11. Percentages: 50% More Fun!

You can have 50% of the fun…or 50% more fun…or half as much fun…or even half-again as much fun. Are these all the same?  They all use 50% or the word "half", but the slight addition of a few different english words changes the meaning drastically.   

Half or 50% of the Fun is giving you 50% of the total - hence you are enjoying this post only half as much as you could.

However, 50% more Fun or Half again as much Fun are providing words that imply adding more to the total.  In this case, you are giggling all of what I would expect, plus another 50% to make a total of 150% total giggling.

In a previous post on Rates, I wrote that Percentages always add up to 100%.  Well, I must have been smokin’ something.  Of course you can have a Percentage more than 100%.  By simply reading this post, you are having 50% more, or 150% of the Fun compared to other people who are having only 100% of the fun reading some other lame math post.   

Let’s try another example of percentages greater than 100%.  You want to borrow $100 from me..and you agree to pay me back the $100 by the end of the week plus an additional 20% interest (I have a friend Guido who will make sure you do).  I stand to realize 120% gain on my investment:  100% being the total amount I loaned to you paid back plus an extra interest of 20%.   

When word problems use standard percentages like 30% or 25%, it is assumed that they are using 100% as the total.  It is the whole pie.  100%.  You cannot have more than the whole pie...unless of course they add more pie to the problem.  My $100 I loaned to you was the 100%.  When I asked for an additional 20% interest, I just added more pie.

Often, word problems will tell us the total amount (the 100%) and ask you to solve for a missing percentage.  For example, there are 30 children in the classroom (Whoa - see what happened there??  It just defined the total...the 100%), and there are 20% boys.  What is the percentage of girls in the class?  In this case, they must add up to 100%.  Obviously the percentage of Girls in the class is 80% (100% - 20% = 80%).  

One last fun point on Percentages.  Common Core may require the ability to describe percentages in a variety of forms.  The tests may provide one form, and ask to define the other forms: 

Percent Fraction:  It is the percent, but instead of showing the “%” sign, we show the number divided by 100.

Percent:  It is the same number as used in the Percent Fraction above except followed by the “%” sign instead of dividing by 100.  Think of the “%” sign meaning “divided by zero”.

Fraction:  One number over another number usually defined in its lowest possible form (i.e. write 1/4 instead of 2/8).  This fraction would be the same as Percent if you were to divide the top number by the bottom number.  For example:  1/4 is the same as 0.25 if you divided the number 1 by the number 4.  

Decimal:  The Decimal number is the same as the Percent Fraction number if you divided the top number by 100.  For example, 0.25 is the same as 25/100.

Below is a table showing some examples of the various forms.

Boy-oh-boy could we have more fun with Percentages?  I think not!  Maybe I should have labeled this Post as 75% more fun.