- TRACHTENBERG SYSTEM OF SPEED MATHEMATICS SOFTWARE DOWNLOAD
- TRACHTENBERG SYSTEM OF SPEED MATHEMATICS PLUS
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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. Same info as in the book but easier to understand (for me) and talks you through every step.The Trachtenberg Speed System of Basic Mathematics
TRACHTENBERG SYSTEM OF SPEED MATHEMATICS FREE
I study once a week for a couple of hours and have been for about 2 months but also practice when out shopping like I said.Ī good free site I found helpful to use alongside the book is Good memory recall is obviously an important skill to have and will need improving if you're going to stand a chance doing sums of that length. The claims of a boy doing very large multiplications doesn't sound like it's impossible but would take a good few months of practice. Give me a pen and paper and I can now do the same sums often in under 10 seconds. 3-4 digit multiplications (ie: 2873 x 231) in my head now generally take me around 15-30 seconds to work out (depending on the numbers) with almost 100% accuracy, about a month ago I would be able to do them in about 30-40 seconds ~80% correct. Your question is hard to answer but I will say that where as before I'd simply give up on trying to do large multiplication in my head (as it would be impossible), now I actually am able to do the large multiplications and check them with good accuracy in my head. Studying and practicing the Trachtenberg System has helped me DRASTICALLY improve my day to day mental arithmetic, especially noticeable when out shopping and working out the cost savings in buying bulk and cost comparisons per kilo.