Episode 71: August 17, 2012
Real World Math
by Jason Marshall
There are tons of practical, real-world applications of math—building skyscrapers, launching satellites, programming video games and movie special effects, and running banks and stock markets. There are also tons of applications of math that aren’t necessarily as practical, but are just as much—if not even more—fun. So today we’re going to focus on this purely fun side of math and talk about a few number tricks that you can use to amaze your friends.
SPONSOR: Get your copy of The Math Dude’s Quick and Dirty Guide to Algebra from Amazon, Barnes & Noble, Powell’s, the iBookstore, or your favorite bookstore!
How to Perform a Number Trick With Years
Start by taking the last two digits from the year in which you were born and then add it to the age you’re going to be at the end of this year. Go ahead and figure out what that number is for you. Again, it’s the last two digits of the year in which you were born plus the age you’ll be at the end of this year. I’m willing to bet that you got an answer of 111, right? How did I know that? Magic? Well, no...it’s not magic. It’s math.
This trick does seem pretty impressive, right? Since I have no idea what year you were born, it means this trick must work for everybody on Earth! Well, actually, it works for everybody who was born in the 20th century. If you were born after the turn of the new millennium and you do this trick, you’ll always get the answer 11 instead of 111. But why?
Number tricks aren’t magic—they’re math!
How the Trick With Years Works
Here’s how it works: Let’s assume you were born in the 1900s. Then you can think of the last two digits of the year in which you were born as the answer to the problem 19xx – 1900 (where 19xx is your birth year). And you can think of the age you’re going to be at the end of this year (which is 2011) as the answer to the problem 2011 – 19xx. Now, you’ll recall that the instructions were to add the last two digits of your birth year, which we’ve seen can be written 19xx – 1900, to the age you’ll be at the end of this year, 2011 – 19xx.
And that’s just 19xx – 1900 + 2011 – 19xx.
Do you see what happened there? We can make it a bit clearer by using the commutative and associative properties of addition (and the fact that subtracting a number is the same as adding its negative) to rearrange the problem to read:
19xx – 19xx + 2011 – 1900
Now do you see what’s happening? The year of your birth—the only thing in the problem that changes from person to person—actually cancels out in the arithmetic: 19xx – 19xx = 0. So when we add the two pieces of the puzzle together (the last two digits of your birth year and the age you’ll be at the end of this year) we end up with 2011 – 1900…which is always equal to 111—no matter what year of the 1900s you were born.
Once you break it down, it’s clear this trick isn’t magic. But now that you know how it works, feel free to pretend that it is and use it to amaze your friends.
How To Guess Your Friend’s Number
Here’s another trick for you to try. First, think of a number between 1 and 10. Now, double that number and then add 10 to the result. Next, divide this new number by 2. Still with me? If you are, subtract your original number from the new result. If you do that, I’m willing to bet that the answer you got is 5. And I’m also willing to bet that if you didn’t get 5, then you made a mistake—because the answer has to be 5…no matter what number you started with. How do I know this? Well, I’m going to let you mull that over and then we’ll talk about it in the next article.
Number of the Week
Before we finish up today, it’s time for this week’s featured number selected from the various numbers of the day posted to the Math Dude’s Facebook page. This week’s number helps answer the age-old question: How much longer is this car ride going to take? The trick is to use the fact that 60 miles per hour is equal to 1 mile per minute, which means that a car traveling at 60 miles per hour (which is in the ballpark of speed limits on typical US highways) covers about 1 mile every minute. You can use this to quickly figure out that if you have 180 miles left in your trip, then you still have about 180 minutes—or 3 hours—left to drive. Hope you brought a snack.
Solutions to Practice Questions
Since the union of multiple sets is the new set containing all the unique elements from all the sets, and since the set of integers is a subset of the set of rational numbers (meaning the rational numbers include all the integers), the union of the sets of rational numbers and integers must just be the set of rational numbers.
How about the second question: What’s the intersection of the set of rational numbers and the set of integers?
This time, since the intersection of several sets is the new set containing just the elements the sets have in common, the intersection of the sets of rational numbers and integers must be the set of integers…since those are the only numbers that are in both sets. Make sense? If not, take another look back at the last few articles and see if that helps. And if you still have questions, feel free to ask me on Twitter, Facebook, or by email.
Math Dude Algebra Book!
As I’m sure you know, algebra is hard for a lot of people. In fact, a lot of people aren’t even sure what algebra is! But things don’t have to be that way. In this book, I invite you to check your confusion at the door and enter a new world in which math—and algebra, in particular—actually makes sense. Using detailed explanations, lots of brain teaser puzzles, and even secret-agent “math-libs,” I’ll take you step-by-step through learning and truly understanding the most important parts of algebra so that you can get rid of that “I have no idea what any of this means” feeling forever. In other words, you’re just one step away from finally making sense of it all. So do yourself a favor and pick up a copy of The Math Dude’s Quick and Dirty Guide to Algebra. Thanks!
Okay, that’s all for today. Remember to become a fan of the Math Dude on Facebook where you’ll find a new number of the day and math puzzle posted each and every weekday. And if you’re on Twitter, please follow me there too. Finally, if you have math questions, feel free to send them my way via Facebook, Twitter, or by email at email@example.com.