Let’s take a break this week.  Let’s go a little lighter, have some fun, and perhaps save or even make you some money in the process.  And all with math, no less! 
I’m aware that many of us have an aversion to anything that can be remotely be labeled as ‘mathematical’.  Nonetheless there are times when knowing or remembering some basic math skills can prevent confusion.  Of many such examples, let’s take a quick look at just three.  

1. Caveat Emptor!

Here’s a tip that might save you money or at least some misery.  Have you ever noticed that carpet is often priced by the square foot, rather than the square yard?  This is partly because it sounds cheaper that way, and not just for obvious reasons.  Because, while there are indeed three (linear) feet in a (linear) yard, there are NINE square feet in a square yard!  (Think of a 3 x 3 block, which would have nine smaller squares inside.)  So, if the carpet is priced at $2/square foot, that translates to $18/square yard, not $6, as one might be hastily tempted to think.  The store wouldn’t mind if you think it’s only $6, of course, but you will know better!

2. Percentages of Increase and Decrease.

This is an often-misunderstood area.  Percents of increase/decrease are measured by comparing the amount of the change with the original amount.  It’s that ‘original amount’ that often catches folks, if they are not careful.  Let’s suppose you buy a stock for $50 and end up selling it for $75.  The ‘change in amount’ is $25, and the ‘original amount’ is $50, so the percent of increase is 25/50, or 50%.  Nice: a 50% profit!

Now, suppose the opposite happened.  Suppose you bought that same stock when it was $75 and then sold it at $50.  The ‘amount of the change’ is still $25, of course, but now the ‘original amount’ is $75, so the percent decrease is 25/75, or 1/3, which is a 33 1/3 % decrease! (Indeed, a 50% profit, followed by a 50% loss never returns you to the starting point.  That’s NOT a break-even situation.)

It can sound tricky, and in case of stockbrokers, these percentages could be used to mislead you. But, if you just keep your terms straight, you’ll not be fooled.

3. Great Bar Bet!

Here’s a fascinating and counter-intuitive math fact that can win bets for you.  Suppose you are in a room with at least 25 people in it.  Did you know that the probability of having duplicate birthdays (month/day only) in the room is better than 50-50?   It doesn’t quite sound logical, but it’s true, and the math verifies it.    If you bet someone to that effect, you won’t always win, of course, but you’ll win more often than you lose.

Before you rush off to start raking in the money, remember:  A) Make sure there are at least 25 in the room.  B) Note that we said ‘duplicate birthdays’ without specifying a date.  You cannot just pick a specific date ahead of time and expect two birthdays to match.  Nor expect someone else with your birthday to appear. You can only expect duplicates somewhere.  Make sense?

I hope you have enjoyed today’s diversions, brought to you by mathematics.  There are many more where those came from – ask your local math expert to get in on the fun and the savings!