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1. TRACHTENBERG SYSTEM OF SPEED MATHEMATICS SOFTWARE DOWNLOAD
2. TRACHTENBERG SYSTEM OF SPEED MATHEMATICS PLUS
3. TRACHTENBERG SYSTEM OF SPEED MATHEMATICS SERIES

The important benefits of the system are greater ease, greater speed, and greater accuracy. Once you have learned them, arithmetic becomes delightfully easy because you will be able to "read" your numbers.

TRACHTENBERG SYSTEM OF SPEED MATHEMATICS SERIES

The method is based on a series of keys which must be memorized. To learn the system you need only be able to count. There are no multiplication tables, no division. 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. This technique works on arbitrarily long columns of figures, and the columns can be dealt with in /conversion/tmp/scratch/375698770.docĪny order desired, except at the very last step. Write down the last digit and carry the other digit, if any, working right-toleft. Now add these two rows using the strange rule of adding the two numbers in any column and the neighbor tick number. When you reach the bottom, write down the running total, and under it write the number of tick marks. Addition The method advocated here involves the following principle: "Never count higher than eleven." If any running column total exceeds 11, subtract 11 and put a tick mark in that column.

Finally, using multipliers of any length is learned by the "two-finger" method. Once the multiplication tables are memorized, using multipliers of two digits is learned. Even better, it gives a way to help memorize them, by allowing one to work out the answer by rule if one cannot remember it by rote. These rules allow one to dispense with memorizing multiplication tables, if that is desired. If you are taking half an odd number, use the integer quotient and ignore the remainder of 1. When the sum exceeds 10, write down the last digit, and carry the first digit. Last step: reduce the lefthand digit of the multiplicand by 1. Middle steps: subtract from 9 and add the neighbor. Last step: Reduce the lefthand digit of the multiplicand by 2.įirst step: subtract from 10. Middle steps: subtract from 9, double, and add the neighbor.

TRACHTENBERG SYSTEM OF SPEED MATHEMATICS PLUS

Use double the number plus half the neighbor, plus five if the number is odd.įirst step: subtract from 10 and double. Use the number plus half the neighbor, plus five if the number is odd. Use half the neighbor, plus 5 if the number is odd. Last step: take half the lefthand digit of the multiplicand and reduce by 1. Middle steps: subtract from 9 and add half the neighbor, plus 5 if the number is odd. Last step: take half the left-hand digit of the multiplicand and reduce by 2.įirst step: subtract from 10, and add 5 if the number is odd. Middle steps: subtract from 9 and double, and add half the neighbor, plus 5 if the number is odd. Here are the rules: Multiplier Rules 0įirst step: subtract from 10 and double, and add 5 if the number is odd. The rules use only addition, subtraction, doubling, and halving. One works from right to left from digit to digit of the multiplicand, writing down the digits of the product. Multiplication Finding the product of multiplicands of any length by small multipliers is accomplished using a set of rules. For information about the life of Professor Jakow Trachtenberg, Founder of the Mathematical Institute in Zurich, see Trachtenberg Speed Math and Trachtenberg Math. While it is impossible to capture the contents of this 270-page book in one Web page, below you will find a part of the content of this system.

The details are given in this reference: Ann Cutler and Rudolph McShane, The Trachtenberg Speed System of Basic Mathematics, (Garden City, NY: Doubleday & Company, Inc., 1960) reprint (Westport, CT: Greenwood Publishing Group, 1983).

TRACHTENBERG SYSTEM OF SPEED MATHEMATICS SOFTWARE DOWNLOAD

Software download This constitutes a system of performing high-speed multiplication, division, addition, subtraction, and square root, all in one's head. The Trachtenberg Speed System of Basic Mathematics