Peter Bone wrote:
>
>
> Yes, well I have a system that I developed (when I was about 15) to sum
> the sub-results as you go so that you just have to keep track of a single
> number. You just have to insert the sub results in the right place in that
> number as you go while taking carries into account. Takes some practice
> but not that difficult.
I go about the same way but it’s still so easy to make one tiny mistake
and then you have to start over. The number you have to keep track of can
be rather large and it’s easy to remember just one digit wrong when at the
same time you are doing some rather hard new sub-task.
But yes, it will become easier if I just practice it more.
> the big divisions always
> slow me down. What's your mental strategy for the divisions?
Divisions also use to slow me down but I can now solve them just as
quickly as multiplications (and much more quickly with large numbers).
Here is my mental strategy for it, it's very similar to what I first
learned to do in primary school. I will be more descriptive than you
probably need me to be just in case it helps someone else.
Let’s take Will’s example of 912 divided by 12.
Of course, it helps a lot to know your math tables up to 12.
What number can I multiply by 12 to get close to 91? *
6 x 12 = 72 = too little (cause 91 minus 72 = more than 12)
8 x 12 = 96 = too much (more than 91)
7 x 12 = 84 = Ok
Type in 7 in the answer box and forget about it.
91 – 84 = 7
7 united with the last digit gives you 72.
72 divided by 12 = 6 (or if you prefer, 6 x 12 = 72) **
Type in 6: you win! (912 divided by 12 = 76)
With practice, the whole process shouldn’t take more than 4 seconds.
You can go about the same way with very large numbers and I think it’s
much easier than multiplications with large numbers. You can always type
each digit of the answer one at a time, forget about it and move on to the
next sub-task. Also the number you have to keep track of is much lower
than with those toff multiplications.
*: If you are working with a number divided by a larger than 12 number,
you now have to estimate the sub-result a little, that may be the hardest
part but still it’s not that bad.
**: If at that point you are confident that the first digits you typed
were correct, one less ethical way to proceed is to try to guess the last
digit, and then quickly erase and type in your next guess until you find
right one. That's not the most efficient way but it can help after you
made a mistake.