Mental calculations can be quite daunting. However, do you know that we can easily do mental calculation for addition and subtraction up 4 digits.
The theory goes like this:
1) Human mind can hold up to 7 bits of information consciously at any one time. (why do you thing most phone numbers are 7 or 8 digits? =D)
2) It is easier to do the addition or subtraction from left to right (most significant digit first).
3) Use some common sense to do some simplification to the questions.
Now for the exciting part:
Lets say we are going to do addition for 56 + 43. Instead of the conventional way of doing from right to left (least significant digit first)
We do addition from the most significant digit
56 + 43 = 56 + 40 + 3
=> 56 + 40 = 96 then 96 + 3 = 99
It may seems trivial at this stage to do mental addition subtraction from left to right. It becomes more apparent as we do number with more digits.
For subtraction:
95 - 48
There is 2 ways. First is the same as above, doing from left to right (the most significant digit first)
95 - 40 = 55 then 55 - 8 = 47
Second, since 48 is close to 50, we can do this:
95 - (50 - 2) = 95 - 50 + 2
95 - 50 = 45 then 45 + 2 = 47.
Now lets take a look at addition and subtraction for the hundred position.
567 + 325
=> 567 + 300 + 20 + 5
=> 867 + 20 + 5
=> 887 + 5
=> 892
786 + 593
=> 786 + 500 + 90 + 3
=> 1286 + 90 + 3
=> 1376 + 3
=> 1379
Try out these sums mentally. You will realized that with practice, doing addition and subtraction mentally is really easier when we do it from left to right (from the most significant digit)
687 - 396
=> 687 - 300 - 90 -6
=> 387 - 90 - 6
=> 297 - 6
=> 291
You will realized that when we need to carry over for subtraction, it is gets a bit more sticky.
And easier approach will be as follows:
Since 396 is close to 400, we can do this:
687 - (400 - 4)
=> 687 - 400 + 4
=> 287 + 4
=> 291
It takes more practice as the number of digits increase, as human's conscious mind can hold up to 7 bits of information, we can easily to up to 4 digit and 3 digit addition and subtraction.
After a bit of practice on this technique, we can easily do mental addition and subtraction without the hassle of using a calculator for anything less than a thousand.
