10 Easy Arithmetic Tricks

1. Reea - September 17th, 2007 at 4:07 am

I always sucked at math, this is useful, another interesting list, love your site!

2. jfrater - September 17th, 2007 at 4:27 am

Reea: same here - this list stems from my trying to find something to help me fix my mess of a mathematical brain.

3. tony3s - September 17th, 2007 at 5:02 am

I didn’t know about trick number 10.
And it seems there is a good reason for that, because it doesn’t work !

e.g.: 58 / 9 = 6r4

but according to the trick: 5r4

e.g.: 587 / 9 = 65r2

but according to the trick: 54r2

So this trick doesn’t work all the time.

The only thing that’s true is that summing all the numbers gives the remainder (I knew that).

But good post to remind people math doesn’t have to be hard.

4. jfrater - September 17th, 2007 at 5:39 am

tony3s: You are right - I have replaced 10 with assorted multiplication rules because the previous number 10 does only work in certain circumstances.

5. dalandzadgad - September 17th, 2007 at 6:12 am

awesome list. i inadvertently learned some of the tricks listed here. but i used to memorize math…

6. blazak - September 17th, 2007 at 10:00 am

The trick for multiplying by 9 is good, but I always thought you’d look like an idiot in math class staring at your fingers, so my trick was simply…the answer will add up to 9, with the first digit being one less than your original multiplier…

ex - 7*9 = 63 (6 is one less than 7, and 6+3=9)

7. jfrater - September 17th, 2007 at 10:33 am

nice addition blazak.

8. Dan - September 17th, 2007 at 12:04 pm

I prefer calculators… but I do know a few of these tricks and they are helpful when I don’t have one.

9. The China Tattler - September 17th, 2007 at 12:39 pm

My brain freezes when numbers and words are combined.

I know most of these things, I can do them without thinking. But, when I read how to do them, I just zone out.

It just seems too confusing, like trying to translate English into Chinese characters using pinyin.

Math has its own language.

10. Shad - September 17th, 2007 at 12:40 pm

#3… 2682 / 2 = 1341 (even number so add 0) …

Isn’t 1341 an odd number? the math still works, but I’m all sorts of confused now. And I’ve always sucked at math

11. Tom Steele - September 17th, 2007 at 12:43 pm

Neat stuff, but #3 appears to be incorrect.

It says if you have an even number, you add a zero to the end and if you have an odd number you add a 5 to the end.

I believe they mean to say, “if you have a WHOLE number add a zero to the end, and if you have a fraction/decimal then add a 5 to the end.”

1341 is an ODD number, not an even number. But it IS a WHOLE number.

12. jfrater - September 17th, 2007 at 1:01 pm

shad and Tom: thanks - corrected.

13. Strath - September 17th, 2007 at 1:43 pm

#3 is just the reverse of #8. Divide by 2 and shift the decimal place. No need to remember even/odd whole/fractional rule.

2682 * 5

Step1: 2682 / 2 = 1341
Step2: Move the decimal: 13410

5887 * 5

Step1: 5887 / 2 = 2943.5
Step2: Move the decimal: 29435

14. Strath - September 17th, 2007 at 1:51 pm

Oh, and #1, simpler method to multiply by 11 and it works for any number of digits.

Multiply by 10 and add the original number.

15. jfrater - September 17th, 2007 at 2:16 pm

Strath: thanks for the additions

16. anteater_sa - September 17th, 2007 at 4:12 pm

Some cool tricks here, heres another, to find if a number is a multiple of 3, add all the numbers together and if they are evenly divisable by 3 then it is. e.g: 9576 –> 9 + 5 + 7 + 6 = 27 therefore 9576 is a multiple of 3

17. ow3n - September 17th, 2007 at 4:30 pm

One trick I use that I didn’t see listed is multiplying large numbers.

Like:

12 x 734

can be broken into ((10×700) + (2×700) + (10×34) + (2×34)) = 7068

or

8 x 6846

can be broken into ((8×6000) + (8×800) + (8×40) + (8×6)) = 54768

basically you break the number into tens, hundreds, thousands, etc and mulitply each group. with some larger numbers it can get hard to remember each “sub-number” but if you’re trying to estimate, its a good way to get a rough idea.

great post otherwise, i learned a lot of tips i wouldn’t have thought of otherwise..

~ow3n

18. ben - September 17th, 2007 at 5:26 pm

I wish I would have had this a few years ago! Now im in high school calculus, its a little harder than these rules apply still great!

19. Miss Cellania - September 17th, 2007 at 5:54 pm

To multiply something by five, I always multiplied by ten, then halved the answer.

20. Fe - September 17th, 2007 at 6:47 pm

Gotta agree with China Tattler, trying to read how to perform math tricks is like trying to sing a fragrance, it just doesn’t work for me. I worked in a fabric store for four years and pretty quick picked up all sorts of tricks to calculate percentages, discounts, fractions and decimals all in my head, but explaining them confuses just about everyone.

21. Ben - September 17th, 2007 at 7:49 pm

Here is a trick…

I turn on the calculator and start typing!

JK

These are great tricks essp for the kids still in high school and middle school. The joys of college math is the same but you dont use numbers just english and greek letters.

22. penny - September 17th, 2007 at 9:36 pm

A better system:
The Tractenberg System Of Speed Math.
Also check out:
Dead Reckoning
For advanced tricks–such as superspeed Langrange
Division.

23. Yanni - September 17th, 2007 at 11:24 pm

We teach many of these “tricks” in our Mathnasium Learning Center (www.mathnasium.com). Sorry for the plug, but here are some interesting “tricks.”

Find 7 % of 300. Sound Difficult?

Percents: First of all you need to understand the word “Percent.” The first part is PER , as in 10 tricks per listverse page. PER = FOR EACH. The second part of the word is CENT, as in 100. Like Century = 100 years. 100 CENTS in 1 dollar… etc. Ok… so PERCENT = For Each 100.

So, it follows that 7 PERCENT of 100, is 7. (7 for each hundred, of only 1 hundred).
8 % of 100 = 8. 35.73% of 100 = 35.73
But how is that useful??

Back to the 7% of 300 question. 7% of the first hundred is 7. 7% of 2nd hundred is also 7, and yep, 7% of the 3rd hundred is also 7. So 7+7+7 = 21.

If 8 % of 100 is 8, it follows that 8% of 50 is half of 8 , or 4.

Break down every number that’s asked into questions of 100, if the number is less then 100, then move the decimal point accordingly.

EXAMPLES:
8%200 = ? 8 + 8 = 16.
8%250 = ? 8 + 8 + 4 = 20.
8%25 = 2.0 (Moving the decimal back).
15%300 = 15+15+15 =45.
15%350 = 15+15+15+7.5 = 52.5

Also it’s usefull to know that you can always flip percents, like 3% of 100 is the same as 100 %of 3.

35% of 8 is the same as 8% of 35.

24. jfrater - September 17th, 2007 at 11:52 pm

Yanni: That is the most useful mathematics tip I have ever heard. Thanks for adding it - brilliant!

25. qureyoon - September 18th, 2007 at 12:45 am

this is amazing ! i only knew few of these tricks

thanks for sharing ^^

26. Andre du Plessis - September 18th, 2007 at 1:26 am

1, 2 and 3 I knew about (you can excercise them with the following feed - http://www.mental-workout.com/)

about 1 : I also worked out you can do the same with 3 numbers eg.

172 * 11

1(1+7)(7+2)2 = 1892

I am pretty sure you will be able expand on that even further.

5 and 6 did seem obvious to me.

9 I would rather go to the nearest 100 eg. 1000 - 700 = 300 and then do an easy 100 subtraction 100 - 48 = 52 then add them up 300 +52 = 352 (may seem longer but actually goes pretty fast in my mind)

Thanks for the others

27. Paul Joakim - September 18th, 2007 at 2:41 am

Another approach is the “is x divisable by y?”-question:

A number is divisable by 2 if it’s an even number.
3: The sum of the individual digits is divisable by 3, e.g. 174 => 1+7+4 = 12 (=> 1+2 = 3)
4: The last two digits is divisable by 4
5: The last digit is 5 or 0
6: The number is divisable by 2 and 3
7: Double the last digit and subtract it from the rest. If the result is divisable by 7, the original number also is. E.g. 483 => 48-(3*2) = 42, divisable by 7
8: The last three digits is divisable by 8
9: The sum of digits is 9
10: The last digit is 0
11: Subtract the sum of “even” digits from the sum of “odd” digits - if divisable by 11 (incl 0), the original number is divisable by 11: E.g. 7084 => (7+8)-(0+4)=11. 7084 is divisable by 11.

28. Robert - September 18th, 2007 at 7:43 am

I always liked the trick to determine if an integer is divisible by 3 - just add up all the digits in the number, and it those digits are divisible by 3, the original number is divisible by 3. 114 = 1+1+4 = 6 - 114 is divisible by 3.

29. Professor Homunculus - September 18th, 2007 at 9:32 am

Check out MathMojo.com for other tricks and tips. There is a link to a good, interactive lesson on multplication by 11 and 12 for huge numbers on the homepage.

30. frogandpig - September 18th, 2007 at 11:39 am

I have always figured out how much a certain percent is by using either 1% or 10%, then easy basic math.
Example:

4% of 430 = ?
1% of 430 = 4.3
4.3 x 4 = 17.2
or
(4×4)+(.3×4)=16+1.2=17.2

15% of 58 = ?

10% of 58 = 5.8
5% of 58 = 5.8/2 = 2.9
15% of 58 = 5.8 + 2.9 = 8.7

or 10% = 5.8 and 1% = .58
.58 x 5 = (.60 x 5) - .1 = 2.9

Rounding works great for tips at restaurants

15% of $58 = ?
15% of $60 = 10%($6) + 5%($3) = $9

And if you round but still want the exact amount, subtract the percent you’re trying to find from the additional amount you rounded. (Works easier for large numbers, but the concept is the same.)

60 - 58 = 2
15% of 2 = .3
9 - .3 = 8.7

Decimal places are moved easily in my mind, so maybe this trick only works for me?

31. imajoebob - September 18th, 2007 at 3:33 pm

Why didn’t you follow your own tax tip rules for multiplying by 15?

Instead of multiplying the first factor by 10, and then the second by 5, which some people may find difficult, just multiply by 10 (i.e. add a zero) then divide by 2 and add it to itself.

237 x 15 =
(237×10) + (237*10)/5 =
2370 + 1185 = 3555

Or you can always multiply by 100 and use your 15% tax formula.

32. Tom H - September 18th, 2007 at 3:48 pm

A better tip for multiplying by 6: multiply by 5 (as stated) and then add the original number.

I find this easier than multiplying by 3 then 2…

33. monsolo - September 18th, 2007 at 4:22 pm

Here’s a quick tip to multiply any two numbers that are between 11-19 (like 13 * 15):

1. Take the first number (13) and multiply by 10

(13*10)=130

2. Take the last digit of the second number (5) and multiply by 10

5*10=50

3. Add the results of steps 1 and 2

130+50=180

4. Get the last digit of the first number (3) and the last digit of the second number (5) and mutiply the two

3*5=15

5. Add the results of step 3 and 4

180+15=195

Try it. It sounds complicated but once you remember it, it gets useful

34. achan - September 18th, 2007 at 5:10 pm

Found this neat trick about the 11 rule - expanded.
What is 51236 X 11.
First step, 051236
Second step, 5(5+1)(1+2)(2+3)(3+6)6
Answer….563596!
Found it here
http://www.angelfire.com/me/ma.....htips.html

35. Ace - September 18th, 2007 at 7:09 pm

Awesome tips guys! Also.. Monsolo, I like yours too. Thanks!

36. sverrirp - September 18th, 2007 at 7:47 pm

Trick number two doesn’t work out:

35*35 = (2x(3+1)) & 25

2 x 4 = 8 = 825 according to the trick

But 35*35 = 1225

37. Jim C. - September 18th, 2007 at 7:53 pm

To convert between ounces and pounds, divide or multiply (as required) by 2 four times.

The same applies for price per ounce and price per pound.

38. hypergene - September 18th, 2007 at 8:10 pm

@sverrip

Trick 2 is correct:

35*35 = 3 x (3+1) & 25 = 12 & 25 = 1225
45*45 = 4 x (4+1) & 25 = 20 & 25 = 2025
55*55 = 5 x 6 & 25 = 30 & 25 = 3025
…

39. onikirol - September 18th, 2007 at 9:02 pm

even numbers multiplied by 6:

6×2= 12
6×4= 24
6×6= 36
6×8= 48

follow this pattern:

the even number is placed as the 2nd digit, and half of it is placed as the first. (the first step always applies, but the 2nd step is only true for 2, 4, 6, and 8 )

and for multiples of 5, I’m like Miss Cellania in that I go for multiply by 10 and then half it

40. MikeB - September 18th, 2007 at 9:43 pm

You might want to look at this book: “The Trachtenberg Speed System of Basic Mathematics” which explains for example how to multiply two large numbers without the need for calculator or paper.

41. jfrater - September 18th, 2007 at 10:44 pm

imajoebob: you are correct, but I wanted to mention as many options as possible because of the very reason you state - some people find different methods easier - two methods are better than one

Thanks guys for the extra tips - they are all really useful and make for an excellent resource.

42. Colin Seymour - September 19th, 2007 at 2:39 am

Fantastic list. I use a fair few of these already, but have certainly learnt a few more. Trick 9 applies to 10 to the power of any number - 10, 100, 1000, 10000 etc too.

43. jfrater - September 19th, 2007 at 2:44 am

Colin Seymour: thanks I am glad it will be of use to you - thanks also for expanding on trick 9. These comments are as useful as the list

44. Rui Martins - September 19th, 2007 at 3:23 am

Actually, Rule Number 3 (Multiply by 5) is a complicated form, of explaining what already is said in in First Item in Rule Number 10 (Multiply by 5: Multiply by 10 and divide by 2)

And this is very simple to understand because, 10/2 = 5

so,

2682 x 5 = 2682 x (10/2) = 26820 / 2 = 13410

or if you prefer to halve first
2682 x (10/2) = (2682/2) * 10 = 1341 * 10 = 13410

No weird rules for 0 or 5 just plain multiplication and halving

Remember that multiply by 10 in decimal (base 10 system) is easy, just add 0 to the right.

And halving something is second nature to any one which had a brother

45. Tuplad - September 19th, 2007 at 4:38 am

This is great, I suck at math so this is very handy!!

46. Woody - September 19th, 2007 at 5:09 am

One trick I learned thats useful is how to do square roots when you don’t have a calculator handy. It’s simple and works quite nicely as follows:

Subtract successive odd numbers, starting at 1, until your remainder is less than the next odd number.
Count the number of odds you subtracted, thats your whole part, then put the next put your remaining value over the next odd to get your fractional part.

The fractional part isn’t exact, but it’s usually close for large numbers.

For example:

9 -1 = 8 -3 = 5 -5 = 0
1 2 3

So the square of 9 = 3 (count of 1,3,5)

You can also use addition to get there as well:

120 = (1+3+5+7+9+11+13+15+17+19)+20
1 2 3 4 5 6 7 8 9 10 remainder

So, the square of 120 is 10 and 20/21 (10.9523)
The square of 120 is actually 10.9544, but 20/21 is pretty close and easier to work with if you’re not using a calculator.

If you have a rough idea of where its at, you can also figure out a quick “jump in” by guessing close. The close value can be multiplied by 2, and added to 1 to get the next odd in the sequence. For example, lets do 10535:

For 10535 we know 100^2 is 10000.
(100 * 2)+1 = 201, the next odd to use.
535 - 201= 334 -203 = 131
So Sqtr(10535) ~= 102 and 131/205 (.639 vs .640)

Hope this is helpful to someone!

47. jfrater - September 19th, 2007 at 5:33 am

I am amazed at how mathematical our users are here! Well done.

Oh - and hi to everyone coming from lifehack.org - thanks for visiting and contributing to the comments!

48. Logi Helgu - September 19th, 2007 at 6:15 am

http://en.wikipedia.org/wiki/Trachtenberg_system

49. portnoy - September 19th, 2007 at 10:30 am

Of course any even number is divisible by two but,

If the last two digits of a number are divisible by 4 then the whole number is divisible by 4.
If the last three digits are divisible by 8 then the whole number is divisible by 8…. etc.

The rules about 3 apply to 6 and 9 too.
If the digits add up to be a multiple of 3 and the number is even then it’s divisible by 6.
If the digits add up to be a multiple of 9 then it’s divisible by 9.

Seven is the only goofball.

50. swimner - September 20th, 2007 at 12:41 am

Relations of square numbers

We can get 15^2 = 225
What about 13^2?
13^2 = 15^2 - (15+13)(15-13) = 225 - 28*2 = 169
17^2 = 15^2 - (15+17)(15-17) = 225 -(-64) = 225 + 64 = 289

Twisting the trick a bit, we can generate ALL Pythagorean Triplets

Most people will recall a 3,4,5 triangle
Some remember the 5,12,13 triangle
Few remember the 7,24,25 triangle
Most don’t know the 121,7320,7321 triangle

Note that the smallest side is odd.

Simply square an odd number such as 9^2 = 81
Divide in half (not evenly)
An uneven split of 81 is 40,41

So 9,40,41 is a pythagorean triplet

ie 9^2 + 40^2 = 41^2

It also works for even numbers, but they have to have at least one odd factor.

Lets try 10. Find the pythagorean triplet for 5.
5,12,13 and then muliply by the other factor of 10 (namely 2) to get 10,24,26.

For powers of 2 we must be really sneaky.
Take 2^6 = 64.
Divide the number by 4 to get 16.

We know 3,4,5 is a pythagorean triplet.

Multiply the triplet by 16 to get 48,64,80.

We owe this to the Babyloneans (3000+ years old).

51. rosy - September 20th, 2007 at 5:44 am

That pretty excellent and good!! I am really impressed with the way you have come up with the math..I will surely use this technique…

52. cybernezumi - September 20th, 2007 at 12:50 pm

For restaurant tips I usually just double the sales tax, which here is about 7.5% — yielding 15%. If yours is a bit lower or higher, just round up or down a little bit to get it close enough.

53. Nazzyon - September 20th, 2007 at 1:01 pm

I am good @ Maths but my problem is speed/time.

Now I will be able to solve faster than usual. My B’s will definitely fire up to A’s if I make use of these tricks.

Thanks for contributing

54. pallav - September 21st, 2007 at 3:38 am

you people are scary!!

55. jfrater - September 21st, 2007 at 5:34 am

pallav: but they will be earning the big bucks one day (if not already!) Nerds rule

56. mamoy - September 25th, 2007 at 5:18 am

its soooooo amazing

57. sahil - September 29th, 2007 at 7:22 am

its simply superb!!!!!!!!!!!

58. flower - September 29th, 2007 at 11:45 pm

Fear of Maths is only mental.I suggest:
1.Instead of saying DIVIDE BY 2, say HALF/HALVE IT.
2.Instead of saying MULTIPLY it by 2, say DOUBLE IT.
3.Never use more than two digit numbers to prove the working of a method.
4.Show the more interesting sides of maths, for example,show the beauty of the table of nine (which really looks cute, simple and well arranged).
After these small things, leave the person to grow up inside herself, by herself. They’ll start with small victories, and keep gathering courage for bigger ones. Maths IS easy and beautiful upto a certain level. Let’s all enjoy this beautiful, universal language.

59. Gaurav Tekriwal - September 30th, 2007 at 6:32 am

HI!
Isnt all this High Speed Vedic Mental Mathematics from India?
Vedic Math is the world’s fastest mental math method from India- You can do calculations much much faster compared to the normal method or even a calculator.
Check out this site on Vedic Maths which has lots of tutorials and resources.

The tutorials given here on Vedic Maths are the best. Do Check them out.

Hope it helps!

Gaurav Tekriwal
www.vedicmathsindia.org

60. Catdancer - October 2nd, 2007 at 6:13 am

Good to know these things! I’m an elementary teacher and have used a few of these before but not all. As for the finger trick when multiplying by 9, I teach that every year. It’s great for elementary age kids and some higher grades, too.
I have a trick for calculating a tip that doesn’t involve anything tricky. I figure out what 10% of the bill is by moving a decimal point, then I add the amount of the sales tax to the 10% figure. My state has a 6% sales tax so it works well for me. If you had 8%, you could just double the amount of the tax. I never worry about an extra 1% for the tip - that’s usually just a few pennies.

61. jfrater - October 2nd, 2007 at 6:15 am

Gaurav Tekriwal - thanks for the additional information - I am sure many people will find it useful.

62. jfrater - October 2nd, 2007 at 6:16 am

Catdancer: great idea about the tip - thanks for mentioning it

63. jackR - October 2nd, 2007 at 2:28 pm

OK, all interesting tips but to me it’s easier to just do the math than to try to remember all these. Now, if there’s one or two that you find you use regularly that’s fine.

64. Lisa - October 2nd, 2007 at 5:22 pm

when multiplying two numbers that differ the same amount from a multiple of 10 (for example, 39 and 41, or 25 and 35), you can just square that multiple of 10 and subtract the square of the difference.

27×33
=30^2- 3^2
= 900-9
=891

(works due to difference of squares)
(30-3)(30+3)

65. Stuart Morrow - October 3rd, 2007 at 2:38 pm

Here’s a quick method I made up was I was younger for squaring any size of number (I mostly use it for 2 digit numbers though), and it’s far handier than Trick #2 of this list.

It’s adapted from the perfect square identity (a+b)^2 = (a^2 + 2ab + b^2) [which I didn’t make up myself, lol].

73^2
=(70 + 3)^2
=70^2 + 2 * 70 * 3 + 3^2 #70^2 is 7^2 * 10^2
=4900 + 420 + 9
=5329, which is right.

Or,

44^2
=(40 + 4)^2
=40^2 + 2 * 40 * 4 + 4^2
=1600 + 320 + 16
=1936, correct again.

For cubing or quarting or whatever higher powers, you could prbably do a binomial expansion on it, although that would probably take a far longer time, unless you’d memorised the binomial coefficients( rather than calculating those factorials each time).

66. Renessaince - October 5th, 2007 at 6:23 am

>> 3. Multiply by 5
What just not to multiply by ten, then divide by two? So you won’t need to check for a reminder.

67. jfrater - October 5th, 2007 at 7:08 am

Renessaince - it is good to have a variety of ways to do the same thing as we all think differently from each other.

Thanks for the additions Lisa and Stuart.

68. Richard - October 22nd, 2007 at 10:28 am

Square numbers with 1
Example 11^2 or 111^2 or 1111^2

1st Count the digits
2nd Start writing 1,2,3… up to the Counted digits and then go back!

e.g. 1111^2 - It has 4 digits
then we have 1,234,321

With 11 -> 111^2 it has 3 digits
then we have 12,321 - count up to 3 (1,2,3) and then go back (2,1) : 12321 =>(12,321)

That’s all Folks
“Viva Chavez”

69. John - October 23rd, 2007 at 6:00 am

Hey this is a great list. I already knew most of them because math was my favorite class in high school. Although, I did number 1 differently. It’s a much easier way and it works no matter how many digits your multiplying by 11. What you do is take the number you’re multiplying by 11 and write it down. Then you write the same number below it but shift the numbers to the right one digit. Then all you have to do is add them together. This would be the same as multiplying by 10 then adding one because the first number has one more digit than the one below. This process just always seemed to work better in my head.

45287 x 11 = ?

45287
+45287
498157

70. John F. - October 23rd, 2007 at 3:54 pm

Have you heard of the Russian Multiplication method. It’s quite fun and you can multiply any two two-or-more-digit numbers together using this method. Not sure if it is easier than the traditional algorithm (method) but it is fun.

1. Write the two number down on a line - write the smaller one first.

2. You will form two columns of numbers.

3. First column - halve the number in the first column write down the answer ignoring the remainder (or fraction). Write down until the first column is reduced to 1.

4. Second Column - double the number in the second column and write down the answers - keep doubling until you come parallel to the 1 of the first column.

5. Go down the list of numbers in the first column and draw a line through or delete the even numbers and their adjacent numbers in the
second column.

6. Add all the remaining numbers in the second column.
Voilá.

Example: 45 x 87 =

45 87
22 deleted 174
11 348
5 696
2 deleted 1392
1 2784

Numbers deleted from columns 22 & 2.
So 45 x 87 = 87 + 348 + 696 + 2784
= 3915

I have tested this on numerous occasions and it has never failed. Two reasons why this is easier than “long multiplication” -
1) Halving and doubling is quite easy mental arithmetic.
2) Addition is easier than multiplication.

I have done the proof to find out why it works.

71. aplspud - November 2nd, 2007 at 5:43 pm

Math scares me.

72. densom - November 14th, 2007 at 5:27 pm

awesome!!!
It is very helpful to me specially I’m majoring in mathematics.

73. Sol Lederman - November 15th, 2007 at 4:03 pm

Hi,

Nice list. I’ve got a similar one, with a few differences, on my blog, http://wildaboutmath.com. I’ve also got an article on a simpler way to square numbers.

74. sajjad - November 23rd, 2007 at 2:00 am

all bodies nice work, i have a better way for squring two digits, and more abt multiplication,
my own made tricks…..

75. Maximus - December 20th, 2007 at 3:55 am

I would like to see a continuation of the topic

76. Sol Lederman - December 20th, 2007 at 7:39 am

My blog now has a few videos about Math tricks. See http://wildaboutmath.com/videos and I’ll be doing more over time, especially about the Vedic techniques, that are not well covered in many other sources.

77. check - December 30th, 2007 at 2:43 pm

How to check if a number is divisible by three:
add separate numbers together and if they are divisible, the entire large number is.

Like for instance 1234: 1+2+3+4=10 - is not divisible.
1233: 1+2+3+6=12 - is.

78. check - December 30th, 2007 at 2:43 pm

sorry, last one was meant to be 1236, but both examples are good.

79. Wendy - January 8th, 2008 at 2:55 pm

I am having trouble with a quick way to figure out this example:

12.5% of 5416

Would appreciate your help.

80. John F. - January 8th, 2008 at 3:25 pm

Dear Wendy,

I am not sure why you are asking for the quick way, but I will not be facetious and say “use a calculator. As a teacher, I would remind children that percentages are just another way of doing a fraction.

It would helpful to have a few standard percentages in mind…

10% = one tenth (divide by ten)
20% = one fifth
25% = one quarter (or fourth depending on which side of the atlantic you dwell)
etc.
12.5% = one eighth

So I divide 8 into 5416.
Is the same as dividing it into
4800 (600)
and 600 (75)
and 16 (2)

Total 677.

Note of Caution: Children must understand the concept of fractions and percentages, and only if they get that link can you suggest this method.

Most Children know that 25% is 1/4 and you can ask what is half of 1/4 (be careful some children might this it is 1/2 because they halve the denominator.) When they have 1/8 then ask what is half of 25 - wait while the work it out, and then say if half of 1/4 is 1/8, and half of 25% is 12.5% then 1/8 is the same as 12.5%

The key is that they can relate common fractions to percentages and visa-versa.

I hope this helps you - I hope you don’t think I am talking down to you.

81. Eric B. - January 31st, 2008 at 10:58 pm

Whilst these math helps are valid ways of making calculations, in the real world one is not often presented with “pre-made” problems, such as:

1. you need to multiply a number by 11

2. you need to square a 2 digit number ending in
5

3. you need to multiply any two numbers that are between 11-19

4. you need to multiply two numbers that differ the same amount from a multiple of 10

These problems are so far-fetched from those encountered by citizens engaged in common jobs relating to commerce, accounting, engineering, administration, clerks, etc.

I don’t see any benefit from the mastery of these very narrow skills except for math contests, which are like spelling bees.

Sure, the winners can spell all those words and the math winners can calculate some obscure problem in a short amount of time, but I ask, in concrete terms, how those abstract math skills translate into stepping into a job:

* cashier
* machinist
* factory worker
* stock worker
* truck driver

82. John F. - January 31st, 2008 at 11:27 pm

You make a good point Erik B. about the “usefulness” of knowing these tricks - and indeed, they are novelties - a bit like a clever card trick - amazing to watch being performed, and fun to do, but really not practical on a day-to-day basis.

However, as a maths teacher, these “card tricks” do have some use, in building a student’s confidence in his/her ability to do maths. Confidence is a very important ingredient in the “learning recipe.” The other aspect is, fun. Sadly, maths is too often NOT regarded as fun. On the contrary, it strikes fear into the hearts of young students. By highlighting the “fun” factor, we hope to coax and lure students into this mysterious world called “Maths” so that they gradually become familiar with the cities called addition, subtraction, multiplication and division. They recognise fractions in their multifarious guises, and begin to see how, in fact, they were in the world of mathematics all along (problem solving).

One can, I suppose have an “essentials only” philosophy of life, but personally, I think spelling bees and maths olympiads add a certain spice to life. Can you imagine a world with no baseball, basketball, football or hockey? Imagine never being able to go to the theatre to watch a play, an opera or a dance? What if there were no circuses? I think you get my point - many of these “tricks” are just for fun - but so what?

83. Richard Williams - February 8th, 2008 at 9:28 am

The very first rule in being a good foreman on a construction job is to surround yourself with lots of talent. The second rule is that when being confronted with a hard task, let someone else do it. Even math. Good tips and I love them.

84. pidro - February 12th, 2008 at 3:36 am

your Math tricks ma help me to work fast and accurate even in our algebra problems. In my 1st time to see this,I told my classmates about this. then, I see now the easy way to solve mathematical problems.

85. pidro - February 12th, 2008 at 3:40 am

This is easy… I can now solve basic math problems using this techniques…

86. sandeep - February 15th, 2008 at 8:26 am

please add more triks this is nice

87. Alan - February 16th, 2008 at 6:11 pm

What a great lot of tips and tricks - thanks. Sevenths are wonderful things too. They are recurring decimals - they never end. So 1/7 is 0.142857142857142857…. - i.e. 0.142857 all recurring. 2/7 is the same group of numbers in the same order but starting with the next largest - 0.285714 all recurring. 3/7 is again the same group of numbers in the same order but starting with the third largest number - you guessed it - 0.428571 all recurring. The pattern follows for the rest of the sevenths as well - 4/7 = 0.571428 all recurring, 5/7 = 0.714285 all recurring and 6/7 = 0.857142 all recurring. And of course the number sequence is easy to remember - 1/7 = 0.(7×2)(7×2x2)(7×2x2+1) = 0.(14)(28)(56+1) = 0.142857 all recurring. Ain’t maths beautiful!

You can also multiply 2 numbers together by simply squaring the average of the 2 numbers and subtracting the square of the difference between a number and the average. E.g. to multiply 58×62 you can find the average (60) square that (60×60=3600) and subtract (60-58)squared - 2 squared = 4. Therefore 58×62 is 3600-4 = 3596. Another - 36×44=(40×40)-(4×4)= 1600-16 = 1584. Obviously this works most easily when the numbers are equidistant each side of a number that is easily squared. But it still works for harder ones, e.g. 27×32 = 29.5×29.5-2.5×2.5 = 870.25-6.25 = 864.

88. moises of philippines - February 17th, 2008 at 8:55 pm

being a math addict is one of the characteristics of being unique… we should love math

89. john fox - February 19th, 2008 at 10:14 pm

nine times table the easy way all the answers add to nine eg.
9*1=9
9*2=18
9*3=27
9*4=36
works to ten

90. Blest - February 20th, 2008 at 4:58 am

This article kicks ass. Thank you so much for writing/publishing it. I really have not had much trouble with math, but many of these “tricks” I did not know. lol. Thank you.

And in terms of the percent”trick”, the other thing that you can do, which I find even easier, is multiply the first number by the first digit of the next number. For example:
8% of 300=21 (8 x 3)
12% of 800=96 (12 x

Again, thank you. Math has always been an enjoyment of mine, and until recently, I had kind of forgotten about it, although still utilizing it for simple calculations. Due to a movie that I saw recently (A Beautiful Mind) and this artcile, I feel a growing fascination within me of reaquainting myself with math and further developing my knowledge and intellect-hungry mind.

91. John F. - February 20th, 2008 at 5:17 am

Yeah that works - but just watch your calculation - 3 x 8 = 24 not 21.

I would suggest that someone useing “Blests” method round of the bigger number to the nearest 100 or, where the number is within 19 of the 50 - eg. 31 - 69 round off to the lower hundred and add a half - e.g. 761 would be rounded off to
7 1/2 and then to find 30% of that would be about 225 - the actual result is 228.3 but it is close enough for estimation.

As I always say, when teaching children make sure they understand WHY the trick works and not merely the mechanics of the trick.

92. John F. - February 20th, 2008 at 5:23 am

Some might argue that I have povided too great a margin for the 1/2 values in the example above. I simply thought it would be easier if you take all the 30’s (except thirt itself, and up to all the 60’s.) rather than quibble about which point the estimation should shift from one to the other. strickly speaking, I suppose it should be the middle third of numbers between each hundred - i.e 34 - 66 but we are talking ESTIMATION here

93. ChiBop - February 20th, 2008 at 5:44 pm

One useful tip my dad always told me for figuring out tip is to take the tax and double it. So if the tip is usually 7%, then it brings you up to 14% (slightly less, but helps anyway.)

94. sponge dude - March 13th, 2008 at 5:40 am

Dear robert, I ALREADY KNOW THAT!

95. sponge dude - March 13th, 2008 at 5:48 am

Hi, I just found a LLLLLLLOOOOOONNNNNNNNNGGGGGG way to find squares:

To find the square in this series:

121,144,169,196,_____

Find the square root of the number before that:
196=14
Add the result to the square:
196+14=210
Then,Add the square root again, but this time add 1.
210+14=224=1=225!

Here’s a simpler one:
1,4,___
4=2
4+2=6
6+2=8+1=9

I bet you don’t know that! :-)8)

96. sponge dude - March 13th, 2008 at 5:50 am

can you go harder?

97. sajjad halai - March 14th, 2008 at 12:14 pm

squaring two or three digits is sound simple……
we know the formula for
(a + b)^2 = a^2 + 2ab + b^2
consider we want the square of number 47
just replace the digits on the place of variables

Step -I
(4 + 7)^2 = 4^2 + 2(4)(7) + 7^2
Plz ignore + Operaor, i m replacing + operator with a blank space…
(4 7)^2 = 4^2 2(4)(7) 7^2
(4 7)^2 = 16 56 49
Step-II
here is a technical sum
start from right, place first digit i,e 9, and other digit i,4 will be added middle column number , i,e 56. 56+4 =60
…..
(4 7)^2 = 16 56 49
(4 7)^2 = 16 (56 + 4)9
(4 7)^2 = 16 (60) 9
repeating above process with middle number,, similiarly for 60 place 0 same and 6 will be added to the left column
(4 7)^2 = (16 + 6)0 9
(4 7)^2 = 22 0 9
and it is the answer 47^2 = 2209
———————————————-
here are other examples
for example number = 69
formula for square is
(a + b)^2 = a^2 + 2ab + b^2 but remove + operator

(6 9)^2 = 6^2 2(6)(9) 9^2
(6 9)^2 = 36 108 81
(6 9)^2 = 36 (108 + 8)1
(6 9)^2 = 36 116 1
(6 9)^2 = (36 + 11)6 1
(6 9)^2 = 47 6 1
69^2=4761
it is the answer
——————————
for example number is 31
(3 1)^2 = 3^2 2(3)(1) 1^2
(3 1)^2 = 9 6 1
31^2=961
and it is the answer
————————-
if u want more….
for squaring three digit number
use (a + b + c)^3
it is also similiar but little trick there.

similiarly for four digit number
use formula of (a + b + c + d)^2
————————————–
OK if you want not square but CUBE of a two digit number then,,
u can use similiarly formula of (a + b^3 ………………..
…………………………………………………………………………
and this never ends ..
U need to A Srong Sum Caculation
and Bionomial Theorem…
if Any Problem Me here…with you..sajjadhalai@gmail.com

98. Raj - March 17th, 2008 at 6:02 am

Really this is very usefull for all. Thanks.

99. Виктор - April 9th, 2008 at 9:19 am

Ну и тупые же вы, американцы. Этому в начальной школе учат.

PS: Хотя то, что я написал, вы, наверняка, тоже прочесть не сможете. :-))

100. jfrater - April 9th, 2008 at 9:38 am

Can someone translate that last comment in to English so I know whether to keep or delete? All I can make out is American on the first line.

101. Kreachure - April 9th, 2008 at 10:01 am

“Well, you stupid Americans. This [is] taught in elementary school.

PS: Despite what I wrote, you probably will not be able to read, too. :-))”

Don’t thank me, thank “GoogleTM Translate”!

102. Kreachure - April 9th, 2008 at 10:08 am

Hmm, that looks too much like I myself was saying it. Oh well…

103. riz - April 19th, 2008 at 3:22 am

Your Tricks is wrong…

Trick number two doesn’t work out:

35*35 = (2x(3+1)) & 25

2 x 4 = 8 = 825 according to the trick

But 35*35 = 1225

Right Tricks:

35*35=1225

(3 x (3+1)) = &25

3 x 4 = 12

ans: 1225

104. kiwiboi - April 19th, 2008 at 3:34 am

riz - huh ? The way you did it correctly is the way Trick 2 tells you how to do it.

Multiply the first digit by itself + 1, and put 25 on the end.

35 x 35

Step One
3 x 4 = 12

Step Two (put 25 on the end)

1225

105. carpe_noctem - April 19th, 2008 at 3:46 am

yeah riz, you just completely made up some random way of doing it and labelled it as incorrect…

106. MrStabby - April 19th, 2008 at 3:59 am

The first one is designed for retards. Just times the number by 10 and add the original number on to the result. If that’s too difficult then you’re also probably having difficulties remembering how to blink.

107. kiwiboi - April 19th, 2008 at 4:11 am

Виктор - засунь себе в жопу…

108. John Morrison - April 29th, 2008 at 6:22 pm

I learn a very good trick for squaring numbers in the 40s and 50s. Think of 50 as 25, and add the ones digit. 51*51 is 25 plus 1. 26, next you square the ones digit. (1 squared is 01, for the answer 2601. Try the next one 52*52 is 2704. 25 plus the 2 is 27, 2 squared is 04.

For the 40s think of 40 as 15, not 16. Add the ones and square the difference between the ones digit and 50. 41*41 is 15 plus 1, 16. The difference between 41 and 50 is 9. Nine squared is 81. Your answer is 1681.

Have fun,
John

109. hero - May 1st, 2008 at 7:37 am

excellent site

110. shan - May 1st, 2008 at 11:01 am

good simple tricks ,good work pal

111. John Morrison - May 6th, 2008 at 7:10 pm

This is a simple way to look at the number 9. Take 45 * 9. you look at the last number and subtract from ten you have 5. Thus, this is the last number of the answer. For 23 * 9, the same is true, subtract 3 from 10 and you have 7. Again this is helpful in coming to answer quickly. As you know with 9 the first number in the problem is alway I greater than the answer. 4 * 9 is 36. 9 * 9 is 81. This is not a hard and fast rule. There are time when the first number does not change. The beauty of 9 is the in the fractional quality of the numbers in the problems. For 45 * 9, you know the last number in the answer is 5. Look at the 4 and think,”what plus 4 is 9?”. ADD that number to the number on the right. 5+5 = 10. Now place the zero in the middle of the answer and the 1 will make the 4 from reducing to a 3. So the answer to 45 * 9 is 405. How do you know your answer is right. 4+5 = 9. 39 * 9. The answer ends with a 1, 3 and 6 make 9, so 6 and 9 are 15. Place the 5 and the carried 1 makes the 3 stay a 3 for the answer 351. (3, 5, and 1 make 9).