One day, 32 of 80 people wore a red shirt to school. What percent of the 80 people did not wear a red shirt to school?

Let me start with finding number of people who wore other colored shirt:

#=80-32 = 48#

Therefore, 48 out of 80 people wore other colored shirt.

As percentage this is:

#=100times48/80 = 60# percent

Your answer is 60%.

Percentage is basically just another fraction. Although, it is a special fraction in that the bottom number (denominator) is fixed at 100.

If the count of red shirts is 32 then the non red shirt count is
#80-32 = 48#

So this count as a fraction of the whole is #48/80#

But for this to be a percentage we need the bottom number (denominator) to be 100. So we write as an 'equivalent fraction'.

Let the unknown count be #x# giving:

#color(green)(48/80-=x/100) #

To find the value of the top number (numerator) of #x# we need to get it on its own. So we need to 'get rid' of the 100. We do this by changing it into 1

Multiply both sides by color(red)(100)

#color(green)(48/80-=x/100 color(white)("dddd")->color(white)("dddd") 48/80color(red)(xx100) color(white)("d") =color(white)("d") x/100color(red)(xx100) )#

#color(green)(color(white)("ddddddddddd.d") ->color(white)("dddd") 48color(red)(xxcancel(100)^(10)/color(green)(cancel(80)^8)) color(white)("d") =color(white)("d") xcolor(red)(xxcancel(100)/color(green)(cancel(100))) )#

#color(green)(color(white)("ddddddddddd.d") ->color(white)("ddddddd") cancel(48)^6xx10/cancel(8)^1 color(white)("d") =color(white)("d") x)#

#color(green)(color(white)("ddddddddddd.d") ->color(white)("ddddddddddd") 60color(white)("dddd") =color(white)("d") x)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#x=60 ->x/100=60/100#

#60/100# is the same thing as #60xx1/100# and #xx1/100# is the same thing as #%#

So #60/100=60%#