8 • THE TRACHTENBERG SPEED SYSTEM OF BASIC MATHEMATICS. The Trachtenberg method is not only speedy but simple. Once one has mastered the . We are giving away free PDF copies of The Trachtenberg Speed System of Basic . Trachtenberg is a good system of becoming a maths calculator great. The Trachtenberg Speed System of Basic Mathematics is a system of mental speed math, created and access to hundreds of downloadable PDF worksheets.
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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. .. The Trachtenberg Speed System of Basic Mathematics. Doubleday and Create a book · Download as PDF · Printable version. PDF | In this paper, we describe the possibilities of using a rapid mental computation system in (). The Trachtenberg Speed System of Basic Mathematics. Download. Download Demo Version With the Demo Version, you can get a good feel of all the features in Trachtenberg Speed Math software. Demo Version.
It was very successful. Trachtenberg developed a set of rules algorithms to multiply long numbers by numbers from 0 to These rules allow one to dispense with memorizing multiplication tables, if that is desired.
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. We perform each rule starting at the far right. When there is no neighbour, we assume it is zero. We also write a zero in front of the multiplicand. If a subtraction results in a negative number you have to back up one digit and reduce that digit of the answer by one.
With enough practice this method can be done in your head. General Addition[ edit ] A method of adding columns of numbers and accurately checking the result without repeating the first operation. An intermediate sum, in the form of two rows of digits, is produced. The answer is obtained by taking the sum of the intermediate results with an L-shaped algorithm.
As a final step, the checking method that is advocated removes both the risk of repeating any original errors and allows the precise column in which an error occurs to be identified at once. It is based on a check or digit sums, such as the nines-remainder method.
For the procedure to be effective, the different operations used in each stage must be kept distinct, otherwise there is a risk of interference. Other multiplication algorithms[ edit ] When performing any of these multiplication algorithms the following "steps" should be applied. The answer must be found one digit at a time starting at the least significant digit and moving left.
The last calculation is on the leading zero of the multiplicand. Each digit has a neighbor, i.
The rightmost digit's neighbor is the trailing zero. The 'halve' operation has a particular meaning to the Trachtenberg system. It is intended to mean "half the digit, rounded down" but for speed reasons people following the Trachtenberg system are encouraged to make this halving process instantaneous.
So 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. In this same way the tables for subtracting digits from 10 or 9 are to be memorized. And whenever the rule calls for adding half of the neighbor, always add 5 if the current digit is odd. Addition The method advocated here involves the following principle: "Never count higher than eleven.
When you reach the bottom, write down the running total, and under it write the number of tick marks. Now add these two rows using the strange rule of adding the two numbers in any column and the neighbor tick number.
Write down the last digit and carry the other digit, if any, working right-to-left.
Example 3 6 8 9 7' 5' 8' 9' 6 6 7' column 1 0 6' 4 of 6 4' 9' 8' figures 8 1 1 3 running totals 1 2 3 3 ticks 2 '1 6 7 6 sum This technique works on arbitrarily long columns of figures, and the columns can be dealt with in any order desired, except at the very last step.
Division and Square Roots The methods for these operations are too long to discuss here, although less complicated than the traditional ones and more adapted for speed and mental calculation. Checking One aspect of calculation which is advocated throughout this book is the importance of checking the correctness of one's work.
The method of Casting Out Nines to check a result is used. For more about casting out nines, see the Dr. Math archives:.