Mentally Calculate Percentages of Large Numbers Quickly without using a calculator

The Infosplit Method

Lesson: Mentally Calculate Percentages of Large Numbers Quickly without using a calculator

Take the following large number:

$145,000

First chop it down

Percentages that end in 0 are simple to calculate mentally:

10% of $145,000 = $14,500

To take 10% We simply dropped a zero.

20% of $145,000 = a bit more thinking. Large percentages are easy to understand as smaller numbers.

Check out this pattern

(it should take you two seconds to make these mental assumptions)
10% = 10 (remove a zero from the end of the number or simply divide by 10)
20% = 5 (100% broken up 5 times creates pieces of 20%)
25% = 4 (100% broken up 4 times creates four pieces of 25%)
30% = 3/10 (divide by 10 and multiply by 3)
40% = 4/10 (divide by 10 and multiply by 4)
50% = 2 (divide by 2 or divide by 10 and multiply by 5)

To understand the above patterns, simply draw some squares on a piece of paper and section them into smaller pieces. These should come to you intuitively if you can visualize the operation.

Lets return to 20% of $145,000.

First, using our understanding that 20% means we are taking one fifth, we note:

145/5 and add three zeros.

Now 145 itself is a bit big, so will chunk this down to third grade math.

145 = 100 + 45.
100/5 = 20. (if you cant do this mentally you might need some help..)
45/5 = 9. (you should have memorized this in grade school..)
20 + 9 = 29.. and VOILA!

20% of 145,000 = 145/5 = 100/5 + 45/5 = 29 and three zeros! $29,000.

Easy when you break it down eh?

Complex Percentages

Some percentages are a bit more complex. For example:

14% of $94,500.

At first this might seem intimidating. Lets break down the percentage first.

14% = 10% + 4%. 4% = 1% + 1% + 1% + 1%. (You’ll see why in a moment).

Now we easily know 10% of $94,500 is $9,450 (we simply removed a zero).

4% is harder to calculate mentally, but we know that 4% is also 1% four times..

In this case, 1% ten times = $9,450 so we know 1% is 945. To get 4%, we simply do 945*4.

(split it up) 945*4 = 900*4 + 45*4.
900*4 = 9*4 (plus two zeros) = 3600.
45*4 = 40*4 + 5*4.
40*4 = 160.
5*4 = 20.
3600 + 160 + 20 = 3780.

So we know 4% = 3780. 9450 + 3780 = 9000 + 3000 + 400 + 700 + 50 + 50 + 30 (split 80 into 50+30).
9 + 3 = 12 (three zeros)
4 + 7 = 11 (one place over)
50 + 50 + 30 = 130 (two places over)
So we have 12000 + 1100 + 100 + 30 = 13230.

So 14% of $94,500 = $13,230. Another one of simply looking at this is 945*10 + 945*4.

The above example was a bit verbose to explain the steps your thoughts should take.

Lets try another one to show the mental math at work.

Mental Magic

Read through this one, then try it in your head. You might be surprised how easy it is.

27% of $132,000

132*10 + 132*10 + 132*7.
1320 + 1320 = 2640. (this shouldnt be too bad to keep in your head while you do the next one)
132*7 = 100*7 + 30*7 + 2*7. 700 + 210 + 14. 910 + 14 = 924.
2640 + 400 + 500 + 24 = 3040 + 400 + 24 = 3540 + 24 = 3564.

Add one zero and.. VOILA! $34,640. So 27% of 132,000 = 35,640.

What if the last two digits don’t end in zero?

We make it end in zero. How? Very easily.

More Complex Numbers

Take this number for example (made this one a bit smaller in case you are not used to big numbers):

83% of $47,139

Ugly eh? This one is more of a toughy and will be split four times. However.. commit 139 to memory and now you have 47,000.

83% can be broken a few different ways. You will likely learn towards one way or another. The more you practice, the less you need to break it down.

50% + 20% + 10% + 3%.
50% of 47 = 23.5
20% of 47 = 47/5 = 45/5 + 2/5 = 9.4 (remainder 2 on division by 5 is always .4)
10% of 47 = 4.7
3% of 47 = .47*3 = .4*3 = 1.2 + .07 * 3 = 1.2 + .21 = 1.41

Add it all up. 23.5 + 9.4 + 4.7 + 1.41 = 39.01.

Now readd the three zeros. 39,010. WAIT! Not done yet.. Remember 139?

83% of 139. Split it through 50/20/10/3 again.
69.5+26.5 = 70.5 + 27.5 – 1 + .3 = 96 + 1.3 + 13.9 = 109.9 + 1.3 + 1.39*3 = 110 – 0.1 + 4.17 + 1.3 = 114.07 + 1.3 = 115.37

39,010 + 115.37 = 39,125.37. Whew. Your brain might hurt after doing that in your head! And that took much longer than it would have on calculator!

You might be saying at this point.. Why place upon yourself such brutal mental torture?

If you’re a gym and exercise type of person, you already know the answer.. if you’re not this type of person.. then you should be! Eating fast food everyday and letting your PC do all your work is holding back your potential as a human being!

Also remember, for many practical purposes, if you’re trying to get a general estimate on something, obtaining a rounded percentage of 47,000 is very quick and easy.

A trick you will learn as you practice is deciding the shortest route to get the numbers you need.

The get 39,010 took me 14 mental very quick steps as written out above. If I wanted I could also figure 1% of 47,000 is 4.7. 4.7*83 = 83*4 + 83*.7 = 332 + 58.1 = 390.1. This is only 7 mental steps compared to 14.

You will notice as you practice more that an operation like 83*4 and 83*.7 will become mentally instantaneous since you have essentially memorized it, reducing the number of steps to three and solving it in about 3 seconds.

Who’s faster?

You might be saying to yourself at this point that either way the calculator will always be faster.. Not true!

Society has taught us to be dependent on machines for many tasks.. this makes you lazy! With some practice, and 15 minutes a day for a few weeks, you can retrain your brain to compute these operations faster than any PC.

Think about how much time you would save every day multiplied across your life if you could manage your finances or purchases without a calculator?

How to computer faster than your PC:

- Write down 10 simple examples ending in zeros and try to do them in your head. Keep the number sizes within the same place size, one hundred thousands etc or start with thousands and move up from there.

- Complexity is not necessarily the size of the number, but how easy the number is to break down.

- Try closing your eyes when calculating. This will help eliminate visual distraction and your brain will focus better.

- Do 10 different examples every day in the evening and when you wake up in the morning.

- Increase the size range of the number over time, maintaining the same number of zeroes at the end and repeat this over the course of a few weeks.

- Challenge your friends or coworkers and they will behold in amazement as your outperform any computer on these operations!

A monkey wrench in all this is technically some numbers cannot be broken down, but after practicing you will be able to spot these quickly and these are highly improbable in your everyday life.

Food for thought

The key to this is memory. Your memory can be a very powerful tool, and like your body, the more you exercise it, the more you will realize learning everything else will become that much easier.

If you have the diligence to try this exercise for at least two months, a phenomenon will happen to you..

- Economics, Stocks and personal financials will begin to seem simpler.

- You won’t get mentally exhausted as easily; you will have more mental stamina.

- Certain trends may become more apparent to you since your mind will begin to add things subconsciously without you even noticing it. You may begin to notice traffic patterns at intersections while driving, cloud patterns on different days, and other interesting details in your everyday life which may change the way you see many things.

Enjoy.

References
Prime Numbers, http://en.wikipedia.org/wiki/Prime_number

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About Ronnie Diaz

Ronnie Diaz is an enterprise software engineer responsible for front-end and back-end development for companies in many industries. Heavily involved in cloud development, online retail, e-commerce and electronic ordering, fulfillment and customer relational systems.

Posted on January 19, 2012, in Math & Programming Puzzles and tagged , , , , , , , , , , , , . Bookmark the permalink. 1 Comment.

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