Do Math Quickly in Your Head
July 14, 2007 – 12:43 pmSome time ago a picked up a cool little book called “Short-Cut Math” by Gerard W. Kelly. It’s promise was to increase my calculation ability (in my head) up to three times. Following are the tips that stayed with me since I read the book and that I found most useful. Now I use these techniques when dealing with our startup ThemBid.com when I’m negotiating over license agreements on the fly during lunch meetings.
1. Round Off to a Quick Approximation
First determine a level of accuracy you are happy with, then round the numbers appropriately before making the calculation. This is also useful to determine a quick ballpark figure before doing the actual calculation.
2. Break Up Into Parts
Say you have to multiply 613 by three. Try multiplying first 600 by 3, then 10 by 3 then 3 by 3 and adding the results.
3. Omit Words
When calculating in your head, think of the results rather than saying out the words. For example to compute 30/2, just think 15 instead of thirty divided by two equals fifiteen.
4. Quickly Find Three Common Percentages
20% -> Divide the number by 5
33.3% -> Divide the number by 3
50% -> Divide the number by 2
5. Finding Percentages by Using 100’s
The percentage of a hundred is the percentage number itself. For example, 15% of 100 is 15. Use this, combined with the Break Up Into Parts method.
The book has many more math shortcuts, but these are the ones that stuck to memory and I find myself using regularly. Have you learned any math shortcuts that allow you to quickly perform calculations in your head?
35 Responses to “Do Math Quickly in Your Head”
You are totally right! Out of five, four of the rules are the ones I use all the time.
By Safak on Jul 15, 2007
Reposted from my Digg comment:
Pretty basic, but helpful nonetheless. Many of you may say “too basic, I already know this” - but the average person can’t do math on the fly. Many do not understand that a fundamental principle of arithmetic, hell, even higher levels of math, is to be able to write something as something else. My first year of HS physics was just making things equal one another.
People struggle calculating 15% tips. My trick is to just take 10% and add it to 5% - just take 1/10th of the bill, cut that number in half, add the two together and there’s your tip!
Another one is being able to calculate Celsius to Fahrenheit on the fly - just double the temperature in C, subtract one-fifth of the original temperature, and add 32 - voila! (Derived from F = [(9/5)C] + 32, bonus points if you can figure out how to get that).
By MikeSty on Jul 15, 2007
Are people seriously not able to do things like that in their head without help from a website? I expected to find amazing tricks when I clicked on the Digg link, but apparently not. Schools are doing a crappy job of teaching math, literacy… and everything else, for that matter.
By JCasto on Jul 15, 2007
A shortcut I have found really useful over the years is to use a calculator.
By Bob Holness on Jul 15, 2007
To quickly get 20% (as in to calculate a 20 percent tip at a restaurant)
1. get an easy 10% by shifting the decimal one space to the left.
2. double the number!
ex. a bill of $120.50
1. 10% is 12.050
2. 20% is $24.00 (round) or add helf of step one for a 15% tip ($18.00)
By Chad on Jul 15, 2007
An awesome way to calculate a tip…
Example: 31.20
Percent = 15%
What is 10 percent of 31.20 = 3.12
So take 3.12/ 2 = 1.56
1.56+ 3.12 = 4.68, round up to be nice and make it even if your using credit card.
So grand total.. 36.00
By Free Nature Photography Wallpaper on Jul 15, 2007
Another tip that I use sometimes…
When multiplying (or dividing) 2 numbers together that may seem difficult…
32 x 62 = ?
This equation is the same as 16 x 124, which is the same as 8 x 248, which is the same as 4 x 496, or 2 x 992… and anything multiplied by 2 is easy… so
32 x 62 = 1984
By Jezza on Jul 15, 2007
I’m holding it with JCasto - this is it? All this rules I learned in school and that people don’t know how to calculate simple percentages is true but really, really sad. And I’m not a math pro, I’m just a normal guy with average marks in maths.
By MuGo on Jul 15, 2007
@MuGo
No, these are just the most common ones I use regularly. The book is filled with many useful Math tips.
Of course, most of us can do these things without thinking, but I find that a refresher on common sense is useful now and then.
By ethomas on Jul 15, 2007
To find a tip, I just divide by 6. It comes to 16.6%, but it’s something I can do really easily in my head and something I can easily divy up to what my friends would owe. For example, $50 would make an $8 tip, if someone got a $6 thing, add another dollar, if they got something that’s $7.50, just round up and add a dollar. It isn’t accurate but it’s easy and fair. I don’t consciously use 1 or 3, I just do them without thinking. As for 2, it’s easier to do 600 and 13, then add 1800 and 39. 4 is also fairly easy, and is something everyone should be able to do with 2. To find a certain percent of something, you can just multiply them by their percent number (15% would be 15x) and then move the decimal left 2.
By David on Jul 15, 2007
Another quick tip calculation, for those living in the US. Tax is 7.75% (here in CA, dunno about other areas), I just double the tax which provides me with 15.5%
By Peter on Jul 15, 2007
Another trick I like to use for tips is like this: 15% of $100 = $15
Take $15 and multiply it by whatever fraction of 100 the bill is. If it’s $30, you can guess that’s about 1/3. $20 = 1/5. $40=2/5 and so forth.
By Dustin on Jul 15, 2007
I used to do statistical sampling and to find the mean or average of five samples you of course add the all findings together and dived by five for the average, So dividing any number by five in your head is easy. 67 ÷ 5 is the same as 67 x 2 and move the decimal one place to the left. 134 is 13.4 or 67 ÷ 5. And 9 ÷ 5 = 1.8, Try a few it’s fun.
By Brodan on Jul 15, 2007
A trick taught to me some time ago for squaring numbers ending in five.
25 x 25 = 625
Take apart the two digits . First digit = 2 add 1 to it . Multiply 2 x 3 = 6
Multiply 5 x 5 = 25
Combine the two parts together …Answer = 625.
55 x 55 would be 3025 (5 x (5+1))= 30 & 25
I don’t use it often, but it’s a hoot to answer a question when someone asks, “What’s 85 squared and you blurt out 7225 in seconds.
By Wahoomcdaniel on Jul 15, 2007
this is what i do to calculate change quickly. let’s say something costs 2.54 and you pay with a 20.00 dollar bill. first subtract 2 from 20, then subtract 50 cents, and then subtract 4 cents. so basically 20-2=18-50 cents=17.50-4 cents=17.46, or vice a versa 20-17=3-40 cents=2.60-6 cents=$2.54. another method (this one works better for me) that i use is this, again using 2.54, do 20-2=18. but now subtract 1 from 18, so 18-1=17. now look at the cents part, 54, and going from left to right subtract 5 from 9 and 4 from 10 to get 46. so here’s how it works, (1) 20-2=18-1=17 - this is your dollar amount, (2) 9-5=4, 10-4=6, so 46 cents is your cents amount. also, if you’re ever stuck in traffic and bored out of your mind, you can exercise by adding numbers from license plates of the cars around you. challenge yourself to find a quickest method.
By aaron on Jul 15, 2007
The easiest way to calculate a tip, which apparently no one except me uses, is to drop the last digit, round up to a single digit followed by zeros, and double that value. That’s your tip.
Example:
Bill: 47.28
1) 4.72
2) 5.00
3) 10
If you’re less generous, drop the last digit, round down, and add half that value again to itself.
Ex:
$63.84
1) 6.38
2) 6.00
3) 9
Of course there’s a variance but if you were mathematically inclined enough to notice, you wouldn’t need a shortcut like that.
By Chaos Motor on Jul 15, 2007
It isn’t particularly useful, but you can tell if any number is divisible by 9 if its digits sum to 9 or a multiple of nine. So 2043? (2+0+4+3=9) Yep. 882,711? Yep.
And Jezza’s idea makes so much sense that I feel stupid for never having looked at it that way.
By BitterOldPunk on Jul 15, 2007
These are all nifty, practical tools. Thanks for sharing. Thanks to all those leaving their replies too.
By Nadadeturbe on Jul 15, 2007
I use all five. I thought everyone did?
I read a website this autistic/aspergers kid made once. He was a math genius who had crazy tricks for super fast four digit multiplication and z-axis 3d stuff. Wish I could find it. It was called Urshilalalu or something. Link anyone?
By agentarsenic on Jul 16, 2007
There are a great deal of books on math tricks.
This one highlights many with lots of exercizes to get the hang of them:
http://www.amazon.com/Rapid-Math-Tricks-Tips-Number/dp/0471575631
http://www.amazon.com/s/ref=nb_ss_b/104-8789556-3305559?initialSearch=1&url=search-alias%3Dstripbooks&field-keywords=edward+h.+julius&Go.x=11&Go.y=8&Go=Go
By Alex in Toronto, ON, CANADA on Jul 16, 2007
If you can’t figure out a 20% tip by now, you shouldn’t be allowed to carry money.
By jim o on Jul 16, 2007
start -> run -> calc.exe does the trick for me
By jarroyo on Jul 16, 2007
- If a number’s last 2 digits are evenly divisible by 4, the number is divisible by 4; if not, not.
- If you add the component digits of a number (a process known as “casting out nines”), then add that number’s component digits together, and keep doing that until you get a single-digit number, if that number is divisible by 3, then so is the original number; if not, not.
- The sum of a + (a + k) + (a + 2k) + … + (a + nk) equals (a + n) times n/2 if the number of terms is even; if the number of terms is even, it equals (a + n) times (n - 1)/2 + a[(n + 1)/2] for n odd. Example 1: 1 + 3 + 5 + … + 20 = (1 + 20) x 10/2 = 21 x 5 = 105. Example 2: 1 + 2 + … + 21 = (1 + 21) x (21 - 1)/2 + a[11] = 22 x 11 + 11 = 242 + 11 = 253.
By James Munroe on Jul 16, 2007
I particularly liked the replies from Jezza,Brodan, and Wahoomcdaniel. Thanks for sharing folks. More informative for me than the actual list of five.
I mostly do things in ratios, percentages, or fractions in my head. I find that American money lends itself well to this kind of mental math. For instance a quarter is 25% of a dollar or .25 or a 1/4. (literally) Simple, I know, but some people might not realize.
I split things up all the time too. I paid $15 dollars for gas(a while ago) and my tank was half full. Tank holds 10 gallons total, so split that for 5. Split that amount filled for 2.5, and again for 1.25. So I split available fuel two times, therefore now I will split price two times. Half of $15 is $7.5 and half of that is $3.25. So I paid approximately $3.25 for 1.25 gallons of gas. You could easily go the extra step and remove 1/5th (.25 is 20% of 1.25, and 10% of $3.25 = $.325 cents. Double that for $.65 cents) of each number for the exact amount per gallon, ( $3.25 minus $.65 cents=$2.60) but it is mostly just for quick estimates.
So basically since my per gallon number came out a little high at 1.25 I had to remove 1/5th (20%)of both sides of the equation to get back to 1. Since ten percent of anything just means scoot the decimal over one place, I did that for $3.25, and then doubled the result to get the full 20% to subtract from the total. $.325 X 2=$.65, then $3.25-$.65=$2.60 for one gallon of gas. (don’t I wish!)
I know it sounds long and drawn out, but it goes pretty fast in my head and I always get reliable numbers.
Does anyone have any good ones for dividing fractions mentally? That seems to mess with me sometimes…
By Dman on Jul 16, 2007
another trick : how to calculate the name of the day fore any date without using a calendar.
http://www.infonosity.be/english/memory/better-improve-memory.html
By Bruno on Jul 17, 2007
Interesting id like to add that you Guys should check out Vedic Math, it basically consists of 16 formulae as written down in age-old sutra’s of India and allows for very easy mental calculation of complex division, multiplication, square roots etc.
http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp
By Martin Möller on Aug 7, 2007
Other thing very cool about squaring number is the following:
Let´s say you don’t know the product of 27×27.
But you commonly know the product of 25×25.
So if you get 25² + (27-25)x(27+25) = 27²
625 + 104 = 729
So…. 27² = 729.
Tip about this technique: is wise to choose a nearby number, so you don’t have to make difficult multiplication operations.
Example: 15² + (27-15)x(27+15) = 225 + 12×42 = 729 (ok, not so difficult this one).
Very cool, huh? =]
I never apreciated my history’s classes, I prefered look for math patterns.
By Leandro Nascimento Camargo on Aug 7, 2007
To multiply any number by 11, use following tip:
34 X 11 = 3 (3+4) 4 => 347
62 X 11 = 6 (6+2) 2 => 682
83 X 11 = 8 (8+3) 3 = > 913 (Note that middle number is 11 so ‘1′ is carried to 8.
Enjoy !!!
By Gajendra on Aug 24, 2007
Or an easier way (for me) to multiply any number by 11 is,
1) multiply by 10
2) add the original number to it.
e.g:
24 x 11 = 240 + 24
= 264
By Danny on Apr 20, 2008
There is this wonderful site which aggregates almost all Mental Math techniques and shows it in an easy to understand animated manner. Guys, you must check out http://www.lazymaths.com
By Amish on Oct 9, 2008