How do you find the percent change given the original number is 48 and new number is 60?

Goes from #48 -> 60#

So this is an increase of #60-40 = 20#

We express this as a change in relation to the original price. So the change expressed as a fraction of the original price is :

#" "color(green)((+20)/48)#

#color(purple)("Using first principles to explain where the "xx100)#
#color(purple)("in the shortcut method comes from")#

#color(green)(20/48color(red)(xx1)" "=" "20/48color(red)(xx100/100) " "=" "(20color(red)(xx100) )/48color(red)( xx1/100)#

But #1/100# is the same as % giving:

#" "=color(green)((20color(red)(xx100) )/48color(red)( %)#

Writing this as in the shortcut method we have:

#" "=(20/48 xx 100)% = 41.6bar(6)%#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Foot note")#

The bar over the last 6 indicates that the value 6 repeats for ever.

It is really helpful to remember that #0.333bar3" is the same as "1/3#

So #0.666bar6# is the same as #2xx1/3=2/3#

Thus: #41.6bar6 = 41 2/3%#