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

Question

Nathan Axel · Accepted Answer

#-26%#

Since reduction necessitates subtraction, the percentage is also negative.

#("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 has the potential to conceal from the public what is truly going on.

#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

Eva Adamson · Answer

undefined To find the percent change, subtract the original number from the new number, then divide the result by the original number. Finally, multiply by 100 to get the percentage.

Percent Change = ((New Number - Original Number) / Original Number) * 100

In this case:

Percent Change = ((45 - 60) / 60) * 100

Percent Change = (-15 / 60) * 100

Percent Change = -0.25 * 100

Percent Change = -25%

The percent change is -25%.