Mental addition/subtraction

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How many digits should the average, fairly well educated, person be able to add in their head?

For instance, is it reasonable to expect oneself to mentally perform computations like this?

-987 - -654

I can't do things like that. The insides of my mathematical lobe are coated with Teflon.

I used to be able to do "mental math" with three digits by visualizing the process in a series of pictures just as if I had written them on paper, but now I can no longer retain the previous frame after moving along to the next one.

Exactly, although I've never been able to do that with numbers.

License plates. I add up the license plates.

That wasn't too difficult. First, it's easy to say -(-654) = +654. Then you can subtract 654 from 987 to get 333. Tack on the negative sign and you've got -333. I did it in my head, I'm not very quick at it, however.

First off make it divisible by 10 ,
so in this case we put aside the 4 in - 650 and we take 987 and add a 3 to it.
Now we have - 650 and 990 ,
we have 3 and 4 - add these two together to get 7.
Then we add - 650 and 990 then subtract by 7.
To get 333.

All it takes is simple working memory to employ the algorithm.

Last edited by DuneyBlues on 21 Dec 2011, 3:04 pm, edited 1 time in total.

Presumably the process of addition and subtraction is trivial to almost any adult- that is, you would not struggle to add/subtract single digit numbers in your head and (given pencil and paper) you should have no trouble computing sums and differences of arbitrary numbers, regardless of how many digits they are. So the only real question here is one of working memory, that is being able to keep all those digits sorted while you work with them. My working memory was measured as comfortably above average but not particularly exceptional; I think I could probably handle a maximum of about 9 or 10 digits (your example has 6 total). The general mantra in psychology is that a typical working memory can handle somewhere around 7 digits at one time.

A fair amount of this will be down to practice, though. Working memory is one aspect of intelligence that appears more responsive to attempts at improvement. In chess, for instance, I can play multiple simultaneous blindfold games (ie, playing without sight of the board), which would seem to contain a lot more information than a simple string of digits, but it comes down to the brain finding more efficient ways to deal with the problems it sees more frequently.

I count inventory in grocery stores for a living by moving down aisles and entering "price times quantity" of the merchandise on the shelves at the rate of 4 thousand plus pieces per hour into a little computer on my belt.

I seem to be unique among my coworkers in being able to calculate what the price of the something that is "three for a dollar", or three for eight dollars is ( 33 cents and 2.67 respectively)without missing a beat.

People who can count faster than I can (including one guy who is also an engineer who youd think would have math aptitude) have to stop and ask me- or have to pause to figure it out on their own-or put their machine into calculator mode. To me its like breathing- I just do it. Its sorta part calculating and part memorizing.

But even I find it hard to subtract three digit numbers in my head like that. I just go " its something like subtracting 650 from 1000- so its about 350", and leave it at that.