Percents, as viewed as a PROPORTION

There are three basic kinds questions we need to answer when it comes to percents;

•  What number is 40% of 24?
•  28 is what percent of 50?
•  15 is 24 percent of what number?   

I recall my son coming home, and being perplexed by these problems.   I ask him,
"If there were a way that you could solve all of these problems with one idea,
would you want to know about it?"As usual he said, "yes dad".  

So I asked him what he knew about a percent, and he told me that it was part
of 100.  I told him that is half of the story.  A number written as a fraction with a
denominator of 100,  we can then say that its NUMERATOR  is a percent.

                                          43/100 = 43%

                                 27/100 = 27%

Now what if I ask about a fraction say ¾.  I said to my son, this is the second part of the story.  

                     3 is what PERCENT of 4?    

                   Therefore,   3/4  =  %/100  or  is/of = percent/100


    Remember we are solving for the NUMBER in the % position.  This is just
    like changing a fraction to a common denominator.  Divide 4 into 100, we
    get 25.  Now we multiply 25 times 3, and we get 75.

                                  Thus ¾ = 75/100  or 75%.

                    3 is 75 PERCENT of 4.
  
 In the previous problem 4 went into 100 evenly, but that will not always occur.  But do not 
 worry.  There is another way to solve for the percent.
      
            3 is what PERCENT of 8?   
                                  
                                  3/8 = %/100

        RETURN TO THE BASIC LAW OF PROPORTIONS

                            8 x % = 3 x 100

                                 % =  300 ÷ 8

                                % = 37.5

                      3 is 37.5% of 8.



   Next, to figure out a Percent of another number, we are wanting a piece of it.
   That piece relates to the the number 100.   That is 30% means 30/100 of an
   amount or .30 of that amount.  Given the following problem, we have two choices.

                     What number is 45% of 20?  

   Choice 1: 45% = 45/100 = .45  Now I can Multiply 20 x .45 = 9

   Choice 2: Rely on my Proportion.    ?/20 = 45/100

       Here we learn another powerful solution method of proportions.  Our "?" is the
       unknown amount.  And as we did above, 20 goes into 100, 5 times.

                                              ?/1 = 45/5 is left

                         But 5 goes into 45, 9 times.  Thus our ? = 9

                                                9 is 45% of 20.

                 

   Now for our last part.  What if the money in your pocket is 15% of your total
   wealth.  What is your total wealth?  If it were me, not much.  To start with we
   need to know what is in your pocket.  Lets say it is $10.00.  So what do we
   already understand.
                                                      
                      15% = 15/100        You have $10.
            
                         10/x  =  15/100     $10.00 "is"    from   "is/of  =  %/100"
           Look at the numbers.  None go in evenly as we go around , but we can
           reduce a fraction.

                              15/100 = 3/20
              
                         Thus 10/x = 3/20
              
                            then 3x = 200


                                      x  = 66⅔


                        $ 66.67 is your total wealth?

    With a single formula we can solve all three types of Percent problems.  Our 100
     is always under the percent and the is, is always over the of.


                            is ÷ of  =  % ÷ 100