,transcrib]'s ,notes3 ,text enclos$ by und]scores is 9 italics 7italics74 ,! :ole numb] "p ( a mix$ fraction is sep>at$ f ! fractional "p ) -1 = example1 #b-a_/b4 ,additional ,transcrib]'s ,notes are at ! end4 99 99 99 99 99 ,multum 9 ,p>vo ,libr>y4 ,vol4 ,i4 ,,febru>y1 #ahid4 ,publi%$ ,mon?ly4 ,no4 #b4 ,h[ to ,become a ,,lightn+ ,,calculator4 ,smalle/ ,magaz9e 9 ! ,_w4 ,subscription price1 #ej cts4 p] ye>4 ,s+le copies1 #e c5ts ea*4 ,,publi%$ ,,by ,a4 ,b4 ,,c\rtney1 #fga ,tremont ,/reet1 ,bo/on4 ,ent]$ at ,po/-,(fice z second-class matt]4 ,in/antane\s ,addition4 ,accuracy %\ld be fir/ consid]$1 !n rapidity4 ,quick add]s1 by ! way1 are ! mo/ accurate4 ,write ! numb]s 9 v]tical l9es1 avoid+ irregul>ity4 ,?is is important4 ,keep y\r ?\ght on results n numb]s !mselves4 ,d n reckon #g & #d are #aa & #h are #ai1 b say #g1 #aa1 #ai & s on4 ,:5 ! same numb] is repeat$ sev]al times1 multiply in/ead ( add+4 ,:5 add+ horizontally beg9 at ! left4 #cacb #bdec #ab #fdga #bj #gcab #ae #bacd #ba ----- --- #baejb ,9 add+ long columns1 prove ! "w1 by add+ ea* column sep>ately 9 ! opposite direction1 be=e add+ ! next column4 ,_m acc\ntants put d[n bo? figures z 9 ! illu/ration4 ,! sum ( ! fir/ column is #ab2 c>ry+ "o1 ! sum ( ! second is #bj2 c>ry+ two1 ! sum ( ! ?ird column is #ae2 c>ry+ "o1 ! sum ( ! f\r? column is #ba1 & ! total1 #baejb1 is f\nd by call+ (f ! la/ two figures & ! "r-h& figures1 foll[+ ! wave l9e 9 ! illu/ration4 ,?is me?od is bett] ?an ! old "o ( p5cil+ d[n ! numb] to c>ry4 ,if "o desires to g back & add a c]ta9 column a second "t1 ! numb] to c>ry is at h& & ! =m] total is kn[n4 ,h[ to ,add ,two ,columns at ,once4 #bcab #cbec #bfaj #abef #caii ----- #abfcj ,to ! inexp]i5c$ x w be a difficult task to add two columns at once1 b _m ( ^? :o h daily practice 9 addition f9d x ab\t z easy to add two columns z "o4 ,say #ii & #ej are #adi1 & #f are #aee1 & #aj & #ej are #bae & #c are #bah1 & #ab are #bcj4 ,c>ry #b1 & say #cc & #ab are #de1 & #bj are #fe1 & #f are #ga1 & #cj are #aja1 & #b are #ajc1 & #bc are #abf4 ,mu* ( ! in=mation "h conta9$ is compil$ f ,w4 ,d4 ,r[l&'s valuable little volume1 entitl$ 8,h[ to become exp]t ) figures40 ,y c get ?is h&y book by s5d+ #be c5ts 9 /amps to ,,am]ican ,,nation ,,co41 ,bo/on4 ,multiplication4 ,to ,multiply ,any ,numb] by #aa4 ,write ! fir/ "r-h& figure1 add ! fir/ & second1 ! second & ?ird1 & s on2 !n write ! left-h& figure4 ,c>ry :5 necess>y4 #baidcd #aa #bdacggd ,put d[n ! "r-h& figure #d4 ,!n say1 #d & #c are #g2 !n1 #c & #d are #g2 !n1 #d & #i are #ac1 put d[n #c & c>ry #a2 !n1 #i & #a & #a are #aa1 put d[n ! #a & c>ry #a2 !n1 #a & #b & #a are #d2 !n write ! left-h& figure #b4 ,9 multiply+ small numb]s1 su* z #bd by #aa1 write ! sum ( ! two figures betwe5 ! two figures1 mak+ #bfd1 ! requir$ product4 ,to ,multiply by #aja1 #ajja1 etc4 ,to multiply by #aja1 add two ciph]s to ! multiplic&1 & add to ?is ! multiplic&4 #bcda #aja #bcdajj #bcda ,to multiply by #ajja1 add ?ree ciph]s to ! multiplic&1 & add to ?is ! multiplic&4 ,to ,multiply by #e1 #be1 #abe4 ,to multiply by #e1 add a ciph] & divide by #b4 ,to multiply by #be1 add two ciph]s & divide by #d4 ,to multiply by #abe1 add ?ree ciph]s & divide by #h4 ,ano!r ,easy ,way to ,multiply4 #hb #ed ---- #ddbh ,to multiply two figures by two figures1 proce$ z foll[s3 ,multiply units by units = ! fir/ figure4 ,c>ry & multiply t5s by units & units by t5s1 7add+7 = ! second figure4 ,c>ry & multiply t5s by t5s = ! rema9+ figure or figures4 ,9 ?is example proce$ z foll[s3 #b #d #h #a/ figure4 7#d #h7 7#e #b7 #db4 ,!re=e #b #b;d figure4 7#e #h7 #d c>ri$ #dd #c;d & #d? figures4 ,by a little practice any "o may become z famili> ) ?is rule & z ready 9 its application z ) ! ord9>y me?od4 ,to multiply any numb] by #b-a_/b1 add "o ciph]1 & divide by #d4 ,to multiply any numb] by #c-a_/c1 add "o ciph]1 & divide by #c4 ,to multiply by #cc-a_/c1 add two ciph]s1 & divide by #c4 ,to multiply any numb] by #a-c_/g1 add "o ciph]1 & divide by #g4 ,to multiply by #af-b_/c1 add two ciph]s1 & divide by #f4 ,to multiply by #ad-b_/g1 add two ciph]s1 & divide by #g4 ,to multiply by #hge1 add ?ree ciph]s1 & divide by #h4 ,to divide by #be1 multiply by #d1 & cut (f two figures4 ,to divide by #abe1 multiply by #h1 & cut (f ?ree figures4 ,to multiply by #ab-a_/b1 add two ciph]s1 & divide by #h4 ,to f9d ! value ( any numb] ( articles at #ge c5ts ea*1 d$uct "o-qu>t] ( ! numb] f itself & call ! rema9d] doll>s4 ,to ,subtract ,any ,numb] ,consi/+ ( ,two ,figures f #ajj4 ,take ! fir/ figure f #i1 & ! second f #aj4 ,= example3 9 subtract+ #gc f #ajj1 or 9 tak+ #gc c5ts *ange out ( a doll>1 say #g f #i & #b1 & #c f #aj & #g1 or #bg c5ts4 ,practice ?is rule4 ,x is simple1 & w be f\nd p>ticul>ly helpful 9 mak+ *ange4 ,divisions4 ,a numb] is divisible by #b :5 ! la/ digit is ev54 ,a numb] is divisible by #d :5 ! la/ two digits are divisible by #d4 ,to divide by #ab-a_/b1 multiply by #h1 & cut (f two figures4 ,simple ,disc\nt ,rule4 ,?is simple rule is 9 use 9 _m h\ses :]e sev]al disc\nts are all[$ f li/ prices4 ,suppose ! li/ price ( a piano to be #ejj1 & y all[ an ag5t #be1 #bj & #aj (f4 #ajj #ajj #ajj #be #bj #aj --- --- --- #ge #hj #ij 4#edjjjj ,subtract ea* f #ajj & multiply & y get 4#ed4 #ejj 4#ed #bgj1 ! ag5t's price4 99 99 99 99 99 ,if y want to get a complete book on quick calculat+1 compris+ all mod]n me?ods1 toge!r ) a va/ am\nt ( o!r valuable matt]1 p]ta9+ to bus9ess1 s5d #be c5ts to ,,am]ican ,,nation ,,co41 ,bo/on1 ,mass41 = a volume ( 8,h[ to ,become ,exp]t at ,figures40 ,p]c5tage4 ,! "n p]c5tage is appli$ to c]ta9 ari?metical ex]cises 9 :i* #ajj is us$ z ! basis ( computation4 ,p] c5t4 is an abbreviation ( ! ,lat9 p] c5tum1 mean+ by ! hundr$4 ,?is sign is us$ = ! words p] c5t4 ,?us1 #aj ( a numb] equals #aj_/ajj1 or #a_/aj ( ! numb]2 #ej equals #ej_/ajj1 or #a_/b1 etc4 ,,fractional ,,equival5ts4 #ej 4#ej #a_/b4 #cc-a_/c 4#cc-a_/c #a_/c4 #be 4#be #a_/d4 #bj 4#bj #a_/e4 #af-b_/c 4#af-b_/c #a_/f4 #ab-a_/b 4#ab-a_/b #a_/h4 #aj 4#aj #a_/aj4 #h-a_/c 4#jh-a_/c #a_/ab4 #f-a_/d 4#jf-a_/d #a_/af4 #e 4#je #a_/bj4 #b-a_/b 4#jb-a_/b #a_/dj4 ,accurate ,int]e/4 ,int]e/ is ! sum *>g$ = ! use ( money4 ,x is really ! use ( money or ! b5efit d]iv$ f its use4 ,! pr9cipal is ! sum = ! use ( :i* int]e/ is paid4 ,! rate ( int]e/ is ! p] c5t4 ( ! pr9cipal *>g$ = its use = "o ye>4 ,simple int]e/ is ! int]e/ on ! pr9cipal only1 = ! full "t2 comp\nd int]e/ is int]e/ on ! pr9cipal = ! full "t1 & int]e/ on ea* int]e/ paym5t aft] x becomes due4 ,to f9d ! accurate int]e/ on any sum ( money at a giv5 rate = "o ye>1 multiply ! sum by ! rate & divide by #ajj4 ,to f9d ! accurate int]e/ on any sum ( money at a giv5 rate = any giv5 numb] ( days1 multiply ! int]e/ = "o ye> by ! numb] ( days & divide ! product by #cfe4 ,equation ( ,paym5ts4 ,equation ( ,paym5ts is ! process ( f9d+ :5 two or m sums due at diff]5t times may be paid at once1 )\t loss to debtor or cr$itor4 ,! "t = su* paym5t is call$ ! equat$ "t4 ,to equate two or m paym5ts1 multiply ea* paym5t by its "t1 & divide ! sum ( ! products by ! sum ( ! paym5ts4 ,! times ( ! sev]al paym5ts mu/ be 9 ! same d5om9ation1 & ?is w be ! d5om9ation ( ! answ]4 ,less ?an #a_/b day is reject$2 #a_/b day or m c\nts z #a day4 ,if ! date is requir$1 reckon ! equat$ "t =w>d f ! giv5 date4 ,! ,lightn+ ,calculator's ,addition4 #dcgicba #efbjfgi #bahdeji #ghaedia #bajefaj #cdecagc -------- #beeehghc ,!re are exp]ts :o c add v rapidly4 ,! be/ ( !m1 h[ev]1 _c add up a column ( ones any fa/] ?an y c4 ,"h is h[ "s ( ! rapid addition is p]=m$4 ,! op]ator writes a l9e ( figures1 !n ano!r1 & s on4 ,! second l9e1 h[ev]1 add$ to ! fir/ makes n9es1 except at ! extreme "r1 :]e ! two figures add to t54 ,! ?ird & f\r? be> ! same relation1 & z _m m z he *ooses to put d[n4 ,! la/ two l9es1 h[ev]1 are put d[n at r&om4 ,n[1 to add ^! columns1 he beg9s any:]e1 p]haps at ! left-h& side1 putt+ d[n #b 7! numb] ( pairs above71 !n by simply add+ ! two bottom l9es1 he gets ! correct sum4 ,bank ,disc\nt4 ,! sum *>g$ by a bank = ca%+ a note or "t draft is call$ bank disc\nt4 ,?is disc\nt is ! simple int]e/1 paid 9 advance1 = ! numb] ( days ! note has to run4 ,:olesale bus9ess h\ses usually sell goods on "t & take notes f ! retail]s 9 paym5t4 ,^! notes are n (t5 = a long] p]iod ?an ?ree mon?s4 ,"s are plac$ 9 ! banks = collection1 o!rs are disc\nt$4 ,:5 a note is disc\nt$ at a bank ! payee endorses x1 mak+ x payable to ! bank4 ,bo? mak] & payee are !n responsible to ! bank = its paym5t4 ,if ! note is draw+ int]e/ ! disc\nt is reckon$ on & d$uct$ f ! am\nt due at maturity4 ,mo/ notes disc\nt$ at banks d n draw int]e/4 ,! "t 9 bank disc\nt is always ! numb] ( days f ! date ( disc\nt+ to ! date ( maturity4 ,example4 ,a note ( #bej1 dat$ ,july #g?1 payable 9 #fj days1 is disc\nt$ ,july #g?1 at #f p] c5t42 f9d ! proce$s4 ,?is note is due 9 #fc days1 or ,septemb] #h?4 ,! accurate int]e/ ( #bej = #fc days at #f p] c5t4 is #b4ei4 ,! proce$s1 !n1 w be #bej - #b4ei1 or #bdg4da4 ,h[ to ,make ,*ange4 ,salesm5 usually make *ange by addition4 ,!y h ! money to c\nt out1 & 9 do+ s !y add to ! am\nt ( ! pur*ase until !y rea* ! am\nt ( ! bill pres5t$4 ,= example1 if y buy some?+ wor? #c4ce & pres5t a t5-doll> bill 9 paym5t1 y w probably receive 9 return #e c5ts1 #aj c5ts1 #ej c5ts1 #a1 & #e2 ! salesman say+ #dj1 #ej1 #d1 #e2 #aj4 ,?is me?od is lea/ liable to error4 ,accuracy & rapidity 9 c\nt+ out *ange c be/ be acquir$ by practice beh9d ! c\nt] or at ! ca%-desk4 ,pro( ( ,multiplication 9 ,t5 ,seconds4 ,! unitate ( a numb] is ! sum ( its digits r$uc$ to a unit4 #beb #i #ed #i #cba #f --- #beb #ejd #gef ----- #hjhib #bg #i ,! unitate ( ! multipli] is #i & ! unitate ( ! multiplic& is #f2 #f times #i equals #ed1 & ! unitate ( #ed is #i4 ,n[ ! unitate ( ! product is f\nd to be #i also1 :i* is a pro( ( ! correctness ( ! "w4 ,! ,canadian ,int]e/ ,rule4 #d #gbd #aha #aa #ai4ia ,?is rule ( comput+ int]e/ appe>s 9 "s ,canadian text-books1 &1 ?\gh simply a modification ( o!r rules1 is wor?y ( notice4 ,to f9d ! int]e/ on #gbd = #e-a_/b mon?s at #f p] c5t41 all y h to d is to divide by #d & multiply by #aa4 ,! rule is to divide ! pr9cipal by #d1 & to multiply ! quoti5t by "o-?ird ( ! product ( ! rate by ! "t 9 mon?s4 ,six times #e-a_/b #cc1 & "o-?ird ( #cc is #aa4 ,if ! "t be express$ 9 ye>s1 multiply "o-fif? ( ! pr9cipal by "o-half ! product ( ! rate by ! numb] ( ye>s1 & remove ! decimal po9t "o place to ! left4 ,table ( ,transpos$ ,numb]s4 ,,diff]5ces4 #i #aj #ba #cb #dc #ed #fe #gf #hg #ih #ja #ab #bc #cd #de #ef #fg #gh #hi #ah #bj #ca #db #ec #fd #ge #hf #ig #jb #ac #bd #ce #df #eg #fh #gi #bg #cj #da #eb #fc #gd #he #if #jc #ad #be #cf #dg #eh #fi #cf #dj #ea #fb #gc #hd #ie #jd #ae #bf #cg #dh #ei #de #ej #fa #gb #hc #id #je #af #bg #ch #di #ed #fj #ga #hb #ic #jf #ag #bh #ci #fc #gj #ha #ib #jg #ah #bi #gb #hj #ia #jh #ai #ha #ij #ji #ij #ajj #jaj #ii #ajj #jja ,explanation ( ,=ego+ ,table4 ,! transposition ( figures is a frequ5t cause ( errors 9 prov+ acc\nts & balance %eets4 ,?is table is f\nd$ on ! fact t all diff]5ces betwe5 transpos$ numb]s are multiples ( n9e4 ,! diff]5ce betwe5 ! figures misplac$ is equal to ! quoti5t ( ! result+ error :5 divid$ by n9e2 ?us1 #ia - #ai #gb2 #gb #i #h2 #i - #a #h1 & ! labor ( se>*+ = x may be conf9$ to exam9+ ^? figures ! transposition ( :i* w\ld make ! diff]5ce1 z !y are ! only ones t c cause ! error4 ,?us3 if ! error 9 ! balance-%eet be #ha c5ts1 x is possibly caus$ by a transposition1 & ! cl]k c fir/ exam9e ! c5ts column ( 8 books = items ( #ij c5ts1 or #ji c5ts1 alone1 ) a /rong probability ( f9d+ ! cause ( ! error )\t fur!r revision4 ,transpositions may occur 9 any decimal or integ] place1 & ! diff]5ces caus$ !reby are divisible by n9e )\t a rema9d]2 b1 beyond ?is table1 ! numb]s asc5d 9 regul> progression1 ea* diff]5ce increas+ by n9e1 z foll[s3 #ajh #abj2 #aag #acj2 #abf #adj2 etc4 #ab #ac #ad ,! quoti5t ( ! diff]5ce 9 a regul> progression1 :5 divid$ by n9e1 gives ! figures transpos$1 ?us3 #acj - #ac #aag #i #ac1 :i* are ! figures to be s\ght = :5 a discrepancy ( #aag is %[n2 b ?is w n apply to diff]5ces bel[ #ha1 nor to mix$ transpositions4 ,an error divisible by two may be caus$ by po/+ an item to ! wrong side ( ! l$g]4 ,%ort ,me?od to ,f9d ! ,int]e/ ( a ,giv5 ,sum4 ,r$uce ! "t to mon?s1 & to ! numb] ?us f\nd annex "o-?ird ( ! days1 :i* :ole numb] multipli$ by "o-half ( y\r pr9cipal w produce y ! requir$ int]e/ 9 doll>s1 c5ts & mills1 at #f p] c5t4 ,if days only are giv51 multiply "o-?ird ( ! days by "o-half ( ! pr9cipal = ! requir$ int]e/ at #f p] c5t4 ,note ^! ex]cises3 #bej at #f = #h mos4 #f ds4 #hb #abe #aj4be4 #bej at #f = #ic ds4 #ca #abe #c4hh4 #bej at #f = #i mos4 #i #abe #aa4be4 ,9 "s respects ?is rule is sup]ior to ! well-kn[n #fj-;day me?od ( reckon+ int]e/4 ,int]e/ ,computations4 #dfb4ej 4#dh ------- #f #cfj ---- #fj #bbb4jjjj #c4gj ,multiply ! pr9cipal 7am\nt ( money at int]e/7 by ! "t1 r$uc$ to days2 !n divide ?is product by ! quoti5t obta9$ by divid+ #cfj 7! numb] ( days 9 ! int]e/ ye>7 by ! p] c5t4 ( int]e/1 & ! quoti5t ?us obta9$ w be ! requir$ int]e/4 ,require ! int]e/ ( #dfb4ej = "o mon? & eighte5 days at #f p] c5t4 ,an int]e/ mon? is #cj days2 "o mon? & #ah days equals #dh days4 #dfb4ej multipli$ by 4#dh gives #bbb4jjjj2 #cfj divid$ by #f 7! p] c5t4 ( int]e/7 gives #fj1 & #bbb4jjjj divid$ by #fj w give y ! exact int]e/1 :i* is #c4gj4 ,if ! rate ( int]e/ 9 ! above example 7 #ab p] c5t41 we w\ld divide ! #bbb4jjjj by #cj 7because #cfj divid$ by #ab gives #cj72 if #d p] c5t41 we w\ld divide by #ij2 if #h p] c5t41 by #de2 & 9 l mann] = any o!r p] c5t4 99 99 99 99 99 ,,our ,,mail ,,directory4 ,e p]son :o receives ?is copy ( ,,multum ,,9 ,,p>vo ,,libr>y w also receive ! b5efit ( ! publicity ( our ,mail ,directory1 "u ! foll[+ arrangem5t3 ,we %all =w>d y\r "n & address dur+ ! next two ye>s to _m conc]ns1 includ+ publi%]s1 :o w mail to y gratuit\sly sample copies ( publications1 circul>s1 catalogues1 etc4 ,y w d\btless receive a great _m ( su*1 & x may be well to rememb] t y are receiv+ !m on acc\nt ( ?is ,directory ( ours4 99 99 99 99 99 ,transcrib]'s ,notes3 ,use ( - to repres5t division 9 "s expressions is /&>diz$ to _/4 ,! foll[+ *ange 0 made3 p4 #ae3 ,extrane\s numb]s 7 remov$ f ! example int]e/ computation4