Lightning-Fast Mental Arithmetic

To complement my university maths studies; I have decided to do some real back to basics, study, to improve my mental arithmetic and calculation speed for long multiplication and division.  I have found a system, that is used by those maths magicians, who seem to calculate huge numbers, in an instant, without writing down any intermediate steps.

The system that I found, is called the Trachtenberg Speed Math System.  It was devised in the 1930's by a Russian engineer who was detained in a Nazi war camp.  During this time, he devised a system for arithmetic, that could be done without paper and pencil or calculator.

I have been studying the system for a few days, and already can see its benefits.  One thing I am planning to do, is to teach my children the system, to compliment their school work.

Just to give you an example of how easy the system is; we will try, for example,  to multiply a large number by a double digit number:

Such as     452413 x 11 =

Now such a number would probably take anyone a few minutes to calculate in a long hand fashion; but with the Trachtenberg system, it can be done mentally, in an instant, without writing down any intermediate steps.  How?  I'll demonstrate:

Just as normal, you write down the answer from right, to left.

In this example, when multiplying by 11, the first digit of the answer, is simply the furthest right hand digit, of 452413 i.e.  3.

For the next digit of the answer, each successive figure of 452413, is added to its right hand neighbour.  In this case, you add  1+3 = 4.

You then repeat this adding.  Thus, next 4+1 = 5.  Then  2+4= 6.  Then 5+2=7.  Then 4+5= 9.  When you only have one number leftover, on the far left, you just write it down.

And that is it.  So 452413 x 11 = 4976543

After practising this for 2 minutes, I managed to do these a in a few seconds.  There are other 'rules' that are slightly different for some multiplications; but the principles are all the same.  When it comes into its own, is where you have a sum such as 3857856 / 843.  By anyone's standards, this sum would take a while to work out.  But with this system, it can be done mentally, in about 10 seconds.

There is a caveat with the system; the rules used for arithmetic are very simple and don't ever require you to add up to more than 11; however, it does take some practise to get it slick.

Plus, it's great fun and a useful diversion from calculus!