The Trachtenberg Speed System of Basic Mathematics and over 2 million other books are available for Amazon Kindle . Learn more

Sign in to turn on 1-Click ordering.
Trade in Yours
For a 0.25 Gift Card
Trade in
More Buying Choices
Have one to sell? Sell yours here
Sorry, this item is not available in
Image not available for
Image not available

Start reading The Trachtenberg Speed System of Basic Mathematics on your Kindle in under a minute.

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

The Trachtenberg Speed System of Basic Mathematics [Paperback]

Jakow Trachtenberg , Ann Cutler
4.7 out of 5 stars  See all reviews (42 customer reviews)
RRP: 9.99
Price: 6.99 & FREE Delivery in the UK on orders over 10. Details
You Save: 3.00 (30%)
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
In stock.
Dispatched from and sold by Amazon. Gift-wrap available.
Want it tomorrow, 14 July? Choose Express delivery at checkout. Details
Trade In this Item for up to 0.25
Trade in The Trachtenberg Speed System of Basic Mathematics for an Amazon Gift Card of up to 0.25, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more

Book Description

29 Jun 1989
Can you multiply 5132437201 by 452736502785 in seventy seconds without reaching for your calculator? Well you could if you used the techniques in this revolutionary book, now available in paperback at a time of growing concern about people's numeracy. The system, described as 'the shorthand of mathematics', only requires the ability to count from one to eleven. It is based on a series of simplified 'keys' and is easy to master giving greater speed, ease of handling numbers and increasing accuracy. Try it for yoursef.

Special Offers and Product Promotions

  • Spend 30 and get Norton 360 21.0 - 3 Computers, 1 Year 2014 for 24.99. Here's how (terms and conditions apply)

Frequently Bought Together

The Trachtenberg Speed System of Basic Mathematics + Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Mental Math Tricks + Rapid Math Tricks and Tips: Thirty Days to Number Power (Mathematics)
Price For All Three: 24.84

Buy the selected items together

Product details

  • Paperback: 272 pages
  • Publisher: Souvenir Press Ltd; New Ed edition (29 Jun 1989)
  • Language: English
  • ISBN-10: 0285629166
  • ISBN-13: 978-0285629165
  • Product Dimensions: 12.9 x 19.8 cm
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (42 customer reviews)
  • Amazon Bestsellers Rank: 36,272 in Books (See Top 100 in Books)

More About the Authors

Discover books, learn about writers, and more.

Product Description


I tried an extract on a well-known woman journalist, very capable in her own field, but barely able to count. The result was magical. --'Sunday Telegraph'

Teachers should read this book and consider deeply the implications of a new technique which could well revolutionise the teaching of mathematics. --'Teachers' World'

About the Author

Jakow Trachtenberg (1888-1953) developed this system during the seven years he spent in Nazi concentration camps during World War II. He had been born in Odessa, Russia on June 17, 1888 and was recognized as a genius at an early age. When the First World War broke out, he was a Pacifist, opposed to the war, and wrote published articles attacking the war. When the Czar of Russia was overthrown, he had to flee to Germany. When Hitler came to power, he did the same thing again, writing magazine articles and books attacking the policies of the Soviet and German governments. His books included “Das Land das blutet. Bilder aus dem heutigen Russland” meaning “The country bleeds. Pictures from today's Russia” in 1928. In 1931, he wrote, “Das Problem der UdSSR”. In 1933, he wrote “Die Greuelpropaganda ist eine Lügenpropaganda sagen die deutschen Juden selbst” meaning “Atrocity propaganda is a Lügenpropaganda says the German Jews themselves” which stated “Some Jewish circles in Germany, who favored German nationalism, felt that the anti-Nazi reactions outside Germany had been exaggerated or distorted. They were afraid, that anti-Nazism would endanger the position of the Jews”. “Die Greuelpropaganda ist eine Lügenpropaganda sagen die deutschen Juden selbst. Atrocity Propaganda is based on Lies say the Jews of Germany themselves. La propagande d'atrocites n'est que mensonges declarent les juifs allemands eux-memes.” Nachdruck der Jakow Trachtenberg Verlag Ausgabe von 1933. Here he is defending the German government from attacks by Jews outside of Germany, calling it “Atrocity Propaganda”. This may explain why he did not flee to the United States as did so many Jewish intellectuals during this period. The immediate prewar years found Professor Trachtenberg living in Vienna and Yugoslavia - almost always as a fugitive. In Vienna in 1936 he wrote “Der russische Bauer heult unter dem Bolschewismus” meaning “The Russian farmer howls under the Bolshevism”. The police state finally caught up with him, and he spent a total of seven years in various concentration camps. It was during these years that Professor Trachtenberg developed his system of speed mathematics. Most of this was done without pencil and paper, since none were available. Thus the majority of the steps are performed mentally. --This text refers to an alternate Paperback edition.

Inside This Book (Learn More)
Browse and search another edition of this book.
Browse Sample Pages
Front Cover | Copyright | Table of Contents | Excerpt | Back Cover
Search inside this book:

Customer Reviews

Most Helpful Customer Reviews
38 of 38 people found the following review helpful
5.0 out of 5 stars Incredible 22 Nov 2005
I have an older edition of this book, and have ordered this edition for a friend. This is an incredible book, you can learn very simple techniques in minutes, that will amaze your friends and family with the speed and ease at which you can do math. You can write the answer down without any calculations as the work is done very simply in your head. This is a book I delve into from time to time, in an effort to really acquaint myself with the techniques. The only prior math’s knowledge you need is the ability to count to 10! Would revolutionise maths if we taught this in schools!
Comment | 
Was this review helpful to you?
18 of 18 people found the following review helpful
5.0 out of 5 stars Definately worth a read! 1 Sep 2000
By A Customer
A good book for those who want better mental arithmetic skills. Whilst a large number of the basic techniques applied were discovered by mathematicians well before Trachtenburg was born (Euler and Cauchy come to mind), this is almost certainly the first time that the thinking was brought to bear on simple arithmetic in such a systematic fashion.
Comment | 
Was this review helpful to you?
15 of 15 people found the following review helpful
5.0 out of 5 stars A Priceless Gem 8 Feb 2000
I read this book 28 years ago in 1972. It was a wonderful insight into the world of arithmetic and maths. I still continue my Jakow inspired interest in things numerical. What a brilliant and resilient man.
Comment | 
Was this review helpful to you?
34 of 35 people found the following review helpful
3.0 out of 5 stars Excellent system but good memory needed! 6 May 2009
While everything other reviewers have written is true as to this books ease at explaining a different method of grasping basic maths. It requires a very good memory to retain the system for daily use without referring back to the book. Especially in those of us that are older!

An example of the first unit (which deals with multiplication) is that learning to multiply by 12 has a different method than 11. You also then have a different method for learning to multiply 5,6 and 7 grouped together. Therefore, if you are prepared to put in many hours learning the 4 basic skills with repeated examples and practice addition,subtraction,multiplication and division again as if you had never learnt it, I think it is a novel and easy method to work through.

But that doesn't change the fact there are a lot of methods to retain in the head and probably better suited to kids fresh to schooling.
Comment | 
Was this review helpful to you?
26 of 27 people found the following review helpful
5.0 out of 5 stars A great resource. 8 Jan 2001
By A Customer
I originally read this book when I was 13 and I have remembered it ever since. When I started vocational teaching of disadvantaged adults I remembered it and bought a copy for my students. I was impressed with what my students achieved and the faculty was astounded.
Comment | 
Was this review helpful to you?
53 of 56 people found the following review helpful
5.0 out of 5 stars Thanks 22 Feb 2006
The contents of this book should be printed on gold leaf!
A person found time to record this work whilst facing death.
A work that removes the shroud of mystery that covers a branch of mathematics that holds painful memories for many people.
Mental Maths.
Mathematicians manipulate numbers with ease; general members of the public or school kids don't.
This book shows worked examples of how to do various calculations easier and quicker than 'conventional' means.
23 x 11
2 is the 'first digit'
3 is the 'last digit'
2 + 3 is the 'middle digit'
So 23 x 11 = 253
Many more examples and information are presented, so that with practice the 'sums' can be done in your head.
It's maths without the tears.
Was this review helpful to you?
7 of 7 people found the following review helpful
5.0 out of 5 stars My Year 3 Class demand it every day! 2 May 2010
When I first saw this book - I thought 'Oh no - another book on Maths!' - however it is a real gem of great ideas!

I sat and read through it, and thought 'Wow - there are so many simple tricks I did not know about!' - and as SATs is coming up, teaching my class how to check their answers is really important.

Another reviewer pointed out that you had to learn a lot of rules - this is true - but for my Year 3 class, they loved having to follow each of these rules and the fact that each rule progressively moved onto the next rule! They all tell me what a wonderful book I have!

Next year, I plan to start in the school a club which is designed to teach Primary School children all about the Trachtenberg Speed system, as if they learn it early enough, I am sure it will prove to be be of great value to them throughout their lives.

I cannot recommend this book enough to anyone who has a child struggling with maths.
Comment | 
Was this review helpful to you?
18 of 19 people found the following review helpful
By A Customer
This book shows you a wonderful step by step method for improving mental calculations that you use everyday without realising. By learning the methods described your confidence in using mathematics will sky rocket. I cannot recommend this book highly enough.
Comment | 
Was this review helpful to you?
Would you like to see more reviews about this item?
Were these reviews helpful?   Let us know
Most Recent Customer Reviews
5.0 out of 5 stars Easy to understand. Big help with my maths.
In all honesty i hate maths. I've had problems with the basic multiplication and division and other formulas that are present in maths. Read more
Published 7 days ago by Matthew Turibamwe
5.0 out of 5 stars Why-o-why
Why do they not teach us these methods in school?

Pretty much every page I read I'm saying out loud, "Oh my God, oh my God! Read more
Published 3 months ago by Wayne Corcoran
5.0 out of 5 stars Don-Hawkwind
I first came across this book in 1963 and learnt to use the method for 11 times tables but had forgotten the other methods for other numbers. Read more
Published 3 months ago by don hawkwind
4.0 out of 5 stars A great system of tackling mathmatics.
I first read this, forty-years ago, and I am glad to have it back on my bookshelf. If you find multiplication difficult - buy it.
Published 3 months ago by angryoldgit
2.0 out of 5 stars The slowest to learn speed system!
OK - the simple examples are fun and easy to apply and offer as a party piece. But to do large numbers requires a huge amount of learning time. Read more
Published 3 months ago by C. L. Roe
4.0 out of 5 stars Done it
Great book and a massive insight into mathmatics
A very good read and source of reference for every body. Read more
Published 8 months ago by Basil
5.0 out of 5 stars Trachtenberg Speed System of Basic Mathematics
I came across an old copy of this book many, many years ago and found it fascinating that maths could be made so easy, so had buy myself a copy (even though I'm years past needing... Read more
Published 8 months ago by P Harris
5.0 out of 5 stars The Trachtenberg Speed System of Basic Mathematics
A fascinating book clearly explaining a different way of doing arithmetic from that taught in most schools which places less reliance on rote learning of tables. Read more
Published 9 months ago by Mr Trevor Cooke
5.0 out of 5 stars The Trachtenberg Speed System of Basic Mathematics
It's good stuff! It takes a little bit of learning and memorisation....but, once you've done that you are set to go. I like it!
Published 9 months ago by Leslie A. Heaps
5.0 out of 5 stars Mind games
Having lost the previous copy, I thought I'd buy another copy, as it is a fascinating book with amazing mathematical calculations and easy ways in which to do so. Read more
Published 13 months ago by susie douglas-smith
Search Customer Reviews
Only search this product's reviews

Customer Discussions

This product's forum
Discussion Replies Latest Post
No discussions yet

Ask questions, Share opinions, Gain insight
Start a new discussion
First post:
Prompts for sign-in

Search Customer Discussions
Search all Amazon discussions

Look for similar items by category