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How to quickly calculate percentages in mind

Posted on 2011-02-26
Medium Priority
Last Modified: 2012-08-14

How can we quickly calculate percentages in mind without using much of a calculator. Are there any short cut methods to quick results so that i can appear to be a clever guy


Question by:Prithvi1976
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LVL 37

Expert Comment

ID: 34989194
10% is easy. Just move the decimal point over one place to the right.
10% of 3452 is 345.2
LVL 22

Expert Comment

ID: 34989196
There are "tricks", but they involve specific percentages.  There is no general "trick" other than to do the basic math.

If you can be more specific about what you are trying to calculate, it would be helpful.

Keep in mind that if you are trying to reduce something by, say, 30%, you can do it the long way (calculate the 30% and then subtract it from the original amount) or the short way (multiply the original amount by .7).  Does that help?
LVL 37

Expert Comment

ID: 34989198
For others, you could find 1% and multiply (7% of 400 is 4*7 or 28)
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Accepted Solution

sshah254 earned 80 total points
ID: 34989200
Quickest way is to get to 1%, 10%, 25% and 50%.

50% is half, 25% is quarter, 10% is one tenth, 1% is one hundredth.

All the other numbers can then be calculated by adding / subtracting these.

Fairly simple.

And - practice, practice, practice.

Above all, a simple math trick isn't going to make you appear "clever".  You should "be" clever ... not "appear" clever.

LVL 37

Expert Comment

by:Neil Russell
ID: 34989271
No good any more cause they put VAT up to 20% but an example of mental maths and percentages is as follows....

VAT WAS 17.5%

so vat on 150 is 150/100*17.5  Not too easy in your head until you realise that 17.5 is just 3 simple divisions

10% of 150 is 75% thats easy.
Now as it happens, half of 10 is 5 and half of 5 is 2.5...
Add those up and you have 10+5+2.5  = 17.5

So if 10% is 75 half of that is 37.5 thats 5%
And half of 37.5 is 18.75 and thats 2.5%

Add them up, 75+37.5 +18.75 = 131.25
LVL 37

Expert Comment

ID: 34989285
Basically, for some you need to be clever to figure out how to figure it out.
So you have to be clever to appear clever. But if you are a little clever and spend some time studying you can appear very clevver.
LVL 17
ID: 34989699
I've always use a rather unusual method for finding percentage amounts. I worked it out for myself when I was quite young and it worked so it stuck.

It's based on ratios.

For instance if you want 8% of 50, you can quickly see that 50 goes twice into 100 so double the 8 and the answer is 16.

or for 15% of 300, 100 goes three times into 300 so you multiply the 15 by 3 to get the answer 45.

Makes my brain itch if I try to understand why these two finish by leaving a multiple each time, but it works.

LVL 17
ID: 34989720
Its late, Im tired, thats ^ wrong!

8% of 50 is 4, for the  same reason as the second example.

50 is half of 100, so half the percent figure to get the result.

LVL 37

Expert Comment

ID: 34990022
Makes my brain itch if I try to understand why these two finish by leaving a multiple each time, but it works.

.08*50 = .08*50*(1) = .08*50*(2/2) = .08*(50*2)/2 = (.08*100)/2

.15*300 = .15*300*(1) = .15*300*(3/3) = .15*(300/3)*3 = (.15*100)*3

Maybe that'll help with the itch.
LVL 22

Expert Comment

ID: 34990192
Though your method works, the math behind it is probably not apparent to one trying to use it.  The reason I argue against such approaches is that there's nothing to keep you from remembering the trick incorrectly.

I would modify your logic a bit for the same results.  For example, when doing 8% of 50, you note two things: 8% of 100 is 8 and 8% of 50 should be half of 8% of 100.  Therefore, 8% of 50 is 4.

The difference may seem trivial, but I think it illustrates the math better and is therefore less likely to be applied incorrectly.
LVL 17
ID: 34991272
>there's nothing to keep you from remembering the trick incorrectly.

I think I proved that:7)

The problem was with trying to explain it, Normally I just 'do the sum' without working out how.

A better explanation would have been:
manipulate the whole number to get it to 100, then perform the same steps on the percent value to get the answer.

The idea is not to have to run through the mathematical proof every time, but to get a quick solution.

LVL 37

Expert Comment

ID: 34991880
It's mathematically sound, you just have to have the common sense to think about the number you came up with and 'know' by inspection if it's right.
If you are finding 8% of 50 and get 16 you should instantly notice that 16 is > 20% or 10% of 50 and start over. This applies to any method. Check your answer and make sure it makes sense.

As a side note, this also applies to any problem. If you calculate that little Johnny's bike is going 3943 mph, you probably made an errror. Your textbook usually isn't trying to trick you. I've seen so many ridiculous answers on tests with no apparent attempts to retry the problem.

Author Comment

ID: 35048071
Thank you all very much for your tips. Some I am already aware of them and rest very new to me.
I think practice makes calculations very easy


Expert Comment

ID: 35457722
Very easy way for this is:
Calculate 1% of a given number by putting decimal 2 digit before from the right side
then multiply the above result with given number for percentage.
Note: the faster calculation time depends on your multiplication skill...

7% of 4876
Step1: 48.76
Step2: 48.76 * 7 = 341.32
LVL 17
ID: 35458641
I think I would expand step 2  bit if I was doing that sum in my head.

48.76 is 1.24 less than 50

7  times 50 is 350

we need to take off 7 x 1.24

1.24 is .01 less than 1.25

7 x 1.25 is 6 x 1.25 = 7.5 and add the extra 1.25 on to get 8.75.

We need .07 less than this so it's 8.68 which is the number we need to subact from the 350.
Take off 9 (341) and add the  difference between 8.68 and 9 (.32) to get the final answer of 341.32.

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