# Mental Calculation



## Psychosmurf (Aug 22, 2010)

With arithmetic calculations I visualize a mental sketchpad and do it in my head the exact same way I would write it out on paper. I can add and subtract up to 5 or 6 digit numbers in my head, multiply up to two 3 digit numbers, and do long division for almost as many digits. I'm also able to estimate logarithms in base 10 fairly well. 

With solving and manipulating equations it's completely different though. I don't experience the equation itself as being written on any kind of surface, it's just floating in a void and can shift shape according to algebraic rules. When I learn a new theorem, I see it as a new kind of super power I can use to transform equations. That way, each theorem I learn, rather than having an explicit representation in my mind, feels like an action I can perform, like breathing or balancing or hitting, etc.

So when I'm solving a problem, I don't have to list out every theorem I know and hope that I find the right combination of steps. Finding a solution feels a lot like walking to a familiar place. You're not thinking about where you're going, and you're not directing your legs anywhere. You just go, and find yourself at the destination.


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## Chinchilla (May 27, 2010)

Psychosmurf said:


> With arithmetic calculations I visualize a mental sketchpad and do it in my head the exact same why I would write it out on paper. I can add and subtract up to 5 or 6 digit numbers in my head, multiply up to two 3 digit numbers, and do long division for almost as many digits. I'm also able to estimate logarithms in base 10 fairly well.
> 
> With solving and manipulating equations it's completely different though. I don't experience the equation itself as being written on any kind of surface, it's just floating in a void and can shift shape according to algebraic rules. When I learn a new theorem, I see it as a new kind of super power I can use to transform equations. That way, each theorem I learn, rather than having an explicit representation in my mind, feels like an action I can perform, like breathing or balancing or hitting, etc.
> 
> So when I'm solving a problem, I don't have to list out every theorem I know and hope that I find the right combination of steps. Finding a solution feels a lot like walking to a familiar place. You're not thinking about where you're going, and you're not directing your legs anywhere. You just go, and find yourself at the destination.



The way I work with equations is much like this. My brain is like an imperfect program in that regards. I don't use rote memorization for each rule and I don't have to remember rules in words if I use them frequently. With an equation rules are like a new set of instructions in a program, allowing me to do something, or restricting me in another matter. I move variables in my head, I manipulate the equation, etc.

I do not use a sketch pad like you do for arithmetic.


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## ALNF1031 (Jul 27, 2011)

absentminded said:


> For me, it's a process of extreme deconstruction.
> 
> 210 x 35 = (200 x 30) + (200 x 5) + (10 x 30) + (10 x 5) = [(2 x 3) x 1000] + [(2 x 5) x 100] + [(1 x 3) x 100] + [(1 x 5) x 10]
> 
> ...


Interesting, in the problem 210 x 35, I would have just done this. (35 x 100 x 2) + (10 x 35)


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## Verrsili (Jun 13, 2010)

absentminded said:


> For me, it's a process of extreme deconstruction.
> 
> 210 x 35 = (200 x 30) + (200 x 5) + (10 x 30) + (10 x 5) = [(2 x 3) x 1000] + [(2 x 5) x 100] + [(1 x 3) x 100] + [(1 x 5) x 10]
> 
> ...


 This, except I only deconstruct it to the lowest level needed. You do it too, it's not necessary to write 10 out as 1 + 1 + 1. . .

(That's an exaggeration of course)


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## Einsteinette (Jan 19, 2011)

Alddous1031 said:


> Interesting, in the problem 210 x 35, I would have just done this. (35 x 100 x 2) + (10 x 35)


I'm great at pure Mathematics and sequential logic programming (C, C++, VHDL, JAVA...) but I'm not good with mental calculation so I use logic and approximation. For instance :
210*35=(200*35)+(10*35) 
= (100*70)+(350)
= (7000+350)
= 7350
Every time I'm splitting a bill with my sister she ends up screaming because she can't keep up with my way of doing mental calculation 

for instance if i wanted to do 54+35+22+62 i'll go like this:
54+35 is almost 55+35 which equals 90
22+62 is almost 20+ 60 which equals 80
90+80=170
we take 1 because we added 1 to 54 and we add 4 because we took 2 for 22 and 2 from 62 
so the final results is 170-1+4=170+3=173 
most people i Know insists on do it automatically by dividing numbers into units and tens like this :
units: 2+2+5+4=10+3 and tens :5+3+2+6=16 add 1=>17 
Results 173 ...:bored:


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## Spades (Aug 31, 2011)

As an INTJ, I find mental calculation a little tricky. I am better at reading a problem and intuiting how to solve it, not with the actual crunching.


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## Zeez Theory (Sep 1, 2011)

Einsteinette said:


> Every time I'm splitting a bill with my sister she ends up screaming because she can't keep up with my way of doing mental calculation
> 
> for instance if i wanted to do 54+35+22+62 i'll go like this:
> 54+35 is almost 55+35 which equals 90
> ...


I think it's really cool the way you do it. Only thing is "why add the extra integer to add an extra subtraction?"  It's unique.

I can do quick math as I go (just feels easier)...
54+35= 89+22=111+62= 173
To each is own. 

And as for 210x35...
(3500x2)+350
I tend to carry the zeros!
That's exactly how it popped in my head... easy enough.


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## HWard (Aug 24, 2011)

I'm not innately good at maths - I can do it when I work hard at it but they have a lot of rather odd concepts.


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## Sonya Awesum (Sep 11, 2011)

Zeez Theory said:


> I think it's really cool the way you do it. Only thing is "why add the extra integer to add an extra subtraction?"  It's unique.
> 
> I can do quick math as I go (just feels easier)...
> 54+35= 89+22=111+62= 173
> ...


Iunno. I'm relatively good with remembering numbers in addition, but I like to keep it as simple and clean as possible. In my head, I would just know 54 + 35 = 89, and 22 + 62 = 84. From there, I would just go 80 + 80 = 160 + 9 + 4 = 173. For the 210 x 35, I haven't been training myself heavily with multiplication, but I would probably go with 21 x 3 = 63, add two 0's, and 210 x 5 is easy, 1050, and then add to 7350. This is assuming I am really concentrating, 'cause for some strange reason with multiplication I can't keep numbers in my head for too long just yet :/

You're way is nice thought, very high-class


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## cantstopthinking (Aug 13, 2011)

I think I would shame alot of INTJ, but this is just me....

I THANK the inventor of the calculator because the time doing calculation would be best done by something more(most) efficient =D


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## dalsgaard (Aug 14, 2010)

I'm pretty good at mental arithmetic now, but I wasn't before I began to study maths more seriously. I have no inherent ability to calculate numbers, but I'm capable of developing it really quickly compared to the majority of people.


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