# The Trachtenberg System of Math

### Learning math the traditional waydoes not make for happy faces.

Many years ago, in the early 1960s, there was an article in Reader’s Digest about the Trachtenberg System of Math. It was an amazing article, that I cut out and saved, carrying it around with me as I moved across country and back several times. I never saw any information about the system anywhere else, so as the years went by, the yellowed Reader’s Digest pages became more and more precious.

So, years and years later, because we home school, I introduced the Trachtenberg System with spectacular results. And the neatest thing is, now with the Internet, I don’t have to rely on my old yellowed copies from the 1960s. Why, I can cut and paste some of the same information for you that was in the Reader’s Digest.

And here it is:

### The Story of Jakow Trachtenberg

The teacher called on a nine-year-old boy who marched firmly to the blackboard upon which was a list of numbers a yard long. Standing tiptoe to reach the top, he arrived at the total with what seemed the speed of light.

A small girl with beribboned braids was asked to find the solution of 735352314 times 11. She came up with the correct answer-8088875454-in less time than you can say the multiplication table. A thin, studious-looking boy wearing silver-rimmed spectacles was told to multiply 5132437201 times 452736502785. He blitzed through the problem, computing the answer-2323641669144374104785-in seventy seconds.

The class was one where the Trachtenberg system of mathematics is taught. What made the exhibition of mathematical wizardry more amazing was that these were children who had repeatedly failed in arithmetic until, in desperation, their parents sent them to learn this method.

The late Jakow Trachtenberg, founder of the Mathematical Institute in Zurich, Switzerland, and originator of the startling new system of arithmetic, was of firm opinion that everyone comes into the world with ‘phenomenal calculation possibilities’.

The only problem is, the Trachtenberg System did revolutionized mathematics all over the world, just not in the United States, because the educational gurus in this country never introduced it. Such a silly decision, but one that you can change, anytime you want to by learning it youself, or by home schooling it to your children. If you would llike to know more about Jakow Trachenberg and his incredible life story, click here.

What is the Trachtenberg system? What can it do for you?

The Trachtenberg system is based on procedures radically different from the conventional methods with which we are familiar. There are no multiplication tables, no division. To learn the system you need only be able to count. The method is based on a series of keys that must be memorized. Once you have learned them, arithmetic becomes delightfully easy because you will be able to ‘read’ your numbers.

The important benefits of the system are greater ease, greater speed, and greater accuracy. Educators have found that the Trachtenberg system, which has a unique theory of checking by nines and elevens, gives an assurance of ninety-nine per cent accuracy-a phenomenal record.

The great practical value of this new system is that, unlike special devices and tricks invented in the past for special situations, it is a complete system. Much easier than conventional arithmetic, the Trachtenberg system makes it possible for people with no aptitude for mathematics to achieve the spectacular results that we expect of a mathematical genius. Known as the ‘shorthand of mathematics’, it is applicable to the most intricate problems.

### Multiplying by 11

Rule: Add the digit to its neighbor. (By “neighbor” we mean the digit on the right.)

Example: $3,425 imes 11 = 37,675$

`  3      7      6      7      5`
`(=0+3) (=3+4) (=4+2) (=2+5) (=5+0)`

To illustrate:
11 = 10 + 1

Thus,

$3425 imes 11 = 3425 imes (10+1)$

$Rightarrow 37675 = 34250 + 3425$

The exercise above is from Wikipedia where the other numbers are illustrated as well. If you are interested in seeing this Wiki entry for yourself, click here.