Reduction requires subtraction so the percentage is negative as well
#("change")/("original value")-> ("2nd number - 1st number")/("original value") = (-15)/60#
#color(blue)("Shortcut method")#
Most people would show this as: #color(purple)(-15/60xx100% = -25%)#
This can hide from people what is actually happening
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#color(blue)("First principle method with full explanation - so it is long")#
Starting point: you need to end up with: #("some number")/100#
Very important point: the symbol % is like a unit of measurement that is worth #1/100#
So: #("some number")/100 -> "some number "xx1/100#
But #1/100# is the same as % so we have:
#("some number")/100 -> "some number "xx%#
which is the same as: #"some number"%#
#color(brown)("The calculations")#
To change the denominator of 60 into 100 multiply by #100/60#
#color(green)(-15/60color(red)(xx1)" "=" "-15/60color(red)(xx(color(white)(.)100/60color(white)(.))/(100/60))" "=" "-26/100)#
Notice that the numerator of #color(green)(15)color(red)(xx100/60) ->15/60xx100# Which is exactly the same as in the shortcut method.
but #color(green)(-26/100)# is the same as #" "color(green)(-26xx1/100)#
but #1/100 -> %# giving:
#-26%# as in the shortcut method
