If 39 is 1% of a number, what is that number?

If you think of it logically, this problem is saying:
#x*1% = 39#
#1%# is #1/100# so it's
#x*1/100 = 39#
Divide both sides by #1/100# and you get
#x=39/(1/100)#
Remember that when there is a fraction in the denominator we flip it and multiply that on top and bottom:
# x = (39*100)/((1/100)*100) #
Therefore
#x = 3900#

You can check this by multiplying our answer by #1%#
#3900*.01 = 39#

#color(blue)("Method 1: ratio")#

Note that #color(magenta)("100% is all of it")#. So we have:

#color(white)("d")#

#color(purple)("Initial ratio")#
#color(white)(".dd")color(purple)(darr)#
#obrace(" 39 : 1%") ->ubrace(100(39 : 1%))color(white)("d")= color(white)("d")3900:"color(magenta)(100%) #
#color(white)("dddddddddddddd")color(purple)(uarr)#
#color(purple)("Multiply everything inside the brackets by 100")#

#color(white)("d")#

So # "39 is 1% of 3900"#

#color(purple)("Alternative ratio format in fractional form:")#

#(1%)/39xx100/100 = (100%)/3900#

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

#color(blue)("Method 2: algebraic manipulation")#

Set the unknown value as #x#

Known that 1% is the same as #1/100#

Then #1/100xx x =39#

Multiply both sides by #color(red)(100/1)#

#color(green)(1/100xx x = 39 color(white)("ddd")-> color(white)("ddd")1/cancel(100)^1 color(red)(xx cancel(100)^1/1)xx x =39 xx color(red)(100/1)#

#color(white)("dddddddddddddd")->color(white)("dddddddddddddddddd")x = 3900#