Nice Math Tricks..

Troberg

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The lines method stops working as soon as you get more than ten dots in any intersection.

It can, however, be generalized as follows (using code tags to get monospace font):

B4X:
Problem: 277 * 524
 
Set it up like this:
      5      2      4
2
7
7
Then multiply all the intersections (normally, you don't write this step).
      5       2       4
2    5*2     2*2     4*2
7    5*7     2*7     7*7
7    5*7     2*7     4*7
to get
    5   2   4
2  10   4   8
7  35  14  28
7  35  14  28
Now, we'll add up the numbers diagonally, starting at the bottom right.
First diagonal:
28. Write down 8, keep the 2.
Next diagonal:
2 + 28 + 14 = 44. Write down the 4 before the 8 so we get 48, keep the other 4.
Next:
4 + 8 + 14 + 35 = 61. Write down the 1 to get 148, keep the 6.
Next:
6 + 4 + 35 = 45. Write down the 5 to get 5148, keep the 4.
Last:
4 + 10 = 14. Write it down to get 145148, which is the correct answer.
If you have decimals, just do the same thing, then count the total number of decimal digits in both numbers (for example, in 1.23 * 4.56, it would be four) and set the point so that you get that number in the result (5.6088).
I like this method, because it's simple and clean. First all multiplications, then all additions, and the carry comes naturally.
 

ilan

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Imagine doing 15x35 by this method
15x35.png


15*35 with this method is very simple (without is also simple) but,
imaging you are in the desert and you want to calculate how much is 937 * 284 and you dont have your iphone with you...
 

Troberg

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imaging you are in the desert and you want to calculate how much is 937 * 284 and you dont have your iphone with you...
Well, "my" method, which is mathematically the same as the lines method, works nicely, even with very large numbers. Try to calculate 897979874 * 3948034 using the lines method...

Also, if I'm lost in the desert, math is low on my list of priorities... :)
 

thedesolatesoul

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The one used in Swedish schools mixes up the operations, so it's some multiplications, then additions, then back to multiplication, then addition and so on.
Thats interesting, made me go to the wikipedia page: http://en.wikipedia.org/wiki/Multiplication
You were probably using th Egpytian method!? lol or maybe modern.
I dont actually know what method i use.

Also, if I'm lost in the desert, math is low on my list of priorities... :)
I wouldnt mind keeping myself preocupied playing in the sand with numbers, till hunger gets the better of me...
 

thedesolatesoul

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Troberg

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Thats interesting, made me go to the wikipedia page: http://en.wikipedia.org/wiki/Multiplication
You were probably using th Egpytian method!? lol or maybe modern.
I was taught the long multiplication (or, rather, a slight variation of it), but that was 35 years ago and it's not the one they teach today. The current method, I'm sad to say, is one I haven't bothered to learn. (And don't get me started on division, I think they've changed method five times since I went to school, each time to the worse...).

But, long and lattice are actually quite similar, just arranged a bit differenly. What I like about lattice is that, right up to the final answer, it keeps the numbers small (large numbers are scary and are a mental hurdle when teaching to newbies) and it makes the carry more natural (just drop of the ones digit and continue). To me, lattice feels more linear.

I haven't tried applying it to polynomial multiplication yet, though.
 

RandomCoder

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I've always found that a calculator works best for me, I was in that generation in which they were widely used in schools (even had the Casio calculator watch). Struggle to do any type of serious math in my head :oops:
 

udg

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I am from the old-school. Seldom used a calculator and, to say it all, I never "trusted" that much a calculator's answer..:eek:
To multiply two numbers, each two-digits long, my mind would suffice and be 100% accurate.
To multiply two numbers, first one three digits long and second one two-digits, I could have done it by mind 100% accurate if not "difficult" digits (7 or 9) were involved expecially on the first operand.
Any other operation went on paper. Generally, the feeling was that my writing hand knew how to compute the result on its own, with little intervention from the mind.
Probably that's the consequence of thousands of math exercises..but I really enjoyed them; just turned on the radio, selected a fast pacing music and began homeworks!

Today I am an ex-teen ager (more or less) and my math abilities faded somewhat, but you won't believe how much I enjoy helping my son with his homeworks..a good excuse to listen to some AC/DC tracks while letting my writing hand fly on paper! :D
 

Troberg

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Licensed User
I am from the old-school. Seldom used a calculator and, to say it all, I never "trusted" that much a calculator's answer..:eek:
I do a lot of math in my head. Usually, you only need an approximate answer, and I can usually find an approximate answer faster in my head than on a calculator. I almost never do arithmetics on paper, although I do use paper for algebra.

Today I am an ex-teen ager (more or less) and my math abilities faded somewhat, but you won't believe how much I enjoy helping my son with his homeworks..a good excuse to listen to some AC/DC tracks while letting my writing hand fly on paper! :D
I know the feeling. I've helped my step daughters and the the eldest girls boyfriend with high school and university (or, rather, the Swedish equivalents, as we cut the line between high school and university a little differently) maths, and it has been very rewarding. It's been fun seeing them grasp "math as a language" and get a feel for it. It's also been very developing for me. When I went to school som 25 years ago, I just learned "how" and pretty much skipped the "why", because that's all that was needed to ace the tests. However, as I helped them, I realized that, from the experience gained by using the math over the years, I've also gained an intuitive understanding of the "whys".

However, helping them also gave me a deep hatred for math book authors. Seriously, math books are the most un-pedagogic crap you can find. Some are better, some are worse, but I've yet to see one actually reach "acceptable". When teaching advanced math, the most important hurdle you need to get the student over is "Why is this important for me? When will I ever have any use of this?". It's by far the most common problem, the student fails to see the relevance, and thus fails to muster interrest in the subject.

So, how does the authors handle this?

They don't. They are usually the kind of mathematician who somehow thinks that "Real world examples sullies their nice, clean math". Seriously, they are about as useless as a car mechanic who doesn't want to get his shiny tools dirty. If there are any real world examples, they are usually token examples thrown in at the end of the chapter, and so abstractly unpractical that they only become ridiculous. They totally fail one of the three basic rhetoric pillars, ethos (why is this important to me?). I could easily come up with dozens of real world examples that feel real and relevant, which were much better than the ones in the books.

Also, when the books explain something, they tend to do it halfway, which just leaves the reader confused. I could "decode" it with my math skills, because I've already knew it, but if you don't already understand what they were trying to explain, it's more or less unintelligble.

Seriously, I almost considered writing a better book myself (perhaps with a little help from a mathematician friend).

Still, that said, help kids with math. It's really rewarding on so many levels.
 
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