,transcriber's ,notes3 ,text enclosed by underscores is in italics 7italics74 ,the whole number part of a mixed fraction is separated from the fractional part with -1 for example1 #b-a_/b4 ,additional ,transcriber's ,notes are at the end4 99 99 99 99 99 ,multum in ,parvo ,library4 ,vol4 ,i4 ,,february1 #ahid4 ,published ,monthly4 ,no4 #b4 ,how to ,become a ,,lightning ,,calculator4 ,smallest ,magazine in the ,world4 ,subscription price1 #ej cts4 per year4 ,single copies1 #e cents each4 ,,published ,,by ,a4 ,b4 ,,courtney1 #fga ,tremont ,street1 ,boston4 ,entered at ,post-,office as second-class matter4 ,instantaneous ,addition4 ,accuracy should be first considered1 then rapidity4 ,quick adders1 by the way1 are the most accurate4 ,write the numbers in vertical lines1 avoiding irregularity4 ,this is important4 ,keep your thought on results not numbers themselves4 ,do not reckon #g and #d are #aa and #h are #ai1 but say #g1 #aa1 #ai and so on4 ,when the same number is repeated several times1 multiply instead of adding4 ,when adding horizontally begin at the left4 #cacb #bdec #ab #fdga #bj #gcab #ae #bacd #ba ----- --- #baejb ,in adding long columns1 prove the work1 by adding each column separately in the opposite direction1 before adding the next column4 ,many accountants put down both figures as in the illustration4 ,the sum of the first column is #ab2 carrying one1 the sum of the second is #bj2 carrying two1 the sum of the third column is #ae2 carrying one1 the sum of the fourth column is #ba1 and the total1 #baejb1 is found by calling off the last two figures and the right-hand figures1 following the wave line in the illustration4 ,this method is better than the old one of penciling down the number to carry4 ,if one desires to go back and add a certain column a second time1 the number to carry is at hand and the former total is known4 ,how to ,add ,two ,columns at ,once4 #bcab #cbec #bfaj #abef #caii ----- #abfcj ,to the inexperienced it will be a difficult task to add two columns at once1 but many of those who have daily practice in addition find it about as easy to add two columns as one4 ,say #ii and #ej are #adi1 and #f are #aee1 and #aj and #ej are #bae and #c are #bah1 and #ab are #bcj4 ,carry #b1 and say #cc and #ab are #de1 and #bj are #fe1 and #f are #ga1 and #cj are #aja1 and #b are #ajc1 and #bc are #abf4 ,much of the information here contained is compiled from ,w4 ,d4 ,rowland's valuable little volume1 entitled 8,how to become expert with figures40 ,you can get this handy book by sending #be cents in stamps to ,,american ,,nation ,,co41 ,boston4 ,multiplication4 ,to ,multiply ,any ,number by #aa4 ,write the first right-hand figure1 add the first and second1 the second and third1 and so on2 then write the left-hand figure4 ,carry when necessary4 #baidcd #aa #bdacggd ,put down the right-hand figure #d4 ,then say1 #d and #c are #g2 then1 #c and #d are #g2 then1 #d and #i are #ac1 put down #c and carry #a2 then1 #i and #a and #a are #aa1 put down the #a and carry #a2 then1 #a and #b and #a are #d2 then write the left-hand figure #b4 ,in multiplying small numbers1 such as #bd by #aa1 write the sum of the two figures between the two figures1 making #bfd1 the required product4 ,to ,multiply by #aja1 #ajja1 etc4 ,to multiply by #aja1 add two ciphers to the multiplicand1 and add to this the multiplicand4 #bcda #aja #bcdajj #bcda ,to multiply by #ajja1 add three ciphers to the multiplicand1 and add to this the multiplicand4 ,to ,multiply by #e1 #be1 #abe4 ,to multiply by #e1 add a cipher and divide by #b4 ,to multiply by #be1 add two ciphers and divide by #d4 ,to multiply by #abe1 add three ciphers and divide by #h4 ,another ,easy ,way to ,multiply4 #hb #ed ---- #ddbh ,to multiply two figures by two figures1 proceed as follows3 ,multiply units by units for the first figure4 ,carry and multiply tens by units and units by tens1 7adding7 for the second figure4 ,carry and multiply tens by tens for the remaining figure or figures4 ,in this example proceed as follows3 #b #d #h #ast figure4 7#d #h7 7#e #b7 #db4 ,therefore #b #b;d figure4 7#e #h7 #d carried #dd #c;d and #dth figures4 ,by a little practice any one may become as familiar with this rule and as ready in its application as with the ordinary method4 ,to multiply any number by #b-a_/b1 add one cipher1 and divide by #d4 ,to multiply any number by #c-a_/c1 add one cipher1 and divide by #c4 ,to multiply by #cc-a_/c1 add two ciphers1 and divide by #c4 ,to multiply any number by #a-c_/g1 add one cipher1 and divide by #g4 ,to multiply by #af-b_/c1 add two ciphers1 and divide by #f4 ,to multiply by #ad-b_/g1 add two ciphers1 and divide by #g4 ,to multiply by #hge1 add three ciphers1 and divide by #h4 ,to divide by #be1 multiply by #d1 and cut off two figures4 ,to divide by #abe1 multiply by #h1 and cut off three figures4 ,to multiply by #ab-a_/b1 add two ciphers1 and divide by #h4 ,to find the value of any number of articles at #ge cents each1 deduct one-quarter of the number from itself and call the remainder dollars4 ,to ,subtract ,any ,number ,consisting of ,two ,figures from #ajj4 ,take the first figure from #i1 and the second from #aj4 ,for example3 in subtracting #gc from #ajj1 or in taking #gc cents change out of a dollar1 say #g from #i and #b1 and #c from #aj and #g1 or #bg cents4 ,practice this rule4 ,it is simple1 and will be found particularly helpful in making change4 ,divisions4 ,a number is divisible by #b when the last digit is even4 ,a number is divisible by #d when the last two digits are divisible by #d4 ,to divide by #ab-a_/b1 multiply by #h1 and cut off two figures4 ,simple ,discount ,rule4 ,this simple rule is in use in many houses where several discounts are allowed from list prices4 ,suppose the list price of a piano to be #ejj1 and you allow an agent #be1 #bj and #aj off4 #ajj #ajj #ajj #be #bj #aj --- --- --- #ge #hj #ij 4#edjjjj ,subtract each from #ajj and multiply and you get 4#ed4 #ejj 4#ed #bgj1 the agent's price4 99 99 99 99 99 ,if you want to get a complete book on quick calculating1 comprising all modern methods1 together with a vast amount of other valuable matter1 pertaining to business1 send #be cents to ,,american ,,nation ,,co41 ,boston1 ,mass41 for a volume of 8,how to ,become ,expert at ,figures40 ,percentage4 ,the name percentage is applied to certain arithmetical exercises in which #ajj is used as the basis of computation4 ,per cent4 is an abbreviation of the ,latin per centum1 meaning by the hundred4 ,this sign is used for the words per cent4 ,thus1 #aj of a number equals #aj_/ajj1 or #a_/aj of the number2 #ej equals #ej_/ajj1 or #a_/b1 etc4 ,,fractional ,,equivalents4 #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 ,interest4 ,interest is the sum charged for the use of money4 ,it is really the use of money or the benefit derived from its use4 ,the principal is the sum for the use of which interest is paid4 ,the rate of interest is the per cent4 of the principal charged for its use for one year4 ,simple interest is the interest on the principal only1 for the full time2 compound interest is interest on the principal for the full time1 and interest on each interest payment after it becomes due4 ,to find the accurate interest on any sum of money at a given rate for one year1 multiply the sum by the rate and divide by #ajj4 ,to find the accurate interest on any sum of money at a given rate for any given number of days1 multiply the interest for one year by the number of days and divide the product by #cfe4 ,equation of ,payments4 ,equation of ,payments is the process of finding when two or more sums due at different times may be paid at once1 without loss to debtor or creditor4 ,the time for such payment is called the equated time4 ,to equate two or more payments1 multiply each payment by its time1 and divide the sum of the products by the sum of the payments4 ,the times of the several payments must be in the same denomination1 and this will be the denomination of the answer4 ,less than #a_/b day is rejected2 #a_/b day or more counts as #a day4 ,if the date is required1 reckon the equated time forward from the given date4 ,the ,lightning ,calculator's ,addition4 #dcgicba #efbjfgi #bahdeji #ghaedia #bajefaj #cdecagc -------- #beeehghc ,there are experts who can add very rapidly4 ,the best of them1 however1 cannot add up a column of ones any faster than you can4 ,here is how some of the rapid addition is performed4 ,the operator writes a line of figures1 then another1 and so on4 ,the second line1 however1 added to the first makes nines1 except at the extreme right1 where the two figures add to ten4 ,the third and fourth bear the same relation1 and as many more as he chooses to put down4 ,the last two lines1 however1 are put down at random4 ,now1 to add these columns1 he begins anywhere1 perhaps at the left-hand side1 putting down #b 7the number of pairs above71 then by simply adding the two bottom lines1 he gets the correct sum4 ,bank ,discount4 ,the sum charged by a bank for cashing a note or time draft is called bank discount4 ,this discount is the simple interest1 paid in advance1 for the number of days the note has to run4 ,wholesale business houses usually sell goods on time and take notes from the retailers in payment4 ,these notes are not often for a longer period than three months4 ,some are placed in the banks for collection1 others are discounted4 ,when a note is discounted at a bank the payee endorses it1 making it payable to the bank4 ,both maker and payee are then responsible to the bank for its payment4 ,if the note is drawing interest the discount is reckoned on and deducted from the amount due at maturity4 ,most notes discounted at banks do not draw interest4 ,the time in bank discount is always the number of days from the date of discounting to the date of maturity4 ,example4 ,a note of #bej1 dated ,july #gth1 payable in #fj days1 is discounted ,july #gth1 at #f per cent42 find the proceeds4 ,this note is due in #fc days1 or ,september #hth4 ,the accurate interest of #bej for #fc days at #f per cent4 is #b4ei4 ,the proceeds1 then1 will be #bej - #b4ei1 or #bdg4da4 ,how to ,make ,change4 ,salesmen usually make change by addition4 ,they have the money to count out1 and in doing so they add to the amount of the purchase until they reach the amount of the bill presented4 ,for example1 if you buy something worth #c4ce and present a ten-dollar bill in payment1 you will probably receive in return #e cents1 #aj cents1 #ej cents1 #a1 and #e2 the salesman saying #dj1 #ej1 #d1 #e2 #aj4 ,this method is least liable to error4 ,accuracy and rapidity in counting out change can best be acquired by practice behind the counter or at the cash-desk4 ,proof of ,multiplication in ,ten ,seconds4 ,the unitate of a number is the sum of its digits reduced to a unit4 #beb #i #ed #i #cba #f --- #beb #ejd #gef ----- #hjhib #bg #i ,the unitate of the multiplier is #i and the unitate of the multiplicand is #f2 #f times #i equals #ed1 and the unitate of #ed is #i4 ,now the unitate of the product is found to be #i also1 which is a proof of the correctness of the work4 ,the ,canadian ,interest ,rule4 #d #gbd #aha #aa #ai4ia ,this rule of computing interest appears in some ,canadian text-books1 and1 though simply a modification of other rules1 is worthy of notice4 ,to find the interest on #gbd for #e-a_/b months at #f per cent41 all you have to do is to divide by #d and multiply by #aa4 ,the rule is to divide the principal by #d1 and to multiply the quotient by one-third of the product of the rate by the time in months4 ,six times #e-a_/b #cc1 and one-third of #cc is #aa4 ,if the time be expressed in years1 multiply one-fifth of the principal by one-half the product of the rate by the number of years1 and remove the decimal point one place to the left4 ,table of ,transposed ,numbers4 ,,differences4 #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 of ,foregoing ,table4 ,the transposition of figures is a frequent cause of errors in proving accounts and balance sheets4 ,this table is founded on the fact that all differences between transposed numbers are multiples of nine4 ,the difference between the figures misplaced is equal to the quotient of the resulting error when divided by nine2 thus1 #ia - #ai #gb2 #gb #i #h2 #i - #a #h1 and the labor of searching for it may be confined to examining those figures the transposition of which would make the difference1 as they are the only ones that can cause the error4 ,thus3 if the error in the balance-sheet be #ha cents1 it is possibly caused by a transposition1 and the clerk can first examine the cents column of his books for items of #ij cents1 or #ji cents1 alone1 with a strong probability of finding the cause of the error without further revision4 ,transpositions may occur in any decimal or integer place1 and the differences caused thereby are divisible by nine without a remainder2 but1 beyond this table1 the numbers ascend in regular progression1 each difference increasing by nine1 as follows3 #ajh #abj2 #aag #acj2 #abf #adj2 etc4 #ab #ac #ad ,the quotient of the difference in a regular progression1 when divided by nine1 gives the figures transposed1 thus3 #acj - #ac #aag #i #ac1 which are the figures to be sought for when a discrepancy of #aag is shown2 but this will not apply to differences below #ha1 nor to mixed transpositions4 ,an error divisible by two may be caused by posting an item to the wrong side of the ledger4 ,short ,method to ,find the ,interest of a ,given ,sum4 ,reduce the time to months1 and to the number thus found annex one-third of the days1 which whole number multiplied by one-half of your principal will produce you the required interest in dollars1 cents and mills1 at #f per cent4 ,if days only are given1 multiply one-third of the days by one-half of the principal for the required interest at #f per cent4 ,note these exercises3 #bej at #f for #h mos4 #f ds4 #hb #abe #aj4be4 #bej at #f for #ic ds4 #ca #abe #c4hh4 #bej at #f for #i mos4 #i #abe #aa4be4 ,in some respects this rule is superior to the well-known #fj-;day method of reckoning interest4 ,interest ,computations4 #dfb4ej 4#dh ------- #f #cfj ---- #fj #bbb4jjjj #c4gj ,multiply the principal 7amount of money at interest7 by the time1 reduced to days2 then divide this product by the quotient obtained by dividing #cfj 7the number of days in the interest year7 by the per cent4 of interest1 and the quotient thus obtained will be the required interest4 ,require the interest of #dfb4ej for one month and eighteen days at #f per cent4 ,an interest month is #cj days2 one month and #ah days equals #dh days4 #dfb4ej multiplied by 4#dh gives #bbb4jjjj2 #cfj divided by #f 7the per cent4 of interest7 gives #fj1 and #bbb4jjjj divided by #fj will give you the exact interest1 which is #c4gj4 ,if the rate of interest in the above example were #ab per cent41 we would divide the #bbb4jjjj by #cj 7because #cfj divided by #ab gives #cj72 if #d per cent41 we would divide by #ij2 if #h per cent41 by #de2 and in like manner for any other per cent4 99 99 99 99 99 ,,our ,,mail ,,directory4 ,every person who receives this copy of ,,multum ,,in ,,parvo ,,library will also receive the benefit of the publicity of our ,mail ,directory1 under the following arrangement3 ,we shall forward your name and address during the next two years to many concerns1 including publishers1 who will mail to you gratuitously sample copies of publications1 circulars1 catalogues1 etc4 ,you will doubtless receive a great many of such1 and it may be well to remember that you are receiving them on account of this ,directory of ours4 99 99 99 99 99 ,transcriber's ,notes3 ,use of - to represent division in some expressions is standardized to _/4 ,the following change was made3 p4 #ae3 ,extraneous numbers were removed from the example interest computation4