How do you find the percent change given the original number is 60 and new number is 45?

1 Answer
Feb 19, 2017

Answer:

#-26%#

Explanation:

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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#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