Subscribe to Listverse10 Easy Arithmetic Tricks
- Published September 17, 2007 - 342 Comments
Math can be terrifying for many people. This list will hopefully improve your general knowledge of mathematical tricks and your speed when you need to do math in your head.
1. The 11 Times Trick
We all know the trick when multiplying by ten – add 0 to the end of the number, but did you know there is an equally easy trick for multiplying a two digit number by 11? This is it:
Take the original number and imagine a space between the two digits (in this example we will use 52:
5_2
Now add the two numbers together and put them in the middle:
5_(5+2)_2
That is it – you have the answer: 572.
If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first:
9_(9+9)_9
(9+1)_8_9
10_8_9
1089 – It works every time.
2. Quick Square
If you need to square a 2 digit number ending in 5, you can do so very easily with this trick. Mulitply the first digit by itself + 1, and put 25 on the end. That is all!
252 = (2x(2+1)) & 25
2 x 3 = 6
625
3. Multiply by 5
Most people memorize the 5 times tables very easily, but when you get in to larger numbers it gets more complex – or does it? This trick is super easy.
Take any number, then divide it by 2 (in other words, halve the number). If the result is whole, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end. It works everytime:
2682 x 5 = (2682 / 2) & 5 or 0
2682 / 2 = 1341 (whole number so add 0)
13410
Let’s try another:
5887 x 5
2943.5 (fractional number (ignore remainder, add 5)
29435
4. Multiply by 9
This one is simple – to multiple any number between 1 and 9 by 9 hold both hands in front of your face – drop the finger that corresponds to the number you are multiplying (for example 9×3 – drop your third finger) – count the fingers before the dropped finger (in the case of 9×3 it is 2) then count the numbers after (in this case 7) – the answer is 27.
5. Multiply by 4
This is a very simple trick which may appear obvious to some, but to others it is not. The trick is to simply multiply by two, then multiply by two again:
58 x 4 = (58 x 2) + (58 x 2) = (116) + (116) = 232
6. Calculate a Tip
If you need to leave a 15% tip, here is the easy way to do it. Work out 10% (divide the number by 10) – then add that number to half its value and you have your answer:
15% of $25 = (10% of 25) + ((10% of 25) / 2)
$2.50 + $1.25 = $3.75
7. Tough Multiplication
If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:
32 x 125, is the same as:
16 x 250 is the same as:
8 x 500 is the same as:
4 x 1000 = 4,000
8. Dividing by 5
Dividing a large number by five is actually very simple. All you do is multiply by 2 and move the decimal point:
195 / 5
Step1: 195 * 2 = 390
Step2: Move the decimal: 39.0 or just 39
2978 / 5
step 1: 2978 * 2 = 5956
Step2: 595.6
9. Subtracting from 1,000
To subtract a large number from 1,000 you can use this basic rule: subtract all but the last number from 9, then subtract the last number from 10:
1000
-648
step1: subtract 6 from 9 = 3
step2: subtract 4 from 9 = 5
step3: subtract 8 from 10 = 2
answer: 352
10. Assorted Multiplication Rules
Multiply by 5: Multiply by 10 and divide by 2.
Multiply by 6: Sometimes multiplying by 3 and then 2 is easy.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number, as above.
Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number (which is obvious from the first step).
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number (which is obvious from the first step).
Multiply by 45: Multiply by 50 and subtract 5 times the original number (which is obvious from the first step).
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number.
Bonus: Percentages
Yanni in comment 23 gave an excellent tip for working out percentages, so I have taken the liberty of duplicating it here:
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.
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September 17th, 2007 at 4:07 am
I always sucked at math, this is useful, another interesting list, love your site!
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.
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.
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.
September 17th, 2007 at 6:12 am
awesome list. i inadvertently learned some of the tricks listed here. but i used to memorize math…
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)
September 17th, 2007 at 10:33 am
nice addition blazak.
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.
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.
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
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.
September 17th, 2007 at 1:01 pm
shad and Tom: thanks – corrected.
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
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.
September 17th, 2007 at 2:16 pm
Strath: thanks for the additions
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
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
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!
September 17th, 2007 at 5:54 pm
To multiply something by five, I always multiplied by ten, then halved the answer.
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.
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.
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.
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.
September 17th, 2007 at 11:52 pm
Yanni: That is the most useful mathematics tip I have ever heard. Thanks for adding it – brilliant!
September 18th, 2007 at 12:45 am
this is amazing ! i only knew few of these tricks
thanks for sharing ^^
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
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.
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.
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.
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?
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.
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…
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
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/marmalade/mathtips.html
September 18th, 2007 at 7:09 pm
Awesome tips guys! Also.. Monsolo, I like yours too. Thanks!
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
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.
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
…
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
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.
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.
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.
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 
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
September 19th, 2007 at 4:38 am
This is great, I suck at math so this is very handy!!
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!
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!
September 19th, 2007 at 6:15 am
http://en.wikipedia.org/wiki/Trachtenberg_system
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.
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).
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…
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.
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
September 21st, 2007 at 3:38 am
you people are scary!!
September 21st, 2007 at 5:34 am
pallav: but they will be earning the big bucks one day (if not already!) Nerds rule
September 25th, 2007 at 5:18 am
its soooooo amazing
September 29th, 2007 at 7:22 am
its simply superb!!!!!!!!!!!
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.
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
http://www.vedicmathsindia.org
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.
October 2nd, 2007 at 6:15 am
Gaurav Tekriwal – thanks for the additional information – I am sure many people will find it useful.
October 2nd, 2007 at 6:16 am
Catdancer: great idea about the tip – thanks for mentioning it
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.
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)
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).
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.
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.
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”
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
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.
November 2nd, 2007 at 5:43 pm
Math scares me.
November 14th, 2007 at 5:27 pm
awesome!!!
It is very helpful to me specially I’m majoring in mathematics.
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.
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…..
December 20th, 2007 at 3:55 am
I would like to see a continuation of the topic
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.
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.
December 30th, 2007 at 2:43 pm
sorry, last one was meant to be 1236, but both examples are good.
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.
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.
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
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?
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.
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.
February 12th, 2008 at 3:40 am
This is easy… I can now solve basic math problems using this techniques…
February 15th, 2008 at 8:26 am
please add more triks this is nice
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.
February 17th, 2008 at 8:55 pm
being a math addict is one of the characteristics of being unique… we should love math
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
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.
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.
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
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.)
March 13th, 2008 at 5:40 am
Dear robert, I ALREADY KNOW THAT!
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)
March 13th, 2008 at 5:50 am
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
March 17th, 2008 at 6:02 am
Really this is very usefull for all. Thanks.
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.
)
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.
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”!
April 9th, 2008 at 10:08 am
Hmm, that looks too much like I myself was saying it. Oh well…
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
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
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…
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.
April 19th, 2008 at 4:11 am
Виктор – засунь себе в жопу…
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
May 1st, 2008 at 7:37 am
excellent site
May 1st, 2008 at 11:01 am
good simple tricks ,good work pal
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).
May 12th, 2008 at 9:23 pm
I LIKED THE 3RD ONE
May 17th, 2008 at 2:42 am
this was a horrible page!!!!!
May 17th, 2008 at 2:59 am
Please if you haven’t got something to contribute to this discussion in terms of Math tricks and techniques – keep your comments to yourself. Posts such as 113 and 107 are as sad as they are irritating. If you think its a waste of time – fine go elsewhere.
Personally I appreciate the different ideas shared here.
John
May 20th, 2008 at 1:51 am
Unbeleivable but Believable
May 27th, 2008 at 6:10 am
MULTIPLY UP TO 20*20 IN YOUR HEAD.
1. TAKE 15 & 16 as an example .
2. Remember to place the larger no of the two on top of your mind
3. Then imagine to cover 16 & 5 from a paper mentally . These are the no.s now needed for the whole operation.
4. Add 16+5=21
5. Place a zero(0) after the last digit to get 210.
6. Multiply the lower covered no. into the single upon it one.(6*5=30)
7. Add 210+30=240
amazing….!
June 2nd, 2008 at 4:37 pm
Giving Lots of Examples could be useful
June 3rd, 2008 at 3:12 am
hi, nice rules,
Kaustubh
ur example is difficult i think,
multiplying 16*15 can be done by
Multiply 15*15 by trick
add 15 to th answer
15*15=225
225+15=240
16*15=240
simple
June 14th, 2008 at 12:10 pm
avery good helpful tricks
June 17th, 2008 at 5:01 pm
I wanted to do a Math list, but I didn’t think there would be any interest. Guess I was wrong. Good list.
June 20th, 2008 at 12:52 am
I needed something for the school project o mathematics. The ‘11 times trick’ and the ‘tip calculating’ ones have got me into atrraction. I’m sure of scoring a full on full for the project.
Please keep adding new tips and traps.
Fabulous! Bravo!
June 22nd, 2008 at 3:07 am
tricks fails at certain times then how can we use them
June 22nd, 2008 at 3:24 am
ranu: read the comments – they don’t fail. They all work.
June 28th, 2008 at 9:05 am
Wow,this was my assignment in Math..good for me to know this website.This one is very helpful for me. Thanks for this!
July 2nd, 2008 at 9:36 am
Fantastic ideas im a teacher but terrible at basic maths, this has been a great help
July 3rd, 2008 at 6:16 am
MAN THIS IS AWESOME PLZ ADD SOME MORE TRICKS ABOUT HOW TO SOLVE TRANSFORMATIONS PLZZ I WILL BE THANK FULL TO U
July 12th, 2008 at 11:00 pm
HI
THIS SITE IS VERY GOOD
DAILY I HAVE TO OPEN THIS SITE . I HAVE BEEN IMPROVING MY MATHS SHORT TRICKS
PLZ SEND SOME OTHER SHORT TRICKS IN MY YAHOO MAIL
THANXXXXXXXXXXXXX
July 12th, 2008 at 11:16 pm
SAM & AJAY: YOUR ENTHUSIASM HAS BEEN NOTED.
July 13th, 2008 at 3:04 am
http://listverse.com/comment-faq/
think there’s a little something about all caps here.
July 13th, 2008 at 8:23 am
Just being smart.
July 17th, 2008 at 11:14 am
with the help of this tricks i really got speed in my calculations .
tfe best part of the tricks was how to find the percentage………….
July 24th, 2008 at 4:52 am
will anyone tell me the addition trick?
July 25th, 2008 at 1:51 am
it is better to give simple breif about quantitative apptitude also
August 8th, 2008 at 12:59 am
hai guyz
August 12th, 2008 at 3:56 am
i sucks at math but when i noticed it,i always recite in math that’s because of this!
August 18th, 2008 at 12:13 pm
can any1 tell me how it is done
this is a 5 digit and 4 line addition. but the next three nos are not displayed but the answer is calculated. plz tell me the steps at nkumar14.1980@gmail.com “NOW REPLY”
eg:-
3 2 3 0 7
- – - – -
- – - – -
- – - – -
- – - – -
————
2 3 2 3 0 5 ANS
How provide the trick how to solve it.
Numbers in the blank are placed upon the above and below lines
August 30th, 2008 at 5:07 am
Any 2 digit number Multiplied by 99……
44*99 = (44-1)(100-44) = 4356
37*99 = (37-1)(100-37) = 3663
78*99 = (78-1)(100-78) = 7722
No multiplication, only addition. amazing… ? .!
M.Bala – mbalasimplythebest@yahoo.co.in
September 4th, 2008 at 1:10 am
after reading this i found a easy way to solve problems thanks for that
September 5th, 2008 at 11:23 pm
or a neat trick for squares of numbers, is…
Problem: find the the square of 51
solution: 50 squared plus two times 51 minus one.
50^2+2(51)-1
September 7th, 2008 at 9:24 am
shit
September 10th, 2008 at 1:15 pm
Here goes another one:
multiplying numbers of 2 digits up to 19.
ej: 16*15
take 16+5=21 add a 0: 210
then 5*6=30
and then 210+30=240
Easy?
September 26th, 2008 at 4:57 am
nice., i really useful this site to my maths .,
September 28th, 2008 at 11:49 pm
here’s a really easy way to calculate a 20% tip, for the non-cheapskates out there:
Double the total and divide it by 10.
Because really, people…15% is the minimum you should tip for good service. Doubling sales tax is certainly easy enough, just don’t do it at the restaurants you like to eat at. Most waiters only make $2.13 an hour, and they really depend on your generosity.
October 2nd, 2008 at 6:09 am
thanks alot
i came to know a few very useful maths tips
thanks 1ce again
al th best
god bless.
October 6th, 2008 at 12:56 am
Thanks a lot for the information. it really helps me a lot. mabuhay web-site nyo!!
October 15th, 2008 at 9:09 pm
tricks for add of odd number in series/43612342513246241443242286541233234242461242
October 16th, 2008 at 7:35 pm
Squaring 2 or 3 digit numbers Trick:
let the number to be squared be called as the BASE.
let the difference of the BASE from 100 be called as the MAGIC NUMBER.
to square: SUBTRACT the MAGIC NUMBER from the base, then APPEND the square of the base.
examples: BASE MAGIC NUMBER = 100 – 97 = 3
97 – 3 = 94 (makes up the first two digits)
3 x 3 = 09 (makes up the last two digits)
thus, 97 x 97 = 9409.
89 x 89 –> MAGIC NUMBER = 100 – 89 = 11
89 – 11 = 78
11 x 11 = 121
121 is 3-digit, so we add it like this:
78 (the first two digits)
121 (we retain the last two, and add the first)
——
7921 –> 89 x 89
examples: BASE > 100
——————————————————
106 x 106 –> MAGIC NUMBER = 100 – 106 = -6
106 – (-6) is like 106 + 6 = 112
6 x 6 = 36
thus, 106 x 106 = 11236.
This works everytime, and is useful as long as you know the square of the base.
For larger numbers, this trick is also applicable using 1000 as the one we subtract from, however, we are using 3 digits now, so we expect 3 digits from both process:
ex. 989 x 989
1000 – 989 = 11 (magic number)
989 – 11 = 978
11 x 11 = 121
———-
989 x 989 = 978121
ex. 1012 x 1012
1000 – 1012 = -12
1012 – (-12) = 1024
12 x 12 = 144
———–
1012 x 1012 = 1024144.
looking at these makes us feel that we can also do these for numbers near 10,000, using 4-digits from each process:
9994 x 9994 –> 9994 – 6 = 9988
6 x 6 = 0036
———————-
99880036.
Hope this helps.
October 19th, 2008 at 11:28 am
I’ve just looked a bit in this site and found lots of good stuff. I’m not a great big fan of math, but I find some of it interesting. I hope you all will look through this site when doing your math. Especially kids.
October 23rd, 2008 at 12:29 pm
this website rocks man!
November 1st, 2008 at 2:55 am
we can find out the total before we add it
steps
1.tell the other person( audience) to tell you a 3 digit number and write that number on a paper
2.subtract that number by 2 and put 2 in front of the answer, that will be your total.
3.then tell the audeince to tell an other 3 digit number, write that down on the paper.
4. subract that number by 999 and write down your answer.
5. now tell the audience to tell an other 3 digit number write down the answer
6. sub. by 999 and write down the answer.
7. now tell the audience to total it up and he/she will be suprised
eg.
(a)- audience
(s)- you
415 (a)
725 (a)
274 (s)
398 (a)
601 (s)
——-
2413
November 2nd, 2008 at 12:44 am
i have 1 fantastic trick 4 multiplication wth 9
November 21st, 2008 at 11:04 am
there is a trick done with 25 pennies… the object is to get the last penny not the most… you play with a partner and you can take as many as 3 or as little as 1… there is a fool proof way to win everytime see if you can figure it out and post it on your site
November 25th, 2008 at 6:59 am
merci boucoup
November 26th, 2008 at 1:32 am
fascinated hehehe hmmm!
November 26th, 2008 at 1:46 am
Here are the tricks,
Copy them
and paste
Easy!
December 7th, 2008 at 9:32 am
i still suck at maths. i didn’t undertand anything on this list
December 7th, 2008 at 4:19 pm
I see now why I have been avoiding this list.
January 21st, 2009 at 2:24 pm
i like this tricks it is very useful i luv dis sites
January 26th, 2009 at 8:14 am
i found it very useful good way to grasp maths techniques.!!****.
January 29th, 2009 at 8:53 am
i know many more such tricks and i have a book called vedic arithmetic which is an extract from the vedas. the tricks are called the sutras(in sanskrit).
February 1st, 2009 at 4:45 pm
Enjoyed these tips.
This is probably a well know trick but my 8 year old son got me with the following:
You pick a number between 1 and 9
Multiply it by 3
Add 3
Multiply that by 3
You will have a two digit number which you add together he “guessed” my number is 9
February 3rd, 2009 at 2:52 pm
hi frens thanx alot for contributing so many underlying facts of maths. It has benefitted a lot to me.
Is ther any trick in dealing with large decimal multiplication problems.
February 4th, 2009 at 5:54 am
yes u can use logarithm for large decimal multiplication.
*edited for email address*
February 4th, 2009 at 2:36 pm
Divide any number by 9 in 6 seconds
12348/9=1372
how to do this
1. copy the first number i.e.1
2. Add it with the second number= 1+2=3
3. add the value 3 with the third number i.e=3+3=6
4. add the fourth no. in the same way= i.e 6+4=10.
5 now the no 6 will be 7 (6 +1) as 1 is the carry over.
6. add 10 with the last number i.e 10+8=18
7.Divide this by 9 and write the quotient over there
In case of 8 if it is 7 then the answer of
12347/9 =1371 +8(remainder)
12346/9=1371 +7(remainder)
February 15th, 2009 at 10:00 am
Thnaks to the original writer of this site and all genuine contributors, site has been very helpful. The rest of you why do you waist your time I. A site you don’t enjoy!!! Keep your comments to yourself and move on.
February 16th, 2009 at 9:59 am
Math tricks are great for understanding the magic of math. But you should be able to do math in a logical manner. I use a method of math to train my mind for logic and pattern recognition. It is the “hidden number” system. Most people should know the times tables by heart. So for example, if you see 2*6 you will call out 12 without much thought. Sadly, there are still many adults who are not able to do simple mental math.
I have come up with a way to focus the mind on the simple parts and discover the hidden parts of math. Start with pen and paper and work your way up to mental math.
Look at this. 23*45. What are the obvious numbers? From left to right, you can see 8 and 15. Because 2*4 is 8 and 3*5 is 15. What you cannot see is the hidden number 22. The hidden number is the secret to the entire problem. It brings the left and right side numbers together. Learn to spot the hidden number and you will be able to solve 2 by 2 multiplications with ease.
Look at the problem again. 23*45 = 8-22-15. Adding for the left only the tens digits, 8 plus 2 is 10, attach the 2 in the ones column. You have partial answer of 102. Add the 1 from 15 and attach the 5 for the final answer 1035.
You will be doing math from the left side (the more natural may) and when you have a single digit number next to a pair. YOU ONLY PLACE IT ALONG SIDE. Practice with the following problems.
24*36 = Left 6, Hidden n 24, right 24. Add 6 + 2 = 8 and 4, add 2 to 4, attach the last 4.
89*47 = Left 32, Hidden n 92, right 63. 32-92-63. 32+9 =41+2, 412 + 6 is 418 attach 3.
56*47 = Left 20, Hidden n 59, right 42. Do it for yourself.
74*85 = Left 56, Hidden n 67, right ?
96*21 = Left 18, Hidden n ?, right ?
This is not a math trick, but a logical step in processing math.
Answers:
24*36 = 864
89*47 = 4183
56*47 = 2632
74*85 = 6290
96*21 = 2016
February 24th, 2009 at 12:54 am
In addition to trick No. 10
Multifly by 25: Divide by 4 then add 00 (2 zero) to last diigit.
For dividision by 25: Move 2 decimal places to left then multify by 4.
More power!
February 28th, 2009 at 9:03 am
Interesting trick – 166 – but notice how the method by which the hidden number is obtained is not revealed?
March 5th, 2009 at 9:30 am
its too long & out of fashion
March 6th, 2009 at 12:59 am
its really great!!!!!!!!!!!!!!!!!!!!
it helped me a lot.
thank u.
March 13th, 2009 at 10:00 am
Trick 9 is from Vedic Math rules. The rule in this case is “All from 9, last from 10″
March 31st, 2009 at 6:31 am
thats a gud site.
u r working nicely dudes……..
March 31st, 2009 at 1:43 pm
im exposed all these tricks were up my sleeve lolz, seriously though this is good stuff thanks
March 31st, 2009 at 1:51 pm
free trick
(by the way by A2 i mean A squared and 2A means 2*A
step 1) let A=B
step 2) A2=AB
step 3) A2+A2=A2+AB
STEP 4) 2A2=A2+AB
STEP 5) 2A2-2AB=A2+AB-2AB
STEP 6) 2A2-2AB=A2-AB (Factorising)
STEP 7) 2(A2-AB)=1(A2-AB) (divide each side by (A2-AB)
2=1
April 2nd, 2009 at 9:01 am
It takes some practice but you can learn to do the multiplication algorithm for two digit numbers in your head (described few times in the comments). To save memory, you have to perform additions after each multiplication and keep a “partly finished answer”. After mastering this method you can multiply any two different numbers from the range 1-100, now that’s 10,000 calculations. (Of course, if you are looking for challenge, you can generalize the method for 3 digit numbers)
Example: 23 * 48
8*3 = 24 # 4 is the last digit of the answer, 2 carries to the next calculation.
2*8 + 3*4 + 2 = 30 # Multiply cross digits and add the carried number. 0 is the second last digit of the answer. 3 carries to the next calculation.
Your “answer” at this point is 0&4 = 04
2*4 + 3 = 11 # Multiply the first digits and add the carried number
and we have 11&04 = 1104 = 23 * 48
Another: 78 * 32
8*2 = 16 # part answer is 6
7*2 + 8*3 + 1 = 39 # part answer is 96
7*3 + 3 = 24 # Answer is 2496
April 2nd, 2009 at 9:01 am
Now, another trick I came up by myself. This may be a bit too advanced to this thread and not even arithmetic but I figure someone can appreciate it. Sqrt means square root. To solve quadratic equations (ax^2 + bx + c = 0) fast:
The general formula you use looks pretty horrible for an untrained eye. Let’s get some sense to it. First divide the equation by ‘a’ so that x^2 will have 1 as the coefficent (the roots won’t change). We are now solving equation x^2+bx+c=0. Notice this, in the formula (with a=1), you can take the 1/2 multiplier inside the square root and it becomes 1/4 (erasing the -4c to just -c). Then you have -(1/2)b outside the root and (1/4)b^2 inside. But the latter is the first one squared! Let’s denote p = -(1/2)b. Now our simplified quadratic formula reads:
x = p +- Sqrt(p^2 – c)
So, to solve a given equation, look at the ‘b’, divide it by -2 and remember this number. Now square it and subtract ‘c’. put a +- between p and the root of the subtraction and you are finished.
Example: x^2 + 6x + 5
b = 6 -> p = -3 ; c = 5
Therefore,
x = -3 +- Sqrt(9-5) = -5 or -1
Another: x^2 – 2x – 8
b = -2 -> p = 1 ; c = -8
Now,
x = 1 +- Sqrt(1+8) = -2 or 4
April 2nd, 2009 at 9:01 am
And the last trick of mine is the coolest, used to solve q.eds with Sqrted and complex roots fast. You need to remember some squares of binomials and the equation should be nice enough (a=1, and then 2 divides b) (Or you can just have insane mental calculation powers and ignore these conditions).
First the examples:
We want to solve x^2 + 2x + 4 = 0 and first notice that there are no integer roots. Luckily ‘b’ is divisable by 2. We can rewrite:
= (x^2 + 2x + 1) + 3 = (x + 1)^2 + 3
Next we focus on the extracted +3. Take it’s negative and square root that. That’s Sqrt(-3) = iSqrt(3). Second focus on the root of (x+1) which is -1. Add these with +- and you’ve got the answer.
x = -1 +- iSqrt(3)
Solve: 0 = x^2 – 6x + 6 = (x-3)^2 – 3 -> x = 3 +- Sqrt(3)
Solve: 0 = x^2 – 6x + 11 = (x-3)^2 + 2 -> x = 3 +- Sqrt(-2)
To prove the method, assume the q.ed. has the roots p+-Sqrt(q). Then derive (x-p-Sqrt(q))*(x-p+Sqrt(q)) = (x-p)^2 – q and ponder a bit. Hope I gave you a good brainteaser! Study maths folks, it’s awesome.
April 10th, 2009 at 12:22 am
there r good maths tricks i m happy
April 14th, 2009 at 2:32 pm
11 times trick…
I just use the follwing…
e.g. 90 x 11
90 x 10 = 900
90 x 1 = 90
therefore 90 x 11 = 990
April 14th, 2009 at 2:41 pm
jp14 – “there is a trick done with 25 pennies… the object is to get the last penny not the most… you play with a partner and you can take as many as 3 or as little as 1… there is a fool proof way to win everytime see if you can figure it out and post it on your site”
make sure when you take the penny you are on odd number..
May 11th, 2009 at 4:50 am
My brain hurts.
May 11th, 2009 at 10:41 pm
Really Very Good Trick of essily Calculation,
i want to trick of big DIGIT Multiply, Divied,
Pls Send ME
May 13th, 2009 at 5:08 am
182. Darshan – May 11th, 2009 at 10:41 pm:
Start => Programs => Accessories => Calculator ;P
…
i remember seeing a book in our college library entitled “the trachtenberg speed system of basic mathematics” or something. their system is more versatile (includes long multiplication, division and square roots, among others) but also more complicated
May 14th, 2009 at 12:29 am
hi all,
I thankyou very much for ur valuable tricks. it helps me a lot. Can any one help me on this
Any trick to find the smallest of these 1/2,3/7,3/5,4/9.
I also want to know if any shortcut method for multiplying and dividing 3 digit number or more
May 14th, 2009 at 9:45 am
No.4 is useless i think. In the 3rd year of school in a romanian school every child has to know the Pitagora’s Chart
1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 15 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100
I think everybody should know this without a calculator
May 14th, 2009 at 9:47 am
it looked nicer when i wrote it
. Sorry about that
May 14th, 2009 at 10:10 am
*jessyb4u
first of all when you have more number use “;” not “,”
1/2; 3/7; 3/5; 4/9
find the smallest number that divides by 2;7;5;9
it takes long to explain how to do that but in this case is 2*5*7*9=63*10=630
now you divide 630 by each (630/2=315;630/7=90;630/5=124;630/9=70)
now multiply each number with the result (Ex: 1*315/2*315=315/630) and you will have the numbers to compare in a more convenient way
315/630; 270/630; 372/630; 280/630
now you can clearly see the biggest, the smallest,etc.
This way works all the time
Another way is to divide them:1/2; 3/7; 3/5; 4/9
1/2=0.50 ; 3/7= ~0.43 ; 3/5=0.60 ; 4/9= ~0.44
(You shouldn’t need a calculator for this small numbers)
But in this situation i would do something else
to find the smallest i would immediatly exclude 1/2 and 3/5 because they are equal or bigger than a half (0.5)
3/7= 0.5-1/7 ; 4/9= 0.5-1/9
1/7 > 1/9 so 3/7 is the smallest
(I would say you shouldn’t need paper to solve this problem, not even mentioning calculator)
May 14th, 2009 at 10:19 am
*177anonymous
This is not a trick and is definetly not yours, is just a way to solve exercises. this is an average problem for a 15 yo kid.
May 14th, 2009 at 10:28 am
174 V-ruz
STEP 7) 2(A2-AB)=1(A2-AB) (divide each side by (A2-AB)
you cannot do this
because A^2-AB=0
You cannot divide by 0 (One of the first rules in Math)
June 9th, 2009 at 3:16 am
1/3 off 10 foot
June 16th, 2009 at 2:58 am
TO answer Nagendra comment No 136
Ask the person to write one more 5 digit No
Below that you write your No by deducting his each digit from 9 (this will be 3rd Number)
Again ask him to write one more 5 digit number(4th No)
Here again in the fifth line write a number after deducting each digit of previous no from 9.
Add all five nos . The total will be the same.
eg.
32307 original no
12345 second no
87654 no you hv written
12345 another one written y him
87654 no you hv written
232305 Total(Written beforehand )
July 8th, 2009 at 12:47 am
plssssssssssss…..show more tricks on how to multiply easily………..tnx…………godspeed
July 11th, 2009 at 8:08 pm
these are the tricks that can only get you so far and can only be used for specific problems
July 12th, 2009 at 6:20 pm
i love these tricks
July 15th, 2009 at 4:04 am
july 15, 2009 i m not smart in math i am bobo
July 19th, 2009 at 5:31 pm
when i looked at this list, all i see is like a big white wall and my mind refuses to even TRY to understand. all my life in school i’ve had traumatic experiences dealing with numbers and math problems.
i’m not stupid. i am south east asian and i can can speak 2 languages and 3 dialects. i excel in english and grammar. i like to read and learn new things everyday. BUT MY MIND REFUSES MATH. what’s wrong with me?!
July 21st, 2009 at 8:28 am
fantastic tips but you need to check the accuracy of it
July 23rd, 2009 at 12:59 pm
Here’s MY nine times trick:
0 9 – 9 x 1
1 8 – 9 x 2
2 7 – 9 x 3 etc etc etc, it works great!!
3 6
4 5
5 4
6 3
7 2
8 1
9 0
July 25th, 2009 at 11:52 pm
IT’S REALLY VERY USEFUL. ONCE WE ARE THROUGH THE EASY TRICKS,IT TAKES HARDLY ANY TIME TO DO CALCULATIONS.WE SHOULD BRING THEM INTO PRACTICE BECAUSE IT’S SOMETHING THAT MAKES US DIFFERENT FROM OTHERS.
July 30th, 2009 at 11:39 am
Lets see my shortcuts of percentage…
1) 128 is increased by 30% . what will be the increased no.
= 128*1.3 = 166.4
2) 40% of ano. is 50 . what will be 20% of that no.
= 50*20/40 = 25
now what about this ……..need other shortcuts email me at koolguyz55@yahoo.com
July 30th, 2009 at 11:47 am
Hi its really very useful…
August 5th, 2009 at 2:59 am
long time reader but just signed up.
love this site.
love jfrater,Randall,mom424 to name a few..
nice to see some of my indian friends makin a fool of themselves here.
but why blame em? blame their english teachers i guess.
even better blame the brits- if they hadnt made english so friggin popular,we indians wuldnt have to go around sounding so friggin funny to everyone.
heard we sound better when speakin french or german.
cheers.
August 14th, 2009 at 11:26 am
Nice set or shortcuts. When I put together my own list at http://www.discreteideas.com/2009/08/the-shortest-path/, only a few of ours overlapped.
August 16th, 2009 at 12:01 am
very nice its so useful for us its is not so fast to do but it is easy to calcuate some one or two tricks is not under stable for me wheather i know i under stand it correct or not any way its so so so so so useful for me thank u thank u so much for your tricks and logic maths
August 19th, 2009 at 11:42 am
I am having a hard time with percentages….I like blog #90 but what do I do if the number you are trying to get the percentage of is not a perfectly round number like for example 120? I am sure it is easy I just need a really quick way to figure this out….for a career test. I am really really really bad at math. Also, if anyone knows any other good math exercises for tests like this to help me practice that would be great!
i love all these quick tips!
August 19th, 2009 at 11:59 am
Ok ignore the comment about the finding a % of a number like 120…I am a loser….I would however like some answers about the other stuff..Also what about multiplying double digits together quickly? I cannot multiply it on paper pretty quick..but not in my head quick. Something not so deep would be great!
August 20th, 2009 at 1:55 am
there is everything means trics are good.
August 24th, 2009 at 10:51 pm
here i’m with my trick
43*11 Its very easy
let do it
take first figure like this 4_3
now 4+3=7
put 7 betwen first figure 4_3
ans is = 473 amazing na!!!!!!
August 29th, 2009 at 9:42 pm
i like so much this tricks ,its very helpfull in compititve exams ,thnx to all who post their tricks
September 1st, 2009 at 12:24 pm
do u know that any digit repeating itself 6 times will be divisible by 3 , 7 , 11 , 13 , 37 and no. itself.
now what abt this one . if like this plz reply…….more tricks cmng soon
September 1st, 2009 at 12:25 pm
do u know that any digit repeating itself 6 times will be divisible by 3 , 7 , 11 , 13 , 37 and no. itself.
example 666666 or 888888
now what abt this one . if like this plz reply…….more tricks cmng soon
September 3rd, 2009 at 9:29 am
I have been teaching mathametics for last 20 years and now i am using tricks to solve maths problems my student .They are very happy and excited . THANKS A LOT
September 4th, 2009 at 1:06 am
thanx for the tricks!!! they all are just awesome!! i like them all!! thnxxxx
September 5th, 2009 at 11:19 am
Running 5/6 of his normal speed a man is 10 min. late. Now what is his usual time and time taken in this case ?
Sol: Multiply 5 and 10 means 50 min is usual time and he takes 60 min. in this case.
I havnt got any reply , thats why i m feeling dscrgmnt…so plz reply.
September 7th, 2009 at 11:57 pm
keep on going
September 10th, 2009 at 11:05 pm
hiiiiiiiiiiiiiiiiiiiiiiiii
September 13th, 2009 at 11:31 pm
these tricks are very helpful if you are preparing for competitive exam.
keep it going.
September 14th, 2009 at 5:27 am
Multiplication of two numbers of any length.
consider PQRS x WXYZ
(a) extreme right digit is S x Z
(b) Extreme left digit is P x W
(c) The middle digits are
R x Z + S x Y
Q x Z + S x X + R x Y
P x Z + S x W + Q x Y + R x X
P x Y + R x W + Q x X
P x X + Q x W
eg.:-
4053
x 7892
———
28219976
+ 37663 (carries)
———-
31986276
similarly
45
x 39
———
1215
+ 54
———
1755
one more eg:-
345
x 253
———
63975
+ 2331
———
87285
September 18th, 2009 at 4:44 am
@Miss Cellania (19):
Hi this is vikas srivastava , i just wanna new tricks for math to solve some and other things
September 24th, 2009 at 10:27 pm
@Reea (1):
hi reea…..how are you..??
i am intersted to being your friend…..call me on 9766871976
September 28th, 2009 at 4:10 am
Dono if someone has already mentioned.
Trick to multiply by 9:(for number from 1 to 9)
9*5=(5-1)_(10-5)=45
9*6=(6-1)_(10-6)=54
October 2nd, 2009 at 10:08 pm
Ialways see math tricks
October 2nd, 2009 at 10:13 pm
I am also support you dude
October 2nd, 2009 at 10:20 pm
IT IS VERY GOOD I LIKE IT VERY MUCH .BUT IAM NOT SO INTRESTED BECAUSE IAM ALREADY KNOW THESE TRICKS AND MORE
October 6th, 2009 at 2:36 am
The tricks mentioned here are almost known to all. please give some more extraordinary ones.
i hereby furnish a game of fun. try it with others.
ASK YOUR FRIEND TO DO THE FOLLOWING:
“Take a number lesser than 10.
multiply the number by 2 and then add 2.
then multiply by 5 and add 5.
then multiply by 10 and add 10.
finally add your age.
tell the result.”
YOU can tell the number that he/she taken initially and the age finally he/she adds.
how?
subtract 160 from the result. the first digit of the answer is the number he taken initially and the remaining digits reveal his/her age.
October 8th, 2009 at 4:11 am
@tony3s (3):th tricks wer given r easi understandable
October 9th, 2009 at 6:11 am
thank you for your help
October 12th, 2009 at 10:15 pm
i want a maths good riddle.please sent to Tenith_adithyaa@yahoo.in
October 15th, 2009 at 2:16 am
I LOVE THIS SITE VERY MUCH.DUDE
October 15th, 2009 at 2:18 am
I LOVE THIS SITE VERY MUCH.DUDEBUT MY FRND VIKAS DOESNOT LIKE THIS BECAUSE HE IS A BIG CHUTIYA
October 15th, 2009 at 3:09 am
I’s Very nice & easy to understand
Thank u
October 15th, 2009 at 6:50 pm
I ENJOYED YOUR SHORTCUTS TRICKS
October 22nd, 2009 at 12:02 am
% trick
It is very easy
Example:
17% of 250=17/100*250=42.5
It is so easy to do in single digit:
4% of 1000= 4/100*1000=40
try it in your exam
October 24th, 2009 at 1:21 am
Thank you very much. It is very helpful to me. I want to know more math tricks.
October 26th, 2009 at 2:37 am
i have a doubt in quick square can any one sort it out.
above mention that:
If you need to square a 2 digit number ending in 5, you can do so very easily with this trick. Mulitply the first digit by itself + 1, and put 25 on the end. That is all!
25 square(2) = (2x(2+1)) & 25
2 x 3 = 6
625
but what about 45 square
45 * 45 = (4*(4+1))&45
= (4*5)& 45
=2045 but
answer is 2025
October 26th, 2009 at 7:35 pm
@pidro (85):
October 26th, 2009 at 7:38 pm
can you tech me about arithtics becuase i don’t know.
October 26th, 2009 at 7:43 pm
hello can you help me asbout math?
October 28th, 2009 at 5:35 am
192*19= ?
October 28th, 2009 at 5:53 am
i have a doubt in quick square can any one sort it out.
above mention that:
If you need to square a 2 digit number ending in 5, you can do so very easily with this trick. Mulitply the first digit by itself + 1, and put 25 on the end. That is all!
25 square(2) = (2x(2+1)) & 25
2 x 3 = 6
625
but what about 45 square
45 * 45 = (4*(4+1))&45
= (4*5)& 45
=2045 but
answer is 2025
October 30th, 2009 at 3:23 pm
wow amazing thing! Ok going to Fishki.lt http://fishki.lt to relax after good mathematic break. Thanks very useful!
November 3rd, 2009 at 12:23 pm
Great Tips! I will share it with my students who take online math tutoring sessions from me. Thanks a lot!
November 6th, 2009 at 9:03 am
take a calendar.ask your friend to mark 9 numbers[in a 3*3grid] in a rectangle in the calendar.ask him/her to add 8 in the smallest number in the rectangle and multiply it by nine.write the total in a piece of paper.this is number a.now tell him to add the nine number.this is number b.now tell your freind to unfold the paper.he wiii be shocked!
November 10th, 2009 at 6:08 am
To add up the numbers 1 to x (any number) :-
multiply x by (x + 1) and then half the result
For example to add the numbers from 1 to 10 :-
10 x 11 = 110
110 / 2 = 55 (you can check this by doing 1+2+3+4+5+6+7+8+9+10 on a calculator or in your head)
This works for any whole number
November 12th, 2009 at 6:37 am
@jaiveer (222): @Online Math Tutor (242): @Gewgaws (244):
November 17th, 2009 at 10:37 am
beautiful list!
November 19th, 2009 at 6:56 am
thankyou!this would help me to do maths in faster and easier way…
thanks a lot!
November 19th, 2009 at 6:58 am
thankyou…..
this would help me to improve my maths and to do it in a faster ,simpler,easier way..
December 1st, 2009 at 8:41 pm
Thank you so much! Finding this was such a pleasant surprise. Doing math is going to be so much easier now that I have this to help me.
December 2nd, 2009 at 11:10 am
this is easy tricks
December 8th, 2009 at 9:20 pm
excellent way of making calculations so easy to do.
December 10th, 2009 at 1:17 am
these tricks are realy good.specially for the preparing of examination.
December 13th, 2009 at 6:34 am
NICE TRICKS!!!
December 15th, 2009 at 12:22 am
tricks are good but give more explanation to percentages & tough multiplication. could u explain that detaily.
December 16th, 2009 at 5:09 am
hiiiiiiiii … this is very cute …. i like this … very much
December 20th, 2009 at 2:23 am
tell your frind think a number between 80and 100 tell him/her to turn it and add then ask your friend to tell that 2digit number or 3digit he/she got then you want to ask which is the last number.if it is 2digit number the last number will be the first numberand if it is 3digit the middle number will be one more than the 3rd number and the first number will be 1
December 22nd, 2009 at 4:11 am
What about getting an Easy square root?
Please post some……..
I’m troubled with square roots
December 22nd, 2009 at 10:34 am
how about this:
You know that the square of 17 is 289. The square of 175(17 & 5) will be what?
289
+ 17
—–
306
—–
therefore 175 square is 306(25) ie 30625.
The square of 32 is 1024. What is the square of 325 (32 & 5)?
1024
+ 32
——
1056
—–
so 325 square is 1056(25) ie 105625.
1 last example
the square of 44 is 1936. What is the square of 445 (44 & 5)?
1936
+ 44
——
1980
——
so the square of 445 is 1980(25) ie 198025
Hope this was useful.
December 22nd, 2009 at 10:43 am
Ok, another one;
What is the square of 125? thats (1 & 25). Look at this carefully…
the square of 1 is 01 and 5 * 1 = 05 so.
01
+ 05
—-
015
—-
that’s 015(625) thats 015625.
what’s the square of 225? That’s 2 & 25. The square of 2 is 04 and 2 * 5 is 10. so.
04
+ 10
—-
050
—-
that’s 050(625) ie 050625
December 23rd, 2009 at 12:00 pm
suare of 289
December 29th, 2009 at 6:39 am
That’s pretty lot of math tricks for a number ignorant like me. Hahaha! I wonder why I haven’t learn those things in high school and college days. I guess I’d had a better chance of getting high grades then if I knew these things.
January 7th, 2010 at 11:41 am
this is sooo cool
I also know a good way of multiplying by 2
DOuble the NUMBER!! lol
JK
Really good website and plus I am amazed by the number of comments!!!!!!!!!!!
January 15th, 2010 at 3:36 am
.thanks for the tricks, it increased my grades in math.
.hope that you can make more awesome math tricks.
.good luck!
January 24th, 2010 at 7:07 am
tricks r so interesting i don’t like maths very much but its amazing & learning
January 24th, 2010 at 11:02 pm
wonderful
January 27th, 2010 at 4:10 am
@kartik (226):
February 3rd, 2010 at 12:38 am
cool its fun too now all these tricks thanks
xd
February 6th, 2010 at 1:39 am
i need maths faster calculation tips please send me
peshaveram@gmail.com
February 6th, 2010 at 5:11 am
It was interesting to me.
I apply this technique in my subjects
i have informed to my friends they where get interested….
February 8th, 2010 at 9:27 am
wow… what a wonderful & L-O-N-G list….lots of tips…lots of knowledge….Tis is COOL..
February 13th, 2010 at 5:35 pm
square root of numbers.e.g find square root of 961.firstly find that of 1,then that of 9.which is 3 and 1,answer=31.
February 16th, 2010 at 3:11 am
After visiting on your site it feels me that i get an ocean of short trics.
Thank you.
Please send me some more short trics for
multiplication of three digits
division of three digits
sqare of two or three digits
on my email id.