The Trachtenberg Speed System of Basic Mathematics ( Free PDF )


  • Basic multiplication
  • Multiply by eleven
  • Multiply by twelve
  • Multiply by six
  • Multiply by seven
  • Multiply by five
  • Multiply eight by nine
  • Multiply by four
  • Multiplication and other numbers
  • Summary
  • Short multiplication: two digits and two digits
  • Long multiplication
  • Multiply three numbers
  • Multiply each length
  • Summary
  • Check answer
  • Multiply by the same number
  • Multiplication by Two Numbers
  • The longest number is a two-digit number
  • Multiply three numbers
  • Summary
  • Search all
  • Check answer
  • General control procedures
  • Easy way to share
  • Fast way to share
  • Distribution method
  • Detailed method
  • Differentiation of three numbers
  • Divide any length
  • Partition control
  • Introduction
  • Fall
  • Three digits
  • Square Roots
  • Number seven and number eight
  • Long number
  • Control
  • Mathematics in general
  • Rows of eleven
  • Algebraic manipulation
  • Trachtenberg system in algebra
  • Generally, out of table multiplication
  • Equal numbers
  • Multiplication by parts per line
  • Numbers of any length


The teacher called out a list of numbers one meter long to a nine-year-old boy who was walking steadily across the blackboard. He rose on tiptoe to reach the top and covered the entire distance at a speed resembling the speed of light.

A little girl wearing a ribbon was asked to find the answer to the number 735352314 11. She found the correct answer (8088875454) in less time than it takes you to recite the multiplication table. A thin, handsome boy with silver glasses was asked to multiply 5132437201 by 452736502785. He solved the problem and calculated the answer 2323641669144374104785 in seventy seconds.

Was a class teaching the Trachtenberg system of mathematics. What made this math wizard show so surprising was that there were kids who failed math over and over until their parents, in desperation, sent them off to learn this method.

The late Jakow Trachtenberg, founder of the Mathematical Institute in Zurich, Switzerland, and pioneer of a new and surprising method of mathematics, held the firm view that every person in the world “has a way of calculating extraordinary things. The Trachtenberg method is not only fast but also simple. Once you learn the rules, counting lightning bolts is as easy as reading a story. It looks like magic, but the rules are based on sound.

A brilliant engineer with a brilliant mind, Trachtenberg developed his simple mathematical system during the years he spent as a political prisoner in Hitler’s prisons. These amazing works cannot arise from a tragedy and cannot be separated from the lives of their founders in the mostcruel situations, for it is quite possible that if Professor Trachtenberg’s life had followed a peaceful path, he would never have thought about the system. this eliminated the drudgery often associated with it. and number.

Trachtenberg’s life is as interesting and fascinating as his magnificent system of mathematics, which many scientists believe will ultimately revolutionize mathematics education in schools around the world. Russian, Jakow Trachtenberg, born in Odessa on June 17, 1888, showed his talent early. St. He graduated with honors from St. Petersburg’s famous Reinstitute (Mining Institute) and joined the world-famous Bischoff ship as a student engineer. He was appointed general manager when he was still in his twenties. At that time, under the leadership of the Tsar, there were grand plans to build the best ships, and 11,000 men were under Trachtenberg’s command. Although he spearheaded the production of the Bischoff, Trachtenberg was a committed pacifist. At the beginning of World War I, he founded the Good Samaritan Society, which trained Russian students in caring for the wounded; This was a work well received by the king.

The assassination of the imperial family in 1918 ended Russia’s naval dream. This also ended Trachtenberg’s personal hope for a happy and peaceful life. Trachtenberg, who opposes cruelty and violence, becomes a victim.

As revolutionaries spread throughout Russia, Trachtenberg fearlessly opposed brutality and rebellion. Criticism ruined his life. In early 1919 he learned that he would be executed. Disguised as a farmer, he travels at night, hides during the day and enters Germany. Berlin, with its wide streets, coolness, air and atmosphere, reminds him of St. It reminded him of St. Petersburg, it became his home. He started a new life in a small room at a foreign address and made friends with young intellectuals who had lost their minds during the war. For the leader. As the paper’s editor, he often appealed to this group when calling for Germany to move towards a peaceful future.

Trachtenberg married a beautiful aristocratic woman. He became famous by writing many important works on Russia and created the first book on Russian industry. He was considered Europe’s leading expert on Russian affairs. His creative mind set a different task. He developed a system for teaching foreign languages ​​that is used in many German schools.

The turmoil of his early years seemed to be behind him. But with the arrival of Hitler, Trachtenberg’s life once again followed the familiar path of conflict. He boldly condemned fascism. Trachtenberg was so popular that Hitler initially chose to ignore his attacks. However, as Trachtenberg’s accusations increased, Hitler dismissed him as forgetful.

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