4 More FAQs About Percentages

How do you quickly calculate 25% of a number? Or 33% of a number? Or 50%? And how can you quickly calculate percentage increases? Keep on reading to learn the answers to these frequently asked questions about percentages.

Jason Marshall, PhD,
January 6, 2017
Episode #297

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FAQWe here at the Math Dude ranch get numerous questions every week from math fans around the world. By far the most common questions we receive have to do with calculating percentages. In particular, how to quickly calculate percentages in your head. You know, things like: What’s 25% of $14,000? Or what’s the final price after a 33% discount on a $25 item? Or what’s the percentage increase from 30 to 40?

It’s not hugely surprising that this is such a popular line of questions since people in lots of different industries love to express changes in terms of percentages. So today we’re going to take a look at four of the most frequently asked questions about percentages.

Holiday Puzzle Solution

But before we dive into percentages, I want to fill you in on the solution to the puzzle I posed last time. Actually, it’s the puzzle tweeted by psychologist, magician, and guest of the show Richard Wiseman. In case you’ve forgotten, here’s how it works. First, grab a calculator. Then do the following:

  • Type your house number (i.e., your address) into a calculator.
  • Now double it.
  • Next add 5 to the result.
  • Then multiply this answer by 50.
  • Now add your age.
  • And then add 365 to the result.
  • Finally, subtract 615 from the whole thing.

What do you get? If you did it right, you should see your house number and age (so long as you’re under 100 years old). Why? It’s actually fairly simple to understand with a bit of algebraic thinking. To begin, let’s call your house number “A” and your age “B”. If you follow the steps in Richard's tweet, you’ll see that the whole sequence of actions is equivalent to the algebraic expression:

(((((2 x A) + 5) x 50) + B) + 365) - 615

Which is quite a mess! How does it help us make sense of the trick? Well, if we simplify the expression a bit, we see that we can combine and arrange the terms to turn it into the equivalent expression:

((2A + 5) x 50) + B - 250

Admittedly, this isn’t much better, but if we simplify this even more we find that we can multiply and then combine terms to arrive at a much simpler equivalent expression:

100A + B

And now we’re getting somewhere. Because this expression tells us that all you're really doing is multiplying your address by 100 (which has the effect of padding the end of it with a pair of zeros) and then adding your age (which has the effect of sticking it on the end). Once you know this, you can see that all of the complicated actions were simply a distraction to keep you from noticing the simple thing happening when you weren’t looking. In other words, it's a magic trick.


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