The methods usually involve less writing down intermediate steps, but all the same calculations are there. One very good thing mentioned in this book is the error checking method "casting out nines," here called the "digit sum method. In fact, the book strongly implies the contrary. The foreword claims that students using this system faced off in a test of arithmetic against "mechanical brains" did people really call computers that??

Well, the mechanical brain sitting on my desk right now can do millions of arithmetic operations per second. Lastly, I have to complain about one more thing. This book strongly encourages a misconception that some people have about mathematics. I'm referring to the idea that arithmetic IS mathematics, and that being good at mathematics means being good at arithmetic.

Arithmetic is to mathematics as spelling is to poetry. View 2 comments. My dad showed it to me in primary school and I was entranced. Dec 24, Richard Craig rated it it was amazing Recommends it for: Everyone. Shelves: science , text-book. If you or perhaps your child,has difficulty with mathematics,the Trachtenberg system is well worth a try.

Trachtenberg developed a clever system of mental mathematics and arithmetic whilst he was being held as a prisoner in a Nazi concentration camp. Trachtenberg was an outspoken pacifist and openly condemned Hitler and the Nazi regime. The Trachtenberg method is not only speedy but simple.

There are no multiplication tables and no long division as we know it. To add long columns of numbers we need n If you or perhaps your child,has difficulty with mathematics,the Trachtenberg system is well worth a try. To add long columns of numbers we need not count higher than eleven! In fact one needs only to count to eleven to master the entire system! It is quite simply brilliant. A book I would recommend to any one who has difficulty with maths or those who simply want to increase the speed of there mental calculations. Every home school should own a copy.

## The Trachtenberg speed system of basic mathematics Jakow Trachtenberg

View 1 comment. Dec 30, Mainak Jas rated it it was amazing. I read this book long ago more than 10 years Yet, it is still crystal clear in my head as if it was yesterday. What I really love about this book is not just the methods but the fact that the author offers proofs in the book's appendices.

### Book information

This is in sharp contrast to many books on Vedic mathematics which also dealt with speed mathematics, but the reader is left to trust the author without any proofs. The techniques themselves are rather ingenious. He not only offers methods to compute the I read this book long ago more than 10 years He not only offers methods to compute the result quickly but also how to check if the result is correct.

The pen and paper version of checksums in computing : This, combined with the backstory of all this being developed in concentration camps makes it such an inspiring read! Jun 19, Smallllama rated it it was amazing. This man should have universities and cities and libraries named after him. Nonetheless, I would not give this book to a child.

Its methods could greatly speed up the child but, until a person is sophisticated enough to understand what is going on behind the scenes and WHY these things work, learning to do math this way provides a weak foundation for learning higher concepts. This system's weakness is that it makes math seem like mystical powers. Jul 16, Priyank rated it really liked it. Simplified techniques to solve the basic day-to-day mathematical problems. Very good book to read at an early stage to get a glimpse of the magic of arithmetic!!!

Although most of the methods need some practice to get a hand-on, some methods are very natural, that we might be doing without consciously knowing about it. Feb 25, Hilary rated it it was amazing Shelves: informational. Genius book! Trachtenberg devised a new system of teaching mathematics while incarcerated in a Nazi concentration camp -- true story! The system works! It is more efficient, effective, and accurate than anything else I have ever seen.

This approach should be used in every public school! Mar 22, voong marked it as abandoned Shelves: nonfic-sciences. I bought the book on impulse, as it looked promising, but never did finish reading it. The new system appears rather interesting, but from what I can gather it seems to require more effort than it is worth. Maybe I'm wrong; one day I'll take a second go at it.

Sep 12, Pandu Reddy rated it it was ok. This review has been hidden because it contains spoilers.

- The Trachtenberg Speed System Of Basic Mathematics!
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To view it, click here. Jul 16, Mazhar Shakeel rated it it was amazing Shelves: fs. Very interesting, somewhat useful. Seems like the authors exaggerate the benefits of the system though. Explanations of the methods are very thorough. A fun read. Lots of cool arithmetic tricks. Jan 21, Tushar Gargava rated it liked it.

I'll re-read it. But in one read, it seems more complicated than what I'd expected it to be.

Maybe once I start working on the methods mentioned, I might understand the significance of it better? Jan 22, Yingtai added it Shelves: did-not-finish , maths. I know it was not part of the brief of this book, but I really would have liked to know why these methods work. Nov 02, Adrian Goh rated it did not like it Shelves: math-and-science. Didn't really find the system effective or quick. Neither did I find it intuitive. The traditional system was more intuitive and more efficient it seems. Gary O'hanlon rated it really liked it Feb 12, The calculations for finding the fourth digit from the example above are illustrated at right.

The arrow from the nine will always point to the digit of the multiplicand directly above the digit of the answer you wish to find, with the other arrows each pointing one digit to the right. The vertical arrow points to the product where we will get the Units digit, and the sloping arrow points to the product where we will get the Tens digits of the Product Pair.

If an arrow points to a space with no digit there is no calculation for that arrow. As you solve for each digit you will move each of the arrows over the multiplicand one digit to the left until all of the arrows point to prefixed zeros. Division in the Trachtenberg System is done much the same as in multiplication but with subtraction instead of addition.

Splitting the dividend into smaller Partial Dividends, then dividing this Partial Dividend by only the left-most digit of the divisor will provide the answer one digit at a time. The Product Pairs are found between the digits of the answer so far and the divisor.

## Trachtenberg system

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. A method of adding columns of numbers and accurately checking the result without repeating the first operation.

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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 both removes the risk of repeating any original errors and identifies the precise column in which an error occurs all at once. It is based on 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. 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.

unikiqirekix.tk 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.

This makes up for dropping 0. For rules 9, 8, 4, and 3 only the first digit is subtracted from After that each digit is subtracted from nine instead.