A New Look at Arithmetic PDF
Preview A New Look at Arithmetic
(SiGNETJ SIGNET SCIENCE LIBRARY 72824/75c rvingAdler A New Look At Arithmetic With diagrams by Ruth Adler Digitized by the InternetArchive in 2011 http://www.archive.org/details/newlookatarithmeOOadle If You Can Count You Can Read This Book. IrvingAdler, renowned mathematician-writer, introduces the parent, the student, and the elementary teacher to the new mathematics that is sweeping the nation's class- rooms. He begins by defining the four basic number systems and developing an understanding of their structure. He — discusses the meaning of elementary arithmetic addi- — tion, subtraction, multiplication, division and the laws governing its use. He tells you just what decimals and fractions are; how to compute a square root. Heexplains principles and paradoxes;whythemeasurementofatwo- inch stick will be mathematically less accurate than a measurement of the distance from earth to moon. A NEW LOOK AT ARITHMETIC conveys all the excite- ment of a revolutionary concept while it explains it in terms chat anyone can grasp and put to use. "He demonstrates that arithmetic is no longer a tiresome exercise in computations but a stimulati—ng exercise in the development of concepts." Denver Post "A book for elementary school teachers who want to findoutwhatarithmeticisallabout." —TheArithmetic Teacher Other Books of Related Interest Breakthroughs in Mathematics, Peter Wolff, ed. Excerpts from the work of nine men who spurred mathematical revolutions, representing the entire his- tory of mathematics. With commentary by the editor. (#T2389—750) TheNewMathematics byIrvingAdler — The first—book to explain in simple, uncomplicated language the fundamental concepts of the revolu- tionary developments in modern mathematics. (#P2099—60£) Magic House of Numbers by IrvingAdler Mathematical curiosities, riddles, tricks, and games that teachthe basic principles of arithmetic. (#P2117—60£) Thinking Machines by Irving Adler How today's amazing electronic brains use logic and algebrato solveagreatvarietyofproblems. (#P2065— 60C) IRVING ABLER A New Look At Arithmetic With Diagrams by Ruth Adler UGll) A SIGNET SCIENCE LIBRARY BOOK PUBLISHEDBYTHENEWAMERICANLIBRARY, New York and Toronto THE NEW ENGLISH LIBRARY LIMITED, London © 1964byIrvingAdler Allrightsreserved.Thisbook,orpartsthereof,mustnotbe reproducedinanyformwithoutpermission.Forinformation addressTheJohnDayCompany,Inc.,62West45thStreet, NewYork, NewYork 10036. PublishedasaSIGNETSCIENCELIBRARYBOOK byarrangementwithTheJohnDayCompany,Inc.,and DennisDobson,whohaveauthorizedthissoftcoveredition. Ahardcovereditionisavailableinthe UnitedStatesfrom TheJohnDayCompany,andinthe UnitedKingdomfrom Dennis Dobson. First Printing, December, 1965 BSEIGGINESTTETBEBDADTEBMAADBEKMABEBGK. TTM.SA.BPOAAT.BEOGFIFS.TABANDDAFOBETGN COUNTRIES HEOHOEN CHICAGO, U.S.A. SIGNETSCIENCELIBRARYBOOKSarepublished inthe UnitedStatesbyTheNewAmericanLibrary,Inc., 1301AvenueoftheAmericas,NewYork,NewYork 10019, inCanadabyTheNewAmericanLibraryofCanadaLimited, 295KingStreetEast,Toronto2,Ontario, intheUnitedKingdombyTheNewEnglishLibraryLimited, Barnard'sInn,Holborn,London,E.C. 1,England PRINTED IN THE UNITED STATES OF AMERICA Contents PartIs NATURAL NUMBERS AND INTEGERS 1 Four Number Systems 3 2 Natural Numbers 3 Numbers and Numerals 36 4 Four Fundamental Operations 63 5 Linear Order 86 6 Primes and Factors 94 7 Special Sums and Ways ofCounting 103 8 Integers 121 PartHi RATIONAL NUMBERS AND REAL NUMBERS 1 Natural Numbers and Integers 147 2 RationalNumbers 156 3 Different Ways ofWritingRationalNumbers 206 4 Measurement 224 5 Ratios 243 6 Real Numbers 263 7 Some Interesting and ImportantNumbers 279 Answers to Exercises 284 Index 303 A New Look At Arithmetic
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