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The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp. The rest of this article presents some methods devised by Trachtenberg. These are for illustration only. To actually learn the method requires practice. Students begin learning the Trachtenberg system using multiplication algorithms. 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 more traditional methods. ==Beginning to Multiply Using the Trachtenberg Method== When performing any of these multiplication algorithms the following "steps" should be applied. Write a zero before the number to be multiplied. The answer must be found one digit at a time starting at the least significant digit ie the digit to the far right. Move left one digit at the time to work. The last calculation is on the leading zero of the multiplicand. ( In 0128 x 6, the 0128 is the multiplicand and the 6 is the multiplier. In 0382 x 28, the 0382 is the multiplicand and the 28 is the multiplier. The answer may be referred to also as the "product".) When working with the multiplicand, one digit at a time has your primary focus. The digit immediately to that digit's right is that digit's ''neighbor''. In the Trachtenberg method, never use the digit immediately to the left as the neighbor. The rightmost digit does not have a neighbor as there is no digit to its right. Some algorithms ask for a value of a digit's neighbor. When the focus is on the last digit to the right, the value used for the neighbor is always zero. The 'halve' operation has a particular meaning to the Trachtenberg system. If a digit is even take half this value. If a digit is odd, mentally subtract one before taking half the value. Alternatively half the odd digit may be taken discarding any decimal, fraction or remainder. For speed reasons people following the Trachtenberg system are encouraged to make this halving process instantaneous. Instead of thinking "half of seven is three and a half, so three" it's suggested that one thinks "seven, three". This speeds up calculation considerably. The Trachtenberg system also uses something called the tens complement. In this same way the tables for subtracting digits from 10 or 9 are to be memorized. This requires subtracting digits from nine except the last digit to the right of a number which is subtracted from 10. The suggestion is to be able to look at the digits 0-9 and immediately know the result if this digit were subtracted from 9 or subtracted from 10. Whenever the rule calls for adding half of the neighbor, always add 5 if the current digit is odd. There will be more discussion on the reasons and details of these methods below. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Trachtenberg system」の詳細全文を読む スポンサード リンク
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