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Tricks to work out percentages without using a calculator

Steve

If you find yourself needing to do a bit of "mental maths" where percentages are concerned, then keep reading for a few tips on calculating these sorts of things in your head!



miniature statue of "the thinker"
This could be you


Calculating 10% of anything


10% of something is really easy to do in your head - all you do is move the decimal point one spot to the left! For example:


To calculate 10% of 35.2, just shift the decimal point one spot to the left and you get 3.52

What if you wanted to calculate 10% of a whole number like 25? There's no decimal point, right? The decimal point for whole numbers is there, it is just not written for convenience. So, in this case, think of it like "25.", in which case it's as easy as above - shift one spot to the left and you get "2.5"


Why does this work? Well it's a special case of a broader trick with numbers. Multiplying by 10, shifts the decimal point one spot the right, and dividing by 10 shifts it one spot to the left. Because 10% is the same as 0.1 which is the same as the fraction 1/10, calculating 10% is the same as multiplying by 1/10 which is the same as dividing by 10. So, you shift one spot to the left.


Calculating 20/30/40% etc. of anything


This is a really simple one which builds on the one above.


Here's the trick - 20% is just double 10%. So, to calculate 20% of something, you just need to calculate 10% of it, and then double whatever that is! So for example:


To calculate 20% of 23.4, first calculate 10% of 23.4, which is 2.34, then double that to get 4.68.

The logic is of course exactly the same for 30%, 40%, etc. To be clear, calculating 30% of something amounts to calculating 10% and then tripling whatever that is.


How easy this actually is to do in your head will depend on how tricky the number is to double, triple, etc. For example, I personally find doubling numbers like "4.98" to be a bit of a pain.


Calculating 50% of anything


This one is easy, depending on the number in question, because 50% is just half! So simply halve the number. For example,


To calculate 50% of 25, divide it in half, giving you 12.5

Switching the order - x% of y is y% of x


This is a lovely trick that can be used to your advantage only in certain situations (so keep your eyes peeled for this one).


It is a mathematical fact that x% of y = y% of x. This means that if you can switch the order of the percentage you need to find, you might be able to do it very quickly! For example:


14% of 50 (which is not immediately obvious) is equal to 50% of 14. That one is easy, it's just 7

Like I said, this is one you need to be on the lookout for because it doesn't always make things easier. By way of example, 23% of 24 is difficult no matter which way round you look at it! In that case, I would just use a calculator.




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