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# How to Amaze Your Friends With Number Tricks Easy number tricks to impress your friends.

By
Jason Marshall, PhD
Episode #71

## 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

At the end of What Are Real Numbers? we asked the question: What’s the union of the set of rational numbers and the set of integers?

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.

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