on the end?")#

Taking a step back we have: #18/15#

Fraction wise we need to change this to #color(white)("d")("something")/100#

Look at the denominator of 15 from #18/15#. If we do this to it #" "15xx100/15# we get 100. What we do to the bottom for multiply or divide we also do to the top.

Now look at the numerator of 18. We do this: #color(green)(" "18xx100/15)# that is the shortcut bit.

However, all of this is over the #color(blue)("final denominator of 100")#. So lets include this giving:

#color(green)(18xx100/15)color(blue)(xx1/100)#

but another way of writing #1/100# is % so we end up with #18/15xx100xx%#

But the same way in algebra we do not write (example) #3xx x# but #3x# then in the same way we do not write the cross for multiply in front of the %

THUS WE HAVE

#(18/15xx100)%-> 120%#

which is another way of saying #120xx1/100#