Additional Math Pages & Resources

Wednesday, January 4, 2012

Geographical Math, Part II

This blog is focused on using math learned in elementary school to understand the adult world around us.

Yesterday I explained a bit about districts, territories and jurisdictions. These are places and people associated with the United States, but not within the US. This subject was only chosen to provide us with some numbers we can investigate - not because I have any special knowledge about it.
Wake Island
In case my previous blog did not provide enough math for you, here are some numbers that describe a few of the places mentioned yesterday:

Territory Area Sq Miles   Land Sq Miles   Water Sq Miles    Water %
Puerto Rico 5,325 3,425 1,900 35.68
Northern Mariana Islands 1,975 179 1,796 90.93
United States Virgin Islands 737 134 604 81.87
American Samoa 584 77 506 86.75
Guam 571 210 361 63.22
United States Minor Outlying Islands 16 16 N/A 0.00

The data came from Wikipedia.


Here's a simple math question related to the chart:

Which columns are essential, and which are discretionary or can be derived from the other(s)?  How little do we need to know to fully populate this table?

This is what we teach kids to answer for themselves.

In our data there is total area, land and water area, and percentage of water for the first 5 rows. We'll ignore the last row because the minor islands don't claim water area.

If we are given total area, we need either land or water area and then we will know everything:

Total - (what ever number you have) =  (the number you don't have)


(Water square miles) ÷ Total =  (Water %)

Or we can derive the unknown data another way. We can start with total and water percentage to learn everything:

Total ÷ (Water %) = (Water square miles)


Total - (Water square miles) = (Land square miles)

Or we can do it yet another way. We start with total and water percentage but use a different operation to derive the land area percentage and square miles.

Total ÷ (1-Water %) = (Land square miles)


TOTAL - (Land square miles)  = (Water square miles)

Now is when I say,

Isn't math fun?

and you say, 

Get a life, Excelmathmike! 

and I say,

Ok, then. Hiho, Hiho, it's off to an atoll I go...