Improving Your Mental Math Skills? 136
Infrared-Archer asks: "I want to learn how to do most math calculations in my head. That way I won't have to reach for the calculator for problems I should be able to do mentally. Of course there are various websites (beat the calculator) that show many tricks, but I am looking for a comprehensive solution (books, websites) that shows how to solve of wide range of math problems mentally. Any suggestions?"
No substitute for hard work (Score:4, Insightful)
Re:No substitute for hard work (Score:3, Interesting)
Re:No substitute for hard work (Score:3, Informative)
Re:No substitute for hard work (Score:5, Informative)
True, but the tricks do help quite a lot, in some cases.
For example, I expect most geeks can add, subtract, and multiply arbitrarily long numbers in their sleep. Division, however, (at least for me) has always proved somewhat tricky when the numbers grow beyond two or three digits.
My solution? Look up "duplation" on Google. The Egyptians used to use it to multiply numbers, basically in what amounts to a bitwise manner (though understanding binary helps to speed up the process, you can do it with nothing more complicated than "multiply by two" and "greater than").
However, as I said, doing multiplication doesn't present much of a problem. But you can also do division by using the inverse of duplation! You basically can break an arbitrary largeish division problem into a set of "divide by 2, compare" operations. Basically just long division in binary, but it requires a shorter mental stack (which seems like the key to all the tricks I've seen - ways to reduce the number of items on the brain's stack during the calculation).
So, I'll agree that nothing can beat plain ol' practice for improving one's math skills. But the tricks can make some operations go from "annoyingly hard" to the almost mindlessly easy "step a, step b, step c, repeat 5 times, get an answer".
Best way (Score:5, Insightful)
Re:Best way (Score:5, Insightful)
Work backwards for dividing by 5.
Re:Best way (Score:5, Funny)
Takes a bit of practice, but once you get the hang of it, it's a piece of cake.
Re:Best way (Score:2)
I hope you don't forget to round 0.5 to the nearest even integer. Don't want any bias creeping into your mental arithmetic!
Re:Best way (Score:3, Interesting)
I use this method a bunch, in various forms...distributing wierd values over things.
What's 19*19?
Well, it's 20*20, minus 20 (20*19) minus 19 (19*19).
Which is (20-1)*(20-1), which is (20*20)-19-19+1, or (20*20)-20-19.
Where did I learn this? I'm not really sure, since it was never actually taught to me, but I think I might have picked it up from Schoolhouse Rock. Go figure.
How that works (Score:3, Interesting)
20*19 - 19 = 19*19
Re:Best way (Score:2)
Re:Best way (Score:2)
Re:Best way (Score:3, Interesting)
95 * 23 = (100 * 23) - (5 * 23) = 2300 - 115 = 2185
I recognize that this is mildy picky, but the point is to show people how easy it is. What you're really trying to do here is to use numbers that you can do easy math on (5, 10, 50, 100, etc) and then account for the differences. This example works because 95 * 23 is the same as (100 - 5) * 23 is the same as (100 * 23) - (5 * 23), which is an easy mental calculation.
You don't have to think about this algebraical
Re:Best way (Score:1)
To me, 95*23 is 100*23 - 23 5's. 23 5's is 1/2 23*10. 230/2=115. 2300-115 = 2185.
Why would I want to work with 5 23's when I can work with 23 5's? :)
Re:Best way (Score:2)
I factor stuff quickly. I'd see that as (19*5)*23, or (19*23)*5. If I hadn't memorized that 19*23=437 (yeah, I memorized the multiplication tables through 200, I'm a geek), then I'd calculate that as (21-2)*(21+2)==21*21-2*2=441-4=437. Tack on the "divide by 2" trick to multiply by five and you get 2185.
First get your arithmetic up to scratch (Score:5, Interesting)
For added challenge translate every letter on there into a number using its place in the alphabet (or even its ascii number) and add them on.
You can then make up your own versions using other arithmetical operators and fractions.
After your arithmetic is up to scratch other areas of maths will be easier to do in your head (although beyond anything simple it is still best to write it down)
Re:First get your arithmetic up to scratch (Score:2)
I quickly upped the accuracy to (minutes
Vedic Mathematics (Score:5, Informative)
You could also try a google search I found some interesting websites
http://www.vedicmaths.comu /~rgupta/vedic.html
http://www1.ics.uci.ed
http://vedmaths.tripod.com
Hope this helps.
Re:Vedic Mathematics (Score:3, Interesting)
Land of serious mental mathematicians, not just Ramanujan the theoretician.
I remember reading, Guiness Book perhaps, of someone in India extracting high roots of many digit numbers.
Sometimes, even in Europe, mental mathematicians lead interesting and unpredictable lives [lk.net].
Re:Vedic Mathematics (Score:3, Informative)
My mathematician wife, by the way, pictures numbers as colors and can somehow do back-of-the-envelope calculations that way. I'm not entirely sure that's a sign of a healthy mind, but it seems to work for her.
Re:Vedic Mathematics (Score:5, Informative)
My mathematician wife, by the way, pictures numbers as colors and can somehow do back-of-the-envelope calculations that way. I'm not entirely sure that's a sign of a healthy mind, but it seems to work for her.
I do. Not really numbers, but letters. It has deteriorated over the years for me. Apparently, it is called synesthesia [go.com]
Re:Vedic Mathematics (Score:2, Insightful)
Re:Vedic Mathematics (Score:4, Funny)
Thanks again.
Re:Vedic Mathematics (Score:5, Interesting)
The guy who wrote it, Tirthaji, was a fraud. Every word and every claim in the book reg. the history is fabrication. The math is also pure junk and utterly useless.
Seriously. I did a term paper on it last year. You don't have to take my word, of course: read this article [tifr.res.in] by Prof. S. G. Dani, School of Mathematics, Tata Inst. of Fundamental research (the premier research inst. in India.) There's also a much more detailed version. [tifr.res.in]
Unfortuntely, the book fits the political ideology of the current Hindu-fascist government in power in India, and so they've been promoting it big time.
Re:Vedic Mathematics (Score:2, Interesting)
The article seems to be picking issues with the author of the book, rather than Vedic Maths itself. OK, Vedic Maths is a misnomer (not much math is from the Vedas)
Also, the sutras are useful to a large extent. (Though most of the sutras have exceptions, and blah blah)
To end, yeah, Vedic Mathematics (sic) is a very useful tool in mental maths.
blind leading the blind (Score:4, Insightful)
My point is that if you want to get quicker with your mental math skills or keep your current pace, you have to keep using it or else it will atrophy like everything else. Translation: college math courses or at home math excercises, but either way don't expect to be able to ever be "done" with it.
Good luck with that by the way, you're a better man than I.
Re:blind leading the blind (Score:3, Interesting)
Re:blind leading the blind (Score:2, Interesting)
If you're really good at math, I'll guess that you're very bad at drawing/sketching. (That's always been my experience, but I'm sure there are plenty of exceptions to that rule, so forgi
good post (Score:2)
Let me say this about being good at math. Not surprisingly, it's (almost) all about practice. I'm not denying the possibility of natural talent playing a role, but I think probably anybody could reach the calculus level without much need for natural talent, as long as there's no time pressure and you do a lot of work.
You have to do lots and lots of example problems. As you do, you start to develop a "feel" for them. If you do it enough to de
Re:blind leading the blind (Score:2)
Cheers!
Re:blind leading the blind (Score:3, Insightful)
I read your comment, boggled appropriately. Thought about the problem for a moment, figured out how to solve it, smiled, moved on. I still don't know what the answer is.
The odd thing that most people don't really get about math is that, the more math you know, the less you deal with actual numbers, and heaven forbid you should ever do any arithmetic. The best math professors I had all had trouble doing extremely easy multiplication. There's a reason comp
Re:blind leading the blind (Score:2)
I recently bought a projector, and was in process of wanting to build a screen for it. I knew the width and height would be 4:3, but I wasn't quite sure how to get the diagonal....
Then I saw on a web page -- just remember "3,4,5" with 3 being the height, 4 the width, and 5 the diagonal... and with that, you can solve any regular TV size image....
My problem being, I had a diagonal I wanted to shoot for (since I knew where I wanted the projector) but didn't know
Re:blind leading the blind (Score:2)
Re:blind leading the blind (Score:2, Informative)
This one is the right way:
(3/3a)^2 + (4/3 a)^2 = 20 ^2
since 3^2+4^2=5^2 we get
(5/3 a)^2 = 20 ^2, so
20 = 5/3 a and a=12.
So: height = 12, width = 16.
Re:blind leading the blind (Score:1)
7/3 * a^2 = 400
to
a^2 = 40 ?
Should be a^2 = 171.429, a = 13.09, dimensions = 13.09" x 17.46"
Reverse it to check gives us 304.85 + 171.35 = c^2
22"....okay, so maybe I'm a bit off too. =P
Just do it! (Score:5, Insightful)
Memory, mental arithmetic and mathematics
Messed up my html - here's the link (Score:3, Interesting)
For the lazy... (Score:3, Informative)
http://www-gap.dcs.st-and.ac.uk/~history/HistTopic s/Mental_arithmetic.html [st-and.ac.uk]
Math Magic by Scott Flansberg (Score:3, Interesting)
It's a really great book.
I went from functionally innumerate to someone who can perform tricks with multiplication/division in my head,
It seems to use some of the vedic tricks mentioned in previous comments, but it's far more simpler to learn and put into practice.
Re:Math Magic by Scott Flansberg (Score:2)
Try an abacus. (Score:4, Interesting)
These days, I have a new baby to worry about (Jaime, a girl, Mar 4, 5 lbs 13 oz) so I haven't had a chance to play with one yet. After meeting those kids, though, I do want to take a look and see if it could help me.
Feynman (Score:5, Interesting)
"Cube roots! He wants to do cube roots by arithmetic! It's hard to find a more difficult fundamental problem in arithmetic. It must have been his topnotch exercize in abacus-land.
"He writes a number on some paper--any old number--and I still remember it: 1729.03. He starts working on it, mumbling and grumbling: "Mmmmmmmmagmmmmbrrr"--he's working like a demon! He's poring away, doing this cube root.
Meanwhile I'm just sitting there.
One of the waiters says, "What are you doing?"
I point to my head. "Thinking!" I say. I write down 12 on the paper. After a little while I've got 12.002.
The man with the abacus wipes the sweat off his forehead: "Twelve!" he says.
"Oh, no!" I say. "More digits! More digits!" I know that in taking a cube root by arithmetic, each new digit is even more work than before. It's a hard job."
Feynman goes on to explain the approximate method he used to get the result, and then gives his analysis:
"I realized something: he doesn't know numbers. With the abacus, you don't have to memorize a lot of arithmetic combinations; all you have to do is learn how to push the little beads up and down. You don't have to memorize 9 + 7 = 16; you just know that when you add 9 you push a ten's bead up and pull a one's bead down. So we're slower at basic arithmetic, but we know numbers.
Furthermore, the whole idea of an approximate method was beyond him, even though a cube root often cannot be computed exactly by any method. So I never could teach him how I did cube roots or explain ho lucky I was that he happened to choose 1729.03."
The rest of that chapter (entitled "Lucky Numbers") talks about his experiences in trying to improve his mental math skills. Definitely worth a read.
Re:Try an abacus. (Score:5, Informative)
Re:Try an abacus. (Score:3, Funny)
Visualisation? (Score:4, Informative)
Some links (click the 1's). Some are for dylexics but still relevent for all since pretty much all of us are capable of visual thought...:
1 [utep.edu] 1 [humboldt.edu] 1 [mathematica.co.kr] 1 [google.com] 1 [sunysb.edu] 1 [artima.com] 1 [suite101.com] 1 [amazon.co.uk] & similar 1 [bda-dyslexia.org.uk] 1 [lboro.ac.uk] 1 [lboro.ac.uk]Re:Visualisation? (Score:3, Funny)
Obviously.
Practice (Score:2, Interesting)
Like everyone else, I say practice makes perfect. I do a lot of UI layout at work, and to conform to interface guidelines, I do a lot of "that control's left plus that control's width plus 14". Little things like that can make all the difference in the world.
Now, so that I don't get modded as redundant ;) Try this:
Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000.Now add 10. What is the total?
Did you get 5000? The correct answer is actual
Actually... (Score:1)
Logarithm tricks: Rule of 72 (Score:5, Informative)
The rule of 72 helps to figure out how long it takes for something to double or halve. Divide 72 by the percentage rate of growth or decrease and you'll get the number of time periods in which something will double or halve. For example, let's assume Moore's law says double CPU speeds every 18 months. 72/18=4. So CPU speeds increase by 4% every month. Or another example: your phat mutual fund gets 12% per year, so 72/12=6. So your money will double in 6 years.
This trick is so simple that even the finance guys always know it.
Re:Logarithm tricks: Rule of 72 (Score:1)
That should say that you'll get an approximation of the number of time periods. Your mutual fund example would take about to 5 years 10 months to double and not exactly six years, and obviously something which increases 72% in a single period has not doubled.
Re:Logarithm tricks: Rule of 72 (Score:2)
The rule of 72 is closest when the number of periods is 9: rule of 72 gives 8%, actual calc gives 8.006%.
When the number of periods is 4, the differences is almost a whole percentage point: Rule of 72 = 18%, actual = 18.921%.
After 9 periods, the rule of 72 starts giving results that are larger than the actual number, but less than a tenth of a percent different:
10 7.200% 7.177%
11 6.545% 6.504%
12 6.000% 5.946%
13 5.538% 5.477%
14 5.143% 5.076%
15
Re:Logarithm tricks: Rule of 72 (Score:1, Troll)
No but thanks for the tip on attention-getting fonts with '<tt>'.
That's fancy... a simple trick (Score:2)
When adding two numbers, say 27 + 36
Round both numbers to next whole multiple of 10
so you get 30 + 40 which is obviously 70
then add the two differences 3 + 4 which is 7
subtract this from the total 70 - 7
which is obviously 63 and there you have the answer in a so much easier fashion than adding those two ugly numbers.
And yes, this is how my mind works.
Re:That's fancy... a simple trick (Score:2)
Here's your method:
27 + 36 = 30 + 40 - ((30-27) + (40-36)) = 70 - (3+4) = 70 - 7 = 63
Here's my method (and what we all learned in school):
27 + 36 = 20 + 30 + (27-20) + (36-30) = 50 + 7 + 6 = 57 + 6 = 63
Your method involves more subtraction, which is harder for most people. And because it's subtraction, it's more difficult to change the grouping in the later calculations. I.e. with 50 + 7 + 6, you can choose to add the first t
Re:Logarithm tricks: Rule of 72 (Score:1, Insightful)
The rule of 72 helps to figure out how long it takes for something to double or halve. Divide 72 by the percentage rate of growth or decrease and you'll get the number of time periods in which something will double or halve. For example, let's assume Moore's law says double CPU speeds every 18 months. 72/18=4. So CPU speeds increase by 4% every month. Or another example: your phat mutual fund gets 12% per year, so 72/12=6. So your money will double in 6 years.
In actual fa
You want to improve your arithmetic skills (Score:1, Insightful)
Easy (Score:2)
This book... (Score:2)
That said, "Rapid Math Tricks and Tips: Thirty Days to Number Power" by Edward H. Julius is great. It is a little cheesy, but very practical. It allows you to do much of the same calculations that a 'child prodgy' can even if you're old.
It does not help with number theory, though it can help give you a much better feel for numbe
You want Trachtenberg Speed-Math. (Score:5, Interesting)
Run a google-search on "trachtenberg math" [google.com].
You're looking for sites like Trachtenberg Speed System [mathforum.org] or Trachtenberg Math [mdc-berlin.de] (Multiplication [mdc-berlin.de]).
Professor Jakow Trachtenberg was a brilliant mathematician. Imprisoned by the nazis during WWII, he kept his mind busy to survive by applying advanced mathematical techniques to numeric computation. Eventually developing a number of techniques that provide for rapid mental computation without massive rote memorization.
For example:
Re:You want Trachtenberg Speed-Math. (Score:2)
I also recall reading a book about him, and there were some really cool techniques for multiplying by multi-digit numbers that required almost no intermediate calculations to be written down. Unfortunately, one of my teachers marked me down when I used them, as she assumed I had to b
Re:You want Trachtenberg Speed-Math. (Score:2)
utilize the subconscious (Score:3, Funny)
The trick then is to let your subconscious do the math for you, and then find a way to "pull out" the answer (like recalling a distant memory, almost). You can train your subconscious to do math a variety of ways, but one of the most effective is to electrically stimulate nerves (in your hand or arm or thigh, whatever) to count out numbers. So for instance, if you wanted to do 22+34, you'd count out 56 quick electic pulses. Practicing this for a few months, your subconscious will eventually get the idea that when you hear numbers, you want them added. The electric shocks will no longer be necessary, but your subconscious will still internall 'tick' out the answer. It works for multiplication, too, and through various mathematical tricks, you can use it to subtract and divide.
The only remaining difficulty is training your conscious mind to retrieve the result. This is accomplished via a hypnosis-like state. You can get good at it so that it only takes you a half-second to pull out the resulting number. No eyes rolling back or chanting or anything like that.
Heh, ok, not really.
Math Tricks (Score:2, Insightful)
Second, knowing a few tricks isn't enough. Understanding the tricks and why they work is the key to improving your math skills. Beyond access to a teacher to help you with this, you may want to try some resources available on the web like MIT's OpenCourseWare [mit.edu]. They have a lot of information available on
Re:Math Tricks (Score:2)
Dear lord, don't do this. Go get yourself a copy of Euclid's Elements [amazon.com] instead. Or take a look at the java-enhanced version [clarku.edu] online.
The Elements is a brilliantly organized treatment of the science of geometry as a whole. While reading it, ask yourself what the subject of each book is (there are 13 books). Ask why they're in the order they're in. Ask why the propositions within each book are done i
You need a different job (Score:2)
It comes down to practice, and the only way you will practice is when you have to do it. So get a job where you have to do this.
When I worked carpendry I got really got a multipling by 1.42 (guess why[1]) because that is something we had to do often, and calculators didn't last more than a week on the job so we rarely had one. (The foreman would buy one if he knew a lot of calculations were coming up, but he often had to do math by hand) In that job there there is plany of surface to work with so we wr
Re:You need a different job (Score:1)
That's what I've been doing wrong... I've been taking jobs in physics laboratories and university faculty positions to sharpen my math skills - I need to apply at McDonald's!
Re:You need a different job (Score:2)
You are mistaking arithmatic for Mathamatics. You will use the latter in a university and the former in low end jobs. Very different skills, are needed.
One thing somebody did to me (Score:2)
Anyway, what he would do is get various slides with various simple multiplication problems of the form xx * x, and show them for all of 1.5 seconds each before skipping the next one. (The x * x form was something learned early on.) The object was to be able to know the answer to said problem immediately on sight. EG, you see 12 * 5, and 60 theoretically registers
Try doing square roots in your head. (Score:2)
Similar story - once, after a trip to a casino, I got it into my head that red/black roulette betting could be won all the time using the simple strategy of "Always bet the same color, and when y
Re:Try doing square roots in your head. (Score:1)
I got it into my head that red/black roulette betting could be won all the time using the simple strategy of "Always bet the same color, and when you lose, double your bet."
Not true. Consider:
Start with $1500
Bet $100 on red, result is black, loss = $100
Bet $200 on red, result is black, loss = $300
Bet $400 on red, result is black, loss = $700
Bet $800 on red, result is black, loss = $1500
Player is broke, and cannot bet again
Keep in mind that probability states that red and black have equal probabilities
Re:Try doing square roots in your head. (Score:2)
Re:Try doing square roots in your head. (Score:2, Informative)
Re:Try doing square roots in your head. (Score:1)
The green numbers fuck this strategy up.
P(red) = 18/38 = .47
P(black) = 18/38 = .47
Eventually, you're going to lose either way.
One Speed Math System (Score:3, Informative)
Visualize (Score:5, Interesting)
As I did these arithmetic problems, I found that my mind developed a kind of blackboard. I could visualize the problem and effectively "write" the answer without worrying about keeping track of everything as separate digits.
My advice: Find a good algorithm, practice a lot (yep, hours and hours), draw a picture in your mind.
The bonus of doing this is that later when I started studying math, the visualization I'd developed helped lots in advanced courses. I could "see" solutions almost instantly that would take others awhile to derive and even then they wouldn't really understand the relationships which led to the solution.
Re:Visualize (Score:1)
Give it enough patterns and the answer pops out. Multiplication tables are one pattern, and fraction tables (1/2 = 0.5, 1/3 is approx.
Memorize the first dozen or so entries of each table that correspond to whole numbers (or whatever logical pattern you can discern) and pretty soon your brain will use the patterns to organize the answer for yo
The book I learned from... (Score:1)
was Calculator's Cunning by Karl Menninger.
I believe it's out of print now, but was an excellent text, covering all of the tricks.
If you search bestwebbuys [bestwebbuys.com] you can see that it is for sale used.
A long long time ago (Score:2)
No tricks involved. I did it just like you would do it on paper.
A benefit seems to be that I'm able to remember phone/pin/account numbers and random passwords easily. And I avoided being brainwashed...
Math as an adult (Score:4, Interesting)
For example, if you knew what you were looking for, such as calories or joules or centimetres, that's one part of it. If you know the formula relevant to the situation, that's another. Then you get to basic arithmetic skills- it doesn't do you any good to know the formula if you can't add or multiply the numbers.
My favourite way to tutor math- and how i learned it as an adult (i never took the SATs and was fortunate to have a tutor who could teach me high school math even though i'm 27) - is to use basic math issues that everyone sees, every day. Like the label on food. If this equals x% of your USRDA, how much is the USRDA? Putting the problems in everyday life situations may make you more comfortable with the math,a nd it will definitely leave you with an idea of the numbers involved.
'An idea of the numbers...' by which i mean a feel for the numbers, and what they stand for. A lot of people have trouble connecting the numbers to reality- and if you can understand in a concrete way the relationship between the distance around a pipe and the distance across it, the math may stick better for real world use later on.
The other trick? Estimate where you can, and use the information that's easily accessible to you..
For example: What's 5% of the time in a week?
well, you know that there's 24 hours per day. Add the big numbers first- 20 times seven, that's 140, right? plus four times seven- 28. Right off the bat, you're up to 168 hours in a week. Ten percent of a number is easy, ten percent of this number is 16.8. Half of that will give you the five percent that you're looking for- 8.4. You've just figured out that 8.4 hours is 5% of a week. Convert that .4 into minutes- forty percent of an hour is a little less than half. (sixty minutes, times ten percent, is six minutes. That's ten percent. Four times six is twenty four minutes. That's forty percent.) The answer? Eight hours, 24 minutes.
I use this with others because it teaches people how to think about numbers, that they are reachable things, not just the provenance of mathemagicians. The biggest barrier to doing math is the belief that math is too difficult. (i also play for people Tom Lehrer's wonderful song, New Math, and assure them that we're going to ignore base 8.)
Good luck with it, and try to use it in the real world where you can get a feel for what the numbers attach to. Figure out what you know and what you need to know, and just practice. There will always be more math to attempt; there will always be stuff that's intimidating. The only way to learn it is to do it, a piece at a time from the information that you can grasp easiest.
Oh, and in high school, in that science class? i got a C. Worked hard for it, i've never been prouder of a grade then or since. And i've never forgotten the real stuff i learned there- that being able to describe what you're reaching for is as important as the math skills to get you that answer.
Re:Math as an adult (Score:1)
Don't forget (Score:1)
Life imitates art (Score:2, Interesting)
"Doomsday" algorithm (Score:1)
What's the point? (Score:1, Interesting)
Re:What's the point? (Score:1)
Here it is. Re:What's the point? (Score:2)
What if you need to program the computer to square numbers that are larger than the word size can contain? (i.e. arbitrary precision arithmetic)
If you know the math tricks, you can do this easily. If you don't, you have to struggle to do it analytically, which is a pain.
Quick, how can you figure out the lowest set bit of a number?
Answer to the previous problem (Score:2)
Everybody else has their opinion too... (Score:3, Insightful)
But there is one thing that I *always* tell my students. That is this: There are many, many, MANY ways of going about doing a math problem. Sometimes the way the book describes it, or the way the prof tells you to do it doesn't make as much sense to you. For instance, some people understand fractions better than decimals, or vice versa. As a statistician (or future statistician at the time) I would always convert fractions to decimal before I worked with them because it made more sense to me. (I just had to remember to convert them back when i was done)
Point being...there are many correct ways to come to a correct answer. When we learned to multiply and do long division in elementry school we were taught an algorithm for doing so. However, as some people have already posted their 'tricks', there are other algorithms out there. You just have to make sure it actually yields a correct answer before you utilize it. (If you don't want to formally prove it, like me, then you can try it on at least 3 different sets of varied number sets. Don't pick simple numbers, they can often lead you to a wrong conclusion)
Find what works best for you. (as long as its correct!) I'm a big fan of rounding numbers, calculating them and then adjusting them from there. e.g. 17 x 4 is almost 20 x 4 = 80, but we left out 3 of the 4's so the answer is 80-12 = 68. (IMHO the algorithm we learned in elementary school for multiplying is the worst way of trying to calculate something in one's head!!!)
A good trick I use when calculating discounts in stores (i.e. 70% off, 25% off etc.) is to figure out how much 10% of the price is. This is easy, just shift the decimal point. Then if its 70% off, I'll take the 10% off price and multiply by 3. Unless it is easier to calculate it the other way around. If it is 25% off, I'll divide the price by 4 and then subtract that.
Anyhow, I haven't really given any specifics or good examples, but explore thinking about the problems in slightly different manners and then making small adjustments to the final answer. Do what makes sense to you.
Hemi-Sync (Score:1)
Listen to this CD every day and your skills will VASTLY improve:
Buy the Numbers CD [hemi-sync.com]
Memory improvement (Score:3, Informative)
One activity you can indulge in can simultanesouly improve your memory, make you feel good and allow you to show off in front of your friends so they will think that you are a really intelligent person (which I am not saying you aren't, but people who aren't really into this kind of brainy and "geeky" activity will surely be very impressed) is to memorize 1000 digits of pi [ernet.in]. It's funner than you may think, as it's a real challenge and over time will increase your capacity to use the full potential of your memory properly.
bookstore... (Score:2)
Tricks for Div 3, Div 7, and Primes (Score:2)
To tell if a number is divisible by 3:
- sum up the digits
- if the sum divides by 3 with no remainder, the orginal number is divisible by 3 with no remainder.
The proof is pretty trivial to work out. It only takes a few lines to prove it.
Another trick, that isn't well know, and that I can't take credit for is
A number is divisible by 7 if
- take the last digit off a number and double it
- subtract the
Re:Tricks for Div 3, Div 7, and Primes (Score:2)
The margin wasn't big enough to write it down?
Two books I have... (Score:3, Informative)
"Consider a Spherical Cow" [amazon.com] and there's a 2nd book "Consider a Cylindrical Cow" :-) - which is about how to do "back-of-the-envelope" estimates. How many pairs of shoes can be made from a single cow? Consider a spherical cow. :-)
And a Dover reprint: "How to Calculate Quickly" [amazon.com] which has many of the tricks and rules of thumb people used to all know before calculators.
From my "antiquarian" collection I have a number of "arithmetic" textbooks (all pre-1930) that have lots of little rules of thumb for checking sums and products - many are familiar to accountants. Also great chapters like "Arithmetic of Thrift", "Arithmetic of Agriculture", etc. with problems like "...girls in a class in millinery need 20 yd. of ribbon..."
Kilometers Miles Tricks (Score:2)
To convert a number, K from kmph to M mph
M = (K / 2) + (K / 10)
i.e.
90 kmp = 45 + 9 = 54
The relative error is 3.4%, which isn't too bad.
I usually drop the fractions, so the formula becomes
M = int(K / 2) + int(K / 10)
Even though the relative error will be a tad higher at low speeds, and oscillate around 3 to 6% for the most part, the absolute error is at most off by 3 mph for speeds less
augment your brain instead! (Score:2)
god bless the public school calculator generation!
Two good sources (Score:1)
and don't forget the Doomsday Algorithm [rudy.ca] which is actually useful on an almost daily basis.
I tend to run out of general purpose registers (Score:2, Funny)
Times tables (Score:2)
Check the way you normally think of things (Score:2)