How important on a scale of 1 to 10 would you say knowing how to do basic percents was? Personally, I cannot think of a more important basic math function than this. Yet most people struggle with the very basics of percent calculations. This should not be the case. My aim in writing Arithmetic Magic was to show people that they can do basic arithmetic, and this once realized would empower them to study math at a higher level and become more interested in this most precious discipline.

Let’s look at what a percent really means. Percent from the Latin literally means “per hundred.” A percent is one part out of a hundred. Ten percent literally means “10 parts out of the hundred,” or “10 parts per hundred.” When we take a percent of a number, we are actually taking a portion of that whole. In other words, when we take 10% of a quantity, we are trying to calculate a portion of that quantity equal to 10 parts out of one hundred. If you read my article “Fractions, Percents, and Decimals,” then you know that these three mathematical entities are one and the same thing: that is a percent is a decimal is a fraction. Consequently 10% is nothing more than 1/10 of the whole.

Now as a decimal, 10% is 0.1. To take 10% of any number we need only shift the decimal point of that number one place to the left. So 10% of 50 is equal to 5. (In a whole number the decimal point is not written but can be found immediately to the right of the last digit. Thus in 50, the invisible decimal point is after the 0, that is 50 can be written as 50. ) Based on this principle, and this principle alone, we have a way of calculating percents very easily.  How you say? Let’s get into this.

We use the following facts: 10% is 1/10 of a number; 1% is 1/100 of a number (a two decimal shift to the left) or 1/10 of 10%; and 5% is half of 10%. To get a percent of a number we use simple combinations of these facts. Watch.

Suppose you want to calculate 20% of 40. Now 20% is twice 10%. So get 10% and multiply by two: thus 10% of 40 is 4 and 20% is 8. Abracadabra. You want 21% of 40. No sweat. 20% is 8 (just done) and 1% is 1/10 of 10% of 40 which is 0.4 (a two decimal shift of the decimal in 40 to the left) Therefore 21% is 8.4. You need 35% of 50. Okay, 10% is 5 and 30% is three times this or 15; 5% is half of 10% or half of 5 or 2.5; put the pieces together and you have 35% of 50 is 15 + 2.5 or 17.5.

To show the sheer beauty of this method, let’s do one more: calculate 28% of 62. We can do this several ways. Let’s break down 28% into 2 x 10% + 8 x 1%. Now 10% of 62 is 6.2, and 20% is double this or 12.4; 1% is 0.62 and 8% is 8 times this or 4.96 (granted this is harder, and you probably need to study my techniques a bit more in-depth to do this. See “Arithmetic Magic” on my website); thus 28% of 62 is 12.4 + 4.96 or 17.36. Nice job!

So you see, working with percents is not difficult at all once you know the tricks. And you should know them since everyone works with percents.  Now you can impress your boss with your new-found math skills.

 

Joe Pagano