Trachtengerg develop TrachtenbergÂ multiplication . It is calledÂ Trachtenberg multiplication. It is very famous trick in mathematics.

**How to Multiply without Table?**

**How to Multiply without Table?**

This is system of rapid mathematical calculation. Hence the system consists of a number of readily memorized operations. It allow one to perform arithmetic computations very quickly. Russian Jewish engineer Jakow Trachtenberg develop this method.

He was a brilliant engineer. He was in the political prison of Hitler. The rest of this article presents some methods devised by Trachtenberg.

**Multiplication Tricks in MathematicsÂ **

**Multiplication Tricks in MathematicsÂ**

These are for illustration only. So to learn the methos you have to practice much. Hence students begin learning the Trachtenberg system using multiplication algorithms. So these initial algorithms are discussed first followed by a more general method for multiplication.

Even if you know well how to do arithmetic, the Trachtenberg method can be faster.

It is also a method you may use to check work done by traditional methods. The Trachtenberg method is not only fast but simple. Once one has mastered the rules the calculation is as easy as reading a story. It looks like magic, but the rules are based on sound logic.

**Trachtenberg Multiplication**

**Trachtenberg Multiplication**

The experts believe that the teaching of arithmetic in schools throughout the world can be revolutionizing by this system. According to Trachtenberg the juggling of figures is not that the arithmetic is hard to comprehend.

But the outmoded system by which we are taught. Most of the students are still found poor in mathematical calculation. Some students in university level require review of high school mathematics. The aim of this system is to make students capable of multiplying. Multiplying bigger numbers without learning tables. To develop fast trick.

Here letâ€™s discuss how to multiply by 11 for larger numbers. Here are 3 rules for multiplication by 11.

**Rule 1.Â ** The last digit of the multiplicand is put down as the right hand figure of the answer.

**Rule 2.**Â Each successive digit of the multiplicand is added to its neighbor at the right.

**Rule 3**.Â The first digit of the multiplicand becomes the left hand digit of the answer.

**Here is an example:**

**First rule:**

According to the first rule the right hand side figure of answer is

6 which is kept down.

326Â Â Â xÂ Â 11Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 6

**Second rule:**

The successive digit will be added to its right hand neighbor.

Â 326Â Â Â xÂ Â 11

In 326Â Â 6 plus 2 is 8.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 86

326Â Â Â xÂ Â 11

Apply the rule again for 3 plus 2 is 5.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 586

**Third rule:**

The first figure of the number 326 becomes the left hand figureÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 326Â Â Â xÂ Â 11

of the answer.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3586

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