Working out percentages - a basic guide, including some simple shortcuts

Part of a series of hubs aimed at demystifying tricky topics in everyday mathematics

Imagine that you and some friends go out for a meal in a restaurant. The conversation's great and the food is fantastic. Then at the end of the meal comes the waiter bearing your bill. Of course you're going to give a tip, because you've had such a great evening. Ten, twelve or fifteen percent would be a suitable amount depending on custom in your country, but you and your friends realise that you just don't have a clue how you'd go about working out these percentages. You're not alone - many people who dislike maths include percentages as one of the topics they find difficult. The following guide aims to demystify the subject of percentages and show you some shortcuts for calculating the more "common" percentages.

Credit: http://www.patric-chocolate.com/store/images/percentage.gif

What is a percentage?

The term "percent" comes from Latin and means "per hundred". So 50 percent (or 50% to write it the short way) is "50 parts per hundred". You could also write it as a fraction, i.e.

50
100

This can be cancelled down to

5
10

and even further, to

1
2

In other words, 50% of something is the same as half of something. And if you want to work out half of something, you just divide it by 2!


Percentage	Fraction	Cancels down to	Divide by
10%	10/100	1/10	10
20%	20/100	2/10, and hence to 1/5	5
25%	25/100	5/20, and hence to 1/4	4

In the same way, several other percentages can be converted to fractions and then cancelled down: 10%, 20% and 25%. The table on the right shows you how.

So if you want to work out 10% of £75.00 you just divide by 10 to get £7.50.

In case you weren't aware, a quick way to divide any sum of money by ten is to move the decimal point one place to the left. So, to use a slightly more complicated example, 10% of £28.50 comes to £2.85 (you just lose that zero at the end, like you did with the £75.00).

If there are no zeros at the end, you'll need to use your judgement about whether to round up or down. So if you're working out 10% of £34.21, the first stage of the calculation gives £3.421. Obviously you can't just leave the 1 there - you have to decide whether to round up or down. In this case, you round down (because the 1 represents a tenth of a penny, which is much nearer to zero than it is to a penny). This gives you £3.42.

Similarly if you've got 2, 3 or 4 as your last digit, then you also round down. If you've got 5, 6, 7, 8 or 9, then you round up. So 10% of £452.67 will initially come to £45.267 which rounds up to £45.27.

Now you know how to work out 10% of something, you can use this technique to work out 20%, 30%, 40% and other multiples of 10.

So to work out 70% of £25.30:

Work out 10%, which is £2.53.
Then multiply by 7, to get £17.71

And if you know how to work out 50% and 25% of something, then you can work out 75%, by adding the two together.

The table below summarises what we've just discussed, with a couple of extras thrown in for good measure:

Percentage	How to calculate it
1%	Divide by 100
5%	Divide by 20, or find 10% and halve the result
10%	Divide by 10
20%	Divide by 5, or find 10% and double it
25%	Divide by 4
30%	Divide by ten, then multiply by 3
50%	Divide by 2
75%	Divide by 4 and multiply by 3, or find 50% and 25%, and add the two together
15%	Find 10% and 5%, then add them
17.5%	Find 10%. Divide by 2 to find 5%. Divide by 2 again to find 2.5%. Then add the three answers together

What about all the others?

What about all the "fiddly" percentages: 28%, 46%, 79% and so on?

One option for doing these is to work out 1%, then multiply.

To work out 1% of a sum of money, you move the decimal point two places to the left. So 1% of £280.00 is £2.80 (after you've "lost" any zeros you don't need). If there are no zeros to lose, you employ the rounding method given above. So 1% of £362.94 comes to £3.6294 initially, which rounds up to £3.63 (use the 9 to decide whether to round up or down; it's much more important than the 4!)

Once you've calculated 1%, you can then multiply by 28, 46, 79 or whatever.

If you're at all comfortable with fractions, then you can lay such calculations out in fraction form. So, to work out 28% of 280, you lay it out like this:

28 x 280
100 1

You can cancel the numbers in pairs (provided one is a numerator and one is a denominator)

So in this case you get

28 x 28 = 784 = £78.40
10 1 10

In my examples, I've stuck to money because that's what most people deal with in their everyday lives. But if you're working out non-monetary percentages, you can use the same principles - you may even find it easier, because you won't necessarily have to worry about rounding to two decimal places!

Hope this guide has helped to clarify the subject. If anyone out there is interested in having other numerical topics explained in hub form, I'm open to suggestions!