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Trachtenberg, a brilliant engineer with an ingenious mind, originated his system of simplified mathematics while spend- ing years in Hitler's concentration camps as a political prisoner. It looks like magic, but the rules are based on sound logic. Once one has mastered the rules, lightning calculation is as easy as reading a story. 8 THE TRACHTENBERG SPEED SYSTEM OF BASIC MATHEMATICS The Trachtenberg method is not only speedy but simple. The late Jakow Trachtenberg, founder of the Mathemati- cal Institute in Zurich, Switzerland, and originator of the startling new system of arithmetic, was of the firm opinion that everyone comes into the world with "phenomenal cal- culation possibilities." What made the exhibition of math- ematical wizardry more amazing was that these were children who had repeatedly failed in arithmetic until, in desperation, their parents sent them to learn this method. The class was one where the Trachtenberg system of mathematics is taught. He blitzed through the problem, com- puting the answer-2323641669144374104785-in seventy seconds. A thin, studious-looking boy wearing silver-rimmed spectacles was told to multiply 5132437201 times 452736502785. She came up with the cor- rect answer-8088875454-in less time than you can say multiplication table.
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A small girl with beribboned braids was asked to find the solution of 735352314 times 11. Standing on tiptoe to reach the top, he arrived at the total with what seemed the speed of light. Foreword The teacher called on a nine-year-old boy who marched firmly to the blackboard upon which was a list of numbers a yard long. THE TRACHTENBERG SPEED SYSTEM OF BASIC MATHEMATICS FIVE: DIVISION-SPEED AND ACCURACY 133 The simple method of division 135 The fast method of division 142 The division process 143 The method in detail 149 Three-digit divisors 158 Divisors of any length 167 Checking the division 176 SIX: SQUARES AND SQUARE ROOTS 185 Introduction 185 Squaring 188 Three-digit numbers 193 Square roots 197 Seven-digit and eight-digit numbers 214 Longer numbers 223 Checking 225 SEVEN: ALGEBRAIC DESCRIPTION OF THE METHOD 227 Numbers in general 230 The rule for eleven 233 Algebraic manipulation 237 The Trachtenberg system in algebra 248 Non-table multiplications in general 252 Squaring numbers 255 Multiplication by the units-and-tens method 257 Numbers of any length 262 EIGHT: POSTSCRIPT 265 Contents FOREWORD 7 ONE: TABLES OR NO TABLES? 21 Basic Multiplication 21 Multiplication by eleven 22 Multiplication by twelve 26 Multiplication by six 28 Multiplication by seven 35 Multiplication by five 39 Multiplication by eight and nine 40 Multiplication by four 46 Multiplication by other digits 49 Summary 52 TWO: RAPID MULTIPLICATION BY THE DIRECT METHOD 55 Short multiplicands: Two digits by two digits 57 Long multiplicands 62 Three-digit multipliers 70 Multipliers of any length 75 Summary 76 Checking the answer 77 THREE: SPEED MULTIPLICATION-"TWO-FINGER" METHOD 81 Multiplication by a single digit 88 Multiplication by two-digit numbers 93 Long number by two-digit multiplier 98 Three-digit multipliers 99 Summary 102 FOUR: ADDITION AND THE RIGHT ANSWER 105 Finding the total 107 Checking the answer 115 General method of checking 122 Library of Congress Catalog Card Number 60-13513 Copyright 1960 by Ann Cutler All Rights Reserved Printed in the United States of America Designed by Alma Reese Cardi THE Trachtenberg SPEED SYSTEM OF Basic Mathematics TRANSLATED AND ADAPTED BY ANN CUTLER AND RUDOLPH McSHANE DOUBLEDAY & COMPANY, INC. MathematicsTranslated and adapted by Ann Cutler and Rudolph McShane
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speed multiplication, aSIC division, addition, subtraction. The Trachtenberg Speed System Of B The revolutionary new method for high.