RAPID ARITHMETIC QUICK AND SPE CIAL METHO DS IN ARITH METICAL CALCULATION TO GETHE R WITH A CO LLE CTION OF PUZZLES AND CURI OSITIES OF NUMBERS ’ D D . T . O CONOR SLOAN E , PH . LL . “ ’ " “ A or o Anda o Ele ri i ta da rd le i a Di ion uth f mfic f ct c ty, S n E ctr c l ct " a Eleme a a i s r n r Elec r a l C lcul on etc . etc y, tp y t ic t , , . NE W Y ORK D VA N NOS D O M N . TRAN C PA Y E mu? WAuw Sum 5 PRINTED IN THE UNITED STATES OF AMERICA which receive little c n in ne or but s a t treatment text books . If o o o f doin i e meth d g an operat on is giv n , it is considered n e ough. But it is certainly interesting to know that there e o f a t are a doz n or more methods adding, th there are a of number of ways applying the other three primary rules , and to find that it is quite within the reach of anyo ne to io add up two columns simultaneously . The multiplicat n table for some reason stops abruptly at twelve times ; it is not to a on or hard c rry it to at least towards twenty times . n e n o too Taking up the questio of xpone ts , it is not g ing far to assert that many college graduates do not under i a nd stand the meaning o a fractional exponent , as few can tell why any number great or small raised to the zero power is equa l to one when it seems a s if it ought to be equal to zero . The multiplication table can be made to give the most curious relations between its constituent figures and quan i o e o for one tit es, and f thes nly a part are given here , can play a regular game o f solitaire with the multiplication table . ’ The book now in the rea der s hands has been a wonder r o f fully inte esting work in its preparation . The sources information and the authorities appealed to were many and in a number o f cases were little known . The collection of the a of m tter presented here was a sort gleaning , picking iv ARITHMETIC t . the up what o hers had left It was also a selective task , o f o accumulating the best fr m many sources . A reference to the table of contents will show that this preface tells only of- a small part of what is to be found in the book . In a certain sense this work is a supplement to the o ordinary text bo k of arithmetic. But it is more than i o f i on e that ; it w ll be found practical appl cati in r al work , for by applying the methods to be found in its pages a greater command o f a rithrnetica l operations will be a c of quired and quick ways calculating will result . Much that is amusing in the way of oddities a nd recre a tions in the science of numbers will be met with in its pages . The compiler hopes that his mixture of the useful with the lighter phases o f his subject will prove acceptable to the reader . CHAPTER I . GN NOTATION AN D SI S . n Th ma o n h um . a c o a o e c . T e Ar bi N t ti . De i l P i t N ber One m Th hm ca h ci a ct o s. Signs in Arit metic. De a l Fr i n e Arit eti l a c n m o s a nd um e s 1 - 10 Co mplement. Pl i g S y b l N b r CHAPTER II . ADDITION h Th a . Notes o n Addition a nd its T eory. e Addition T ble n fi f n . n Ho t . Di erent a Ca rryi g O e. w o Add W ys O Addi g ’ o e on G ou on. nd tio . B okkeep r s Additi . r p Additi I ex Addi n d n o om ina o . o Period Ad itio . Additi n by C b ti n Additi n by a i ca i n o u ca o . c Aver ge Multipl t o . Additi n by M ltipli ti n De i m l Two a nd h e o umn on. f a Addition. T re C l Additi Le t o w hou a r n f om o umn to Ha nd Addition. Additi n it t C ryi g r C l umn c ma iz o . S h a n Col . De i l ed Additi n ig t Re di g in Addi m m n Ad n r f a n o . o a tion. I verted o Le t H d Additi n C ple e t ry dition CHAPTER III . UBTRA CT O S I N . Su o nc f a ci iz o u r . ma btra cti n. Pri iples S bt ction De l ed Sub a cti ubt a c on n I o . ut a c o n tr n S r ti in Couples. S b r ti by spec . c i n o r ef n tion Subtra tion by Add tion. I verted L t Ha d Sub a c m m o . m n u a c on. Su a c o O f S tr ti n Co ple e t S btr ti btr ti n u s. om m o e O f ubtr c C plement Subtra ction o f Su s. A Pr p rty S a vi ARITHMETIC CHAPTER IV. c o S o The Multipli ati n a h rt Method Of Additi on. Multi c o . E i the Multi limtion pli ati n Table xtend ng p Table. Mul ti liea tion o l o r Two t m p by D ub e Digi Nu bers. Multiplica ti liea tion o f Two m ut l c o p Digit Nu bers. M l ip i a ti n o f Three i a nd h m . I m u Dig t Hig er Nu bers ncre ent M ltiplication. o h ho o f m c o An t er Met d Incre ent Multipli ati n. Special Memod h Of Multiplying T ree Digit Numbers . Multiplica o o f o ti n Special Cases f Polynomials . Inverted or Left l c o o r o o Hand Mu tipli ation. Fact rial Prop rti nal Multiplica l uo o . f tion. A iq t Part Multiplicati n Practical Use o Aliquot c a c o . T Parts in Multipli ation. F t r Multiplying o Multiply ut T u H To . o un by Nine. M l iply by Eleven M ltiply by One m l m dred a nd Eleven. Co p e ent Multiplicatio n. Multiplica o f um r wi h l Two tion N be s Ending t Five. Mu tiplying by u a n m w Numbers at Once. M ltiplying by y Nu ber bet een h T e s. Twelve a nd Twenty. Multiplying by t een Cross S ul i c o . ce o f Multiplication. lide M tipl ati n Ex ss Nines h Proo f o f Multiplication. Curiosities o f t e Multiplication l A C o ho of . in Tab e. uri us Met d Multiplying Oddities Mul R CHAPTE v. o D o . Factor Division. Abbreviated L ng ivisi n Italian c s o f i in s o . Re Method o f Long Division. Ex es N ne Divi i n Di isibifit o f m s. S meinders in Division. v y Nu ber pecial - i . w C Ca se o f Division . Dividing by Ninety N ne Le is ar te rs Short Cut RA N S F CTIO . c Cha nging the Value Of a Fraction. Reducing Fra tions to r o the Same Class o to a Common Denominator. Additi n ul o a nd v o a nd Subtraction o f Fra ctions . M tiplicati n Di isi n o o rs o o f o o D m f Fractions. C nve i n Vulgar Fracti ns int eci al 94- 100 CHAPTER VII . THE Decma r. O T P IN . o s Due t s c m o o f Err r o Mi pla ed Deci al Point. Additi n ° f o o f c m s. u Decimals. Subtracti n De i al M ltiplica tion o Deci f tor- 108 mals . Division o Decimal s CHAPTER VIII . E E T ERCE AGE AL CULATI N S . I NT R ST AN D DiscouN . P NT C O E c s xpression Of Rate o f Interest. Cal ulating Intere t. h o f S o rt Ways o f Calculating Interest. Reducti n o Interest ’ s . so for a o f Peri ods. One Day s Intere t Divi rs R tes Inter t. c es Cancellation ih Interest Ca lculations . Per entage Cal cula tions o m u o c J o - 1 1 .