IMAGE EVALUATION TEST TARGET (MT-3) &c // ^/ :/. ^0 ks5 ^ 1.0 SK^ Ki — lu 1^ I.I ^.-^KS m 1.25 1 1.4 |J.:.6 '/] /i /: .^ V' ^ %^ ?^^ Oy^^ Photographic Sciences Corporation <^ a>' « i\ ... * 33 WEST MAIN STRICT WEBSTER, N.Y. M5B0 (716) S73.4S03 '^.>" ;\ '<^ CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques ^ Technical and BibHographic Notaa/Notas tachniquaa at bibliographiquaa Tha Instituta haa attamptad to obtain tha baat original copy avaiiabia for filming. Faaturaa of thia copy which may ba bibliographicaliy uniqua, which may altar any of tha imagaa in tha raproduction, or which may significantly changa tha usual mathod of filming, ara chockad balow. □ Colourad covars/ Couvartura da couiaur I I Covars damagad/ D Couvartura andommag^ Covars rastorad and/or laminatad/ Couvartura rastaurAa at/ou palliculte □ Cover titia missing/ La titra da couvartura manqua Colourad mapa/ Cartas gtegraphiquaa vn couiaur Colourad ink (i.a. othar than blua or black)/ Encra da couiaur (i.a. autra qua blaua ou noiral Colourad plataa and/or iiluatratlons/ Planchaa At/ou illustrations an couiaur Bound with othar matarial/ Rali* avac d'autraa documants n D D Tight binding may causa shadow* or distortion along interior margin/ La re liure serrte peut cauaar da I'ombre ou de la distorsion la long da la marga intiriaura Blank leaves added during restoration may appear within tha text. Whenever possible, these have been omined from filming/ II se peut que certainaa pages blanches ajoutAes lofs d'une restau ration apparaiasant dans la taxte, mais. lorsqua cela 4tait possible, ce* pages n'ont paa *tA filmiaa. Additional comments:/ Commentaires supplAmentaires; L'Institut a microfilm* la mailleur exemplaire qu'il lui a M possible de se procurer. Les d*tsils de cet exemplaire qui sont peut-«tre uniques du point de vue bibliographique, qui peuvent modifier una image reproduite. ou qui peuvent exiger une modification dans la m^thoda normale de filmage sont indiquia ci-daasous. D D D E D D D D D Colourad pages/ Pagaa da couiaur Pagaa damaged/ Pages endommagtes Pages restored and/or laminated/ Pages restaurAes at/ou pelliculAes Pages discoloured, stained or foxed/ Pagaa dAcolorAes, tachaties ou piqutes Pages detached/ Pages dAtachias Showthrough/ Transparence Quality of print varies/ Qualit* inAgala de t'impression Includes supplementary material/ Comprand du matiriel suppl^mentaira Only edition available/ Seule Edition disponible Pages wholly or partially obscured by errata slips, tissues, etc., have been refilmed to ensure the best possible image/ Lea pages totaiement ou partieltement obscurcies par un feuillet d'errata. une pelure. etc.. ont M fllmtes A nouveau da fapon i obtanir la meilleure image possible. This item is filmed at the reduction ratio checked below/ Ca document est film* au taux da reduction indiquA ei-daaaous. 10X 14X 18X 22X / 12X 16X 20X 26X 30X 24X 28X J 32X Th« copy fllinad h«r« has b««n reproduced thank* to th« gonoroshy of: TtM Nom Scotia LagitlathM LilKary L'oxomplairo fllm« fut roproduh grieo i la gAn^rosM da: Ttw Nova Scotia LagMativa Library Tho imagos appearing here are the beet quality poeaibia conaidoring the condition and ieribillty of the original copy and in keeping with the filming contract apecificationa. Original copie* in printed paper cover* ere filmed beginning with the front cover and ending on the laat page with a printed or illuatratad impree- aion, or the beck cover when eppropriate. All other original copie* are filmed beginning on the firat pege with a printed or illuatrated impree- aion, and ending on the laat page with a printed or illuatrated impre**ion. The laat recorded frame on each microfiche ahall contain the aymboi -^ (meaning "CON- TINUED"), or the aymboi V (meaning "END"), whichever applie*. La* image* *uh^*nte* ont «t« reproduitee avec ie plu* grand *oin, compta tanu de la condition at da la nettet* de i'exemplaire film*, et •>> conformM evec Ie* condition* du cnntrat de fllmege. Le* exemplaire* onglnaux dont la couvarture en papier eet imprim«e eont fiimte en commen^nt par le premier plat et en termlnant *oit par la dernlAre page qui comporte une empreinte d'impreeeion ou d'illuatratjion. *oit par le eeoond plat, aelon le ca*. Tou* lee autre* exemplaire* orlginaux s.nt film** en commenpant par la pramiire page qui comporte une empreinte d'impre**ion ou d'iilustration et en termlnant par la derni*re pege qui comporte une telle empreinte. Un de* eymbole* *uhrant* apparattra *ur la dernl*re imege de cheque microfiche, **lon ie ca*: i* eymbole — *> eignHI* "A 8UIVRE", le eymbole ▼ eignifie "FIN". IMaps, plate*, chart*, etc.. may be filmed et different reduction ratio*. Tho*e too lerge to be entirely included in one expoeure are filmed beginning in the upper left hand corner, left to right end top to bottom, e* many frame* a* required. The following diegram* iliuatrata the method: Le* certee, plenchee, tableeux, etc., peuvent *tre filmte i de* taux de reduction dlff«rent*. Lor*que le document eet trop grand pour Atre reproduit en un eeui cllch*, 11 eet film* i pertir de I'engle eup*rieur gauche, de gauchn * droite, et de haut en baa, en prenent le nombre d'imagee n*ceeealre. Lee diegremmee auivant* illu*trent la m*thode. 12 3 1 2 3 4 5 6 ^mwmmi's^i^mmv^^'^^^'^^^'^^ ^ J^^^u^y^ ^f^^ft^C'^-^ ^v^. ^OVA SCOTI4 PROVINCE HOUSE •/i\ FRAZEE & WHISTON'S [^ t COMMERCIAL ARITHMETIC. <^ 1 J- o. P. fra2:e]e, A«OCX.„ PH„„„^ „ ,,. ^^^^^^^ ^^^^_^ ^^^^^^ Halifax, n. s.. fUBUSHEi) BY FRAZEB 4 WHISTON. 18M. ITt. • m^i ^W\ \\S, Entered acoordinK to Act of Parliament of CanRcla, in the year 1884, By J. C. P. Frazm, In the Office of the Minister of Agriculture, Ottawa. . -. -1 1 PRINTKD BT THB NOVA SCOTIA PRINTINO CO. i PREFACE. The author of this work desires only to say to such of the pubhc as may feel an interest in it, that he has pre- pared it principally for use in the Halifax Business College, and has consulted only the requirements and interests of that institution in its preparation. That he lays no claim to literary merit for the work ; nor has he always confined himself to the insertion of purely original matter. The subject is so old. and so much the common property of so many authors, that about the only originality any one can lay claim to in such a work is his manner of pre- senting the subject. Some of the material of Eaton & Frazee's Arithmetic, now out of print, has been appropri- ated. Many other works have been consulted, and occasional exercises, modified to suit the requirements of this work, have been used. The author's thanks are due. and are here tendered, to several practical accountants and business men of Halifax for valuable information and assistance, always cheerfully rendered when asked for. Haupax, N. S., December, 1883. ;7^:^§o .^:^-^ • CONTENTS. Pbiliminakt ExracTs^s ^'■** Numeration ^ Notation ^ Definitions * PhOPERTIK OF Nf IIBBH8 ' PrimeFactors ^ Oreatest Common Divisor Least Common M\jltiple Fractions 1* Reduction Multiplication ^ Division I'east Common Denominator ^ Addition * Subtraction * Decimal Fractions ...........'.''" 29 Addition and Subtraction ' " ' ^ Multiplication ^ Division ^ Denominate Numbers ' ' ^ Canadian Currency British or Sterling Currency ^ United States Currency Dominion Standards of Weight ' ^^ Avoirdupois Weight Troy Weight ^ Linear, or Long Measure Surveyors' Linear Measure ■** Square Measure ^ Surveyors' Square Measure ^ Cubic or Solid Measure. . ^^ Measure of Capacity __^ AO Liquid Measure Apothecaries' Fluid Measum * 18 h^.m^M VI CONTENTS. DKNOMiifATE NtTiiBKRB— Dry MoMure 49 Produce Weight 49 Measure of Time jO Marine, Angular, or Circular Measure 51 Miscellaneous Measures 52 Thk Metric Symtkii 52 Linear Meaiiure 53 Square Measure 53 Land Measure 54 Cubic Measure 54 Dry and Liquid Measure !i4 Weight 54 Reduction of Denominate Numbers ^ 55 Addition of Denfiminate Numbers 64 Subtraction of Denominate Numbers 67 Multi]ilication of Denominate Numbers (!9 Division of Denominate Numbers 7I The Cental ' 73 Foreign Moneys of Account and their values in Canadian Currency 75 Longitude and Time 76 Aliquot Parts 78 Peucbntaob 83 Special Methods and Exercises 90 IfTTEBEST 96 Accounts Current with Interest 108 Discount and Present Worth 113 Compound Interest 114 Table of amounts of $1 at Compound Interest 117 Annuities II9 Table of amounts of an Annuity of 81 122 Table of Present Worths of an Annuity of $1 123 Commercial Paper 124 Demand Note 125 9 Note with Interest 126 Joint and Several Note 126 Sight Draft I27 Time Draft 127 Set of Sterling Exchange 128 Bank Discount 128 Partial Payments I33 Commission and Brokerage 140 CONTENTS. vu Stocks awd Bondh Insuranoi... 144 Pkowt and Lo« but F Ju away ^f J73 , how many dollars have I left ? an/sold^Srbrff '":'^'"'" ''^ •'"'"^^'^ ^««3 bushels of apples sold 558 bushels ; how many bushels had he left 1 4. How much did the 558 bushels bring @ $2 per bushel ? 1C3 poundtTottroro' '"',*' ™"'^^ ' ^«°^^ °- -i^'h-l 197 pounds ano he .lo ''"^ '' '"°''" ''^ P^"'^^^' «"o".er 256 pounds how In '"",''' T'*^" '' P''"'^^^' ^^ -other pounds , how many pounds of pork did he have to sell ? 6. How much a.. 1758 lb. of pork worth @ 7 cents per lb i" one dty tttt wlff" U'ff ' °"^^^ '™™ ^^« -«^« PRELIMINARY EXERCISES. 9. If a man were worth $3112 on new year's day, and gained during the year $849, how much would he be v,orth the next new year's day ? 10. If a man were worth $4000 on new year's day, and lost $1943 during the year, how much would he be worth the next new year's day ] 11. A man intending to move from the counttj to the city sold his farm for $1743, his harses for $395, his cows for $98, his sheep for $137, his farming utensils for $249, his hay for $217, his gram for $75, and his poultry for $29, how many dollars worth did he sell altogether ? 12. In the last question how much more did ^1.3 man get for his hpy than for his grain] 13. In 1871 the population of the counties of New Brunswick was as follows: St John, 52120 ; Charlotte, 25882 ; King's, 24593 ; Queen's, 13847; Sunbury, 6824; York, 27140; Carleton, 19938; Victoria, 11641; Restigouche, 5575; Gloucester, 18810; North- umberland, 20116; Kent, 19101; Westmoreland, 29335; Albert, 10672 ; what was the population of the whole Province] 14. If one yard of cloth cost 75 cents, how many cents will 25 yards cost ] 15. If 1 pound of cheese cost 18 cents, how many cents must I give for 9 pounds ] • 16. If 7 boxes contain 144 pens each, how many in them alii 17. If a laborer earn $7 a week, how many dollars would he eani in 35 weeks] 18. How many bricks would a t«amster remove at 23 loads, if he took 1625 at a load] 19. If a wagon wheel make 586 revolutions in a mile, how many revolutions would it make in a journey of 67 miles 1 20. An ordinary clock strikes 156 strokes in a day, how many strokes does it strike in a year of 365 days ] 21. A bushel of potatoes weighs 60 pounds, what is the weight of 350 bushels ] 22. At $15 pet acre, what would be the price of a field mea- suring 29 acres 1 PRELIMINARY EXERCISES. 3 2i. What is the half of 9786 ? 25. What is the one-third of 768594 ? 26. Find on«-eighth of 673915. 27. Find one-foitieth of 976183. ^ JO. If I» yda of cloth CO.. 1805 cent., rt.t ,-, a, p^„ ^.^ ^. .M pi't'^e:*":: ir;r ^'"''"™ '■»' "•--' -«" -^ .ach t. "o,!l™ „7, *~'= '° • ^"' '">»' " "" '-"^ »' or o!t, afz rZfiric «:»? ^'"^"-^ "" '"•-"■ 35. If each family in a city consume 72 eg-s in a war ,«^ •* STn^c;;^ '''' '' -^^'^' ^^^ -^' ^ "-". Si::t thaf per busheU '"'^'^ ^ "" ^°^^ ^'^^^ -^^' ^^ -ch . 37. What is the cost of 1 7 acres of land at $52.50 per acre f 52 ,vtk .V'""'' ^''*"'^ *"'"' ""* 3^"*^^ h^'""^'-^ in a year of ^2 weeks, how many is that per week, on an average ? for $1:8of " """^ '"'' '' ""^° ® ' '^'^'^ P" y'"d can I buy purctsed^rS' ''^' '' "'"^^ ® ^^ ^^"*« P- >-^ - ^ l,n„*^" i '"^'^ l^ *"''' °^ ^""''■' ^««^ containing 25 lb for how much was that per pound ? ' ii 4 PRELIMINARY EXERCISES. 42. Bought 21 barrels of apples @ $1.05 per barrel, what did they cost me ] 43. If 11 tons of hay cost $214.50, what will 1 ton cost? What will 27 tons cost 1 44. 1125 bbls. fish were sold for $5906.25, how much per barrel ? 45. 2G9 persons pay a tax of $1312.72, what is the average tax on each ] 4G. Suppose a manufacturing company employs 250 men, and pays them on an average $1.75 per day, what is the cost to the company for 1 day? for 1 week? for 1 year? 47. If the houses in a town are worth on an average $950 each, and their total value is $1168£00, how many houses are iu the town ? 48. If the total value of 1230 houses be $1039350, what i.- the value of each house on an average ? 49. What would be the total valu« of 1230 houses, if the average value were $845 each ? 50. What is the value of 437 sheep at $4.75 each ? 51. If a man travel 3 miles an hour every day for 40 days of 12 hours each, how many miles will he travel. 52. If a railway train runs 264 miles in 12 hours, wbat is the average rate per hour ? 53. At 45 cents per bushel, what must be paid for 1195 bushels of potatoes 1 54. A cargo of 4700 bushels oats sold for $1504, how much is that per bushel ? 55. What is the weight of a cargo of 5000 bushels of wheat weighing 60 lbs. per bushel. 56. 180 chaldrons of coal were sold for $1035, what was the price of 1 chaldron ? :aEt£^.3S3a=ss%t&:.'^^^3XS^ML^i^jT:i NUMERATIOX, Numeration. Numeration is the art of reading numbers or letters, Th expressed by figureg, EngliT "" *"' "'''''^ ^ ^^^umeration. the French and the The French method is almost universally used; Tt separate. FREXCH ^UMERATION TABLE. a o ^ 2 H o •5 ° 2 Oth Perifxl. Trillions. 05 a " 00 u O 15 n ".2 4tb 'eriod. Billions. a o s § o 1^ 00 .< p cw 2 Ut o 13 o C X ^ s *-« 7^3 )— < 3^ h— ( M-i rH -5 3n] Period. Millions. rrj n c 0-2 Ci CO 3 3 = 2 Snd Period. Thousands. o5 g 00 S Ist Period, t'uitg. -■-'^i^ooioH each period uith ih name. " ' "''''' ' '''' " 'iili^^ NOTATIOy. EXERCISES IN NUMERATION. EIAMPLE.-368271927. Eeadthua:- 125. 372. 864. 1076. 1884. 2750. 6890. 9759. 10864. 17651. 42414. 1 a .2 -=! 11 2 58763. 86552. 155731. 196472. 251103. 564989. 2285432. 2711511. 5318754. 9871832. 118G7438. a a a ^ o a ^ - - -S-a^ 3. ® -, » > g _a g o 'S 7 1,» 2 7 25643287. 87418389V 254656431. 761118445. 4519676314. 57965432819. &8740811087. 880195038604. &1086301 06543. 86419038765789; 386480967318640. j^ OTATION. Notation is th« art of writing numbers by fi ^:L ^{'-■A>» ■ DEFINITIONS. 1. Fort3'-8ix thousand, seven hundred and one. ^. bix thousand, six hundred and sixty and'.iJ""""""""" "■' '''«'"''-"8" ".o«»-d, eight h„„d.d 5. Eight hundred thousand and nine. Ten millions, ten thousand and ten. Ten millions and ten. ^inety millions, nine thousand and ninety Ninety millions, nine hundred and nine Seven hundred and seventy billions, five thousand and Eleven millions and eleven Eleven billions eleven millions, one hundred and eleven. Two trillions, thirty millions and thirty 7 . 6. 7. 8. 9. 10. seven. 11. 12. 13. 14. Definitions. Figures are characters representing numbers. A Digit is a single figure. An Integer is a whole number. A Unit is one, or a single thinfr respectively addition, subtraction, muItipUcation and S^LZ These processes are often indicated by signs, as follows: The sign of addition is -f, read plus. The sign of subtraction is -, read minus. The sign of multiplication is X, read multiplied by nr fl> The sign of division is -^, read divided bv. nr t,.» ....,.:„,. .. ^ aui.... .«ed in tiie division in this position, Y;"which"means !>'; PROPERTIES OP NUMBERS. tl.at the upper nun.her is to be divi.led by the lower numbor • or n las pos,t.o,, 4)12, uhich means that the number on the riJht to be divided by the number on the left. ^ The Sum is the result of addition. traded. "^""'"'^ " " """'^" '"" ''^''^ ''•"^^^^^ ""'"^er is sub- The Subtrahend is a number subtracted from another number. The Difference or Remainder is the result of subtraction. The Multiplicand is a number multiplied by another number, pliel ^ ^^ " " """'" '^ "^"^'^ '''-^'^- -'-ter is multi- The Product is the result of multiplication. The Dividend is a number divided by another number The Divisor is a number by which another number is divided. The Quotient is the result of division. J^f^OPEl^TlES OF NUMBEI^S. Every number is either odd or even. An Odd Number is one that cannot be divided bv o ,vifJ,. f making a fraction, as, 1, 3, 5, 7, 9. 11 &c ^ " ""'"* ■livide evenly into'anyev'en 'nib;. ' ^'"' ^"' ''''''''' ' '''' 3 ^^^:^^f' ^"^^ ^"^ "-^^ ^^- -- of who. digits .^ 5..n divide evenly into any number whose right-hand figure "•ii^ J ^i^Jitfi'x^^^ r.-^.. PROPERTIES OF NUMBERS. 9 div- iJ^ve!;;:'^ evemy into an, even n„n,ber into which 3 will 8 will divide evenly into any number if if ^vU^ ,!;,•> into .he „„..„ ro^ed b, e,„ f,,^. .^J.^/^^"' '""'^ .t -m'laMivT'^ '"*" ™^ ■™"'" "■' " »' "'»- Jiti" 10 „ill Jivido „™lj in ,„, „„„,t^, n„i ^„,,, ^.j,^ ^ ^ folio J!n'' '""' """'"" "^^ ^"^'^^ ^^^" ^^«» -- i-l"ded in th^i TABLE OF PRIME NUMBERS. 1 2 3 5 7 11 13 17 19 23 2,^S» JL.J:^ S I „. , -jSJ' - ,1^ «1 •' ' 4L ■ ' *" OBEATEST COMMON DIVISOR. ' n To find the greatest common divisor of two or more nnmbers. tjfpZulZT'r I""' "'""" ""'"*''■* '"'" ^^^'-r prime /actors ; thej^uct of tUe factor, common to all u,ill U the greatest common Example.— Find the greatest common divisor of 18, 27 and 36. 18 = 2X3X3. 2" = 3X3X3. 36 = 2X2X3X3, The prime factors common to air «re3and3. 3 X 3 = 9, the greate.t •oromon divisor. EXERCISES. 1. Find the greatest common divisor of 16, 40 and 70 -. ^ind the greatest common divisor of 36, 54, 90 and 70 J. ^ind the greatest common divisor of 126, 210, 84 and"l68 *. J-ind the greatest common divisor of 175 and 245. V.W ""'^.fTf^'^'"'' *' '"^^ '"'" ""'»*^'-«' '^'^'^'^ '^« greater h, ^rl^VZT ZZ T T """'^-'-^"^ ^'- 'Jreatest common ;;;: 4:r """"' ''"'" """ '^ *'' ^^^^^^^^ —^ '^-w ExAMPLK-Find thM greatest eommon divisor of 21 and 98. 21)98(4 84 U)21(l 14 7)14 ~2 Tlie last divisor, 7, is the greatest common divisor. EXERCISES. 1. Find the greatest noBimon divisor .-.f 50 .-.,-.1 oc-r- 2. Find the greatest common divisor of 108 and"9342. I« PHOPEBTIES OP NUMBEBS '■ wit ;: ,'h! '"Tl """""" '"""»' "'■ '"•'« »■' 21"" 1 j^ ■•.«,..». U.C ,^.. „„„„„„„ ,.,;„::r^,;«;-;j„^;^ 8- A gentleman's cnrden iq ir.o <- ^ i "e wi«hes to set posts'for L nil Th '"'' ""' ''' '"■^ "''■''- tl'at will „,ake equal spaces on !7' ^^'^ ^'^''test distance apart *-t fro,n centre t'o coZll ^ '""' "'^ ""'"'^'- "^ LEAST COMMON MULTIPLE. so is 21. ' ^^ '^ » nmltiple of 3; so is 12 ; cant's f;s:v/.t :.r r'"^^-^ --^ -^ --^^ -^^^'^ a common mmtipl '3 and 5 ^T '' ""''"'"• ^^"^^' ^'^ ■■^ and 6. -J ana 5, 24 is a common multiple of 2, 4 T" W the tat common mmpl, of soveral .nmbera '" "- '«< ',■». „w «f S TX ; f?"'"' "" '"'""- '■-««A-«t 6 because it is a factor of 12. The divisors are all pnme numberH. and the numhen, in the last line are prime o each other. Then 2X2X3X2X5 = ,20, which I the leut common multiple of 6, 8. 12 and J 5 EXERCISES. o" pint T I'"'! '"'"™'" ™"'''P^^ °^ ^-' ^6> ^8. 30 and 48. :• ,","." ^^''«t,co,nmon multiple of 3, 4, 5, 6, and 7. and 56 ? " ''""^'" "'"^''^'^ "^ - *' 7' 12. 16, 21, 4. mat is tho least common multiple of 2, 9, 1 1, and 33 G F nd tt n '""""" "'"''•''' '^^ - '' ^' '' «' 7' 8. «nd 0. 7 mat f^, '7™''" '""l^'Pl^ «'• 8. 12, 16, 24, and 33. '. V\ hat IS the least number into which 2 4 8 Ifi "^o «! and 128 will divide without a remainder ' ' ' ^^' I' mV^''/r,' '°"™''" "'"^''P'^ °^ ^' ^' 27, 81, 243 and 72». ^- v> nat IS the least common multiple of 2, 3, 5, 7 ] ]? ^g^^ ^^M^m^m^^^'^m^m^m^Mxm.^^^^im^^ H'v FRACTIONS. "nit i. divide,! iMo Si , r ?"" " '""*''■ "'''" ">« , iiiw,,, lourtlw, fifth, or „j,|„^ respeclivelv. 01 equ.il parts into which the unit is divided. by l:!LZT' ^'"^^ '-'- "^"^ ^' ''^- P-*« - ^-^P-ed mon Thus, the value of the fraction J ,8 4 Whlt.e 1^!^ - proper the division cannot be ,>erformed. but i« mer^^y nl^ 7 and the quotient can only be expressed in the fractional ;ot^''' REDUCTION OF FRACTIONS. alte!!:f ttr vl^""' '''''''' '' ^"-«<" ^^^'"^ ^-« ^^'hout A fraction is in its lotce^a terr,u, when ita numerator and deno- minator ar^ prnue to each other, as f f |. but not f Since the numerator and denon.inator of a fraction are a dividend and a d.visor, they may be divided by the san.e nun.ber without changing the quotient, or value of the fraction. CASE I. To reduce a fracdon to its lowest terms. "'e process m the resulting terms are prime to each other O. dnude both terms hy their greatest comJn divisor. ' Example. -Reduce f| to its lowest terms. S.'ll = il, and 4|H = \ Ans. Or, 8jH=f Ans. EXERCISES. Ueduce the following fractions to their lowest terms -^ H- 6- m- 11. HU- tWt- 12. ^le^. «o 1 2 8 10. J 7 « «ttl- fit- ':?;,! IG FRACTIONS, CASE II. To reduce an improper fraction to a whole or mixed nnmber. KL-LE.-D/,vVfc tf,e numerator hy the denominator; the quotient )idl he the whole or mixed number. Note. -If there be a fraction in the answer, reduce it to its lowest term,. ExAMPLE.-Reduce JJ to a whole or mixed number. The denominator 8ho,.s that the unit h dirideJ into 16 equal mrts- .«nce ,G s,:cteeuths make I. and there are as many uuita in SjL T J coutained times n S7 nn,? '' " '" u as ib u 16)87(5,V 80 1 j: EXERCISES. Reduce tlie following improper fractions to whoL numbers : — e or mi.xed 1- H^. 2. y^K 3. 3^. 4. ^, 5. ^^i. 6- ft- 7. l?p. 8. ^l. 9. Vi^. 10. 5/^. 12. ^^^K CASE III. To reduce a mixed number to an improper fraction. T.ULE.-Multiply the whote number by the denominator of th,> no.tor under the sum. and writing the proposed denommator under the product. """'"'■*'»'■ Example.— Reduce 4^ to an improper fract'on, 5 „ 'l ? ', '''"^f''^^' '!'« «"«''" i^ to be halves, and as two halves make a unit, there will be twice as many halves as unif, th.t \ and the I half expressed by the fraction added ^Z1^;:^.Xl '' l> < «-1( .. F^i..>>:! MULTIPLICATION OF FRACTIONS. 17 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. EXERCISES. Eoduce 4J to an improper fraction. Reduce 27^ to an improper fraction. Reduce 66* to an improper fraction. Reduce 18f to an improper fraction. How many sevenths in 9f f lu $7| how many eights of a dollar J In 17f gallons how many thirds of a gallon ('hange 27 to a fraction. Express 9 as a fraction having 7 for its denominator. Reduce 19 to twelfths. Reduce 28 to a fraction having 19 for its denominator. MULTIPLICATION OF FRACTIONS. CASE I. To multiply a fraction by a whole namber. i/nen uhole number, and set the product over the denominator n- •vhen It can he done rolthout a remainder ^«^"^'««^«'- 0. , Example.— Multiply § by 8. §X8 = y = 5|. Multiply, 1. I by 3. 2. J by 8. «• A by 9, EXLrtCISES. 4. ^V^ys. 6. myi7. H by 3. W by 7. 7. 8. 9. 11 K.. c 18 FRACliONS. CASE II. To multiply a whole number by a firaction. lluLE. — Miiltiphj the given whole ninnher Inj fhe nnmeraior of flie (jlmi fraction, and set the pwdiict over the denominator. Example. — Multiply 8 by I 8X5 = ¥ = 5J. Multiply, EXERCISES. 1. 7by|. 2. 12by|. 3. 18 by f 4. 5by,V 5. 4783 by ^\. 6. 39by^V CASE III. 7. 8. 9. 408 by |. 5781 by T^ 78 by H- ijii To multiply one fraction by another, or several fractions together. liuLE. — Midtij)7i/ fdl the numerators tor/ether for a ncv: ninnern- tor, and all fhe denominators for a neic denominator. Note.— ■\Vhen some of the factors are mixed numbers, they must be reduced to simple fractions. Example. — Multiply § by f. 1st, Multiply 3 by 5 = ^ ; but as 5 is 7 times the l X T= si Ans. multiplier, 4, the product, i^-, is 7 times the required product; iu other words, the required product must be li as much as Y- Now, if ' be divided into 7 equal parts, each of the parts will be -^^, or |. as much as -| ; therefore, 4 as much as i^ is 1 3, which is what is re(iuired. Therefore, 2ud, multiply the denomiuator, 8, l)y the denominator, 7, for the denomiuator of the product. i m EXERCISES. 1. Alultiply ^ l,y I. 2. :\Iultiply I by f .3. Arultiply I, f and 5 together. 4. Multiply I, I, I and f together. Observe the following methods of doing the last exercise. m il-.-^-_-^:*»ii If PAXCELLIN'G. IST ArETHOD. fO- redncin- the fraction 5^/;^ by the frmiiest common divi sor of its terms, viz : 420. 2nd :^^ETHOD. lxlxix-i=i. ^ y 7 6 2 3 19 1st. Divide the numerator, 4, and the de- nominator, 8, ly 4, which will divide both "actly; next cancel the numerator, 5, and the .cnom ,t,r.5; ne.xt cancel the two 7's; la.,,ly •bvide the numerator, ,3, and the denominator of the original numbers. The second metliod is called CANCELLING, XoTE.-M-hen a quotient is 1, it may be omitted. iAfultipIy A 1^ 4 ,.^„,, ^ to-cfher J^"ltipiy A, 3;,, 2^„,d 4to,retl,er f "Itiply 0^', 44 M.ul H toKether ^"I'il'ly 31, \l, .,K and c^ (ogetl.er .5. C. 7. l^^tter expre.i„n indicates uA ^^^;V''" ^ '^ ^ ^ ^^ '"'^^ «re units in |. Now" I , t '^ ,' .^'' ''^'"'^"' '^^ «"^^ "^ there of a unit ; therefore Vol t TT ',"'''' ^"* ^"'^ ^^^-**>>^^^ . "e:orc, i t., to be taken two-thirds of once, wliicli M'ill ' <^(l"al to :? of itself: or s ot iiicrciuii 'w^m SO FRACTIONS. To reduce a compound fraction to a simple fraction, \lvLE.— Multiply all the numerators for a mto numerator, ami all the denominaturs fur a new denominator, cancelling as before, whenever practicable. 9. Reduce | of U to a simple fraction. 10. Reduce ^ of 4^ of /» to a simple fraction, 1 1. What is the value of f of ^ of if of ^ ? 1 2. What is the value of j of ^ of | of H ^ 13. What is the value of f of 5| of i of ^h of 4 1 14. What is the cpst of 3 of J of a pound of tea at | of a dollar per pound 1 15. Multiply f of M by A of M- 16. Multiply i, H, f and 2^ together. 17. What is the product of i| of f of 4 by ^ of 3| 1 CASE IV. To multiply a whole number by a mixed number. HuLE.—Multiplij by the fractional part and the whole number separately, and add the products. Note.— It wiU be found more convenient to multiply by the fraction fiiat. \ Example.— Iklnltiply 320 by 8^. 2)320 8i IGO 2560 2720 Ana. EXERCISES. Multiply, 1. 4629 by 5J. 3. 4763 by 7|. 2. 198 by 61. 'i. 1875 by 83. .J V DIVISION OF FRACTIONS. 01 1875 Or. 4)5025 = product by 3 14061= " f 15000 = " 8 1C40G|=: " gT" 5. G428 by 9f 2)1875 937i = product by J 468|= " ' 15000 = « 6. 7. 8. 9. 5630 by 23f. 2769 by 14|, 764 by 105|. 785 by 631. 16406^ = 10. 215 by 73A. 11. 612by87J. 12. 652by92|. la 739 by 751. 14. 575 by 84^. I 8 8f -cr:;:s::i:e:^:-^:- :^,;-- - - .^.o, o. .. 15. Multiply 79C0 by 3|. 7960 3| 4)23880 5970 16. 17. barrel ? 18. 19. 20. 29850 Ans. If a ton of hay cost $17.60. .vhnt is the price of 3f tons ? A\ hat 1. the price of 14| barrels of apples at es'sO per mi*''',r.l"r?r'^ '"'' '^ ^^"^ '' ^^-^-SS per acre. ^^ hat w,]l 41 bushel.s of wheat cost at $1.75 per bush ■>! ? Multiply 7598 by 2^ ; by 3. , by 4| ; by 7^ DIVISION OF FRACTIONS. Division of Fractions is the process of division when tne divisor or dividend or both are fractional. CASE I. To divide a fraction by a whole number. ,h>^'''^^,~?'""^' *'" ''"'-m/or h,, Ike u-hoh number, if it can he 22 FRACTION'S. EXERCISES. ExAMPLK — Divide t by 2. i -f- 2 = ^ Aii8. Or, ^.2=1*0 = § Ans. To tlivide any quantity by 2 gives the half of tliat quantity; and as thf> half of f is |, the correctness of the first methoil is evident. The second method may he explained thus: | indicates that the unit i,'* divided into five equal iiarLt, of whicli 4 are expres.scd. If the ■ '^"»»«"«nt. and ttiose generally adopted. ''" 20 FRACTIONS. LEAST COMMON DENOMINATOR. It has alreaily beon sIkiwii tJiat to ilivide both terms of a fraction hy the same number does not change the value of the fraction. Ileiice, also, To multiply both terms of a fraction by tlic same nuinbcr does not change the value of the fraction. Two or more fractions have a common denominator when their ilcnomiiiator.s are alike. Thus, S, 4 and S have a common denomi- nator, 7. Any two or more fractions may be reduced to ciinivaleut frac- tions, having a common denominator. A common denominator of two or more fractions must be a common multiple of their deuDminators, in order that the equivalent fractions having the common denominator .shall be simple fractions. Thus a common denominator for the fractions | and | must be a common multiple of 3 and 4, as 12, 24, 36, &c., and 5 and -^ may be reduced to equivalent fractions having 12, 24, 30 or any other common multiple of 3 ami 4 for their common derKuninator. The Least Common Denominator of two or more fractions is the Least Common Multiple of their denominators. To reduce two or more fractions to equivalent fractions having a common denominator. RcLE. — Multlphj both terms of each fraction hi/ the product of alt the deninainators cxc^'pt its own. Example. — Reduce § and | to equivalent fractions having a C'juimon denominator. 2X4 = s 3"X4 = n 3X3 = 9 4X3 = 12 Take 12 for a common denominator. Then, since tlio niimorator and denominator of a fractiun ninv be multiplied by the same number without .altering its value, multiply both terms of f by 4, l)ec.au.se it makes tlie denominator 12; and multijily both terms of f bv :i, for a like reaxon ; and we obtain 1^ r.nd j\ .as equivalent fractions having a common denominator. 1. Reduce f, ^ and 3 to equivalent fractions having a common denominator. • LEAST COMMON- DENOMINATOR. 27 5 XS X .3=120 3X«X3=: Dt 2XCXHz= ». r f ". 28 FRACTIONS. ADDITIOiN OF FRACTIONS. Addition of FractloiS is tho process of fimling the sum / the same aenoZJo -A^ce /;..« to a common ,en.,nlnntor, take the aiff:^Z^;. th^ nc. numerators, and set it aver tke com.^on denominuL Prom, 1- ,\take^»r. EXERCISES. 2. 3. 6. 7. 8. \ take f A take /,. 1^1-1*1 = ^ Ans. 4. |i take Jf 5- I take f MtaLV\ '^- ***^^«iV ** ''^- "• if take jj. irAer. a m/.r«c? n«m6.r occurs it may he reduced to an improper fracuonand tke sultraction performed according to the rul^' rately, hut d must be ohserved to add 1 to the fraction in the nnnuend ^f a he less than that in the suhtrahendandcar^yto fhe unit's figure of the subtrahend. ■ ^ 12. From 4 J take '2^. H H 2^ Ans. 30 FRACTIONS. From, l.r 5^ take 3f. 14. im take 12i^. Ij. 9G;4i take 4375. 16. 3 J take 1 J. Here it is easier to suLtract the fraction and whole nunilicvs separately. Thus, I'J Subtract | from 1 (0 and | remain, carry 1 to 3= 4 : 17. 8 J take 3 J. 18. 7f take 4f 10. 27| take I'jj^,- 20. 16 take 3i. 3.^ 4 from 16 = 12. 1-21 Alls. 21. From 3912 take 14 7|. 391^ Add 1 to f =!§ = !; then, 1472- fxHfS — - f X i = /^ ; and ?5 - {-^= ^ Carry 1 to tl,e -*'^i2 whole numbers. From, 22. 3201 take 249f 2.3. 164| take 8 7 J. 24. 231, '5 take 148 J. 25. 943^ take 583 jV 26. 480 take 127,\. 27. 364|take96if 28. 75j\take57^V 29. 185,7j take 9||. 30. A has §725|, and B has $G90|, iiow much inoie his A tlian B? 31. A man owned f| of a ship, and sold | of his share, Iiow much had he left ? 32. What is the diifercnce between | of U and --- ? 33. After selling 4 of J + i of f of a farm, wlmt part of it reniuined ? When the numerator of each fraction is 1, T/ie dip.rence of Hie denotninafor.i will he the nimeraf'-r, ana then- product the dent- ruinator, of the difference. •4 J EXERCISES. ■rom, 1. \ take \. 2. 4 take |. 3. i take f 4. ^ take l 5. I take l- 6. i take ^^ DECIMAL FRACTIONS. A Decimal Fraction is o„e that has lO, or some power of 10 for >ts denonunatur, as ,V, rh, .U,, .te. ' '" '' '' The won decimal is derived ln.,„ the Latin, J.cnn, ten Observe the relation between the d.cin.al fractio ,s "., ,.,, Tile first is six tenths, or ,V of fi nt U<= ■ i\,^ , • , ■>"^^>-. o. A of ft ; ...e .M,;,: „: ir ,:ut :t '/.'If IX'nod (.) called the Jecnnal point, or separatrix. ° ^ " TABLE OF DECIMAL ORDEHS. i a » . i ■" »=' 5 "- £ ^ V 3 • — = 5:= ■=~ s£ • - s ? = 5" 5^ ; 5.5 'nd'"'' ';•■■••• •••-'™'^'^^-ths. 4 » -^J^: " thonsandth«. i I =■■ ■' -"Si.,.. . »tli ^0000_U08 '< Sbillionths. Sum — .54C73''0 1S <« r i , , 32 DECIMAL FRACTIONS. And it will be found that if each of these decimals bo expressed in the connnon fractional form, viz : y"';,, ^J^, j^%^, &c., and added together by the rule for adding common fractions, the sum will be Ji 4 t'l 7 121) I 8 To 0.1 570 (J ff- By examining the above table and what has been said, it will be seen that the value of a decimal figure depends on the place the figure occupies, and diminishes in a one tenth ratio for every place tlie figure is removed farther from the decimal point. Hence, to place a cipher on the right of a decimal docs not alter the value of the decimal, because the cipher is nothing in itself, and, so placed, does not change the place of the other figures. Eut a cipher placed on the left, between the decimal and the point, removes the figures one place to the right, and thus divides the value of the decimal by 10. To read decimals expressed by figures. Rule. — Read the decimal as a whole vumber, and give it the name of the right Itund figure. EXERCISES. Eead the following : 1. .2. 7. .8004. 13. 48.7804. 2. .04. 8. .4010. 14. 83.0084. 3. .138. 9. .21042. 15. 121.18005. 4. .4531. 10. .000014. 15. 345.000018. 5. .0098. 1 1. .1743196. 17. 909.000999. 6. .00006. 12. .0008980. 18. 1203.080764 To write decimals in figures. Rule.— TFr/Ve the decimal figures as a whole number; then place the point so that the right hand figure shall have its expressed value, placing ciphers to the left of the significant figures if necessary. EXERCISES. Write decimally the following quantities 1. Five tenths. 2. Tw nty-two hundredtha. r^KCniAL FHACTI OXS. 33 3. Eighty-seven thoiisaiulths. 4. Fifty-six teu-thousnu.lths. 5. TJ.ree hundred and four ten-thousandtl>3. sandths " ''"'^"' '''-' ^'^'"^-^ -^ ^-ty-sevon ten thou- 7. Eighty-eight millionths. 1. Seven thous..nd and seven ten-nnllionths. onelnn;^!:;!:'""'''"' '"'^"'^ ^^'^"^^"^' °- ^-^red and ti.ousandan"i.r::;,Ho:r' "'"^ ^'""^^^^ ^"^ '-'-' ^-^y division indicated. Thus, i n ea ToJ 1 * -'/"V-™"^ '^ -'its e,ual 40 tenths, he ;« o 4 .I'l" 1;' ' ""^ ^"^ ^ tenths = 8 tenths, or 8 ^,:,i„ \''''\^'-^,f ^0 teaths, or -V-. a-1 § of a tenth over that S:. i ^' ';","' ^^"^^'^ = -«' hundredth over that s 4 t, ^ /\""'^'-^'^l^''« = -07 and * of a th-ee parts togeih hey ^ak^';?^ =?•'''' "" "'"^"'^ ^l^- Therefore, ^ ' '^^ '^'^ '^ "'^^^'"^^ equivalent to {. To deduce a decimal from a common fraction. Example. -Deduce an equivalent decimal from ]. le- 4)1.00 .25 Ans. -cuuce equivalent decimals from the following comni.u fractions : 34 DECIMAL FRACTI , S. EXERCISES. 1. o 4. 5. 6. 1^,;. 8. 9. hi 10. f 11. foff^. 12. 7» In deducing decimals from common fractions wlien any quotient figure or figures are found to continually rejieat, as in exercises 10 and 11 above, the decimal is called an Infinite OF Circulating Decimal. The part of tlie decimal which repeats is called a Repetend. A repeiend of a single figure may be ter.minated at any point by making it the numerator of a common fraction, M'ith 9 for denominator, and annexing the fraction to the preceding decimal figures, if any. A repetend of more than one figure may be terminated at any point where the period ends by making the repeating figures the numerator of a common fraction, and as many 9's for denominator, and annexing the fraction to the preceding decimal figures, if any. Of course, in all cases the common fraction sliould be reduced to its lowest terms. Thu^, I is equal to .8333, &c., in which the figure 3 is a repetend. This decimal is correctly expressed thus, .8J, or .83J, or .833:",, d'c, that is the | is ^ reduced to its lowest terms. Again, J is equal to ,714285 repeated ad hifinitum, and is correctly expressed Utis^ = 7, or .714285J, or .7142857142855, tl'C. A repetend of one figure is distinguished by a point placed above it, thus, .83. A repi.-tend of more than one figure is denoted by a point over both the first and the last figures, thus, .714285. Reduce to dcciraiiis the following : 13. 14. 15. 1 y IG. 17. 18. 7 1 1- 19. 20. 21. 11. A- To reduce a decimal to a common fraction. DECIMAL FRACTIONS. 35 Jl.LK-WrUe the decimal for a numerator, omltfh,r, the pohf a I apl.rs on tJ,e lejt ; an.l for a denonunator, 1 rcitk as L.„ n act ton to tts lowest terms. EXERCISES. r.educe the following deciinal. to common fractions : 11. .390625. 1. .5. G. .125. 9_ .25. 7. .312.5. 3. .75. 8. 2.125. 4. .875. 9. 10.002. 5. .0G25. 10. .0175. 12. 13. 14. 15. .003125. .15234375. .804. .08125. 7. « /,. dec^maI ts a rr-petend, mal-e the decimal ulth the point "ndted the numerator, und as man, .V.s as there are renLln,, .mresfor denominator, and reduce the fraction c^ before. ^ Eeduce the following decimals to common fractions : ^•5- •^- 18. .8888. 20. .307092. 17. .8. 19. .<: 21. .857142. men the decimal Is composed of a finite part and a rep.t^nd ronrert the repetend Into a common fraction, and annej to th^ J^^^'^Pfl under this urlte the denominator of the decimal, and reduce the complex fraction thus fanned to a simple one. Example. -Reduce .83 to a common fraction. 81 5 n. .83 = .8§=.8J,thatis,f^ = 8^^10 = ?LV = ^^ 10 •* 3^10 «• 2 Reduce the following decimals to common fractions • 22. .910. 24. .7083. 20. .78545. Ans. 23. .583. 25. .027. 27. .78545. The following rule deduced from the above will be found con- venient m solving questions like the last six : 'RvLK.-SnUract the finite part of the decimal from thr whole >i^e the remainder for a numerator, and for a denominator as man, •'^ ^ «* there are figures m the repetend, and as many ciphers anm^^d J"J'^' <-" '"■ c he Jinlle part. 3G DKCIM.VL FRACTION'S. ADDITION AND SUBTRACTION OF DECIMALS. As ilecimald are m(Mv]y an extension of tlie common Ara])ic system, they are added and subtracted in tho same manner a.i whole numbers; and it sliould be remembered that X'/'"'tA' of the mme order munt he j)Jaced under one another, that is tenths nnder tenths, hundredths under hundredths, ^-c. In nther words. Arrange the (piantltics to be added or sulifracted so that the d'uhnat points sho/l stand, in a vertical column, add or subtract as in whole numbers, and place the decimal point in the suui or difference directly under those in the numbers added or subtracted. Example.— Add togetlier .0 75, .0456, .73, and .1042.5. Observe that the decimal points arc in a column, so that tenths are under tenths, hundredths under hundredths, &c. The colnran of tenths, with what is carried to it, amounts to 15 tenths = 1 unit and 5 tenths. .575 .0450 .1?, .1642.- 1.51485 EXERCISES. Add the following decimals : 1. 21.611,0888.32,3.4107. 6.01 630.1, 0510.14, 07.1234, 1233. 14.034, 25, .0000025, .0034. 10 75, .375, 5, 3.4375, .00087.5. 173, 7000.0005, 1.7, 125.728, .000.5. .10, 39.."), .7283. 700.83, 10.765, .72835, 81.9. .142857, .0180, 920, .0139428571, What is the sum of .70, .410, .4-5, .048, .231 Reduce to decimals and find the sum of 2^, 4| and 5yV Find tlie sum of .427, .410, l.:328, 3.029, 5.470. 13. Find the sum of 35 units, 35 tenths, 35 hundredths and 35 thousandths. 2. 3. 4. 5. 6. 7. 8. 9. 10. 12. 14. From 8.53 subtract 3.643. Arrange the numbers so that the points shall be in the 8.53 same column, and subtr.aet as in whole numbers. The 3.043 place of thousandths being vacant in the minuend, we borrow one from the hundredths, which is 10 thousandths, 4.887 Ans. subtract 3 thousandths and carry oue as in whole numbers. I 16. 17. 18. 10. 20. 21. f)0 MULTIPLICATIOX OF DECIMALS. 15. From 20.03G5 subtract 8.77|. 20.03G;i 8.7733 11.2632 Or, Ant. 20.0365 11.263^ From 24.0042 take 1.3.7013. From 170.0035 take 68.00181. From .0142 take .005. Wliat is the difrereiice between .05 ami .0024 ? ■V^ hat IS the diJlerence between 72.01 and 72.0001 1 From 19 take 8.9981. From .4 take .04.1 37 23. From 2f take li.' 24. From i.l69^ take .93.2.. 25. What is the difference between 24.'. tenths and 3701 thou,^andths? 26. Subtract IJ hundredths from 49^ tenths. MULTIPLICATION OF DECIMALS. Multiply .375 by 7. upt.ation by common fractions. .375 7 iVo^ X{ = nU = 2AVa = 2.625 Multiply 2 75 by .9. Operation by common fractions. 0PK|Ano!f. -iV;r = ?J^,then,ni;XV\, = ?^-=2,Vo^ = o.475 Hence, to multiply decimals. JivLK-Mul/iph, as in whole vnmhcrs, and point off in fh. pro, net as many decimal plaees as there are in the multiplicand and multiplier tcjethcv. If there he not enoncjh figures in the product to r/ive the required ninnhev „f ,U.-u.,..i .,7 ,/<.ft-,.;..,>..„ J... ^. ■ . . - ' i'---~> detit ij prefixiitij cipher^ :qrp:y 38 DECIMAL FRACTIOXS. Multiply, 1. 2.r)4 by .31. 2. 4.16 by .OU. 3. 4.5 by 4. 4. .01 by. 15. 5. .08 by 80. EXERCISES. r>. 7. 8. 'J. 10. 11 12 18. jf, by 1.007. . 00070 by .0015. 7.4i» by 0.3,1. .0021 by 21. .007 by 4000. Fiiul the continual prmluet of .2, .2, .2, .2, .2 .2. Find tlie continual product of .10], .011, .11, 1.1, and 1 1 13. Multiply .144 by .144. 14. Multiply 14.583 by 2.75. 14.583.33 .tc. 2.75' 72910 00 itc. 1020833 33 (tc. 291G0CC.0G &c. 40.1041g! In thi.s exercise the Last fisuro in the multipli- < ami is a repeteml, aud mn.n be treated ns such. In multiplying by 5 we must carry 1 from the jtroduct of 3 understood on the ri-lit, and the 6 in the product is a repetcnd. In a similar manner we c arry two when we begin to multiply by 7, and the •■! in the product is also a repetcnd, for which ren.son we fill up the place on the right of the product usually left blank. Also in multiplying by 2, as I he 3 in the multiplicand is a repetend, ^o is the 6 in the product aud we must fill up the two places on the right with e's. Then in ad.liug the partial products, we must allow for other columns on the right, made up of the repeating figures, aud so carry 1 at the beginning. Note. -The above method answers very well when the multiplicand .ilone oontams a repetend of only one figure ; bnt when the repetend consists of more than one figure, .r when there is a repetend in both multiplicand and multiplier the process becomes complicated, and it is usual to proceed by the following ' Hm.E.—Iiedace the decimals to common fmcHons, and pcrfor-, the multiplication reqnired; then reduce the fraction, if any, in the product to a decimal. Multiply, 15. 7.416 by 8.5. 10. .078 by 7. 17. 5.G38 by .2754. 18. .73 by 2.6. 19. 5.736 by .410. 20. 9.4571428 by .538401. To multiply by 10 or any power of 10, as 100, 1000, 10000, &c. llm.K.~Muve the decimal point as many places to the rijht ;/.■. ;here are. rinhfr^ in flif «n<7/ ;.,/.■,,« MULTIPLICATION OF DECIMALS. 39 f EXERCISES, Multiply, ^- *■•' ^'y 1^- 4. .0G25 by 1000. 2. .007 by 100. r.. 4.8(1 by 1000. 3. 170.5 by 100. Q, 4.83J by 10000. ^lo'o? ^"^^ ^""""^ '^'"'''"'° '' "'""' '^^■^^^' '"^'^^ '' ''*'' ''"^"^ "^ 8. Wl.iit will 1000 barrels of flour cost at 86.73 per barrel ? 9. AVhat is the cost of 100 acres of land at $17.37i per acre t 10. What is a million pounds sterling worth at $4.80* each 1 11. Multiply J by 100000. To multiply by 15. Move the point oxe phice to the rhjld, and add one-half. To multiply by 25. Move thepohit jy^o places to the right, and divide hj I To multiply by 250. Move the point three placets to the right, and divide hy I To multiply by 75. Move the point two places to the rljht, and euhtract a fourth paH. To multiply by 7J. Move the point ose place to the right, and .vihtrad a fourth part. To multiply by 12i. Move the 2x,lnt two places to the right, and divide hj 8. To multiply by 2i. Move ihepoiHt osk place to the right, and divide hij 4. Multiply, 1. 25.764 by 25. 2. .0896 by 15. 3. .7985 by 250. 4. 240.8 by 7^. 0.. 5.987 by 75, EXERCISES. 6. 19.50 by 2i. 7. 160.5 by 150, 8. .00032 by 250. 9. 73.5 by 750. 10. 99 by 2^. ■vf% 40 DECIMAL FnACTinxs. DIVISION OF DECIMALS. Division is tlie convorse and proof of niuiti|iIication,— tlie pro,lu,:t becoming the .Hvi.Iend, tlio inuitipiicr or imiltiplican.l tlio •livi.sor, and the nndtij)liciind or niultipiicr the nuotii-nt. Hence, since tiie product contains as ni^my decimal places as^ the two factors to-cther, it follows that the dividend contains as many decimal i)Iaces as the divisor and quotient togetlier, or T/te quotient m v.vC nmtaiit ii« uinny (hriuntl plurr^ as thfi dlcnh'wl has more than the dirisor. From this, again, it follows that the dividend ranst contain, at least, as many decimal figures as the divisor. Tlierefore, JlVLK.— When the dividend does not contain as many dee I mat figures as the dhusor, annex ciphers to make up the mimf>er. Then dlrlde as In irhole numbers, and the quotient will he a whole number. If there he w, quotient so far, or if there he a remuluder, and It />e desired to carry the division further, annex as many more ciphers us necessary, continue the division, and the addltlon(tl'ji,jures obfainat In the quotient will be decimals. NoTE.-When there are not enough figures in the quotient to give the required number of decimal places, the deficiency must be sui-plied by prefi.un(i ciphers. ■' ' ** Example.— Divide 1728 by .12. .12)1728.00 14400 Ans. Divide c /\ c r tVylOC 1. 28 by .4. IK 2. 21 hy J,. 12. 3. 86.07.) by 27.5. 4. 24.73704 by 3.44. 13. 5. .21318 by .19. 14. 6. 9.9. by .022.5. 1.5. 7. 81.2090 by 1.28. IG. 8. 3.15 by 375. 9. .88425 by 176.85. 17. 10. .09201 bv 7 .-. 1 8 57.G by .128. 1.07654 by 240 to six places of decimals. 873,3.724 by .9. 724.5 /'3 by .7. 573 183 by .6, 6927.8510 by 78.5 to seven places of decimals. 9.6 by .55. -_J_-. DIVISION' OF Dfc IMAI.S. 3.111(;)lL>17.1.<).-.8;),,(3S7.-> Ans. 1'74S95h.,, 2r)13 33,>,,3 i.';5.i(ii>r)„„ 210 lrici; 15 708S.I 1.') 7nS3.-i The al,ovo motl,o.l „f divi.Iinj;, wl.,.,, tl.e ,]ivi..or contains .'^ n-potcn.i, IS .son.owl.at to.Hou.s an.! m,,m,..s great care. The more- usual method is tu reduce the repetend to a common fraction, and then divi.le by tlie mixed nuniher. Thus, 3.14l3')li>173.9r)8:3(387.-, Ans. 3 3 9.42.-))3Gr)i'1.875 Divide, 19. .8 by 2.(1. o] 20. 6020.00 by 4.86. 22. 1.77075 by 2542").' 3480.40 by 4.85. To divide by 10 or any power of 10, as 100, 1000, 10000, &c. 'iivLF..~More tho dechnul pond a..- mmu, places to the hff as f/ierc are ciphers in the du-isor. EXERCISES. Divide, 1. 3425.5 by 10. 4. 8.39 by 100. 2. 57.75 by 100. -). .75 by 10000. ^ 3. 1444.755 by 1000. 6. 5863.72 by 100000. .. If It xost $7000 to furnish a meal for an army of 100000 men, what is the cost of each man's meal ? DENOMINATE NUMBERS. ' All Abstract Number ia simply a numLer wit'iuut reference to any i.hj^-ct, us, 7, 1(5, 39, &c. A Concrete Number is a number in connection with .some olijict or ol.jects n.iiiieil, as, 1 liorse, 7 men, 30 siiips, &c. Denominate Numbers are concrete numbers applied to tiie derio- minations of weights and measures. CANADIAN CURRENCY. 100 Cents (ets.) = 1 Dolhir $. BRITISH OR STERLING CURRENCY. TABLE. 4 Farthinj,'s= 1 l\nny ,?. 12 Pencti =r 1 .Sliiliinj,' .v. ■-'0 Siiillings = 1 Pound or Sovereign. .£ I £ «. d. /'tr. 1 = 20 = 240 = 900 1= 12= 4H 1= t 5 .Shillings = 1 Crown, and 21 Shillings = 1 Guinea, UNITED STATES CURRENCY, TABLE. 10 Mills = 1 Cent rf. 10 Cents = 1 Dime d. 10 Dimes =: 1 Dollar .$ 10 Dollars = 1 Eagle E. E. 9 rU Mllh. 1 = 10 = 100 = 1000 = 10000 1= 10= 100= 1000 1= 10= 100 1= 10 ^'''^^.■~'^'*,'^°"^'' *'''* '^^^^'^ " '" t'leory tho U. S. table of currency, in ( AVOIRDUPOIS WEKJHT. 43 i DOMINION STANDARDS OF WEIGHT. Tl,.. l,.^-;il 8tan.Inr.l8 of ^v,.i;-l.t in the Domi.non of Cana.la arc llie I,np..ri.l i„„n„l, Avoii.Iiipois, containing 7000 grains, and the ounce iroy, """taining 480 grains. The I).mi„ion Staml.-vnl for .leterminint' tho weight of the Donnnio,, tan,ar. ,,o,.,,,| H of ,,Iat,,.nm-iri,li,.,n. the ,orn. being that of a cvlin.ler toarlv I .15 ,„.h ,n lieight. an.l Ii,^ Inch in diameter, with a grJove or ■ ,.' f 7" '• «■''•''« ""''i'llo i" ahont 0-34 i„oh below the ton of ,he .- of platinnm-iridium, the form being that of a truncated .one, w„b a knob, nearly }^th.s of an inch in height, including the knob, the knob bemg nearly i .nch, an.l the ba«e of the cone J inch in diameter, respec- tively, an,! such standar.I troy ounce is marked "A." The weight of thi, stand.ir.l in terms of the Imperial standard is 479 99197 grains wlieu both are weighed ,n vacuo, and 48003648 grains when both are weighed in air at the temperature of r.2" of Fahrenheit's thermometer, the barometer feeing at .30 inches, (or which .lue allowance is to be made when comparing other standards.— M eijltts and ^fe(^su)■es Act of 1879. AVOIRDUPOIS WEIGHT. Avoirdupois Weight is used in weigliing all artides c.xcopt gold, silver, iilatiauui and precious stones, and articles made thereof." TABLE. 1 G Drams (dr-^.J = 1 Ounce „-. IG Ounces = 1 Pound /i. 100 Pounds = / ^ Hundred-weight . . . cwt. \ 1 Cental c. 20 Hundred-weight = 1 Ton T. T. act. Jh, oz. dr. 1 = 20 = 2000 = 32000 = 512000 1 = 100 = IGO = 25000 1 = 1 n = •>:".n 1 = IG 44 DEXOMINATE NUMBERS. IG Jr. =1 oz. IG oz. =1 lb. -'8 lb. =1 ,^r. 4 qr. or ) 112 1b. 20 cwt. = 1 cwt. = 1 ton. BRITISH TABLE. T. art. (jr. 1 = 20 = 80 : 1= 4: 1: ^f'- oz. fir ; 2240 = 3.5840 = 573440 112= 1792= 28672 28= 448= 7168 i= 1G= 200 1= IG Pv,I!" ^f'"^ "*^!^ ^^ ''""^ "^'"'' '" ""^ ^°»"'"-. ^nd "till is in a fe,v >oncl t ,u Gre.t Britain are invoiced by this method. 112 lbs. ar a nSa o h.h; and coal is .old at the amines by the ton of 2240 lbs, oao'cwto 1 2 bs. each. By the " AVeight.s and Mea.sures Act of 1 879 " the le "al on i. hxed at 2000 lbs and no other is lawfnl. This will probabiy hav rh ffe a.p^^t:-=,ir:;i:;trj;,ShrScS'- ^^'^ — - ^^ and i:dStin°ui"heT> '"''T'""' "' '''''"' '''''' ''' ' '^ ^^ '''^ '-' avoirdupois, and .9 d,^tlu<;^I^hed from the ton measurement, as " dead weight " inter^:!:?;r„;:;;r^ °^ ''''-'' '- ^^^'--^ - -- -^^ ■"» -»"-^ ^eet. Vessels are reckoned to carry of me.isured tons about IJfor every ton register, and of dead weight about Ij for every ton register. ' TROY WEIGHT. Troy Weight is used in weighing ^^oIJ, silver, platinum and precious stones, and articles made thereof. TABLE. . ^'^- OZ. jvvt. -4 (, rains (,,r.) = 1 Peunyweiglit. .;;«•/.! 1 = 12 = "40 -'0 Pennyweights = 1 Ounce „,.l j __ .^q 12 Ounces = IPound . oz. .lb.\ r»7G0 480 24 i APOTHECARIES' WEIGHT. Apothecaries mix their mediciues l)y this weight, using the -""CO Iroy, but they buy and sell by Avoirdupois. LINEAR OR LONG MEASURE. 45 TABLE 20 nn\ns(fl,:) = 1 Scruple . •^ Scruples = 1 Dram... ■ 3 ■ 3 8 Drams = l Ounce . . . r 12 Ounces =IPouaa.. . lb. ^'- Z- 3. 3. qr. 1 = 1-2 = 06 = 288 = 5700 1= 8= 24 3= 4S0 1 = 3 = GO 1 = 20 LINEAR OR LONG MEASURE. Tlieoretically, the yard is equal to ;-;?,!};;!? of the length of a pendulum that vibrates seconds in a vacuum, at the level of the sea in the latitude of London. The ImjuTial yard is the standard measure of lenqth, from ^^'h.ch all other measures of length, whether lineal, superficial or solid, are derived. stanlanwr,'"""" ^T!^"^ ^'' determining the length of the Donumon »tandard yar,i ,s a sol>,I square bar, thirty-eight inches long and one ind ^ZVinr'" "^"■°°' "" '''' ^^"^^^ ^' ^-"- - ^- -tal (known ai Ba.lys metal); near to ea-^h end a cylindrical hole \. sank (the distance between the centres of the two holes being thirty-six inches) to' the d pth of Jh 1 or' n ' ■ K : ''°"''" '' ''"'' ''"'^ '"^ ■"^"'^'^ - - -'^"^r '-'•-> ' gold P "g or p,u. abont one-tenth of an inch in diameter, and upon the surLe of each p.„ are cut a fine line transverse to the axis of the bar, and two at an mterval of about one-hundredth of an inch parallel to he axis of the bar the measure of length of the Dominion standard yard is given bv tie n erval between the transverse line at one end and the transv r let the o.her end, the part of each line which is emploved being the poi,! m.dway between the longitudinal lines; and the said'pdnts are In 1 isT m ke^ T ; ;t""-«^ '^ll'^r'^ g^l-i .""*^« or pins, and such baf marked Mr. Ba.ly s metal." "Standard Yard," "A,-' "Troughton and S.mms. London." There are al.,o. on the upper side of the bar, two hole, for he ,„sert,on of the bulbs of suitable thermometers for the det rminatio. of the teniperature.- Weights and Measures Act of ' 879. "'"'"a^'O* 12 Inches (in.) 3 Feet 5 1 Yards : 40 lloda : 8 Knrl nrinTi.To T.\BLE. ; 1 Foot ff ^ Yard y^_ 1 Kod, Pole, or Perch rd. 1 Furlong y,,^, * -'•^"■'-' .;«. II DKXOMINATE NUMBERS. »i. /"' >;l. U'i. ff. '«. 1 = 8 = ^^■20 =: 1700 = 52S() =: G3300 1 = 40 = 220 = GGO T= 7920 1 = H ^ m =^ 198 1 = 3 1 ^^^ 3G 12 Notes. -1. Tlie inch is usually divided into Imlvcs, (luarters, eiglitlis, und sixtcentliH. 2. In measuring "dry goods" the yard is usually divided into halvis., quarters, ciglitlis, and sixtoentiis. ^ 3. Tht •lilo of the table is that fixed by law, in England, Canada, and the t'ldted States, and is therefore often spoken of as the statute mile. 4. A Hand » inoho.^, used in measuring the height of horses. A Fathom t; feet, used in measuring cordage and depths at sea. A Cable Icngtii r. 120 fathoms, or LMO yards. 5. French measures are recognized for the measures of length and super- ficies, for land comprised in those parts of the Province of Quebec originally granted umler the Seigniorial tenure-the foot, "French measure" or "Paris foot" being equal to 12.71) inches of the Dominion standard. The " Arpont " when used aa a measure of length is 180 French jeet ; and wlien used as 'a measure of superfuies is [Vim square French feet. The Percli, as a measure of length, is equal to 18 French feet, and as a measure of superficies is equal to ,324 square French feet. I SURVEYORS' LINEAR MEASURE. Survoyoi-a' Linear Mt'asure is iise.l in nieasurinj,' liin.ls, roads, Sec. The unit used, wl'ich is also the instrument for nit-asuring, is a idiaiii, 4 nxls. or GG foet long, called Ounter's Chain. It is dh'idud iuto 100 links, eacli 7.92 inches in len>;th. ii; TABL& "'• cJi. I. ;„. ch. 1 =80 = 8000 = C33GO m. \= 100= 792 1= 7.92 Note.— Links are written decimally as hundredths of a chain. hHI Links r/.;= 1 Chain 80 Chains = 1 Mile . SQUARE MEASURE. Square Measure is used in measuring' surfaces. i CUBIC OR SOLID MEASURE. Tlio unit for tJiis measure is a square whose siile is some linear nnit. Thus, a square foot is a square whose side is 1 linear f.xit, and a square mile is a square whose side is one mile in length. TABLE, 144 Square Indies (xq.'iu.) = \ Square Foot 9 " Feet =1 .< Yar,i. 30^ " Yards = 1 <« Kod 102400 " Rods = 1 " :Miie ...sq. ft. . . sq. yd. . . sq. rd, ■ . . sq. VI. SURVEYORS' SQUARE MEASURE, Or LAND MEASURE. For small areas of land, the scjuare foot, yard and rod are used as m the above table. For larger areas, as below. T.Uit.E. 10000 S(iuare Links (.^q. /.)=l Square Chain .... sq. ch. 10 Square Chains = 1 Acre a. C-iO Acres = l Square Mile ,q. vi Note.— An acre, which is the common unit of land measure, is equal to ICO .square rods. A rood is i of au acre, or 40 square rods. The term rood is no* much useJ. CUBIC OR SOLID MEASURE. Cubic or Solid Measure is used in measuring the volume or contents of bodies having length, breadth and thickness, or height or depth. ° The nnit for this measure \» a cube, each of u hose oides is the sqnare of wmo linear uuit. Thn... a cubic foot is a cube, each of whose six si.les is a square foot, that is, the s(iiiare of a linear foot. 1728 Cubic IncheK (,-u. In.) = 1 Cubic Foot cu. ft. '2-1 Cubic Feet = 1 Cubic Yard .... cu. yd. Note. -128 cubic feet are 1 cord of wood or bark. Such cor.Is are usually neasured by piling sticks of wood or bark 4 feet long, into piles 4 feet high and 4» DENOMINATE NUMBERS. MEASURE OF CAPACITY. The Measure of Capacity inchides Liquid Measure and Diy Me isure. Tiie former is use.l f„r measuring liquids, and tl.e latter lor measuring siieli commodities as grains, salt, roots, fruits, etc. The Dominion Standard Measure ef Capacity is the Imperial Gallon containing 10 pounds weight of di.stilled water, weiglied in air, against hras^ weights. w,il, the water and air at the temperature of 62 degrees Fahrenheit and with the haroincter at 30 inches. The Imperial or Standard Gallon contains 277.274 cubic inches. The Standard Gallon of the United States (which wa.s also until recent'y tlin standard in Canada) is the Wine Gallon, containing 231 cubic inches. It will therefore he seen that 12 Wine Gallons = 10 Standard Gallon.s. Therefore, to reduce Wine Gallons in Imperial Gallons, Deduct J, and To reduce Imperial Gallons to Wine Gallons, Add J. Since 8 standard gallons = 1 standard bushel, the standard bushel contains 2218.192 cubic uiclio.s, wliich is the Imperial bushel of England. In the United Sta.es the Wiudieiter bushel containing 2159 40 cubic inches, is used. LIQUID MEASURE. 4 r.uufg.) 2 Pints 4 (Quarts 25 Gallons TABLE. 1 Tint, pt, 1 '.4»iiart q,-f. 1 (iaiioii ifal. 1 liarrel /,W. (jrd. 'jif. pf. rj, 1 = 4 = 8 = 32 1=2= 8 1 = 4 APOTHECARIES' FLUID MEASURE. The British Pliarmacopieia is adopted by tlie Pluirmacentical Society of Xova Scotia, and is understood to be used in all pre- scriptions, nnles.? otherwise siiprifiefl. PRODUCE WEIGHT. TABLE. 1 Minim fm.) = .91 Grains. GO Minims =54.G8 " = 1 Fluid Dram . . /f. J,-, or y. ". 8 Fluid Drams = 437.5 " = 1 Fluid Ounce . ./. „:. or'f. - 20 Fluid Ounces = I ^ lb. =1 Pi„t ^,/. or 6 8 Pints = 10 " =1 Gallon r/a/. or C. Also, IG Fluid Ounces = 1 Fluid Pound. The ounce and pound are equivalent to the ounce and pound avoirdupois which are used in custom. The gallon i.- the Imperial gallon, containing 277.27* cubic inches. DRY MEASURE. \ 2 Pints C/;)'.)=l Quart ..q,-f 4 Quarts =- 1 Gallon, .gal. 2Gakor )_,p , 8 Quarts / = 1 F^'ck . . . ;;/•. 4 Pecks = 1 Bushel. iW/. 3 J Busliels =1 Barrel . . iW. TABLE. hbl. bu.'ih. ^;/,-. ffi(J. qrf. j,f, 1 = 3J = 1 2i = 25 = 100 = 200 I = 4 = 8= 32= G4 1 = 2= 8= IG 1= 2 Although the "Weights and Measures Act of 1879" fixes the barrel at 25 standard gallons, in commerce neither the barrel nor tlie hogsliead is a fixed measure, but their capacity is found by guagiug or actual melisuromcnt. PRODUCE WEIGHT. By the " Weights and Measures Act of 1879," the weiglits of produce arc fixed as in the following table, and it is enactell that " in contracts for the sale and delivery of any of the undermentioned articles, the busliel shall be determined by weighing, unless a busliel by measure be si^pcially agreed upon." Commodities. lb. AVheat CO Indian Corn . . . . 5G Kye 5G Barley 48 Pease GO Malt 3G Oats ii TAm.K. Commodities. lb. Beans GO Clover S«ed GO Timothy Seed .... 48 Flax Seed 50 Buckwlieat 48 Hemp Seed 44 Blue G russ Seed ..14 Gommod'ties. lb. Castor Beans. . . .40 Potatoes GO Turnips Go Parsnips GO Carrots GO Beets 60 Onions GO so DENOMIN/TE NUMBERS. Heaped measuren are not lawfal. Measares of grains or small sepJs must be stricken with a ronnd, rtraight stick; and where the size or shape of the article measured will not adnnit of the measure being stricken, "it shall be filled in all parts as nearly to the level of the brim as the size and shape of the article will admit." MEASURE OP TIME. The natural divisions of time are the Solar Year and the Solar Day. The Solar Year is the time in which the earth niakca one revolution around the sun. The Solar Day is the time in which the earth performs one revolution on its axis, and is not of exact uniform len[.;th at nil seasons of the year. Tlie average of all the days is taken na tlte length of each in measuring time for civil purposes. TABLE. 60 Seconds (s.)-=. 1 Minute m, CO Minutes = 1 Hour /;. 24 Hours = 1 Day (/. 365 Days = 1 Common Year y. Also, 7 days = 1 week; .')2 weeks and 1 day = 1 year; 12 calendar montlis = 1 year; 100 years = 1 century. The above divisions of time make the year consist of 365 davs ; but the solar year is 365 d. 5 h. 48 in. 50 »., or nearly 365i days. To prevent the loss of i of a day each year, Julius Ciesar, in b. c. 46, established the calendar which makes every fourth year one day longer, or 366 days. This long year, which occurs every year whose number is exactly divisible by 4, is called leap year. But this correction is too great by II m. lOs per year, making an opposite error of about 3 days in 400 years. The error had amounted to 10 days in the time of Pope Gregory XIII. who, to correct it, decreed that 10 days should be omitted from October, 1582, and, to prevent future error, it was further decreed that the leap year should be omitted 3 times in every 400 years, that is to say, that only such centennial years as are exactly divisible by 400, as 1600, 2000, 2400, &c., should be leap years. The calendar of Julins Cajsar is known as the Julian Calendar or Old Style, and is still in use in Russia. That of Gregory is known as the Gregorian Calendar or New Style, and is in use in all other civilized countries. Since the original difference in 1582 was 10 days, and as the years 1700 and 1800 were leap years by the old style and not by the new, the difference is now 12 days. Any date is therefore 12 days later in Russia than in other iHi MARINE, ANGULAR OR CIRCULAR MEASURE. 51 THE CALENDAR MONTHS OF THE YEAH, •Tamiary has 31 days. Febniary " 28 " " in leap }'«ar. .29 " March has 31 <« April " 30 ■« May " 31 « June " 30 ■" July has.. ..31 days. Aiif^ust " . . ..31 « September " . . . . 30 " October " . . ..31 " November " . . . . 30 « December " . . ...31 " i I Rule for Finding the Leap YEXR.-D!v;de the ttco rhjJd f>',n.1 jtgures of the number denoting the year by 4; If there be no remainder, it is leap year. Exception.— No centennial year, that is, no year whose number «nds in two ciphers, is leap year, except its number can be divided by 400 without a remainder. MARINE, ANGULAR OR CIRCULAR MEASURE. The unit of this measure is the degree which is ^i„ of Mie circumference of any circle. TABLE. CO Seconds (") = 1 Minute or :Mile '. CO Minutes = 1 Decree ° 300 Degrees = 1 Circle c Also, ir-15'= 1 point of the Compass, and 32poiuts=:l Circle. A quadmnt is one-fourth of a circle, or 90 degrees. A sextant is one-sixth of a circle, or 60 decrees. Among seamen a fathom is 6 feet, and a knot is a division of the lo- Ime. about 4/ feet in length, used in expressing the rate of a vessel's speed" When a ship sa.ls at the rate of 6 miles an hour, her speed is said to be 6 knots A degree of latitude, or of longitude on the equator is ji^ of the earth's "" »" '^■' '•"- "cgrcc S3 a miaute or iiiarine miie, equal to 1 15 statute mJej, or about 2025 yards. 3 miles = 1 leaeoe. 52 DEXOMIXATE NUMBERS. MISCELLANEOUS MEASURES. 12 Ar tides 1 Dozen 20 « ■ — 1 Score. 144 u = 1 Gross. 24 Sheets of 1 'aper ^IZ 1 Quire. 20 (^)iiires z^ 1 lieani. lOG lbs. Flour ~~ 1 Barrel, 200 " lleef or Pork z^z 1 Barrel. 100 " ^'aih ^zz 1 Ke-'. OF BOOKS. A sheet folded in 2 leaves is called a folio. i " " quarto, or 4 to. 8 " " an octavo, or 8 vo. 1 2 ," " a duodecimo, or 1 2 nio, 1^ " " an 18 mo. a (1 It C u (I M (< I The M ETP^jc System. Tlie Metric System of weights and measures is a system emiiluy- iug entirely the decimal notation. By this system, throughout all the tables, 10, (or 100 in square measure, or 1000 in cubic measure) of one denomination, make one of the next higher ; which fact enables the denominations to be written in decimal form, and added, subtracted, multiplied and divided with the same facility as simple numbers. It is, without doubt, destined to come into universal use. It has already superseded the uktb complex and variable systems formerly in use in several countries of Europe and America, and has been legaliz,^d and partially adopted in many more, including Great Britain, Canada and the United States. I THE METRIC SYSTEM. 53 The Metre is tho Imsis of tlio system, and gives it its name. J I is the unit (.f tlie lueasup: of leii-th, ami is e(iUiil to t>iiu-teii- miilioiith jiart of the length of a meri.iian between the equator and ilie pole. To assist till' ttuilcnt in learning the names of the denominations, it may be noted that there are only four units to remember, viz : tlie Metro (length), the v\rc (land surface), the Crim (weight), and the Litre (capacity), "ilie nain<;s of the denominations which are ■/n-lsiuna of these are formed, beginning with the lowest, by prefixing to the units the Latin numerals, milli, ^ ,,',„.; centi, ,'„; deci, ^\■, and the higher denominations, or multiples of the units, are formed in like manner, by prefixing the (ireek numerals, deea, 10; hecto, 100; kilo, 1000; and myria, 10000. LINEAR MEASURE. TABLE. 1 !>[illimetre (mm ) 10 mm. = 1 Centimetre (cm.) 10 cm, = 1 Decimetre (-/w.) 10 (hn. = i Metse (/;(.) 10 m. = 1 Decametre (Dm.) 10 Dm. = 1 Hectometre (rim.) 10 II m. r= 1 Kilometre (Km.) 10 Km. = 1 Myriametre(J/?«.) Tlie Metre, like the yard, is used i vlotlis, ribbons and siiort distances. The kilometre, equal to about i of a '.li-itaiicea. METRE-). r„\M7 = .039382 Inches, lb = .39382 ;' ,\, = 3.9382 1 = 3.281833 Feet. 10 = 32.818333 " 100 = 109.394444 Yards. 1000 = 1093.944444 " 10000= G. 2 15593 Miles. u e.xpressing the measurements of mile, is used as the unit for Ions; SQUARE MEASURE. 100 Square Centimetres {s,,. cm.) = 1 Scitiarc Decimetre = 15. .5 sq. in. iOO " Decimetres (s./. ■''■»6 cu. ft. ) 1 .309 cu. vds. I DRY AND LIQUID MEASURE. Tlie unit of Dry and Liquid Measure i3 the litre, equal to a cubic decimetre, or .i'202 of a shmdavJi gallon, or .8S0S of a quart. T.\BLE. LITKXM. 1 Millilitre,T„V„= .001008 cu. in., or 10 na. = 1 Centilitre, T^\o = .ClOGS cu. in., or 10c/. =1 Decilitre, ^\, = 0.1068 cu. in., or 10.«. =1 Litre, 1 = 1.7610 pt., or 10/. =] Decalitre, 10 = 1.1012? pit., or 10/)/. =1 Hectolitre, 100= 2.753 bush., 10///. =1 Kilolitre, 1000=27..d3 bush.. .03.321 a /.o.r. .35219.//. (-,- .70478 gUl. or .881 '/rt. or 2.202 'jaK or 22.024 r^aJ. or 220.2U >jal. The litre is used in measuring liquors, milk, &c. It is about eoaal to th^ old wine quart. The hectolitre, equal to about 21 bushels, is used in measuring crain. WEIGHT. The unit of weiglit is the gram, which is the weight of a cubic centimetre of distilled water in a vacuum, at a temnerafire of 3*> ••'' Fahrciiliuit. iu la c-quai Lu LoAo2 grains. s-W 10 W.7. 10 c(i. \Othj. 10 i/. \OD.j. 10 IIr, DEXOMINATE XUMIIERS. - W Icurr d.nomlnat 'nn ma/v / ,/ this hhjl,,;; nwl to II,. \,,,(„cf ^ n, r,yard t„ l,„r,r ,ln>o,nu>.t;,,,. ,„ .rhirh thr rr.lurtlon !s fn he vxiemJvd, lUifd the rrqnired druouiiw,!!,.,, /,y rmchal. KxAMPi.K.-l. lioduco .£20 i„ ,,l,illi„„<,. We multiply hy 20 ),o,-,iuse thorf> ar^ ?0 .|,il!i„j>, i„ £, t^it H, -Oof the l„wer n;irno make <.,ie .f the hfj.er. Or l„.can«o swue there .arc 20 .hillinjjs i„ CI, there arc l>« time»2o'or -'O tiiiicij 26 shilliiigH in f26. ExAM.-r.p„-2. Kodnco 18 aays, 10 h. 23 »,. tO .... to .econls. 1^'/. 10/;. 23?rt. 40 .y. 442 //. r.o .i:2G 20 52U <*. Multiply hy 24. horanse 24 :.„„r8 make I ,l.iy. A,M in 'T^ri iV,'"'"''' *'""''''-^ '•'' ^"' ''"^"""^ «0«. make 1 hour. -^oUm. AM „> 23 mir.H.H. M„l,ipiy ,,^. go, because GO uc. makf on 1 minute. AtM in 40 .seconds. i:)y2G20 A EXERCISES. Tieiluce : 1. .£25 12.s\ to poiiof. 1. £.'52^) 19a'. 7d. in pencp. 3. .£19 to farthinpts. 1. i:27 17,s', 11],/. to fartliings. '). £128 4„-. 107. to pence. 1B*\ ^\d. to larthin''.s. •?273 to cents. -?478.2"» to cents. •SlG to mills. ] 7 rY/. 7 (/o/. 3,?. to cents. 3 tons, ! 7 art. to pounds. 759 lbs. 7 hz. 12 rZr. to drams. 18 tons to oiince.s. 24 cci. 1 qr. 18 Uk to pounds. ••• •-•.•::; iu c,c,-. o .jfv. i'o (6. to poiinds. G. 7. 8. 9. 10. 11. 12. 13. 14. i?i REDUCTION OF DKNOMINATK NCMIIKIIS. .'7 / 1 1 tons 7 nrt. 73 /'. to iioiinds. -•"i III. Troy to ;;riiiiiH. <> //'. 8 (/;. 1,") jiirt. to i't'iinywoij,'}itt<. y.3 'c. \ 11, . to gniins by A|iotlR'Ciitici.' taMi-. T) III. C) (z. 4 (//•. 1 ,vtv. 8 ijr. to gr.tins. 7 (C. to scruples. ■_'.") hu.siifl.s (jf wlicat to pounds. 'IX't biisliels of oats to por.inLs. 17 bushels of potatoes to poumls. 7 miles to rods. 4(1 rods to yards. 47 miles to feet. 15 m. .")/ 3r> rd. 3 ij:^ 1 7 7, ,,..7, f^ 54. 12 bush, c pk. 5 qrt. to pint :)S DKXOMINATE NUMBERS. S-"). 40 hu^ih. 1 2>k. to pints. SG. 1873 years (305] ,1.) to days. 240 ,1. 12 /(. 42 m. 3G *. to seconds. 2 y. 136 d. 16 /i. 9 rn. to minutes. 47= r,0' 25" to seconds. 58' 24' 50" to seconds. 5 reams paper to sheets. 12i reams to quires. How many days in tlie first six months of the year? How many days in tiie last six months of the year ? 57. 58. 59. CO. Gl. 62. 63. 64. KlT.E FOR liEDUCTioN AscENDiXG. -Z)/f/c/e fhe given nnniher h ihd nnmher which exi,rcmes how man>, of that denomlnatim Ki'iht 1 of the next hltjher, reoervln.j the remulmler, If awj, a* part if tliK (i)istcer. Treat the quotient, and the succrmlve quotients obtained in the some n-ay in ngnrd to higher denominations to which the reduction li in he extended, uniU the required denomination Is reached. The ia^f quotient with the remainders will form the answer. KxAMPLE.— 1. Ileduce 520 shillings to pounds. -.0)j^-^0 Since there are 20 ghillings in .£] the number of pounds _ i:2G Am. in nny number of shillings is ^^ of tl, number of shillings; and this id found by dividing by 20. ExiMPLE.— 2. Reduce 1592620 seconds to days. 6.0)159262.0.v. G 0")2G.")4 3~ 40.V. 24)442^7 23«i. Ms. 24 iJU^ (18 d. 10 h 23 m. 40 s. Ahs. 192 10/i. l3t ?tep, from ser-nd^ to nlroites—iWvide by 60 be.ause the numl)er of minutes will be ^\- of the number of seconds. This gives the minutes and a I'tiiiiainder of 40 s. ind step, from miiotrei, to Ao^'j-divide by 60 because the number of hours will 1)6 j'j5 of the number of minutes. This gives the hours and a remainder of 23 m. 40 s. REDUCTION OF DENOMINATE NUMBERS. 5!> 3rd step, from hours to days-AWxA^ by 24 because the nnmbcr of days will be if of the number of hours. This Rives 18 d. and a remainder of 10 A. 23 Hi. 40 s. The answer is, therefore, 18 d 10 A 23 m 40 s. ^ Thp. remainder after each divlsim is of the same name as lie iliindend. EXERCISES. Heduce 1. o_ 3. 4. 5. 6. 7. 8. _9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 23. 26. 27. 28. 29. SO. 6144 pence to ponnrls. 78235 pence to i)Oiintlf). 18240 farthings to poinul?. 26781 fiirthings to pounds. 30778 pence to pounds. 882 fartliing o .shillings. 27300 conts to dollars. 47825 cents to dollars. 16000 mills to dollars. 17730 cents to eagles. 7700 1h. to tons. 194428 r/>-. to pounds. 576000 oz. to tons. 2734 Ih. to cwt. (Englisli taWe). 31022 lb. to tons (English table). 8773 lb. to tons. 144000 gr. to pounds Troj'. 1615 pwt. to Ih. Troy. 1842 gr. to our 144000 gr. to inds by apothecaries' table. 31948 gr. to pounds by apothecaries' table. 168 scr. to ounces. 1500 lb. of wheat to bnshels. 8330 Ih. of oats to bushels. .1020 lb. of potatoes to bushels. 2240 rods to miles. 220 yd. to rods. 248160//. to miles. 997057 in. to miles, d-c. 20257i ft. to milt>s. .^-r-. €0 I 31, 32, 33. 34. 3:). 3G. 37. 38. 39. 40. 41. i2. 43. 44. 45. 4G. -47. 48. 49. 50. 51. 52., 53. 54. 55. 5G. 57. 58. 59. <;o. (51. <>2. DENOMINATE NUMBERS. 2.13004 links to miles, Sic. 000 chains to miles. 32G7 .yq. ft. to xq. rods. 014400^7/. rods to^vy. miles. G99S4 sq. i„. to sq. yards. 480 gq. rods to acres. 40I59G7044*-/. m. to «,/. miles, .te. 128000 sq. ch. to ^q. miles. 40000 *vy. links to ,q. chains. 270 t«i. ch. to acres. I47G0000.V7. links to acres. 559872 ci; in. to cu. yards. "24032 t7<. !n. to f?<. feet. COO id. to gallons. 1500 7^-^. to barrels. 702 gills to gallons, Sect. 180 standard >.875jj. ji-.i^jZio Alia. C4 DliIN'OMINATE KUMBEUS. Reduce the following to the decimal of a pound : (r,9) 17.--. G.l. ■ (70) ITk iU ; (71) 13.'. 3rA ; (72) IG.,'. Ol'l. ; (73) 10^,/.; (74) 1^7.; (75) 'o.'. ; (7G) 1^. id.; (77) 19.^., Od. , (78) Uf!. 79. Keduce 3 cirL 32 ///. to the decimal of a ton. 80. Ileducc 13 net. 3 '/r. 21 lb. to the decimal of a ton. 81. lieduce 1 ijr. 14 //■. to the decimal of a od. 82. IJeduce 37 rods to the decimal of a mile. 83. lieduce 5 A. 48 m, -50 *•. to the decimal of a day. ADDITION OF DENOMINATE NUMBERS. IlCLE. — Wi'ite the (inanfitlc.t tn he added so tJidf inunhcr'i of tin s'-nne dennmuirilon uunj .v/?/; to the next hiijlier denomination, the number of vhirh carry to the column to wJiich it helonjs, and set the re- vi'iinder, if any, under the column added. Note. --The pupil should carefully study these aflditions to see that the principle is the same as in addition of simple numbers ; the only difference arising from the v.arying scale, instead of the uniform scale of 10. EXERCI.SES. £ •>•. d. £' .«. d. £ s. d. £ .< d. 17 11 4.\ 4.1 IG 3] IIG 12 H. 8 17 -4 09 19 9 17 11 Ih 74 5 9 6 4 4 11 11 11 43 7 lOj 57 18 llj 1 15 n (17 15 lO.V G.5 4 n 94 8 7.^ 2 3 w-l 79 19 9 93 9 5\ 3G 13 3 4 IG 8 28 12 1 G7 13 1 -4 55 2 u 9 5 3,', i"13 8 A\ 119 10 8 81 19 8\ 11 12 1 5. Add together 1 3 eui. 2 ^z-. IG Ih., 10 cwt. 1 qr. 18 Ih., 15 art. 3 ./r. 27 Ih., 18 Ctrl. 3 yr. 21 Ih., 7 cwt. 2 (jr. 25 Ih. G. Add togetlier 3 /. \1 cwt. 3 qr. 5 lb., It.U cwt. 3 qr. \Mh., 8 /, 7 act, 24 Ih,., 14 t. 18 cwt. 1 '/*•. 20 Rk and 5 /. 19 cwt. 3 '.'/•. ADDITION OF DENOMINATE NUMBERS. fK 1 7. Find the sum of 4 /. 7 acf. 8G fh., 2 f. 9 act. iSlb., 1 / vS rwt 90 /h., 1 /. Id acf. 33 lb., 4^8 acf: 41 //>., 2 f. 1 7 act. 89 /a! 8. What is the sum of 13 If). 14 r;2. 10 ^/y., 15 Ifj. 1 1 „?. 10 rfr., U /ft. 4 OS. 9 f?r., 8 /ft. 1 2 o.-. ] 3 (/,-., 15 /ft. 7 oz. 8 r/r., 10 /ft. 13 ox. 1 1 f//-., 8 /ft. 9 02. 6 dr., 4 /ft. 15 02. 15 dr. 9. Add together 3 /ft. 1 1 02. 16 pwf. 21 i/r., 5 /ft. 802. 7 pwf. n.7/-., 7 /ft. 9 02. 18/jJc/. 23;jr., 11 /ft, 10 02. 15^r/. 17^r., 12 /ft. *■'«. 9/JW/. 8.7;-., IG/ft. 10o;a llpwf. •22;/r. 18/ft.8o2. 19^«,^. \8,jr. 10. Find the sum of 5 /ft. 11 re. 7 ^/r. 2 scr. 19 pr., 4 /ft. 10 02. 4.//-. \8cr. 7gr., 3 /ft. 11 02. 6./;-. 2srr. Uf/;., 1 /ft. 9,/2. 3 dr. \ scr. 1 2 !7r., 2 /ft. 4 ,c. 5 dr. \Q ,jr., fi /ft. 7 vz. 2 dr. 2 *c/-. 9 gr., 2 /ft. 8 oz. 1 v/. 3 yd., 81 r>i. 2/«r. 31 rd. 1 yr/., 79 /«. 21 rd. 2 yr/., 18 m. 3 fir. 33 rd. 3 yd.l 12. Fiiid the sum of 18 yd. 2 ft. 1 1 ///., 14 yd. 2 ft. 7 In., 8 i/d. \ ft. 10 in., 11 yd. 7 hi., 7 yd. 2 ft. 8 in., 16 yd. 2 ft. 9 hi., 8 vd. I //. 7 /«. ^ 13. Add together 39 .vy.U3d.\\ ft. 48 m. 485., 17^! <»7 ,/ 1 O fc 1 OAT i'J 6., iz yy. Hi a. GG iJKNuMINATE NUMBERS, 19. Ada to-.ther 1-2 ud. 2 ft. din., \6 yd. \ft. 11 in., 28//'/. 8 in., 37 yd. C ///. When it is required to find the sum of several fractions of different denominations. Rule. — Rodncf th<' /rartions to the same name, add them itn'l tiiid the value of th>'ir ■•"nn, or, Find the va!'ir.< nf tha several fractions nepnratehj, and ad/ thrse values. KxAMPLE. — Add tojjether J of a pound and g of a shilling. S. — rz: — ■<. IS or, ^^X^0^25^^- <'^ » 2 25 '2 l^fi 80 = 1 .3 .". 4 d. An!>. — .I. 5 x;;^ 10 13.V. 4(/. Am. 20. Add togetli.T £. ,•„ and I .«. 21. Add togetlier i.' ,\,, | s. I d. 22. Add f of ii toil to ^.^ of a cwt. 23. Add togetlipr * of a 7?i., J of a//fr., and fV r/f. 24. Add together ,',, of a cwt., I of a ^, and 5 of a lb. 25. Add together £{,-. and .£75 of a a. When the frai-ti'■>. The decimal part of wliich reduced t- /6. -11.48125 lb. IG ' 7."7O0OO oz. 10 IGcvW. Wiij. to:., li. 2 (ir. Ana. ii."-- (»/•. SURTRACTIOX OF DENOMINATE NUMBERS. C7 26. Find the sum of .075 of a //>. Troy, and .97025 of an i.z. Troy. 27. What is the sum of £.79062r>, M\b s. and .75 d 28. What is the sum of £.70375 and .375 sA 29. Find the sum of .896875 /., .875 art. and .25 or. fBriti'.li Wci-ht.) 30. Find the sum of .393 /., .9 ,7(7. and .5025 /i. (Canadian Weight. ^ \ SUBTRACTION OF DENOMINATE NUMBERS. . Rule.— TI>/7e the smaller (/iiantify under the hn-jet; gettii,,/ inatihers of the game denomiimtion wider ench other. Beijhi at the right, mid take the ninnlters in the snhtrahend from those immediately above them in the mitniend. When any number in the subtrahend exceeds that of the saw denomination in the minuend, add to the number in the minuend, OS many of that denomination as rnal-e one of the next higher, subtract the number in the subtrahend from the sum, and carry one to the next denonmudion as yon proceed ; or conisder the next number in the minuend diminished by 1. (!•) EXERCISES. (2) (3) £ s. d. t. net. lb. tn. fur. rd. From 1573 11 U 47 17 43 1407" 1 16 Take 976 15 m 29 18 97 161 1 2i» 4. A farmer possessed 1279 a. 2 roods 21 rd. of land, and bv his will left 789 «. S roods 36 n?. to the elder of his two sons"; how much was left for the younger? 5. The latitude of London, England, is 51° 30' 49" N., and that of Gibraltar 30° 6' 30" X., how many degrees is Gibraltar soutli of London ? 0. The eartli perforins a revolution round the sun in about 365 rZ. 5/;. 48 m. f>^ s., and the planet Jupiter in about 4332 . take 12 nrf. 2 qr. 27 l/>. 15. From £42 7 .•*. 4 d. fake £27 10^. 8 d. 16. From £56 16 ^^ 7i d. take £49 12 «. 10 d. 17. From £114 s. 8| d. take £19 19 ^•. 5\ d. 18. From £34 5 *•. take £27 13k 1 J . 25. Find the difference between .£.76825 and .925 n. 26. From .690484375 of a ton take .87796875 of a arf. 27. Find the diff-erence between .875 of a quart and .90625 ot a gallon. 28. What is the diff-erence between I of a ton and A of a nrf by the British table? MULTIPLICATION of DENOMINATE NUMBERS. Rule.- &/ tfte inultipller under the Invest denmnmation of th- multqMcand, and nmltiply each denomination in succession, ohserr. >ng to reduce each product to the next hiyher denomination. Write th« remainder, if any, from each reduction, and can-y the quotient to the next product. Example.— Multiply £27 17 a-. 5^ d. by 6. 8. 17 d. H 6' IG 4 n Six times \ fur. are 6/((r., which are = 1 rf. o fa'. S«t down the -2 far. and carry the 1 penny to the product of the pence. Sis tiroes 5 d. are 30 d., and 1 d. adde.i makes 31 rf, which are = 2 s. 7 to the product of the pounds. Six times ,£27 are £162, and £5 added m.ike £167, which set in the pounds column. EXERCISES. (!•) (2.) (3.) £ s. d. £ s. d. £ s. d. fi4 11 Qi TO r. 11 .1 117 ij 'T 3 9 12 ro DFNOMINATE NUM iKRS. (4.) (5.) (0.) 5 17 29 5 17 11 13 6 7 "3. y »//'/. gr. 4 15 21 7 (7.) (8.) (!).) Ih. 3 02. (/;•. j*fr. 7 6 1 (10.) 15 11 m. fin: /•-/. 5 7 15 8 />-/ I) 1 3 1 10 (11.) (12.) h. 5 31 42 4 7/. 7 12 55 7 4 56 28 5 When the multiplier is more than 12, it is usual to muUiphj hij factors. Thus, £ 8. ll. Example.— 1. Multiply 24 18 lOJ by 28. 28 = 7X4. 7_ 174 12 3i 4^ 698 9 1 product by 28. Example.— 2. Multiply 16 ^ 12fic/. 76 /&. by 243. t. net. lb. 16 12 76X3(l0xl0X2)+(10X4)+3=243 H) Product by 10= 166 7 60X4 10 Product by 100=1663 16 00 o Product by 200=3327 12 00 Product by 40= 665 10 40 Product by 3= 49 18 28 Product by 243=4043 68 Ans. '"^'-ryri'.;- DIVISION OF UKNOMINATK MMBEUS. 7l 13. Multiply £18 Ms. / -/. hy 15. 1 4. Multiply £V> ly«. ,j\ ,1. by 21. 1 "). Multiply X49 7 «. ."i^ d. by 29. 16. Multiply 18/. \2cwt. 61 /^<. by 84. 17. Multiply 16c^ys! 22. If a ntan saw a conl of wood in 8 A. -I.'i ,a. 50 s., how lout; Mill he Ik; sawing,' 11 cords t 23. If 12;/a/. Sijrt. \ pt. of nioIasscK b« \is.d in a hotel in a week, how much would be used in a year at the same rate 1 24. If 13 wagons carry 3 t. 15 act. 40 //,. -iuli, how much do tiicy all carry ? DIVISION OF DENOMINATE NUMBERS. 1{VLE.—Bcff;n trith the highest denonuiiativN. and diclde ewh in mrceMion, m-ititig the -jiiotieut tjenralh. When a remahuhr <>'-rHr.i, rediu-e !t tn the nejrt lower denominutio),, „dd !n the numf^er of that denomination, and km the mm ew fhr i^j-f dicidend. &j l>roceed to tlie end. Example.— Divide £47 13 a 81 rf. by 7. £ «. 7)47 13 d. 7 into 47. 6 times iiiul t.i over; write C, and reduce Ch to Bhillinsrs, thus, .5 x 20 = 100, ail'l 6 16 2J^. Ans. '3 = 113; 7 iuto 113, 16 times and 1 shilling over; reduce the I .■s wore than 12 >rc marj either dh-ide sucra sireli/ by its f adorn, or employ the pmce)th. 3j>k. 2qrt. of grain can be packed in 37 equal- sized barrels, how much will there be in each ? ^18. In a coal mine 1459/. A cwt. 3 yr. 14/i. were raised in (•7 days, how much was that per day on an average] 19. If $15.50 be the value of 1 lb. of silver, what will be the weight of $500,000 worth ? 20. If 13 hogsheads of sugar weigh G /. Q cwt. \ qr. Mil., what is the weight of each ? 21. What is the twenty-third part 137 /t. 9 oc. \9, pid. 22 rjr.] 22. A shipment of sugar consi.^^ted of 8003/. Srui. 1 qr. /U Woz. net weight, it was to be shared ecjually by 451 grocere, how much did each get? 23. If a horse runs 174 m. 2G ni. in 14 hours, what is his speed per hour? 24. A farmer divided his farm conUining 322 a. 8 fq. cli. equally among his seven sons and si.\ sons-in-law, what was the shave of each \ THE CENTAL. In some markets grain is bought and sold by tJie 100 Ih. or cental. Railway freight tariffs are sometimes reckoned in th.- same way. The following rules show how to find what price per ccnt.l corresponds to a given price per bushel, an«. A.M., at St. John, X. B., what is the longitude of St. John? 4. What is the longitude of Montreal, if, when it is noon at (Irecnwich, it is 7 //. 5 m. is. a.m., at Montreal 1 5. What is the longitude of a ship whose correct time is found to be 5 h. 35 m. 40 g. fniitnr than the time at Greenwich? 6. What is the longitude of a ship whose correct time is 8 /(. 43 ??t. slower tliaii the time at (Greenwich? ALIQUOT PARTS. An Aliquot Part of a number or quantity is a factor contained in it an integral nuniljer of times, and is therefore always expressed by a fraction whose numerator is 1, and whose denominator is a whole number. Hence, for example, when the price of any given quantity of a '•ommodity is known, tlie yirice of any portion of such quantity, which is an aliquot p.irt of it, maj' be readily found by taking the same part of the ])rice of the given quantity ; and this can always be done by simply dividing by the denominator of the fraction expressing the aliquot part. Example. — I. What is the price of 65 lb. of beef® $9 per cici. ALIQUOT PARTS. 79 OrERATIOX. 50 Ih.~l of 1 cirf. 2)89.00 10 lh.=}f of 50 ///. 5) 4.50 = i of $9.00 = price of .'iO U>. 5/?..=^of 10/6. 2) .90=^ of 4.50= " 10 M. ■ 45 = ^ of .90 = " 5 /b. Sum, $5.85 = price of Ijb /L Ans. Example.— 2. Wliat is the price of G cwt. 3 ijr. 23 lb. @ $17.G0 l»cr ton ? OPKRATIO.t. 5cwt.=:\onf. 4)!?17.f)0 1 cwt.=)s of 5cirt. 5) 4.40=} of $1 7.60=price oCicui. 2 f/r. =i of 1 cirf. 2) 1 '/r. =iof 27?-. 2) 14//*. =iof If/n 2) 7/&. =iof 14M, 2) ■2 lb. =}ioni/b.7) .88=]iof .44=1 of .22=A of .ll=iof .055=i of .01G=^of 4.40=s: 88= 44= 22= 11= 11= 1 '.'/>: un,. 7 " o « Sum, $0.12 = price of Gcid. 3'jr. 2'dih,' Example.— 3. "Wiiat will 156 yd. of cloth cost @ 3 4^ per ijd. 2 s.=^ of XI 10 y£15G = price @ £1 per ?jd. 1 *-. = J of 2 «. 2) 1 5 1 2.*. = jijj of 1 56 = price @ 2«. per yd. id.= \ons. 3) 7 IG = I of 1512 = " 1*. i. ®£0 13 6 3 art qr. 1 9 /6. @ £2 5 16f«/. 3qr. 27 lb. @ £3 15 11 net. 2qr. 18/6. ^£4 6 13tvc/. ]qr. 9 /6. @ £5 8 4 360 articles @ 1 0/ each. 5a 410 articles @ 6/8 each. « « « « 56. 57. 436 580 141 396 1224 1840 i( 5/ 15/ « 2/6 " 1/3 « 12/6 " 17/6 " 59. 60. 61. 62. 63. 64. 2463 247 1420 860 1000 HOO 18/9 13/4 3/4 5/6 11/ 1/6 8t DEXOMINATK NUMBERS. 65. 1725 articles® 6 d. each. 66. 2100 " " 3d. « 67. 2250 " " 9d. i< 68. 300 " " lid. « 69. 1300 " " ^d. <( 70. 624 " " lid. )i 71. 1260 " " lO^d. t< 72. 720 " " 1/4 « 73. 3627 " " 3/9 « 74, 1220 " " 6/3 (( 75. 843 " " 7/6 u i4yg a 82. 330 " " 3/lOi <( 83. 6G0 " " 2/8 t< 84. 148 " " 4/7i « 85. 284 " " 7/3 (( 86. 428 " " 8/4 « 87. 75 « " 9/8 II 88. 235 " " 11/3 i< • 89. 240 " " 11/9 % 1.0 I.I ^5 2.0 L25 lu I I iinii m 1.6 6" — %. J^ y] /a V Photographic Sdences Corporation 23 WEST MAIN STREET WEBSTER, NY. USSO (716) 872-4S03 " \- ; J >■'. .f ■'•';''- ■ -■• ^ m^m' ffi PERCENTAGE. tSOO IS the ba«e. and 10 expresses the rate. Now when thj fiundCths w P«^"J»««. conveniently expressed decimally i„ Tlllll^' i' ' ^"^ '^"*- = -^2 ; 2J per cent = .02J or .025. eQu"tor^^''^r'' '°'^^"' -^^ "»"y*»»« rates^peruni equal to the corresponding raiss per hundred. meat to use the common fraction expressing that pait. The student should thoroughly master the following: 100% s the whole of anything, therefore, 50 per cent = .50 = J. 20 per cent = .20 = I. 25 H 16f 8J 1 = .25 = i = .I2J=i. = .06i=^, = .33}= i. = .16§=i. = •08}=^. = -01 = rh. 10 5 H 2 4 = .10= A. = .05 = ^. = -02^= ^,. = -OU=bV. = -02 = ^. = .04=3',. J i f I i i I I i per cent, that is, } of 1 per cent = .005 = „l^ « « « « <( (( (( « (( (( iof 1 I of I iof 1 |of 1 |of 1 Jof 1 iVofl 3H.0fl iof 1 f of 1 fof 1 JoM Aofl f*ofl Aon = .0025 =r,J^. = .0075 = ,g„. = . 00125 = ,i^. = .00375 = T^^. = .00625 = , 5^ = = .00875 = ,J„. = .000625 = ^^^. = .0003125 = ^^,^ = .002 = ,i^.. = -004 = ,i,, = •006 = ,8^. = .008 = -rty. = .003 = T^^. = .007 = W&T. — .OOt = x,^5. rio- ^■•■^•«^>iiB^>^gfcT*rs fc'L'JTi.tj^^igii'^^ir^' PERCENTAGE. 85 Taking exampfe r above, we hare the following forn^ul,: Bow. Rate. 500 X. 08 = 40 percentage; therefore, Peroentace. Bue. 40 -i- 500 = .08 rate, and Percentage. Rate. 40 -f- .08 = 500 base. From which we have the following : I^iven the Bwe and Bate to Itad tfie pewentage. n.--fliy(m tlh, Baae and ftrtentage to «ad the rate. in.-6Iven the Peroentage and Rate to find the Baee. EXERCISES. Find the percentage on : 1. 630 2. 540 3. 1825 4. 2648 5. $428.20 " 8 6. 1 1724.50" n 7. $1728 " J 8. $975 « l| @ 6 per cent. «« 7 « " 2i « "12" ♦« 9. 10. 11. 12. 13. 14. 15. 16. Find the base when the percentage is : 17. $37.50 and the rate 6. 21 18. $39.45 " « 5. 4'- 19. $6.60 « « 2. 23 20. 45 centa " «« 3, 24 $8000 (g 19 percent. $789 765 4800 $1300 $2500 " 37 " 44 " 65 " 62| " 17} $176.40" 9i 877.5 " 90 « K $23.75 and the rate 9|. $57.03 " « 7j $62.69^ " u gj[' 147.685 " " 46,"' ■ -A'.'"' m 86 23. '-'6. 27. 28. 29. 30. PERCENTAGE. 12.125 and the rate 12.i. 297.081 688.856 $4.35 ^86.34f 12.25 « 18. 28. 25. 18|. h 31. 32. 33. 34. 35. 36. 13J and the rate g. 68 cents •' $152.19 8.4 $1U.80 216 " 23f " A- Find the rate when base is : 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 62. $560 and the percentage $33.60 $4.60 $2460 ' $1568 ' 20000 " 1800 ' 1728 " 4600 " 25000 " 32 $1275 « 600 bush. " 1800 " « $720 " $125.50 " $120.80 « $.826. $246. $172.48. 3000. 27. 43.2. 3220. 1875. 24. $63.75. 3 buslu 459" $1.80. $.753. $.75i. 53. A merchant bought goods costing $580, and sold them at a proBt of 35%. What was his gain t 54. A commission merchant sold goods for another to the amount of $625.40, and chained 5i% for his trouble. How much did he earn ? 55. An auctioneer who charged 1^% for selling goods for another earned in one day $1 9.50. What did his sales amount to ? 56. If the interest of $750 for 1 year is $33.75, what rate per cent, is the money earning 1 57. A man bought a horse for $1 25, and by selling him gained $26.50. What rate per cent of profit (M he make 1 58. The regular price of a mualjilinstrument was $520, but the vendor sold it for $443. What nlU of discount did he allow ? '^4 <'^ ^ PERCENTAQE. 87 59. The retail price of a book WM $2.50 per copy. What would the discount to a wholesale buyer amount to ou 125 copies at 35%. 60. What rate per cent of profit would the buyer, as in the last question, make by selling the book at the retail price? As already explained, the amount is the base plus the percentage, and the net is the base minus the percentage. Taking 1 as the base, the aniouut is 1 + the rate expresst-d decimally. Thus, @ 7% the amount of 1 is 1.07, and @ i7 the amount of 1 is 1.005, &c. Also the net of 1 is 1 — the rate expressed decimally. Thus /fnc/c the given amount % Vie amount of 1 ; the qmi- tient will be the bate. m.— Given the Amonnt and Base to find the Rate. Rule.— £>jt;/rfe the given nmmnt hj the ham; the quotient irill he the amount ofl, from which ou^rad 1, and t/ie remainder wiU be the rate expressed deeiimlly. t^'^m^sm (^jrf^-i^if i^mmmti ^ PEBCEKTAGE. Also, L— Given the Baae and Rate to lid the Ket RvLE.—yt>dt;pfi, the given bast hj the net of 1 , the prtxlacl Will be the net required, IL— Given the Net and Rate to find the Saw.. RoLt— Z)/j;/ u « Aliif ' f "''*:^""* ^*'""** t*"** l>'« Profit on an investment was $1365, and that it was 21% ; how much was his investment! 127. The capital of a bank was $800,000, and its profits in or^e^year amounted to $108,000; what was the rate per cent, of ^ Janv 7^" 7^'"^^? P"" °^ "'^'^ ^^ '2.45 per yard, which was m)/^ from the reUil price.; what was the retail nrieal M PERCENTAGE, 1 29. A stationer sells pens which cost him 50 cents per ffross at 73 cents per gross ; what is his mte per cent of profit ? 130. The invoice price of goods imported was $140, and the tost of importation was 22 J% ; what was the full cost? 131 A manufacturing company imported a steam engine and boUer. the maker^ price of which was $7600, and the full cost to the importer $10222 ; what rate per cent, did it cost to import J 132^ Purchased a draft for $1628 on Montreal for $1632 07 • at what pat« was it purchased 1 -^ > , 133. I have $641.70 to invest in a draft which I can buy (? i/^ premium ; what will be the face of the draft ? 134. The population of a city increased from 25000 to 27750 what was the rate per cent, of increase ? $13500, and at the end of the same year it was $1575C : what rate per cent, of profit did he make during the year? -to-ilf;. ^ }''V^' ^^^^^'^^^ t2785 for a client, and paid over f-545.75, retaining the balance as commission ; what rate per cent was his commission ? and had $48024 left ; wiiat was his capital ? ^ 138. A citizen neglected to pay his taxes until 2i% was added on account of delay, he then had to pay $48.79 ; what was his original tax bill ? '*iii?i^' '^\ *"""*" ""^ " ^*"^'™P* "" ^^^268, and his liabiUties JPJ48U0 ; what per cent, can the estate pay ? *Jn^n ^.'"•"'^*"' P^i-i for goods $438, and sold them for *J0U.40 ; what per cent, of the cost did he lose ? 141 A commission merchant sold for a miller 450 barrels flour @ $5.75 per barrel, and remitted the net proceeds by a draft • what was the face of the draft if the merchant's commission and charges were equal to 4%, and the draft was purchased at T/ discount. » '■ »/o SPECIAL METHODS AND EXERCISES. A- ^l"""^ \L" ^^'" ^^"^ ""'^^ *° fi"^ tAit of any number is to divide by 100, and since to divide by 100 is to move the decimal I- PERCENTAQE. 91 point, expressed or understood, two places to the le/t, or the figures t>ro places to the right, therefore. To find 1% of any number. Move the decima{ point two placet to the left ; or, leasing th,- decimal point in the same place or column, nuyve the figures two places to the bight. EXERCISES. I^*'*r^% °^ *»ch of the foIlowinK quantities: |l40- $750 • 117.50; $2384.50; $1625.25; $986.75; $1.90; $16- $10- $12.50; $.90; $.75; 180; 5300; 10000; 1346; 1563720. Write under each of tj as required, 1% of the eai $630; $955; $1865; $180.50; $16.20; $584.50; $4 444- $4.86§; $486,661; $484.44| ; $480; $4,875; $5; $10; JuOU ! $4.83i; «4-8H; 980; 71.6; 1750; 8.43; 4883; 20000- 416- 3.1416; $4.82f; 745 tons. tB following numbers, to add or subtract life: Since 100% of anything is the whole of it, 10% is ,\j ; a since ^ oi & number is found by dividing it by 10, and to divi by 10 is to move the decimal point one place to the left, or t figures one place to the right, therefore, To find 10% of any nmnber. Move the decimal point one place to the left ; or, leaving the decimal point in the same place or column, move the figures onk place to tlie right. EXERCISES. Read 10% of each of the following quantities : $648; $246; $366; $240; $360; $750; $3oO ; $29 40- $976.80; $453.25; $15.68; $35.28; $3504.90; $4.50; $4500- 186; 940.5; 725.^. Write under each of the following numbers, to add or subtract as required, 10% of the same : $1023: $1812: 230390: ftl.fsi Rn- *,^(\R m. «qik >7n. «<><>i in- m: r>2 PERCENTAGE. ' 4 1419.80; fI5O4.50; $305.55; $898.29; $201.44; 172.90- 1U"0- 4.86|; 44.4 ; $4.44 J ; $4.88| ; $4.83. Of coarse 2% is twice 1%, and 3% is 3 times 1%. and so on. i\ow as 1/ of any number is simply the figures of that number shifted two places to the right, 2% is twice those figures shifte,! two places to the right, and 3% is 3 times, &c., and so on to 97. Therefore, '" If it be required to add to. or sabtract from, any base any percentage at any Integral rate from 2 to 9 Inclusive. Write the product of the base hy the rate render the ham, but two places to tlie right; then perform the addition or subtract im. Example.— 1. To $538 add 6%. OmATIOM. $538 base. 32.28 6 % add. $570.28 amount. Example.— 2. From $428.50 take 87 '0* • oruunox. $428.50 base. 34.28 8% subtract. $394.22 net N. B.-The multipUcation « to be performed without writing the multiplier, EXERCISES. 1. 2. To 24 " 460 add 5 per cent. " 5 " 10. 11. From 550 take 4 per " 1240 " 5 " 3. " 325 " 6 " 12. " $3 " 2 " 4. " $145 <( ^ « 13. " $43.50 " 6 " 5. ■ " $630 " 8 " 14. " $1.50 " 8 " 6. " $12365 " 2 " 15. " $1700 " 9 " 7. " $4667.20 " 3 " 16. " $910 " 3 " 8. " $528.50 " 7 « 17. " $625 " 7 " 9. " $1500 « 9 '« 18. " $485.50" 6 •♦ ^jRg^ iSiabiasi ..^iti -; =>:i PERCENTAOE. 93 Since 10% of any number is simply the fi. 20. 21. 22. 23. 24. 26. To 400 add 20 per cent 27. From 1 700 take 90 per cent " 1850 " 40 " 720 " 60 " $1625 " 60 " $564.20 " 70 " $392.25 " 80 " $63.75 " 90 " 600 . " 30 28 29. 30. 31. 32. 33. 34. 7C0 " 650 " 270 " 385 " $574 " $87.50" " $12.25" 80 70 60 50 40 30 20 « « « « be by The percentage at any other rate not containing a fraction may readily written below a eiven base, convpniont f« o^^ v.-.. combining the last two cases. ^^^^irnrn 94 PERCENTAQE. Example.— 1. To $825 add 27%. OrttATIOll. |825 base. 165.0 20%. __57J^7%. • 1047.75 amount at 27%. Example.— 2. From 1458.60 take 36%. OriKATIOit. 1458.60 base. 137.580 30%. 27^5160 e%. 1 1 65. 1 sum 36% subtract from the base, net to the nearest cent @ 36%. $293.50 35. 36. 37. 38. 39. EXERCISES. To 480 add 35 per cent. 40. To $.56 add 37 per cent " 368 " 67 " 725 " 42 " $1260" 71 " $1.85 " 18 41. " $12.40 " 29 42. " $1900 " 64 43. " $824.50 " 58 44. " $1272 " 75 45. Prom 590 take 85 per ct 50. From $60 take 31 per ct. 46. " 14000 « 79 " 51. « $846.25 " 28 « 47. " 4210 " 14 " 52. " $1612.80" 65 " 48. " $19.20" 45 " 53. " $525 " 19 " 49. " $625 " 55 " 54. " $16.40 " 72 «' Fractional rates are similar fractional parts of 17 Thus IV ;. i of 1 %. and i% is i of 1 %, and so on. ' *^^ When a percentage at a fractional rate is to be added to, or subtracted from, a given base, it may be readily written below the base convenient for that purpose, by taking such part or parts of the base as arc expressed by the rate, and setting them under the base, two places to the right. Thus, Example.— 1. To $240 add J%. opiiunox. $240.00 base. i ~ •^^ = i ^^ *240 set two places to th« riffht $-40.30 amount (S) 1°/. PERCENTAGE. : M ExAMPLi— 2. From f 1264 take J%. OriKATIOH. tl 264.00 base. i% = 6.32 = J of 1264 set two places to the right. i% = ^ofr /o = 3.16 9-48 = 3% subtract from the base. 11254.52 net ^ 3%. EXERCISES. Give the answers to the nearest cent 55. To 2000 add J per cent r>6. " 1200 " I 57. " $1680 " J 58. " 1480 "tV 59. " 11900 " J 60. " $225 " I 61. " $1080 " I 62. " $462.50 " I 63. " $875 " I 64. " $770 " J 65. " $478.20" 34 77. From $125 take i per cent 81. 78. " $960 " \ " 82. 79. " $75 " i " 83. 80. " $84 " I " 84. It « « . duct by 100. ' EXERCISES. Find the interests of the following sums for 1 year, at the rates 98 INTEREST. 1. $15 3. $120 4. $2.25 @ 3 per cent •' 5 " '< 7 It u 8 ■( 5. $175.50" 6 6. $6.40 @ 8J per cent 7. $260 « 9J « 8. $760.40 " 7 J 9. $964.50 " 6J 10. $568.^5 " 7\ « u « n.— To And the interest of any principal for any nnmber of years. RvLK—Fuul the interest for 1 year, and multiply, it by tite number of years, EXERCISES. What are the interests of the following sums for the periods, and at the rates given : 1. $4.60 for 3 (/. @ 6 per ct 2. $570 " 5 j^, " 7 $680 " 4 y. " 7J $460.50 " 3 It. " 6i $17.40 " 3y. " 8J $321.05 " 8 y. " 5 J " 4 y. " 10 " " 3 y. " lOJ" 7. $1650.45 for 2 y. at 9 per ot. 8. $964.75 9. $1674.50 10. $640.80 " 5 y. " 4|" 11. 965.50 " 7 y. " 5 J " 12. 2460.20 " iy. "7 « niL-To find the interest of any snm of money for any nnm- ber of months. j *" Rcj. K—Find t/ie interest for one year, and take aliquot parf, Jor the montfis ; or, Find the interest for one year, divide by 12, and multiply the ijttofient by (he number of months. EXERCISES. What are the interests of the following sums for the periods, and at the rates given : 1. $740 for 6 months @ 7 per cent 2. $684.20 " 4 " "6 « 3. $529.30 " 3 " "7 « 4. $76a50 «• 2 « « 7 a ;/ -^^mi 5. 6. 7. 8. S, 10. 11. 12. 13. 14. 15. 16. 17. 18. 11728.28 for 11575.64 " $1500 1899.99 " $964.50 " $1560 " $268.25 « $1569.45 " $643 " $560.45 " $48.50 " $560.80 " $2360.40 " $2500 " INTEREST. 9 months @ 8 " " 7 5 10 11 13 ly. ly- ly. 3y. 2y. 19to. 7 m. 99 3 m. 5 m. 6 TO. 9 m. 8 m. 8 J per cent. 6| " 10 « 7 « 9 '• n 7 8 10 9i lOJ llj 12 5J « K <( « TTAen the Urns la expressed in months and days, find the interest for the months as above, and take aliquot parts for the days. For this purpose a month is reckoned as SO days. Find the interests of the following sums 19. 20. 21. 22. 23. 24, 25. 26. 27. 28. 29. 30. 31. 32. 33, 34. 35. 36. $468.75 $1654.40 $34.5.65 $74.85 $673.75 $57.45 $1763.25 $485.15 $48.90 $193.70 $2647 $268.40 $2345.50 $4268.45 $642.20 $64.50" $746.25 $680 for 1 m. 15 d. " 7 m. 18 d. " 8 TO. 20 d. " 2 m. 22 d. " 8 TO. 25 d. " \y.2m.l2d. " 3?n. 18 d. 25 d. 27 d. 19 d. 5 TO. 18 d. 2y.lm.ld. 3y. 7 m. 20 d. iy. Um. Ud. 2y.7 m. 24 d. 2y. 1 1 TO. 2 d. ly. 10 TO. 12 rf. 4y. 9to. 29ci @ 7 per cent. 5 " « 11 TO. 6 TO. 10 m. ly. 6 9 n 6 H H 6 7 6i 8 10 llf 12 7 5 6 IV.— The practice of finding the time between two dates in INTEREST. months and days and working the interest therefor is attended with some inaccuracy, since the same interest is, by such a method, allowed for one month as for another, whereas the months are of unequal lengths. In order to be accurate and uniform we must find the exact number of days and reckon them as so many 365th of a year. This is the usual method employed in banks and mer- chants' offices. KxAMPLE.— What is the interest of ?528 for 65 days @ 5% ? First find the interest for 1 year, then, if the interest for 1 year be divided by 365, the quotient will be the interest for 1 day ; and if the interest for 1 day be multiplied by any number the product will be the interest for as many davg. Now, of course, we may, if we choose, invert the order of the last two processes without affecting the result, and it will be found the easier method to do so. That is, multiply the interest for 1 year by the number of days, and divide the product by 365. The whole operation will then stand thus : $528 5 $26.40 65 13200 15»40 principal, rate per cent, interest for 1 year, number of days. 365)1716.00(4.70, that is, $4.70 interest for 65 days ^57 1460 ^ ^ /o- 2560 2555 50 From the above we have the following • To find the interest for any number of days. RvLK.— First find the interest for 1 year, then m?t?tfpfi/ tlug Interest by the number of days, and divide the product by 365, A method somewhat shorter than the above will be arrived at by examining the following : INTEREST. 101 The interest of |1 @ 5 per cent, for 365 days is 5 cents, therefore " " « « 73 » ^ ^^^^ ^°en*°^ ^' PRINCIPAL, the interest, time and rate liuLK.~Div;de the given interest by the interest of $1 for the given time, and at the (jiven rate. Example 1. What principal will produce $26.60 interest in 1 year at 7% 1 The interest of «1 for 1 y«ir @ 7% i, 7 cents ; and as every 7 cent« of interest represents 81 of principal, there will be as many dollars in the principal as the number of times that 7 cants are contained in the given interest. ExAMPLB 2.— What principal will produce $1,28 in 3 months @8//? op.RAT,ox. The interest of «1 for 1 year fe. 8% is 8 cents, and there- .02 )1.28 fore for 3 mos. is 2 oente, which is the divisor. $64 Ans. Example 3.— What principal will produce $12.70 in 89 days OPKKATION, .07)26.60 $380 Ans. I INTEREST. 105 Interest of $1 for 89 days @ 5% = || of a cent, and at 67 .?"n8 = M*ofacent = 3ejaofa«. ^' Then 112.70 -- ^eja = ^■^■^^j^'^Pi^^ = 868.07 Ans. IS EXERCISES. What principal will produce 1. 2, 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 84.50 interest in 1 y. 3 m. 77 cents 810.71 $1235 849.81 831.50 879.30 8387.40 8290 8456 872.10 8231.504 " 7i " H 3 m. 9 d. Sm. 12 rf. li/.Sm. 12 d. " 6 9 m. 24 d. 2y.6m. 15 d. " 6^ 2 //. 8 w. " 4| 2 y. 6 m. «< 7J[ 93 c/. " 6 125 r/. « 5 261 d. «. 7 @ 6 per cent.? " 7 « bei Jg-iivl""' ''' '''^'^^^ *'^ ^^°^^ «"« ^°d ^^ llULE.-Z?iV/(fe //te i7/;,w a»wo««/ by the amount of $1 for the gn-cn time, and at the given rate. OPERATIOS. ][.04U 391.25/ 8 3.13/ 3i375 Ans. 1173.75 939 2347 2191 81.04J is the amount of U at the end of 8 OT. 20 d. ; that is, SI is principal, and «t.04A is 4WJ1. Jo, 18 found to hfi 375 times 81.04J • that IS, It is 87.5 times «.04i for interest and 375 times «1 for principal. The required princi- pal IS therefore $375. 15G5 f I I I i: 106 INTKREST. EXERCISES. What principal will amount t. 1. 2. 3. 4. 6. 6. 7. ^8. 9. 10. 11. 12. 13186 $168.30 $777.71 $617.11 $697.99 $1358.40 $400.18 $607.81 1255.84 $1188.34 $996.52 $5440 in 3 years " 1 y. 8 ra. " 6 m. 10 d. " 8 m. 24 d. " " 1 y. 5 m. 27 d. " " 2y. 2 m. 12 c/. " " 9 rtu 27 d. " 95 days " " 186 days " " 368 days " " 75 days " 13 years " @ 6 per cent T " 8 " " J « " 5 " 7 " 6 " 4 " 5 " 6 " 7 " 8 " 3 " Vn-To llQd the RATE, the principal, interest and time being given. B.vhR.— Divide the given intered by the interest of the given principal for the given time ® 1 %. ExAMPLt— At what rate will $150 produce $15.75 interest in 1 y. 4 m. 24 d/ OPIRATION. 2.10)15.75(7i 1470 105 iiO :=j The interest of $150 for ly.im. 24d. @1% ig $2.10, and the given interest ig found to be 7 J times 12.10. The rate mugt therefore be 7J times 1%, that ig 7J%. EXERCISES At what rate will 1. 2. 3. 4. 5. 6. 7. 8. $60 $40 $75 $30 $425 $125 $292 $373.70 $365 produce $3 interest in 1 year 1 $13.36 $1 $2.25 $11.73 $14 $3.92 $14.83 2y.9m.\2dt 2 months 1 9 months? 3 m. 18 rf/ 1 y. 7 m. 6 c?. ; 140 days 1 207 days? $13.92 " 174 days? INTEREST. 107 10. At what rate must any sum of money be on interest to double itself in 12 years Y 1 1. At what rate must any sum be on interest to amount to three times itself in 25 years t 1 2. At what rate will any sum double itself in 16 y. 8 m. / Vm— To find th« TIME, the principal, iatenst and rate being given Hvhti—Divule the girev hitertfi hj the interest of the given principal /or 1 year at the given rale. ExAMPLt— In what time will $125 produce $13.75 @ 8% I OFBRATION. 125 principal. 8 rate. Int. for 1 year |10.00)m75, given interest. 1.375, years— quotient by 10. 12^ 4.500 months. 30 15.000 days. Ans. 1 y. i m. 15 d. EXERCISES. In what time will 1. 2. 3. 4. 5. 6. $12 $1800 $1200 $3825 $40 148.20 @ 8 per cent produce $2.88 interest] " 7 "6 "H "6i "6 $315 $338 " $151. 93f" 75 cts. " amount to $167.32? In how many days will 7. $672.50 @ 7 per cent amount to $683.33 » 8. $856.88 "5 " prmluce $7.63 interest f <|iiOuO $76.8.1 10. In what time will any sum double itself at 6%t .a »» i 106 INTEREST. It! 11. In what time will any sum qumlniplo itself (? 9 %T 12. borrowed n sum of money on .Tune 3, 1808 (<,. 7% agreeing to settle the account when the inlarest should bo equal to tl!« principal. When was it due ? ACCOUNTS CURRENT WITH INTEREST. It is customary for wholesale merchants in rendering therr regular half-yearly accounts to their cuetomers, to charge interest up to the time of rcnderii,., the account on such items of the Dr. side as fall due prior to that date, and also on such items of the Cr. 8-ide as fall drte after said date, from the time of rendering the account to the dates on which they severally fall due ; and allow interest in like manner on such items of the Cr. side as fall duo More the said date, and also on such items of the Dr. side as fall due after said date. SucU an account with the interest reckoned in it is called an Account Current with Interest. As an illustration let us suppose the following account to he rendered ou June 30th, and the mdse. items to be on 3 months' credit : Db. John Smith. Cr. Jan. 18 Feb. 6 Mar. 10 Apl. 25 May 17 June 4 To Mdse. (( << « (( 150 00 The rndse. items being on 3 months" cmiit, all the iteniR on the Dr. side, and the third item on the Cr. side fall due 3 months after their .several dates' that is, the first item, on April 18, the second, on May C, ic. ' On the first item interest is reckoned from April 18 to .Tune ,W-73 days • on the second item, from May C to .Tune 30-r>r> days ; on the third item', from June 10 to June .30—20 days ; and these items of interest go to increase the I)r side ofthe account. The last three items on the Dr. side do not fall due until after June 30. That of April 25 falls due on July 25, and on this interest is reckoned from June 30 to July 25-25 days ; on the next from Juno 30 to Aug 17-48 days, and on the last from June 30 to .Sep. 4-66 days, and these items of int.prft«t pro todimini-h the Dr. ?.iHr: nr -i-HirK sTT-..-.---.fi, t.. ti... ^t ■ increase the Cr. side of the account. They are written in red ink on the Dr. ■"t£*2:^*" l^l^'i£3iaS4l.£U!C ACCOUNTS CURRENT. 100 oide, and their wiin m tnuwferrod to the interent colinnn on thn Cr. »icle in Muck with the explanation " Intereiit in red," and there added with the intercut on that aid*. The fir«t item on the Cr. iiide in Caiih, and interest in reckoned on thi« from •March 27 t«) .Ijino 30-t« days ; on the wpind it.iii intert.«t i« reckoned from May 17 to June .JO-M dayn, and on the fourth item fnmi June 21 to June 80— !t 05 •»iuu »« ■^ ao b» ov »*< 1^ O O lO o O O t- o •c a. O O (M o o ic ■«»< ic C-I -v s-i ^< -f< 00 eo CO t- CI oo o £ * a. o E CO 2 3 = p;5 = : ^i: s c2i; l^ t-» to — o 1.0(J0 iKM) 1.071 225 l.OMl (KX) 1.102 .500 1.123 600 1.144 900 :i 1.0'.»2 727 1.108 718 1.124 ,S64 1.1,57 625 1.191 016 1.225 043 4 1.125 50!) 1.147 523 1.169 8.59 1.215 506 1.262 477 1.310 7'.N5 ii l.l.it) 274 1.187 cm 1.216 653 1.276 282 l.:m 226 1.402 ,5,52 fi 1.194 or,2 1.229 2,55 1.2()5 319 1.340 096 1.418 .519 1..500 730 7 1.220 874 1.272 279 1.315 932 1.407 100 l.,503 6:« l.fK>6 781 H 1.2(;6 770 1.316 809 1.368 569 1.477 4.55 1,.593 848 1.718 186 !) 1.304 773 1.3(i2 897 1.423 312 1.551 328 1.689 479 1.838 459 10 1.343 916 1.410 .599 1.480 244 1.628 895 1.790 848 l.%7 1.51 11 1..384 234 1.4.59 970 1..5,39 4.54 1.710 :«9 1.898 299 2.104 852 12 1.425 7(51 1.511 0<)9 l.<501 032 1.795 S,5«; 2.012 196 2.2.52 192 1 13 1.4('^ ,534 1.563 95 2.156 591 2.445 9,59 2.772 470 3.555 673 4.549 :183 5.807 353 27 2.221 289 2,531 567 2.883 369 3.733 456 4.822 346 6.213 868 28 2.287 928 2.620 172 2.i»8 703 3.920 129 5.111 687 6.648 838 21> 2.a56 566 2.711 878 3.118 651 4.116 136 5.418 :J88 7.114 257 30 2.427 262 2.806 794 3.243 398 4.321 942 5.743 491 7.612 2.55 31 2.500 080 2.905 031 3.373 i;« 4.538 039 6.088 101 8.145 113 32 2.575 083 3.006 708 3. .508 059 4.764 941 6.4.53 387 8.715 271 as 2.652 335 3.111 942 3.648 381 5.003 189 6.840 590 9.:i25 340 34 2.731 !K)5 3.220 860 3.794 316 5.25.3 348 7.2.51 025 9.978 114 35 2.813 862 3.333 590 3.946 089 5.516 015 7.o«6 087 10.676 581 3»; 2.898 278 3.4.50 266 4.103 9;53 5.791 816 8.147 252 11.423 942 37 2.98;j 227 3..571 025 4.268 090 6.081 407 8.636 087 12.223 618 3.H 3.074 783 3.(i9(i Oil 4.438 813 6.385 477 9.154 2.52 13.079 271 3!t 3.167 027 3.825 372 4.616 366 0.704 751 9.703 507 13.994 820 40 3.262 038 3.959 260 4.801 021 7.0:« 989 10.285 718 14.974 458 41 3.a">9 899 4.097 834 4.<)93 o<;i 7.:?91 988 10.902 861 16.022 670 42 3.4(!0 696 4.241 258 5.1i)2 784 7.761 588 : 11..557 o;« 17.144 257 43 3. .564 517 4.389 702 5.400 495 8.149 667 12.2.50 4,55 18.344 .355 44 3.(!71 452 4.543 342 5.616 515 8.5,57 150 12,985 482 19.628 460 45 3.781 rm 4.702 3;)9 5.841 176 8.985 008 13.764 611 21.002 4,52 4(; 3.895 044 4.m> 941 6.074 823 9.4;U 258 14.590 487 22,472 623 47 4.011 895 5.037 284 (i.;il7 816 9.905 971 15.465 917 24.045 707 4« 4.132 2.52 5.213 589 6.570 528 10.401 270 16.;«»3 872 25.728 907 4.. ...ill ^n.,nfn ^u„ :..»„. 1. „c at ;„,.* 1 ^r ;* ^^if^i^^^j^iS^ 118 INTEREST. To flad the PRINCIPAL, the amount at compound intereet, time and rate being given. RvLK—Dhide the given amouut by the amount of $1 for the given time and rate. Example. —What principal will amount to $2315.25 in 3 years e 5^ compound interest ? OPHATIOX. tl.OO .05 1.05 ■0525 1.1025 .055125 Amt. of II for 3 y. at 5% l.!57625)2315.25O000(200O Ana. EXERCISES. What principal will, at compound interest, amount to 1. «1 085.40 in 2 years @ 6 per cent. 2. $14802 44 " 10 " " 4 «« 3. $2873.37 " 12 " "5 <« 4. $51428.59 " 40 " " 6 " 5. $216.73 '< 20 " " s " 6. What is the present value of a debt of $1000 payable at the end of 25 years, money being worth 6%, compound interest 1 7. What sum must be invested in the Savings Bank at 4°/ compound interest on the birth of a child so that when the child becomes of age he may draw $5000 f 8. Suppose a person at the ago of 58 has a paid up life insur- ance policy for $2000, what is its cash value on the basis of 47 compound interest, his expectancy of life being 15 years ? 9. As in the last exercise what should be the cash value of a pohcy of $5000 paid up at the age of 65, when the expectancy of life 13 1 1 years t r j 10. In like manner what should be the cash value of a paid-up policy for $1000 at the age of 52, when the expectuncv of life i^ iS.S2" years I ANNUITIES. An Annuity is an annual payment continuing fur a given number of years, for an uncertoin period, as for life, or forever. An Annuitj'fCertaln is one that ia payable for a definite length of time. An Annuity Contingent is one continuing for an uncertain period, as during the life of a person. A Deferred Annuity, or Annuity in Reversion is one that begins at a future time. An Immediate Annuity or Annuity in Possession, is one that begins immediately. An Annuity Forborne or in Arrears is one the payments of which have not been made when due, but have been allowed to accumulate. The Amount, or final value of an annuity is the sum of th« amounts of all its payments at compound interest to the end of the annuity. Thus, the amount of an annuity of |1 for 5 years at 5% Is the sum of the amounts of all its payments at the date for the 5th or last payment, and may be shown ais 'allows : The amt. of the lat pajrment, 81, for 4 years = SI. 215506 " " " 2nd " " " a " 11.157625 " " " 3rd " " " 2 " $1.102500 4th " " " 1 " $1.050000 " 5th payment $1.000000 Amount or final value $5.525631 The Present Value of an annuity is such a sum as, at compound interest, would amount, at the end of the annuity, to its final value. A complete discussion of the subject of annuities would occupy too much snacs and be trso !nt.rif*-Jitft fav this TrorVr Thft f*-btpf practical problems, viz. : to find the amount and to find the pre««nt ^^1^:-' ISO ANKUITIES. value of an annuity are readily solve.! by tl.o use „f the tables on pages 122 and 123. and exerci.es fur these purposes are all that can l>e hero introduced. Rule. -3/,,////,/,/ ^/,g a»w«n/ of an nnnmf,, of 91 for the aiven Inne and rate (Table p. 122) hy the gu'en annuity. ' Example.- -Find the amount of an annuity of $500 forborne 7 years @ .")%, OPIRATIOX. $8.142008 amt. of an annuity of «1, per table, p. •'^00 given annuity. 14071.0040 Ans. EXERCISES. Find the amount of an annuity of 1. $fi00 for 10 years @ 6 per cent. 2. $1000 " 25 " 5 «« 3. $800 ■' 40 " 3 it 4. $750 " 30 '< 4 « 6. $1200 " .50 " 7 « 6. $325 "12 " 3i « interest^* ^^"^ ^'^^'^°* ^^^''^ °^ *° ^""'"^ ** compound nuLE.~Mu?t;pIy the present r,lne of an annuity of $1 for the :ncen time and rate (Table p. 12S) by the given annuity. Ex.xMPLE.— What is the present value of an annuity of $120 to continue for 20 years @ 5 % ? j v ^^j OPKRATIOK, $12.46221 pre.sent value of an annuity of $1, per table p. \^ given annuity. -j.-r^:£7 '■^tt^^i :-*H--'- " 30 7''! ;U.O.; . 954 :«5.785 ,591 40.!>95 492 21 28.676 486| 30.269 4711 31.90.. m2\ 3.5.719 2.52 ,59.992 727 44.»(;6 177 22 30..5;«5 780, 32.328 902, 34.247 970 38.505 214 43.392 2.9!»5 828 .53.4,36 141 24 34.426 470| 36.666 528: 39.082 60l! 44.501 !>99 ,50.815 577 .5«.176 (571 25 36.459 264 38.949 8571 41.645 908, 47.727 09i> .54.8(54 512 63.249 0.50 26 38.5.53 042; 41.313 102 44.311 745 51.113 454 .59.156 383 68.(576 470 27 40.709 634i 42.759 060 47.084 214 54.609 126 63.7a5 766 74.48:5 823 28 42.930 923 46.290 627 j 49.'.»67 583 ,58.402 .583 (58..528 112 80.697 691 29 45.218 850 48.910 799! 52.iH!6 286 62.322 712 73.(539 798 87.346 .529 30 47.575 416! 51.622 677 i .56.084 9;W 6<).438 848 79.0.58 18(5 94.460 786 31 50.002 6781 54.429 471! 59.32.S 335 70.7(iO 790 84.801 677 102.073 041 32 52. ,502 759 57.334 .502! 62.701 469 75.298 825* !»0.889 778 110.218 1.54 33 55.077 841 60.341 210 6<).209 .527 80.063 771 97.343. 1(55 118.9.33 425 34 -57.730 177 63.4.53 1.52, 69.857 909 8.5.066 a59 104.183 7.55 128.258 7(55 a5 60.462 082 66.674 013 73.6,52 225 90.320 307 111.434 780 138.236 878 36 63.271 944 70.007 603 77.598 314 95.83(5 323 119.120 867 148.913 4(50 37 66.174 223 73.4.57 869 81.702 246 101.628 139 127.268 119 16().:5.37 400 38 6'.). 1,59 449 77.028 895 a-).970 ;}36 107.709 546' 1.^5.904 2iH5 172..V;i 020 39 72.2:U 233 80.724 906 90.409 1.50 114.1-95 023 145.0,58 4.581185.640 292 40 75.401 260 84..5.50 278 9.5.025 516 120.799 77411,54.761 96li!lit.047 684i2U.609 .570 42 82.023 19(5; 92.M7 371 104.819 .598 13.5.231 75l|l75.9,5(l 645 2.J<).(!.32 240 43 8.5.483 892| 96.848 629 110.012 ;{82 142.993 339:187.507 577!2«7.776 496 44 89.048 409,101.238 331 11,5.412 877 151.143 OOo|l99.758 032'266.120 8,51 45 02.719 861 105.781 673 121.029 392 1,59.700 1.5»i'212.743 .514 2^5.749 311 46 9X501 457 110.484 031 126.870 ,568 168.685 164^226.508 125 306.751 76.3 l'tO.396 .501 115.350 973 132.945 390 178.119 422J241.098 612'329.224 ;{86 47 48 104.408 396 120.388 297 139.263 20f> 188.02.5 393 2.56. ,564 .52<.t 108.540 648 125.(W1 846 145.8.33 734 198.426 66;} 272.958 401 35:5.270 093 49 378.999 000 60 112.796 867 130.999 910 152.667 084 209.347 976,290.335 9a5 406.528 929 1 1 1 1 m^ fUESENT WORTH OF ANNUITIES. 123 TABLE, • HOWINO THS PREHENT WORTH OF AN ANNtlITT OF ONE DOLLAR PER ANNUM, f CONTI.VLg POB AHy Nt'MUEU OT VBARS NOT KXCKUMNO riK"r, No 1 2 3 4 5 6 7 8 •9 10 11 12 13 14 15 16 17 18 19 20 21 "22 23 24 2S 26 27 US 29 30 31 32 ;u 34 35 3(i 37 38 39 4U 41 42 43 44 45 46 47 48 49 50 » ptr c«nt. I ^ ptr cent. | 4 per cenl. I K per cent. | « p«r cnt. ^1 0.970 874 1.913 470 2.H2S 611 3.717 098 4..'>79 707 5.417 191 6.2:«) 3ft3 7.019 682 7.786 109 H.XiO 208 9.2.V2 624 9.954 004 lO.tfcM itrtSl 11.29(1 073 11.937 »;«! 12.561 102' i:i.l66 118 13.753 513! 14.323 799; 14.877 475] 15. 4 1^ 0?4 16.443 608' 16.935 542 17.413 148 17.876 842 18.327 031i 18.764 108' 19.188 45,j 19.(H)0 441 20.000 428 20.338 766' 20.765 792 21.131 8371 21.487 220, 21.832 2.".2 22.167 235; 22.492 462 22.808 215 1 23.114 772, 23.412 400 23.701 359; 23.981 902 24.254 274 24.518 713 24.775 449 25.024 708 25.206 707 2».501 657 23.729 764 0.966 1H4 1.899 694 2.H01 637 1 3.673 079 4.515 0.'.2 5.328 55.3 6.114 544! 6.873 956! 7.607 6871 8.316 606 1 9.001 56r 9.66;i 334! 10..302 738 lO.iKW 520 11.517 411! 12.094 117 12.(>51 321 13.189 682 13.709 837 14.212 40:i 14.697 074 15.167 125 15.620 nio 16.058 ,168 16.481 515 16.890 352 17.285 366 17.()67 019 18.035 767 IH.39^ 045 18.736 276 19.068 865 19.390 208 19.700 684 20.000 (Wl 20.290 494 20.570 535 20.S41 087 21.102 .5001 21.3,-.5 072 21.599 1041 21.834 SS3! 22.062 689 i 22.282 7911 22.495 450 1 22.700 918 22.899 438 23.091 244 23.276 .564 23.455 618 0.961 KJS l.88«i 095 2.775 mi 3.62!> 895 4.451 822 5.242 137 6.002 056 6.732 745 7.435 ;m 8.110 8!>6 8.760 477 074 9.985 648 10..563 123 11.118 387 ll.9 3;<4 11.663 583 11.825 779 11.986 709 12.137 111 12.277 674 12.409 041 12.,531 814 12.646 ,5.55 12.7.53 790 12.854 (m 12.M7 672 13.035 208 13.117 or 13 193 473 i;?.264 928 13;«1 709 13.394 120 13.452 449 13.,506 963 13.557 908 13.605 522 13.6.50 020 13.691 603 13.730 474 13.760 799 13.800 746 COMMERCIAL PAPER. The most usual forms of commercial paper are notes, drafts and bills of exchange. A Note, or as it is often called, a Promissory Note, is an abso- lute promise m writing to pay a specified sum at a specified time, or at sight, or on demand, to a person named in the note, or to his order, or to bearer. FORM OF PROMISSORY NOTE. *^*^ ^"'f- Halifax, N. S., Not. 22, 1882. Three months after date, for value received, I promise to pay frazee t the legal rate tlieiw- after till paid. 126 «325.,Vff COMMERCIAL PAPER. NOTE WITH INTEREST. Halifax, Nov. 23rd, 1882. One year after date, for value received, we promise to pay to the order of \ ,ctor G. Fraz.e, tl.ree hundred and twenty-five and y\<% dollars, with interest at 7 per cent. Newman Casey & Co. This note bears interest at 7?; frojn its date tiU paW. If the word. " at 7°' " ^.L! "° '"""/■°" °' '"*«■••«' >« "'ade in a note, it bears none until after maturiv'b.t"f \f /r '^'^" ' ""*" '* ""* *° ^" -*--* befor, "wth int .^^' *'"''' '^.'^* P""*' ^* ''"y "*''" ^•t" 'hao 6-. the word* inlrted " "'^""'^ ''" ^"^'''^^" "^' •* '^^^'^ "P->' >--» be A JOINT AND SEVERAL NOTE. ^^^•^^- , Halifax, Oct. 31st, 1882. Four n.oNths after date, for value received, we, jointly and severa ,, promise to p^iy .James Xorthcote, or order, six hundred dollars. Arthur Crawford, C. Weston Frazee. For the payment of the above note, the makers may be sued jointly, and iTrr^' .Tu '^^"'''^y- " the words " jointly and severally "wer* omitted they would be liable jointly, but not separately. The four months mentioned expire on the la»t day of February, 1883. ToulH rf ' "• Tk""* "" ^^"^ '^""^ ^^y thereafter-March 3rd. This not«y would mature on the same day, whether dated October 2«h, 29th, .tOth or FebraTry '"°" "'°"''* ^"^'^ '" ^'^^^ *""' °° ^^^ ^Sth or last day of A Bill of Exchange is a written order, whereby one person orders another to pay to a third, or his order, or to bearer, a sun» of nH)aey at a certain time. The parties to a bill of exchange are three,-the drawer, or the person who gives the onler; the draweft or the person who f, ordered to pay the money; and the payee, or the person to whom the money is ordererl to be paid. When the drawer and the drawee are both residents of the same country, the bill is called an inland bill, or more commonly a draft. DRAFTS. 127 When the dniwer and the drawee are residents of different countries, the bill is called a f(irei<4n bill, and this is what ia com- monly meant by the term " bill of exchange." Drafts and bills of exchange are made payable " at sight," that is, on presentation, or at a specified time after sight, or at a speci- fied time after date, or on demand. A draft or bill of exchange is accepted when the drawer nnder- takes to do what he is ordered to do, and he (iocs this by writing the word " accepted " across the face of the bill, followed by the date, if the bill is payable after sight, and his signature. He is then called the acceptor. When a bill or draft is made payable a certain time after sight, the time is counted from the date of Jicceptance. When a certain time after date, the time is dunted from th& date of the instrument. All drafts and bills, except those to be paid " on demand," are subject to three days of grace, if the words without grace are not inserted. Demand drafts are payable when the demand for pay- ment is made. A SIGHT DRAFT. $400.00. Halifax, Nov. 20th, 1882. At sight, pay to the order ot Hiram Dodge, four hundred dol- lars, value received. Frazee & Whiston. To Doddridge Dwyer, Pidon. TIME DRAFT. $1000. Halifax, Nov. 25th, 1882. Thirty days after sight (or date), pay to the order of I'rown & Jones, one thousand dollars, value received, and charge to the account of Frazee & Whiston. To Jno. W. S.MITH & Co, Montreal. Forei;^ hilla, that is, hilla drawn in Canada and payable in Great Britain or any foreign comitry, are (except thuHe on the United States) usually drawn in sets of two or three, one of which being honored the others are void. Bills on the United States, though they are foreign bills, are drawn singly in the i; i; ^^^ COMMERCIAL PAPER. A SET OF STERLING EXCHANGE. ^240 12,. 9d. HAurAX. N. S., Nov. 25th, 1882. thirfl'onh'" '"'[ ""'^' °' '•'"' '"■• '^"^ of exchange (second and thzrf of the same date and tenor unpaid) pay to the orl.r of John B. Cumnungs two hundred and forty pounds, twelve shilling, anS nineponce, value received, and charge to the account of ' To H. a Glad3to^b, London. ^""^'"^ * Wuibto^. Halifax, K S., Nov. 25th, 1882. X240 12*. 9d. thirT'/n'^' *^^' "'^''* °^ '^'^ ""^ «^'=«"'I of "Change (first and third of the same date and tenor unpaid) pay. Ac. ^240 12,. 9J. Halifax, N. S.. Nov. 25th, 1882. Sixty day, after sight of this, our third of exchange (first and «wond of tne same date and tenor unpaid), pay. &c. BANK DISCOUNT. note, nd bdls, tha .s, purchasing notes and bills from merchant .nd other,, pay.ng for each a sum e^ual to its face, less the inter^^ on the same for the number of day, it has to run after the day o when r . " -"^"^^ '' ""^'* '''' ^^'''^^^ -<^ ^he remainder pit worth 1 " T''"'^ '"™ *'^ ^''^^ ''' ^^« -'•- « -ll«' •/ 17. A holds a note against B for I478.&2, dated May 10th, 1883, at one year after date, drawing 7^^ per cent, interest. I pur- chase this note from A on Augu.st 18th following, paying for it such a sum as will allow me 20 per cent, interest on my money. What do I pay for it 1 To 'find the face of a note such that, when disconnted at a bank, its proceeds shall be a given sam. Rule. — Divide the given sum by the proceeds of $1 fur the given time andf rate. The qnoiient will he the face of the note. Ivn i— Tl'is ia the lame m Case IT, page 88, with the element of time added. Example. — What must be the face of a note dated Jan. 6th, 1883, at three months, to be worth, on the same day, $400 — bank discount at 7 /{ ? OrBRATtOV. Time is 93 days. The interest of %\ for 93 days (^ 5 % is f J of a cent, and @ 7%i8iof fjofacent = §5iofacent = $.0mf. Then, $1.00 Proceeds of $1,00, .98^^\ ) 400 ( 407.26, that is, $-107.26, the face of the note required. NoTR.— Since .S400 is the rroceedg of a note, the face of that note mimt rnn. tain il as often an f-KK) ouutaiiis the proceed)) of $1. it 132 COMMERCIAL PAPER. Or, tlie follo\7ing method may be used : RvLn.-Find the inUrest of the given mm for the given time, at the gn,en rate; then the interest of that interest, and so on, till the interest of the last interest obtained is less than a cent, that is insignificantly small. Add the successive items of interest thus found to the given mm for the face of the note required. -..?*'"''^''~^*'''"^ *^^ """^ problem as before, the interest of 1400, for 93 days at 7% is $7.13, and the interest of $7.13 for the same tin.e, at the same rate is 13 cents, while the interest of 13 cents is practically nothing, being less than half a cent. Thea |400 + $7.13 + |.13 = |407.26, the answer as before. .o aT;;"?'?!.!"*,"',*'''^; '^"''''^ ""^ theoretically correct, is practically I^ffl^lt, \^"i "i '"^'""^ *^^'^'' '"">• ^ ''>^'^y "-«d with result •uffioiently accurate for business purposes resu..» EXERCISES. 1. For what sum must a note be given so as to produce a net •um of $375, when discounted at a bank for 95 days at 6% t 2. A man owes you $750 now due ; for how large a sum should he give you his note to be discounted at a bank for 184 days at '/o> and ywW the net amount of the debt I 3. Your note for $800 lies at the College Bank, due .n th« 8th January, 1883; what is the face of a renewal in full for 2 mot., bank discount at 7% t 4. Your note for $1200 is due at a bank on March 28. You pay $500 cash, and renew for 4 months for the balance; what U the face of the lenewal note,— bank rate 8% t $oOO ; for what sum should he write his note at 6 months to U discounted at 6%, and pay the debt! . ^' I/^'nf chant wishes to obtain $550 from a bank, discount- me at 7*/.. for wha'' «■"»" »»>"'•«• i-- --•-- < ■ . -_ . PARTIAL PAYMENTS. 133 7. Lsold A. Mills niercliandise to the amount of $918.16, for which he was to pay me cash ; but being disappointed in receiving money expected, he gave nie his note at 90 days for such a sum as "."hen discounted at 7%, produced the price of the merchandise. What was the face of the note I 8. I owe R Harrington an acci., now due, of $168.45 ; he also holds a note against me for $210, which will be due in 34 days, including days of grace ; he allows me a discount of 8% on the note, and takes a new note at 60 days large enour^h to settle, when discounted at a bank at 6%, both debts. What is the face of tha new note 1 9. Samuel Johnson has been owing me $274.48 for 84 dayji, I charge him interest at 6% per annum for this time, and he gives me his note, at 90 days, so that when I get the note discounted at 8%, the proceeds will equal the amount due. What is the face of the note 1 / >' 10. I got my note for $2000 discounted at a bank. May 20, 1882, at two months, and immediately invested the sum received in flour. June 7, 1882, I sold half the fl.iur at 10 per cent, less than cast, and put the money on interest at 9 per cent. August 13, 1882, I sold the remainder of the flour at 18 per cent, advance, and expended the money for cloth at $1 per yard; 12 days after I sold the cloth at $1,161 per yard, receiving half the price in cash, which I lent on interest at 7 J per cent, and a note for the other half, bearing interest from October 4, 1882, at 6| per cent. When my note at the bank became due I renewed it for 5 months, and when this note became dne I renewed it for 2 months, and when this note became due I renewed it for such a time that it became due July 20, 1883, at which time I collected the amounts due me, and paid ray note at the bank. Required the loss or gain by the transaction. PARTIAL PAYMENTS. It is often required to find the balance due on a note, mortfr.'jge. or other interest bearing obligation where par' payments have been I I 134 COMMERCIAL PAPER. made at viirlniis times, and no otlxT «ettlutn('iit.s arrived at tlian the eiidorHciiKMit on the instrument of the suras paid, or n-ceipt* given on ancouiit. Tho usual course, in sucli cases, is to apply the payment, or lO much of it as is necessary to tlie dischar^'e of tiiu interest duo at the tiuK! tlie payment is made, and tho balance, if any, to tlie dis- charge of the principal. If tlie payment is not sufficient to pay the interest then due, the balance ot interest must not bo a.lded to tho principal for the piir|»ose of charj,'iii;,' interest thereon r that would be charging interesL on interest, which, in general, is not allowable. To carry out the above adopt the following Eui.E. — Find the amoiiht oj the pn'nci/Hil to the iiiiie i,f th« first />iti/,ii"itt, if that paymi'iit exreeilx tli^ interr.'it dm: it that time; if not thill to the time when the xnm of tli^ paytaentH exceeds the interest, and suljtract the paijinent, or tlie s'l^ of the poymeidsfrum such amount. Consider the remainder as a new principal, ant pro- ceed as lufore with other payments, and so on, to the time of settle- meirt. Example— Find the balance due on the following note on December 31st, 1882 : — • 1600. PiCTOu, Feb. 16th, 1880. 0,1 demand I promise to pay Jacob Amh^rson, or order, one thousand six hnndred dollars, with interest at 7 per cent. - John Fortune, Jr. There was paid on this note,— June 19th, 1880 $460 January 22, 1881 1.50 February 2.'?. ISS), 50 May 1 0, 1882 100 November 4th, 1882 700 :A PARTIAL PAYMKNTS. 135 eruiATioii. PrinripHl Interest troiii F.h. 16,'80, to June 19,'80— 124 Jay«,a(ld Amount June 19, *80 First (mynient — subtract Halnnco — new principal Int. from June 19, '«0, to Jan. 22, '81—217 tluys, mlil Amount January 22, '8 1 Second payment lialanc(? — new principal Interest Iruni Jan. 22, '81, to Feby. 25, '82—399 »biy8 Interest on same principal from Feby. 25, '82, to May 10, '82—74 (lays Amount May 10, '82 Thin! and fourth payments Kalance — new ])rincipal Interest from May 10, '82, to Nov. 4, '82-178 days Amount Nov. 4, '82 Fiftli payment Balance- new principal Int-rest from Nov. 4, '82, to Dec. 31, '82- -57 days. .. Amount Det. 31, '82 — balance due $1(100.00 38.07 1038.07 4()0.00 uTko^ 49.03 1227.10 l.'iO.OO 1077.10 82.42 15.29 1174.81 150 00 llj24^ 34.98 lor)9.79 700.00 '359.79 3.93 EXERCrSES. 1. How much remained due on the following note on Juno 12th, 1883: — $800.00. IIamfax, N. S., Oct. 21st, 1880. One year after date, for value received, I promise to pay Smith & Hunter, or order, eight hundred dollars, with interest. L. J. McLeod. Payments : — October 2l8t, 1881 |300 March 1st, 1882 100 y November ICth, 1882 '. . 150 February 27»h, 1883 80 h ^^ COMMERCIAL PAPER. ^^2^ Wl.at wa, the balanc. of th, following note on April 5th, •350. oo ^ WrN-DsoR, N. S., May l.,t, 1876. On floman,! I promise to n.iv Williim p, James Wktow. Paymenta : — December 25th, 1876 ^-^ June 30th, 1877 * ,' '"" August 22, 1878 .....'.*.' .' . June 4th, 1879 ." ' .''*,' ' [ ' " * " " " j^^ I 1609. «» ^ KB.VTvaLB, N.S., June 8tb, 1881 Six months aftor .late, we jointly and severally, promise to par Samuel Gkauam, T. B. Bearman, Jrayment. Principal «600.00 Interest from Jan. 2nd to Dec. 31—363 days 35.81 Amount of principal to Dec 31 $635.81 1st payment ^120.00 Interest from March 14 to Dec. 31—292 days. ... 5.76 2nd payment 150.00 Int from June 20 to Dec. 31—194 days. 4.78 3rd payment 200.00 Int. from Sept 9 to Dec. 31—113 days 3.71 Amt. of payments — subtract HSi.25 BaldueDec 31, '82 $151.56 EXERCISES. 7. How much was due on the following note on Decembgr 28th, 18821 $400.00. JklAiTLAND, N. S., January 1st, 1882. For value received, I piuriiise to pay J. B. Smith & Co., or order, on demand, four hundred dollars, with interest at 6 per cent. A. R. CASSBLa The following payments were receipted on the back of this note Fobniary 4th, 1882, received SlOO May 16th, " " 75 . August 28th " " 100 W««»™>^«l. «>Kf>l •• " 80 ^ERCHANTS^ RULE. 139 ^. "What remained due on the following note on May 6tli, 1883 : 4^950.00. Dartmouth, Jan. 3ni, 1881. Two years after date I promise to pay A. R. Tennison or order, nine hundred and fifty dollars, with interest at seven per cent Jas. S. Parmbmte& Payments : Feby. Ist, 1882 $500 Nov, 1 4th, « ,... 100 Jan. 12th, 1883 300 9. "What was due on the following note on August 7th, 1883^ t240.0a KiidTAX, May 4th, 1882. Three months after date I promise to pay A. K. Frost & Co^ "or order, two hundred and forty dollars. Value received. David Rloak. Payments : Sept 10th, 1882 ..$60 !/ Jau. 16th, 1883 90 10. How much was due on the following aote at the time of settlement — Aug. 10th, 1883.- — ^340.75. Antigonish, June 16th, 1882. Three months after date, for value received, I pwmi^ to p»y 3). Graham Whidden, or order, th'-ee hundred and forty dollars •and seventy-five cents with interost at 7 per cent '.FiLLIAM J. PCOH. PajTneirts ; October Uth, 1882 $86 Feh. 12th, 1883 40 May 27th, 1883 90 f 1 1 1 i I 1 ' : ' I COMMISSION AND BROKERAGE. DEFINITIONS. A ComMssion Merchant ia one who sells, usually in his own name, goods intrusted to him for that purpose by ethers. He is sometimes called a factor. A Broker is one who makes contracts in the names of those who employ him, but who does not have possession of the property he buys or sells. Commission merchants and brokers are agents, and the parties for whom they act are the principals. Gommission and Brokerage are the charges made by these agents for transacting business for others. It is usually computed at so much per cent, of the outlay in case of buying, or, of the gross amount of the sales in case of selling. A Gonsig^nment is a quantity of goods sent or consigned by one person to another. The party who sends it is the Consignor, and the party to whom it is sent is the Consignee. The Gross Proceeds of a consignment are the total amount realized by the sale of the goods. The Net Proceeds are what remains of the gross proceeds after all expenses and charges have been deducted. An Account Sales is a detailed statement of the sales, expenso» and charges of a consignment. ACCOUNT SALES. 141 ACCOUNT SALES. Haupax, N. S., April Ist, 1883. Soldjor Account of Ja». Styiith ^ Co. By Frazee ^ Whiston. Mar. Mar. 3 10 18 30 1 30 5 boxes Soap, A. No. 1, 83.00. 10 " " "TlieT}ustIo,"2.75. 736 11)8. Butter, 18c 5 boxes Soap, A. No. 1, 3.00.. . . CHARGES. Freight ex. Rail Express from Depot Commisflien, 8% Net Proceeds. 15 00 27 50 132 48 15 00 8 90 50 9 50 ■ . 189 _ 13 98 90 $17608 An AOMOnt Porohase is a detailed statement of the coat of goods purchased for another, and the expenses and charges attend- ing the purchase ACCOUNT PURCHASE. Toronto, Nov. SOth, 1882, Purchaged hy W. C. Douglas, , For acct. and risk of Frazee Sf Whiston. 100 bbls. " Major," @ 86.50 100 " "Walzen,"@7.25 ■250 " «« "White Swan," @ 5. 80 CHARGES. Cartage Commission @ 1^% on $2833.25. Charge vour Acct 650 725 00 1450 8 42 00 00 2825 00 5075 3875 75 142 COaMrSSrON and BROKERAOff. EXEROI8E8. 1. An agent sold for a manufacturer agricultural implements: for $1875.75 ; what was hia commission at 2^ % f 2. Bought 25 chests of Tea^ averaging 64 lbs, each, @ 37f eents per lb., on commission @ If %; what was my commission t 3. My cMTespondent purchased for me 2768 Ibe. Bacon„@ 12 J cents per lb. ; what was his commission at 3^ % t 4. A salesman sells on a ccanmission of 2 J % ; what must \» his annual sales that he may have a yearly income of $2500 T 5. A lawyer cdlected debts to the amount of |3275 on a com- mission of 5 % ; how much should he pay over to im principal t 6. My Agent in. Toronto, buys for me, on commission, @ 2 J %> 750 bbls. flour @ $5»10 per bbl.; how much do I owe him T 7. A collecting agent collected $2876, and paid over $2807. 38, retaining the difierence as his ccnnmissioD ; what was the rate- > charged T 8. Remitted an agent in Montreal $968, which paid for a pur- chaw of flour, and his commission @ 4 % ; what was the cost of - the flour, and what was his commission f 9. An agent purchased wheat on commissiMi @ 2^ %, and received from his principal in full for the wheat aad his commission $779 ; what did the wheat cost,, and what was the agent's com- mission 7 10. Remitted a commissioQ naerchant at Brantford $3641.40 to. invest in flour, and to pay his commission @ 2 % on the sum invested; how many barrels of flour would he purchase® $4.25 per bbL 1 11. What WDuld be the net proceeds of sales erf mdse. amount- ing in groes to $4825.90, the charges being: for transportation $106.28, for advertising $12.60, for storage $19.20, and for com. mission 2J % T 12. An agent sold 84 sewing machines @ $25.00 each, and his commission was $262.50 ; at what rate was he paid t 13. A book agent sold books for Day A Co., Montreal for $487.60, and received $73.14; what was the rate of his com,- V EXERCISES. 143 14. An English commisnon agent buys for a Halifax house goods to the value of jE576.10s. ; what is his commission in sterling 15. What £ the commission in sterling @ 7^ % on a purchase of £534. 4sL worth of goods Y 16. An English commission agent sold cattle for a Canadian exporting firm to the amount of £1325.188. 9d., and his commis- sion was £66 5& ll^d. ; what was the rate per centt 17. J. Flemming, Hamilton, purchased for me a lot of butter, at 25 cents per lb., his bill for which, together with his commis- , eion, @ 1} %, amounted to $779.52. How many lbs, of butter should I have received, and what was his commission t 18. Graham Bros, purchase for me bacon and hams, for which they pay $1560, and charge 5| %, and the charge for lading is $76.15. How much do I owe them t 19. My agent in Toronto bought for me 276,448 centals of wheat @ $2,245 per cental What was hi" commission at J % 1 20. An auctioneer having sold a lot of fumitnrc on commis- sion @ 3 J %, paid his principal $2393.20. What did his commis- sion amount to 1 21. I remit J. Purdy, New Orleans, $1142.40, instructing him to invest ia cotton, which he does, at 16 cents per lb., retaining his commission on the investment @ 2 %. How many Ibs^ of cotton should I receive t 22. Morrison ^ Thomson have sold for me 1 1 2 bbls. of fish @ $9.50 per bbl., and 85 bbls. flour (5 $12.40, commission at 2^ %. I have instructed them to invest the net proceeds in bacon. They charge IJ % for investing, and pay 13^ cents a pound for the bacon. How many lbs. of bacon should I receive, and what is the total amount of their commission t 23. An accountant being employed to make schedules of the liabilities and assets of a bankrupt, charges 2^ % on the former, and 5| % on the latter. How much does he get altogether, the liabilities being $2786, and the assets $6181 24. A broker received $36 foj^selling bonds @ ^ % brokerage on the par value. What was the4B0(raiue of the bonds sold I 144 STOCKS AND BONDS. 25. A commission merchant sold 255 bales of cotton, averaging 460 lbs. per bale, @ 16.3 cents, on commission @ l\ %, other charges amounting to $242.50. He purchased for his coMignor 720 quintals dried fish @ $2.75 per quintal, and 1500 bbls. pickled fish @ $4.30 per barrel, charging 3 %. How much is still due the consignor J 26. A Montreal merchant shipped a commission merchant in New Orleans 8000 busL wheat and 600 bbls. flour, with instruc- tions to seU and invest the proceeds in sugar. The wheat was sold @ $1.55 per busL, and the flour @ $5.20 per bbl. The freight, cartage, ^c, amounted to $2430, and the commission for selling was @ 2J % for the flour, and 1 cent per bush, for the wheat How many lbs. of sugar could be purchased @ 6Jc. per lb., the commission for the purchase being ©3/1 STOCKS AND BONDS. DEFINITIONS. A Joint Stock Company is an association of individuals with a joint capital contributed by the members of the company, who are empowered by act of parliament to act as one person in the prose- cution of business enterprises. The capital of such a company is called its Capital StOCk, or more generally Stock. It is usually divided into shares, each share representing a specified portion of the capital, and a person sub- scribing this specified sum, or any multiple of it becomes a share- holder or stockholder with one or more shares according to the sum he subscribea A Stock Certificate is a written instrument signed by the proper officers of the Company certifying that the person to whom it id issued is the owner of a certain number of shares of its capital stock. Preferred or Preferential Stock is stock taking preference of the ordinary stock of a Company. Preferred stock is often issued where additional capital which cannot be otherwise raised is necessary to the success or existence of a company ; as when a company becomes embarrassed, and would otherwise lose its property, or is unable to profitably can-y on its business for want DEFINITIONS. 145 ^ of sufficient capital. A stipulated dividend must be paid to the holders of preferred stock, before the holders of ordinary stock are entitled to anything. The par valae of a share is the sum which each share originally represented, and is often $100 for the sake of convenience, but may be any sum the projectors of the company choose to make it. A Dividend is the whole or part of the profits of a company during a given time which are divided among, and paid to, the shareholders. The stock of a company is desirable or otherwise according as the dividends are large or small, or none. When the dividends are large the stock is in demand, and the price rises above the par, or original value, and is then said to be at a premium. Wlien there are no dividends, or when they are very small, the stock is not sought after, while those who hold it are likely to want to selL Then the price falls below th« par value, and is said to be at a discount. The rates of premium or discount are expressed by percentage of the par value. Thus when $110 can be got for a share which was originally $100, the stock is at a premium of 10% and is so expressed, or it is spoken of as being at 110. And when a similar share is sold for $90 it is at a discount of 10%, or is said to be at 90. In like manner when a share, the par value of which is $20, sells for $21, it is at 5% premium, or 105, and when a similar share sells for $16 it is at 20% discount, or bu. A Bond is the obligation of a nation, province, city, town or company, to pay a sum of money ft a specified time with interest at a stipulated rate, usually payable half-yearly. Bonds have the force of promissory notes against the government or corporation issuing them. The bonds of governments and municipal corporations are often called debentures. Those of business corporations are frequently secured by mortgage of the whole or some portion of the com- pany's property, and are thence called mortgage bonds. They are j>^fr»y» •» Vipi-*^™ sr:;^ ca'fiir ^ri'i-^sf— .-. -.■;-.'f iV. .-■;-. i\, ^i.^»1- ^S il, oompany \ t 4f i m : '4. i! STOCKS AND BONDS. Coapon Bonds are bonds wiUi coupons attached for the regular payment of interest during the life of the bonds. As the pay- ments of interest are made the coupons are detached and returned to the party who issued the bonds. The income derived from bonds is called " interest," because it is received for the use of money loaned ; while that derived from an investment in stock is known as " dividend," because it is a division of the profits of the company. Stocks are usually sold "flat," that is, all future dividends accrue to the buyer, and are included in the quoted price of the ■tock ; but the buyer of bonds bearing a fixed interest usually pays to the selltr the accrued unpaid interest in addition to the price at the rate agreed upon. In large centres where regular stock exchanges are established ttocks are bought and sold either " cash," that is, deliverable on the day sold ; " regular," that is, to be delivered and paid for the next day ; " seller three," which gives the seller the option of de- livery any time within three days, or " buyer three," which gives the buyer the option to demand delivery of the stock at any time ■within three daya Sometimes the option is for more than three days, in which case interest is paid by the buyer to the seller, and one day's notice is required to terminate the option. Should a stock pay a dividend during the pendency of a contraet the dividend belongs to the purchaser of the stock, unless other wise previously agreed. A Margin is a deposit made with a broker by a person who em- ploys him to buy or sell stock for speculation to enable the broker " to carry " the stock, and preset himself against loss should the price of the stock decline. It is usually 10 % of the par value of the stock. The commission for buying and selling stocks and bonds is reckoned by per centage of the par value, or market value, according to the custom of the place where the business is done. In New York and probably in other places where stock boards are established it is on the par value, and | % is the customary rate, except for mining stocks, which have special mtefi In Halifax the 'iommis- •ioQ is from ^ % to J % on the market value. 1 i STOCK QUOTATIONS. 147 List of the principal lo< ' stocks as quoted by J. C, Mackintosh, Banker and Broker, 166 HoUis Street, Halifax, N. S. : Averaffe prieea of Stock, ^e., on Thursday, 10th May, 1883. t 20 00 100 00 843 33 50 00 80 00 100 00 40 00 40 00 800 00 100 00 50 00 40 00 106 00 50 00 5* 00 lUO 00 SO 00 90 00 S 00 S5 00 ^100 £500 $600 00 lOOO 00 SOOO 00 100 00 5*0 00 S 40 00 100 00 100 00 25 00 40 00 50 00 iCu 00 100 00 Halifax Banking Company Bank of Nova Scotia Bank of B. N. America Union Bank of Ilalifax People* Bank of Halifax Merchanto' Bank of Halifax Commercial Bank, Windier Pictoa Bank Bank of Montreal Merchants' Bank of Canada. Canadian Bank of Commerce Ontorio " " Bank of New firnniwick Molion'i Bank La Banqne da People Bank of Toronto IXSUKAHCX COMPAMiaS. Halifax Fire Insnrance Company yicadia Fire Insurance Company (old) do. do. (newl Merchants' Marine Insnrance Oo. of n^lif sx, DCBBHTUBSa. ) Sterling Prorincial Debentures ) 1885 } City Debentnres ( 5 per cent > School do ) Dartmouth do Montreal City Bonds Toronto do St. John do Cbarlottetown de MlBCBLLXVEOUS. Halifax Gas Light Company Montreal Gas Light Company Starr Mannfacturing Company Do. Preferential Chebucto Marine Railway Company Montreal Telegraph Company Dominion Telegraph Company NoTa Scotia Sugar Refinery do. do. Cotton Company., ........... « 6 6 7 8 « 10 7 8 6 8 8 6 8 10 15 15 loe 150^ 114 115 no 189 135 110 203 126 1361 1154 140 126 81 140 180 138 131 75 102 102 1121 108 140 173i 105 112 1231 87i| II " ii I07i 149 118 lis 109i 128i 1381 106 808i 185 136 115 13* 125 80 138 1174 188 187 M 108^ 101 111 lOi 117 IIT 111 104 1371 173 100 109 107 1881 881 "i -.'^^ J. ;■! 148 STOCKS AND BONDS. EXER0I8E8. Find the market prices of the following at the rates given :— No. or Bkari STOCK. QuoTATioaa. 1 5 a 10 3 15 4 la 5 25 6 100 7 17 8 80 9 8 10 SO 11 24 19 18 IS 100 14 31 15 20 I« 80 17 40 18 12 19 15 SO ts Halifax Baokino; Co Peoples Bank or Halifax' Union Bank of Halifax Merchants' Bank of Halifax... Bank of Nova Scotia Commercial Bank of Windsor. Ontario Bank Bank of B. N. A ','.'.[ Picton Bank La Banqae dn Peaple Bank of Toronto Bank of New Brnnswick M«rchant8' Bank of Canada.... Bank of Montreal Halifax f'm> lasaranre Co Halifax Gas Lijtht Co Starr Maanfactoring Co Chebacto Marine Railway Co.., Nova Scotia Sugar Refinerj. . . , Nova Scotia Cotton Co 108 no 115 1281 150 1071 80 139 I38( 125} 2021 117* 137t 100 > 107 82 80 21. What will be the cost of 7 shares Bank of N. S. stock @ 143^, and brokerage @ J% on the market value ? 22. What will be the cost of 18 shares People's Bank stock @ 111 J, and brokerage @ J% on market value? 23. What will the sale of 25 shares Merchants' Bank stock realize if sold @ 127^ by a broker charging f% on the market valne? 24. Sold through a broker 40 shares Bank of Montreal stock Jf® 201 1, brokerage on market value @ ^ %. How much was realized? 25. Bought 5 shares Bank of N. S. stock (g 151 J, and sold the same @ 147^. How much did I lose 1 26. Bought 10 shares Bank of Montreal stock @ 201J, and sold them at 195^. How much did I lose ? 27. Bought 25 shares Union Bank stocks 1151. and anld them @ 121f. How much did I gain J EXERCISES. ^ <^ 28. A broker purchaaed for Mr. A 50 sbaree Peoples Bank J^- stock @ 110 J, and sold them at 117|, charging J% commission on ([y ' ^ ^he market value, each transactioa What was A's gain t ^ y 29. Bought through a broker 16 shares Bank of B. N. A. stock ' J*" @ 103 J, and sold the same @ 104|, brokerage on market value @ vO i^ ^^^ transaction. What did I gain or lose t 30. A bank with a capital of $800000 declares a dividend of 3%. What is the amount of the dividend, and what does a stock- ^ holder receive who owns S5 shares of $50 each T 31. An Insurance Company divides among its shareholders $21000. What is the rate of the dividend, the capital stock being $600000, and how much is paid to Mr. A. who owns 26 shares o£ $40 each 1 32. A manufacturing company declared a dividend of 4%, and it amounted to $3000. What was the capital stock 1 33. A gas company declared a half-yearly dividend of 3J%, and it amounted to $10500. How many shares of $40 each in the capital stock t 34. The profits of a half-year's business of a bonk amounted* to $16485.26. What was the surplus after a dividend of 2J% on a capital stock of $600000 vas provided for t 35. How many shares or the N. S. Sugar Eefijxeiy stock eaa be purchased for $1 764 @ 84 ? ,^ 36. How many shares of the Halifax Banking Ca's stock can be purchased for $1510.50 @ 108^1 37. What is the par value of stock which cost $7286.25, including brokerage on the market value @ J %, when purchased @145? 38. What is the par value of stock which cost $7275, including brokerage on the par value @ J %, when purchased @ 145 ] ,. ^ j(f^' 39- How many shares of the Chabucto Marine Railway Co.'s "^P^tock can be purchased for $2346.01, including J % commisaion on ttJ^ tlie market value, @ 110^ t 40. How many shares of R R stock, (par value $100), can be . purchased for $81 12.50, including brokerage ® ^ % on the par value, @81l 150 STOCKS AND B0KD8. 41. What income will be derired from an investment of ♦6125in6%bonda@ 102^1 42. If the stock of a certain bank can be purchased @ 137 J, wid you make a investment at that rate through a broker who charges ^ % on the market value, what will be your income from an expenditure of $9649.06, providek ."i ' transaction, and how much money being worth 6 % ] 65. On the 14th of March 1883, a broker purchased for me ^ shares Erie R R. stock @ 71 ; 50 shares C. & R. I. R R stock f , @ 95 J ; 200 shares N. Y. C. R R stock at 103^, and a seven- ^ . '" thirty bond for $6000, (interest @ 7^ 7^ payable Ist June and \P * December.) at 1061. They were sold out on ADnl-12th 684-j 97i, lOSJ and 106J respectively. What was the brokerage at \ 7, y /■> v^ (£■ / STOCKS AND BONDS. on the par value for buying and \ % for selling, and what was my gain or loss by the transaction ? 66. I have received from a correspondent f4781.25 with instructions to invest the same in five-twenties® 105 J first deduct- ing my commission @ | % on the par value. What is the broker- age, and ft'hat amount of fivo-twonties can I purchase? 67. On the 20th Feb'y 1883 a broker purchased for me 100 ^^ shares of the Bank of N. S. stock @ 151^, 80 shares Peoples Bank ^.j stock® lllf, 120 shares Merchants' Marino Ins. Co.'s stock @ ' \^ o ^^'^ °^*^ debentures to the face value of $6000, (interest at ^ ' 5 % payable half-yearly, March 1st and Sept 1st,) @ 102. They > were sold out at my order on May 17 @ 153, 109^, 65 and 102J respectively. What was the brokerage @ J 7, on the market value each transaction, and what wis my gain or loss on the transaction? , 68. In a certain company only 40 % of the subscribed capital IS paid up when a cash dividend of 3^ % on the subscribed capital 13 declared. WTiat rate per cent, does an original subscriber receive on his investment ? 69. The stockholders of a certain bank have paid in but "5 "/ i «tinn'' '"^"''••'P^'"^^' «nd A ;. a subscriber to the extent of -^ 7^^ o f" ''^^ dividend of 4 % on the paid-up capital is declared, ' and 10 /„ of the paid-up capital is carried to the credit of the stockholders. How much is A's. cash dividend, what per cent of subscribed capital is carried to credit of stockholders, and how much has A. stUl to pay on his stock ? )^, 70. An investor purchased railroad bonds @ 40 % below par and thus realized 10 % on the price of the bonds when the annual interest on same was paid. He purchased also State securities beanng the same rate of inteiest 20 % below par, and received annually on the latter $2400. What did he pay for the State securities. -AaHt-^f! r\ INSURANCE Insnrance is a contract by which one party, called the Insurer or Underwriter, engages for a stipulated consideration, called the Premium, to indemnify another party called the Insured, against loss to which he or his family may be liable. Insurance is effected on property against loss or damage by fire, water, Ac, and on lives of persons, against sickness, accident aid death. It receives different names, according -i the kind of loss covered, as Marine, Fire, Life, Accident, &o. Guarantee ii another kind of insurance recently adopted, by which the insurer g^uarantees the honesty of eaipluyes in places of trust. Insurance is usually carried on by companies or corporations, each company confining itself usually to one particular kind of insurance, although some of the larger companies combine two or more kinds. Insurance companies may be classed as, 1. Stock ; 2. Mutual ; 3. Mixed. A Stock Insnrance Company is one in which the capital is owned by individuals called stockholders, who alone share the profits and assume to bear tbe losses that may be sustained. A Matnal Inaorano- Jompany is one in which there are no stockholders, and the piofits or losses of which are shared ariong those who are insured. A Mixed Insurance Company is one conducted upon a combin. ation of the stock and mutual plans. The Policy is the written contract between the insurer or underwriter and the insured. In marine insurance, in case of loss or damage, th<» insurer pays only such proportion of the loss as the amount of the insurance bears to the total value of the property ; but in ordinary fire insurance the total losa is made up if it does not exceed the amount of the insurance. 154 INSURANCE. III. The Preminm ia the amount paid for insurance. Premium rates are expressed as so much per cent, of the amount insured, or, where the rate is less than one per cent, it is often expressed as so many cents per hundred dollars ; thus, " 75 cents " means 75 cents on $100, or | of 1 per cent. Life insurance premiums are determired by a scale which each company adopts for its own business, showing the premium on 81000 at the various annual stages of human life. The scales are all formed, with more or less modification to suit the financial policy of the various companies, upon statistics from which the average expectation of life at any age is deduced. EXERCISES. 1. Find the premium on an insurance of $1280 @ 5J %. 2. A ship and cargo are insured for $58,000 @ 2^ % ; what ia the premium ? 3. A ship is insured for $35,000 @ 1 J %, and her cargo for $55,000 @ 2 J % ; what is the whole premium t 4. A house is insured for $3500 @ 75 cents per $100 ; what is the premium 1 , 5. A house is insured for $4000 @ 90 cents; what is the premium 1 6. What is the total premium of the following insurances : $5000 @ 1| %, $7000 @ 45 cents, $1500 @ 76 cents, $2000 @ 4^ %, $3500 @ 45 cents, $2000 @ 70 cents, $4000 @ U %, $2000 @ 60 cents, $4500 @ 25 cents> $3600 @ IJ %, and $3000 @ 2f % 1 7. A village store was insured for 6 years for $1200 ; the rate for the first year was 3^ %, with a reduction of J each succeeding year. The stock was insured for $1600 each of the six years @ 2^ %. How much did the owner pay for insurance during the six years ? 8. $40 was paid for an insurance of $2500; what was the rate of premium 1 9. $26.20 was paid for an insurance of $3600; what was the rate I i K E^KERCISES. 155 ^^ 10. A Uiilding was insured for $3000 @ 1^ % for 5 years, from June Ist, 1881 ; what was the value of the unearned premium on June Ist, 1883? • 11. A shipment of goods, valued at $5000, was insured for $4000. If the goods were lost, how much of the Joss would be paid by the insurance company ? 12. A factory (worth $3000) and its contents are insured for $10,000 @ 2| % as follows : $2000 on building, $3000 on machi- nery (worth $6000), and $5000 on stock (worth $8000). The building is damaged by fire to the extent of $1000, the machinery, $4000, and the stock is a total loss. How much is the claim against the underwriters, and hotv much does the owner lose, including tlie premium ? 13. If it cost $22.50 to insure a house for $5000, wiat was the rate ? 14. If it cost $56.87^ for an insurance on merchaiidise ®l°/, what was the amount of the policy ? 15. A building is inwired for $30,000, and is damaged by fire to the extent of $12,000; what per cent of its risk is paid by the insurance company ? 16. Effected insurance on a cargo from Liverpool worth ^1872 lis. 5i. at 1 J %. What is the premium ? 17. What will be the premium of insurance on a cargo from Havre, value 32450 francs, @ 1 7^ the franc being worth 19.3 cento? PROFIT AND LOSS. Profit and Loss treats of the actual gains and losses, and of the gain and loss per cent, arising from business transactions. Gaia or loss per cent, is always estimated on the cort price which therefore is always to be considered as the base. The actual gain or loss, which is the difference between the cd price and selling price, is the percentage reckoned on the base or cost. The selling price, wben a gain is made, is the sum of the cost (base) and the gain (percentage) and ia therefore the amount. When a loss is sustained the selling price is the net. EXEROI8E8. 1. If 224 lbs. of tea be bought @ 60 cents per lb., and sold @ 95 cents per lb., how much is gained t 2. A grocer bought 24 bbls. flour @ $5.80 per bbl., and sold 12 bbls. 01 it@ $6.10, 9 bbls. @ $6.20, and the remainder® $6.25 ; how much did he gain 1 3. A Lian bought 216 yards flannel for $86.40, aL 1 sold it @ 37 Jc. per yard ; how much did he lose 1 4. A dealer bought 78 busk potatoes @ 62J cents, and sold them @ 87 J cents ; how much did he gain 1 5. If I buy a horse for $225, and sell it at a gain of 16 % ; what will be my profit t 6. Bought a building lot for $450, and sold it at a loss of 20 % ; how much did I lose 1 7. Cloth is bought @ $3 per yard and sold @ 30 % advance; what is the selling price 1 8. A farm cost me $5''00; what must I get for it to gain 22 J % 1 9. Flour cost 7 per bbl., and was sold @ a loss of 10 %; what was the selling price ? EXERCISES. 157 10. If hats cost $21 per dozen, what is the retail price to gain 33J%1 11. If rubber coats cost at the manufacturer's $96 per dozen, and if the cost of importation is 40 %, what must be the selling price to gain 20 % ? 12. A merchant purchased goods to the amount of |6280, and sold them for $7222 ; what was the gain per cent, t 13. A quantity of goods was bought for $318.50, and sold for $299.39 ; what M'as the loss per cent t 14. A grocer bought butter @ 24 cents and sold it @ 30 cents; what was his gain per cent. ? 15. Bought 125 bbls. flour for $600, and sold it @ $5.52 per bbl. ; what was my gain per cent 1 16. A tobacconist bought a quantity of tobacco for $75, which brought him only $60 ; what per cent did he lose 1 17. A cattle dealer bought 20 cows at an average price of $20 per head, and paid 50 cents for the freight of each per railroad ; what pQj cent, did he gain by selling them @ $25.62 j per head 1 18. A man paid $1015 for merchandise, and sold it for $875 ; what per cent, did he lose ? 19. Find the rate per cent, of profit on goods bought for $432 and sold for $486. 20. If the Dr. side-^f your merchandise acct amount to $42,460, and the Cr. side to $40,960.50, and the cost price of the goods remaining unsold be $7600, what gain per cent does the account show 1 21. The Dr. side of a merchandise acct is $145,250, the Cr. side $131,763.75, and the inventory $16700; what is the gain per cent f 22. If flaxseed is sold @ $17.40 per bushel, and 13 % lost, what was the cost price 1 $17.40 is the net @ 13 %. To find the coat price (base) divide tlie given net by the net of 1, that is $17.40 -r .87 = $20, Ang. 23. How much was paid for a horse which was sold for $108 158 PROFIT AND LOSS. t i! m ^ 24. A dealer sold 116 hogs for 8725, and thereby gain 25 % ; what waa the coat each to him, on an kverage ? 26. If 13 sheep were sold for 850.70 and 20 % gained, what was the first cost per head 1 26. If 16f % be lost by the sale of linen @ $1.25 per yard, what waa the first cost T 27. A man ?oId goods @ 12J % profit >»nd made $76 ; what was the cost of the goods 7 28. If a man buy a house, and lose 37 J % by selling it for $810 less than it cost him, how much did he get for it t 29. If a grocer sells wine @ 90 cents per bottle, and thereby gains 20 %, what per cent, would he gain by selling it @ $1 per bottle t 30. If a hatter sells hats @ $1.25 and loses 23 %, what would be the result of selling @ $1.60 each 1 31. If cloth is sold @ $1.25 per yard and 15 % lost, what would be the result of selling @ $ 65 pex yard ? 32. If I sell cloth @ $5 per yard and gain 25 %, what will be my rate of gain if I sell @ $5.30 per yard T 33. If cloth be sold @ $5 per yard at a loss of 25%, what win be the result of selling @ $6.40 per yard? 34. A milliner sold bonnets® $1.25 and lost 25% ; would she have gained or loat, and how much per cent, if she had sold @$1.40t 35. A grocer sold tea @ 45 cents per ft., and gained 12J % ; what would he have gained per cent, if he had sold the tea @ 54 cents per ft. ? 36. A farmer sold com @ 65 cents per bushel, and gained 6 "i^ ; what per cent, would he have gained if he had aold the com @ 70 cents per bushel 1 37. li I^ny a lot of wheat @ $1.15 per bushel, what must I get per bushel for it so as to gain 15 % ? 38. A man bought a horse for $150 and a chaise for $250, and sold the chaise for $350 and the horse for $100] what was his "9.1 n nf^r f.p.Ti'h ? EXERCISES. 159 39. In one year the principal and interest of a certain note amounted to $810 @ 8 % ; what was the face of the note ? 40. A carpenter built a house for $990 which was 10 % less than it was worth ; how much should he havi' received for it so as to have made 40 % profit 1 41. A broker bought stocks @ $96 per share, and sold them @ $102 per share ; what was his gain per cent. 1 42. A merchant sold sugar @ 6J cents a B)., which was 10 % less than it cost him ; what was tlie cost price 1 43. A merchant sold broadcloth @ $4.75 per yard, and gained 12^ %; what would he have gained per cent, if he had sold it@ $5.25 per yard? 44. A watch which cost me $30, cash, I sold for $35 on a j_ credit of 8 months ; what did I gain^ allowing true discount @6%? 45. Sold a horse at a gain of 33 J % and with the proceeds purchased another horse which I sold for $120 @ a loss of 20 % ; what was the gain or loss 1 46. If books are bought at 30 % discount from the list price, what is the gain % by selling at the list price 1 47. What per cent, is gained by selling tin paB»,@ 21 cente, that cost $2.56 per dozen less 20 and 12^ %? ^.- 1 48. Bought a lot of broadcloth @ $5 per yard ; what must be i-s ^,\^\ '•'■'' my asking price so that I may fall 10 % and still make 10 % on Uv y.y the cost ? 49. A gentleman sold two horses at $240 each. On one he gained 60 per cent., and on the other he lost 60 per cent. Did he gain or lose by the operation, and how much 1 ^^ 50. What must I ask per yard for cloth that cost me $3.52 per yard, so that I may fall 8 %, and still make 1 5 %, allowing 12 % of sales to be in bad debts 1 51. A merchant's retail price for boots is $4.75 per pair, by which he makes a profit of 33^- %. He sells to a wholesale cus- j tomer at a discount of 20 % from the retail price. What per cent. V of Jiis wholesales does he gain or lose ? ' 52. If an article is bought at|jif list price, 10 and 5 off, and sold at the list price 5 oil, what is the gain per cent. i« . ji 160 BANKRUPTCY OR INSOLVENCY. 53. A merchant purchased goods to the amount of $7200, sold in 40 days to the amount of $4900, had then on hand gcjoda which cost $3000. Find the total gain and the gain per cent., the average daily sales, and the average daily profita 54. Sold merchandise at 30 % advance on cost, and then deducted 20 % from the face of the invoice. Required the net per cent of gain. 65. Bought Bank of Montreal stock @ 180, and sold it @ 190 ; what was my gain per cent. 1 56. Bought Union Bank stock @ 118J, and sold it @ 115; what was my loss per cent. 1 BANKRUPTCY OR INSOLVENCY. If M| Bankruptcy or Insolvency is that condition of a business man's aflFairs in which his property is not sufficient to meet his liabilities. A Bankrupt is one whose affairs are in a state of bankruptcy. A Debtor is one who owes the bankrupt. A Creditor is one to whom the bankrupt is indebted. The Assets of a bankrupt are his entire property including the debts owing to him. The Liabilities of a bankrupt are the debts which ho owes. An Assig*''iient is a formal surrender of his property by a bankrupt for the benefit of a part or the whole of his creditors. An Assignee is one to whom the property of a bankrupt is assigned. A Preferred Creditor is one whom a bankrupt in his deed of assignment directs to be paid in full before any provision is made for the other creditors. Canada is at present without a bankrupt law, so that preferred creditors, and frequent injustice are common in. the settlement of insolvent estates which were not foimerly permitted, and which a grood bankrupt law should and would prevent. It is to be hoped that this state of affairs will not be permitted much longer to exist. The rate per cent of liabilities which an estate can pay is cttlieu liie Dividend. To find the dividend, and thence the share EXERCISES. 161 of each creditor — the available assets and liabilities being given is the only problem with which we have to deal RuLK. — Divide the net assets by the number denoting the lia- bilities; the quotient will show the rate per cent., or dividend. Then find the percentage of the several liabilities at this rate fen- the sum to be paid the several creditors. EXERCISES. 1. A bankrupt owes A 8400, B, f350, and C, $600; his net assets amount to $810. What is the dividend, and how much should each creditor receive 1 2. A becomes bankrupt. He owes B |800 ; C, $500 ; D, $1100, and E, $600. The net assets are $1110. How much can the estate pay on the dollar, and how much does each creditor receive ? 3. A house becomes bankrupt with liabilities $17,940, and assets $8970. The expenses are 5 % of the assets. What is the rate of dividend, arid what is the share of the chief creditor whose claim is $1282? 4. A shipbuilder becomes bankrupt with liabilities $303,000. The premises, building and stock are worth $220,000, and he ^ has in cash and notes $12,842. The creditors allow him $3000 for maintenance of his family, and the costs are 3J % of the remainder of the assets. What is the dividend, and how much does a creditor get whose claim is $1360.60? 5. A Halifax house failed, owing in London $22,000, in Glasgow $18,000, in New York $17,100, in Montreal $16,000, in Toronto $4400, and in Halifax $4200. Their assets were real estate $7200, cash $4400, railway stock $4200, merchandise $9000, and good debts $20,135. The expenses were 4 % of the assets. What was the dividend, and how much went to each city? 6. A merchant went into bankruptcy owing A $1080, B, $850, C, $1720, D, $1580, E, $970. The assets were house and store which realized $848, merchandise in stock which brought $420, sundry debts collected $220. ITie expensfl« were 12i "/. What did the estate pay, and what was the share of each creditor ? S EXCHANGE. Exchange is the system by which merchants living in different countries, or in different parte of the same country, discharge their liabilities to each other without the transmission of money. Suppose, for example : A, of Halifax, owesB, of Toronto, $1000, and at the same time C, of Toronto owes I), of Halifax a like sum. Instead of A sending $1000 to B, and C sending the same sum to D, A will purchase of D his order or draft on C, and send it to B, who will collect the money of C in Toronto. Thus D will get his money from A, his neighbor in Halifax, and B will get his from his neighbor, C, in Toronto. Now, of course, it does not always or often happen, that one debt can be set oflF against another in this way. The business of exchange is mostly carried on through the medium of the banks and exchange brokers who make it their business to buy and sell these drafts in sums to suit. Thus, if A, of Halifax, who owes B, of Toronto, wishes to pay B, he goes to a bank or broker who will sell him a draft on some one in Toronto. This draft A forwards to B, who collects the money in Toronto ; or B, of Toronto may draw a draft on A, of Halifax, and sell it to a bank or broker there, and receive his money, and A will pay the draft when presented to him in Halifax. The price of these drafts, or, as it is usually called, the price of exchange, varies according to the state of trade between the two places, but it is never very far removed, where the currency of the two places is the same, from the face or par value. To take the two places above mentioned, when Halifax buys much more largely from Toronio than Toronto from Halifax, exchange on Toronto will be high in Halifax, and exchange on Halifax will be low in Toronto. On the other hand wlien Toronto buys much more largely from Halifax than Halifax from Toronto the price of exchange will be exactly opposite. DOMESTIC EXCHANGE. 163 When exchange can be bought dollar for dollar it is said to be at par. Wlion a dollar of exchange can be bought for less than a dollar it is at a discount. When a dollar of exchange costs more than a dollar it is at a premium. The rate of discount or premium is expressed in percentage of one dollar. DOMESTIC EXCHANGE. Domestic Exchange is that between diflerent parts of the same country. Although a bill drawn in Canada and payable in the United States, or one drawn in the United States and payable in Canada is a foreign bill, yet as the monetary denominationi of the two countries and their values are the same, bills between Canada and the United States are treated arithmetically as domestic or inland bills. To find the cost or market value of a draft at a given rate of premium or discount EvLE.~Add the percentage at the rjiven rate of premium to, or subtract the percentage at tJie given rate of discount from, the face of the draft; the mm, or difference will be the market value. 1. 2. 3. 4. EXERCISES. Find the market values of the following drafts : 83000 @ J percent, prem. 9. $ 725.60 @ If perct. prem. disct $4600 @ ^ $5600 @ I $8425 @ I 5. $1875.50 @ I 6. $7629.80 @ I 7. $ 948.30 @ f 8. $5824.90® I CI (< il (( (I (( l( << II 10. $5243.40® J 11. $2785.10® J 12. $1280 @ I 13. $4782.12® 3J 14. $3900 @ ^ 15. $3794.75® f 16. $2500 @ I i< i( CI 17. "WTiat will be the cost of a bill on Montreal for $2864.25 @ i % premium ? 18. A merchant in New York owing me $3750 payable there, I drew on him for that amount, and sold the bill S- JL °/ discount; what did I get for it? 164 KXCHANOB. To find the face of a bill which will cost, or sell for, a given sum. at a given rate of premiam or diaooont. RuLB. — Divide the given market price hij the cott or gelling price of $1 of tke draft. The quotient will be the face of the bill required, EXERCISES. Find how large a bill can be had for 19. 14000 @ 2 per ct. prem. 22. $8706.18 @ ^ per ct. disct. 20. 13638.10® J " " 23. $2735.22 @ § « prem. 21. tl8U.88 @l " diact. 24. | 869.99 @ f " disct. The same result to the nearest cent may be obtained as follows : ExAKPL* 1. How large a draft can be had for $100,000 @ 5 % piamium t flOOOOO — ^^Q = 5 % of the given sum. $95000 + 250 = 5 % of $5000. $95250 — 12.50 = 5 % of $250. 95237.60 + .62 5 = 5 % of $12.50. 95238.125 — .0 31 = 5 % of $.625 95238.094 = Face of draft required. EzAMPLB 2. — How large a draft can be had for. %4285 @ ^ °/ discount 1 OPBKATIOa. $4285 =: cost or market value given. + 21.425 = J % of the given sum. + .107 = ^ % of $21,425. $4306.53 == Face of draft required. Of course where the given inm or rate or both are very large, the rate may be required to be applied several time^ In any case the operation vnnaf Kn /irkn4^niiA/1 ii rtfil fkf. 1a»4- »._.._x * f • • /. . u ,„r. 11^.,. j,-^:.._ii-.sjjcisiii=:ij:iiscu.r.; is T;Uue. /rt^miiV.i- ^-if^fm^^^^^^if^^^^^. 'm. FOREIGN EXCHANGE. 166 28. What will a drut on Toronto for |1 878.60 coat @ | % premium t 26. Bought goods of A, at Montreal to the amount of $2796 ; for what smn should I accept his draft, exchange on Halifax in Montreal being \ % premium t 27. A commimiou merchant has $963.78, net proceeds of a consignment sold for T. H. & Co., Chicago. What is the face of the draft he should remit them — Exchange on Chicago being J % discoiuit 1 28. I have in my posflassion the net proceeds of a sale of cotton amounting to $3765 which my correspondent desires me to i-eroit him by a draft on New Orleans. Exchange on New Orleans is at a discount of 2^ %, and I invest the whole in a draft at that rate. What is the face of the draft t 29. . T. N. C. of Winnipeg owing J. B. P. of Halifax $8432.80 payable in Halifax remits him a check on a Winnipeg bank, to cash which J. R P. is obliged to allow a discount of ^ %. How much is the payment short, and what should have been the face of the draft 1 FOREIGN EXCHANGE. Foreign Ezohuig^ is exchange between different countries. Foreign bills of exchange Me usually drawn at sif^t (3 days) or at sixty (63) days' sig^t, and in the ourrenc}' of the country in which they are payable. Sight bills are sometime* spoken of as " short" exohange, and sixty days' bills as " long" exchange. Foreign bills are usually drawn in sets of two or three, of the same tenor and date. The separate bills are sent by difFerent mails, and when one has been paid or accepted the others are void. For sample of a set of sterling exchange see page 128. A Letter of Credit is an instrument issued by a bank or banker, and addressed to another, or other banks or bankers requesting the payment to the holdsr on demand of such sums as he may require, — the total amount not to exceed a sum mentioned in the letter. The Bate of Ezckange between two countries is the market value in one of drafts on the other. It is regulated partly by the course of trade between the two countries, and partly by the cost of transporting gold. K^axLvl 166 FOREIGN EXCHANOB. Tno Oommerclal Par of Exchange is the market value in one country of the coins of another. The Intrinsic Par of Exchange is the real value of the taonetary unit of one country expressed in that of another It 18 ascertained by a comparison of the fineness and weignt of ^he coins of the two countries* The Old Par Value of the pound sterling, and the base of the quotations of sterling exchange in Canada, is $4.44J. This value was fixec' many years ago when the dollar represented a greater comparative value than at present The rate of exchange is still expressed by percentage of this old par value. The commercial par of exchange between Canada and Great Britain is 9i 7 higher than the old par value, making the pound equal to $4.86f° The rate of exchange with other countries is generally given by eq,nvalents Thus, quotations of French exchange is by gmng the number of francs and centimes which make a dollar or by giving the equivalent of a franc in cents. In >he Fnited Spates the quotation of sterling exchange by percentage of the olu par value has been discontinued, and there the quotations are now expressed by giving the value of £1 in dollars and cents. Documentary Exchange is a bill drawn by a shipper on his consi^mee against merchandise shipped, accompanied by the bill ot Icding and the insurance certificates covering the property against which the bill is drawn. f i y To find the value of £1 steriing at any rate of exchange. RcLE.-ro the old par value ($4.44J) add the percentage at tlie given rate of premium. Since 1 % of $4.44| is 4| cents, when the value at any rate is known, for a higher mte add, and for a lower rate subLct, as lows : for 1 % 4 J cents, for ^ % 2^ cents, for i % ^ cents, l\^°fl Vr''-'" ^ ^ '^ ^^"^^ ^''^ '^^ it i« W t<^ construct the following " ' TABLE OP VALUES. 167 Tablb of Valcks of £l^£TERLmO. At the old par rate, $4.44f At 9^ per cent. prem. S4.85f " 1 per cent prem. 4.48| II 9| II II 4.86J " 2 (( II 4.53J M 9i it u 4.86f " 3 CI II 4.57J II H 11 II 4.87J « 4 II II 4.62f II n 11 II 4.87i " 5 II 11 4.66f II H II II 4.88J " 6 II II 4.7H II 10 11 II 4.88| " 7 It II 4.75^ II m II II 4.89J " 8 « II 4.80 II m II II 4.90 "8i II II 4.80ft II m II II 4.91^ " 8^ l< II 4.81i II m II II 4.92| "8f ■1 II 4.81f i: 11 II II 4.93| " 8^ II II 4.82f II Hi II CI 4.94| " 8f 11 II 4.82J II lU II IC 4.95f " 8| iW FOREIGN EXCHANGE. To redace Dominion oorrency to sterling, Bulb. — Divide the given amount of Dominion currency by th* vdltie of £1 ai the given rate. Example. — What is the face of a sterling bill which can be bought for $61.44 @ 109^1 4.86§)61.44(£12 12». 6d. Ans. 37. What amount of sterling money @ 9J % prem. can be bought for $1000 1 38. What is the value of £50 sterling @ 110 1 39. At 12 7o premium what will a draft on Liverpool for £1800 cost? 40. A merchant sold a bill of exchange cm London for £7000 @ 11 % premium. What did he receive for it mora than its commercial par value t 41. What must I pay for a bill on London for £1266 15«. @ 109Jt 42. How much sterling exchange @ 108 J^ can I buy for $822 1 43. Bought £168 15«. sterling exchange for $817.50. What as the ratel 44. If a bill of exchange for £427 12». cost $2073.86, what is the rate t 45. What must be paid for a draft on Paris for 15750 francs, exchange being 5.19 (5 francs, 19 centimes per dollar) 1 46. What will a French bill for 31895.50 francs cost when exchange is quoted @ IS-jS^ (18^ cents per franc) 1 47. When $1566.20 is paid for a draft for 8200 francs, what is the rate of exchange by the method of quotation used in Ex. No. 46 ? 48. A draft on Havre for 7419.50 francs was bought for $1420; what was the rate of exchange, by the method of quotation employed in Ex. No. 45 1 49. Paid for a draft on Paris and brokerage @ J % $3460.32; what was the face of the draft, exchange being 5.19§t EXERCISES. 171 50. Bought through a broker exchange on Geneva for 8000 francs ; what did it cost me, exchange 5.20f and brokerage ^ % t 61. A merchant, having a biU of exchange for 18000 franca to sell, sent a cJerk to two bankers to sell to the best advantage. The first applied to offered to buy the biU .§ 5.25, the second @ O.^Si. The clerk took the latter offer. How much did the merchant lose by his clerk's ignorance! 62. A merchant in Halifax owes 12000 francs in Paris- how touch wiU a sterling bill to setJe the account cost him, exchange on London m Paris being 2' .20 francs per pound, and sterlin- billsm Halifax 109^? 63. A merchant in Halifax wishes to purchase for i^mittance to Haii>bui:g a biU „f exchange for £358 Us. 9d. Sterling -exchange m Halifax is (S 109^, in New York i.85i. His c«^ respondent in New York will reinvest and remit for him at V/ commission, and drafts on New York ar, at ^ % premium. How , . much will he lose or gain by remitting via New York J y JV 64. A broker sold for a merchant on commission a bUl of A V exchange for £2000. He was to receive ,V % on the commercial ' par value of the bill, and 5 % on whatever he obtained more than the commercial par value. What did his commissioa amount to I 55. I owe A. N. McDonald & Ca, of Liverpool, $7218, net proceeds of sales of merchandise effected for them, which I am t« remit them in a bill of exchange on London for such amount as will close the transaction, le^ ^ per cent, for my commission for investing. Bills on London are at 109J, -Required the amount of the bill, m sterling money, to be remitted. 56. When exchange between Montr il and Hamburg is at 24 cents per mark, and between Hamburg and 3t. Petersburg is 2i marks per rouble, how much should be paid in St. Petersburg for a draft on Montreal for $6501 57. A merehant shipped 2560 barrels of flour to his agent ^ m Liverpool, who sold it at £1 8.. 6d. per barrel, and charged 2 percent commission; what was the net amount of the t in dec-mal nwney, allowing exchange to be at a premium of 8 per / 172 FOBEIQN EXCHANQE. 58. Paris, Jan'y, 4ih, 1883. Messrs. S. E. Whiston ^ Co., Halt/ax, N. S. Bought of Paris Branch, Grimanlt & Co. 5 dot asst'd Perfume, 20.80 fr f. 104.00 28 " gross asst'd Soaps, 16.10 450.80 " 554.80 15 % discount 83.22 471.58 Less Freight to Liverpool .... 34.08 f. 437.50 What must be the face of a sterling draft to pay the above bill reckoning 25f. per pound sterling, and what will it cost when sterVng exchange in Halifax is 109 J. 59. A merchant in St. John having to remit £434 15«. to Liverpool, wishes to kno^ which is the most profitable, to buy a set of exchange on Liverpool at 10 J per cent premium, or send it by way of France ; exchange on the latter place being 19| cents per franc, and exchange on Liverpool can be bought in France at the rate of 24A francs per pound sterling, and he has to pay his correspondent in Rouen J of 1 per cent, for purchasing the bill on Liverpool 60. Hughes Bros. & Co. purchase of R Chaffey & Co., a sterling bill at 60 days ca Gladstone & Hart, of London, for £3956 IOa They remit this biU to James Alder, in London, where it is accepted by Gladstone & Hart, and falls due on the 20th November, at which time it is protested causing an expense of £2 19«. Gladstone & Hart having failed, K Chaflfey & Co.'s agent in London pays James / 'do- '"n the 20th No"ember, £2000 " on account How much must E. Chatfey & Co. pay to Hughes, Bros. & Co., on the 24th December, to cover the amount still due in London, allowing interest at ilie rate of 10 per cent from November 20th, to the maturity of a 60 days' bill at date of 24th December, and ^ of 1 per cent commission for their trouble in negotiating a new bill 1 TAXES AND DUTIES. A Tax is a mouey payment, assessed upon the subjects of a State, or the members of any community for the support of the government, and sometimes for the protection of home industry. A Direct Tax is an assessment made on all citizens in propor- tion to the value of their property, or a levy upon the persons of individuals without regard to property. In the latter case it is called a Poll Tax. ^ Indirect Taxes are called duties, and are either cugiorm or excise. Castoms Daties are taxes levied upon imported merchandise. Excise Dnties are taxes levied upon merchandise manufactured in the country. AU duties are paid directly by the iHiportere or manufacturer* of the goods taxed, but indirectly by those who buy and consume them. Duties are either specijic or ad valorem. A Specific Duty is a tax assessed at a certain sum per ton, pound, yard, gallon, or other weight, or measure, without regard to the value of the goods. ••^ An Ad Valorem Duty is a tax assessed at a certain Ate per cent, on the actual or fair market value of the goods in the Country from which they were imported. The dutiable value of imported merchandise is^nerally ascertained frotu the mvoice given by the seller or shipper at the place of shipment. But dutiable goods are nibject to appraisement, so that the invoice price is not always ta^en aa the dutiable value. Before duties are calculated certain aUowances are deducted which vary *ccordirg to the kind of goods upon which the duties are levvjd. Among thesa are the iuilowing : Geo. c- ,- Shelb. OX, N.S. APitv / L .. and 20 % t 7. Imported from London 10 doz. ready made cotton shirts @ 48/ per doz., 15 doz. cotton undershirts @ 17/6 per doz., and 10 jz. pairs cottcai drawers @ 15/3 per doz. What was the duty @30%? 8. What is the duty on 425 gross steel pens costing 30 cents per gross, less 10 % j dutj 20 %t y KXEBCISES. 175 9. What is the total amount of duty on the following, viz : 1 case felt hat«, value i,\\ U. 9d. @ 25 %. 1 " prints, " £30 5«. 9d. " 20 %. 1 " mantles, " £55 19». Id. weight 166 lbs. @ 10 cts. per lb. and 25 %. 1 case girdles value £37 9«. Id. @ 30 %. 1 " trimmings " £9 13». 5d. @ 20 %. 1 " feathers " £80 18«. 6d. @ 25 %. 1 " flowers " £60 15«. 7rf. @ 25 %. 1 " laces " £132 8s. 5d. @ 20 £ 10. McLeod & Co. import from Cadiz 10 casks port wine containing 48 gallons each @ 2 J pesetas per gaUon ; 20 casks sherry wine 48 gallons each @ 2 pesetas per gallon, and 80 baskets champagne, 1 dozen bottles each at 10 pesetas per basket. The allowance for leakage was one gallon per cask, and for breakage 5 %, The duty on the port and sherry was 52 cents per gallon, and 30 %, and on the champagne $3 per dozen and 30 %. What did it amount to, the peseta being 19,^ cents ? 11. What is the duty at one cent per square yard, and 15 % on an importation of unbleached cotton cloth all one yard wide" vii: 132 yds. @ 8c., 257 yds. @ 7ic., 47 yds, @ 9c., 334 yds. @ SJc, 95 yds. @ 9i c, 226 yds. @ 10c, and what rate percent, is the whole duty equal to 1 12. What is the duty at 2c. per square yard and 15 % on a lot of cotton cloth as follows : 475 yds., | of a yd, wide, @**11 c, 372 yds., II yds. wide, @ 13c, 136 yds., 30 inches wide, @ 12c', and 567 yds., 33 inches wide @ 22^ c1 Find also what rate per cent, the duty on each lot is of its dutiable value, and what is the average rate on the whole 1 13. J. Johnson & Co. import from Liverpool 10 pieces carpet, 40 yds. each, f of a yd, wide, and invoiced @ 5/ per yd., on which the duty is 10c per square yd. and 20 %: 200 yds. hair cloth @ 4/, duty 20 % ; 100 pairs woolen blankets @ 7/6 per pair, weight 472 lbs., duty 7Jc per lb. and 20 %, and shoe lasting to the amount of £60, duty 25 %. Required the whole duty, and what rate per cent, it is of the invoice price. 14. Find the rate per cent, of advance on the net amount of the following invoice that will cover expenses, the total cost in t 176 TAXES AND DUTIES. store, and the rate per cent., the total cost is of the gross amount of the invoice ; also what must be the selling price per gross of / each sort to make a profit of 20 %. TflRMs Cash. NEW YORK, JuLT 5th, 1883, S. E. Whibton, Esq., Halifax, N. 8. Bought of J. C. P. Frazeb & Co. 19 BlackweU St 168 gross 8 oz. bottles $2.88 Z 483.84 91 " 16 oz. " 5.11 465.01 40 " 18 oz. " 8.27 330.80 (Gross) ei279.65 . Trade discount 66§ % 853.10 $ 426.55 10% 42.65 $ 383.90 8% 19.20 Net $ 364.70 Cartage to Pier 5.25 Freight to Boston 18.96 8 388.91 Duty 30 %♦, truckage to store $3.75, freight Boston to Halifax $9.30. 15. What figures should fill the blanks in the following invoice and entry 1 • The customs authorities add 2 % to the nat amount of cash American iuvoices when making up for duties. Mark TxA H EXERCISES. lf\ BiBMixaHAM, M*y 30th, 1883. Mess. Theakstoic k Angwin, Bought of Per " Nova Scotian" SS. B. & S. H. Thompson. -1 caak Shovel* 40- 6 doz "ElweU'i" Iron Shovel., ea 1 & 2, cwt. 8, 2, 0, @ 36/6 C*^ 6/6 DeUvered • • • • •• • -Cask 4L- 18/ 26/ 2 doz. fine ward Stock Locks, ea 8 10 in, 62^' 1 " best " 18/ 26/ ea 8 lOin, 62i% iNwhtCoc 1 " " lock " ' " 2 'I BrassNiijhtCocks, No. 0, Jin, 18/ >in, 21/ 60% 12 " Japd. Padlocks, 2i in ea, 337, 339 6 ;; ;; " 2* in ea, 339y 3W^ 8 ^ ' •• 2jinea,346 6/ 2 bright Chest Locks, 47664, 4 in, 9/ 6 47639, ea 8%^/n 6 " , " " 47645, ea 3^^J hx Cask etc, 9/8, lined with waterproof paper ) Carriage to Ijverpool cwt 3, 1, 20 4/ J Brought forward amount of 1 cask Shovels, 40 1 " Hardware, 41 / • •• • • • • • • • • •• • • • • I on £25 o, . . „ Commission 7J % on Shipping Charges and Bills of Lading Insurance to Halifax against all risks ® 12/6, Policy 9d. E. & O. E. B. & S. H. Thompson. 3 16 9 15 18 7 19 16 4 3 10 3 6 6 3 16 9 113 1 11 18 6 • •• • • • • • •» • • • • • •• • 15 18 7 19 16 4 • * • 8 9 • • •• £21 ^ ^> IMAGE EVALUATION TEST TARGET (MT-3) // A /. %i^ w^^ 1.0 I.I 12.0 2.2 1-25 1 1.4 1.6 % /a ^,. e. >^ y Photographic Sdences CoiDoration s. m a>' fV <^ \ \ V O 73 WEST MAIN STRICT WEBSTER, N.Y. 14S80 (716) S73-4S03 S*,rV- ■jV T?!-*" r.^'.W ^fe,\-% i^Vjif^- a'.*-/ir ^.r ^1 ^ |£lu££ ^78 EQUATION OF PAYMENTS. FOR DUTY. Port of Halifax. 18th June. 1883. ^"^"^ ^' Entry No Imported by Theakston & Angwir. per SS Nova Scotian, RiVhard- son master, from Liverpool I' TxA H40 41 ft. Description of Qooda. Valuct Dollara. Cts. Cask Shovels £3 10b. w| •• Cask. Locks £1S 168. M. Mfre. BrsM £1 Ss. 6d. Theakston k Angwin. Qu'ntity •• Rate Amount of of Duty. Duty |DoU'8.Ctfc 30% 927 •» 80 t The value is extended to the nearest dollar TOThlTTkl 1 ZZ — •WW the dcUars are increased by 1° *^^ cents are 50 or EQUATION OF PAYMENTS. Equation of Payments is the process of finding at what date several debts which are due at different times may all be ^d a^ once so that neither party may lose by interest ^ '^ "^ ^'^ "' th^r^"^ T"^ ^"^^ "" ^"'^ ''' '^«'«"* ^^ ^ th« whole of them be paid m one sum the day on which the first of them is due xt IS evxaent that all the others wiU be paid beforeThev are due. and that the payer will lose the use or Vterest of ihZ thTlt *T.\^r«- *h« ^^y - -l^ich he paid them aTd the dates on which they are sevexaly due. On the cont,«y U he do not pay any tiU the last becomes due. aad then pay the whole at once, he will gala the use or interest of those sumi T*\ EQUATION OF PAYMENTS. 179 ti^t were due before that time from the dates on which they were severally due to the date of payment, and the payee wiU omewhere between the date for the first payment and thatT« the last on which if the whole be paid thVpayer wiU gat « much interest on what he retains after it is due^as he wS lo" on what he pays before it is due. This daU is the AveraTl^te which la sought in Equation of Paymenta ^^ r.rntTTf^T "*"'*^ ^''^' *^« *^«"*« «late Will be .8 far «m.ved from hxs pomt as the time during which the sum of the would from the same starting point to the dates on whTcrthey are payable. n,us suppose A owes B $1200 which he is to ply whl the 4 T'. ,^''°"°»" ^'^^ «t«rtin^ point the date from which the 4, 6 and lOJ mos. count, A is to have the use of $300 for 4 moa. interest «6 $500 for 6 mos.. interest |15. and |400 «42. and then pay the whole sum at once, it will be the same to him so far as interest is concerned; and if the same to him it will be the same to his creditor. The interest of $1200 will mount to 142 in 7 months, therefore 7 months is the equa^ $300 X 4 = 1200 600 X 6 = 3000 400 X 10^= 4200 11200 ) 8400 (7 months, 8400 equated time. «1 T^'lo^cT' V^^ '"' * °^°^ '' '^' ^« •« ^^ i«t«"st of «1 for 1200 months ; the interest of $500 for 6 months is the same «t^ie interest of $1 for 3000 months; and the interest of |400 for 10^ months i, the same a. the interest of $1 for 4200 months, ^e sum of aU these is 8400 months; therefore the interest of the whole 18 the same as the interest of $1 for 8400 mrthl 180 EQUATION OF PAYMENTS. Now, if Jl require 8400 months to produce a certain interest, LUdl tf ' ^''''' "^ "^"" °°^^ ^^- P^^ <>' that time Irf. r^' T*"™'*' "^'^ 8400-M200=7. Hence the equated tuna is 7 months. ^.J*?!.^'"""^""'^^ "^^P^y^^ ^ ^"^ «"»«. and divide the turn of the products by the mm of the payments. Another method of producing the same result is the foUowing : Interest of $300 for 4 months= 812.00 @ 12 per cent 500 for 6 monthfl=s 30.00 @ " « _400 for lOJ month8= 42.00 @ ." " $1200 for 1 month=$l"2J8r00 ( 7 months. Rule 2.-F,r,d the irderest of each imtalment f^ its time, at tnterest of th'- '.hole debt at the same rate for one month, of the prind^Tr TZa Th I 'l^l^''.'^*!-- ^''^ *« hundredth part phKses of decimal.. "*"*'"• *"** Pointing off two The procew by Rnle 2 becomes identical with that hv R„i« i u mg the interest at 1200 per cent ^ ^* ^ ''^ '**'^«"»- EXERCISES. theL^fif«!«%'^''11*^' '"' '^^ P*y°^«"* °^ tl"«« debts, tZ o1 ?;:ontt'' ^^"^^ ^^ ''' ^^^ ^- *^^' ^- - the OPIRATIOV. $45X 6=270 70X11=770 75X13=975 ■ $190 ) 2015 ( 10.61 30. 18.30 10 mos. 18 days. Ana. >^ZZ:t£^ " "^*' '^' ""'*^"- •* *•> *-» P^ of decimals. EXERCISES. 181 2. If a person owes «1200, to be paid in four instalments, JlOO in 3 months; |200 in 10 months; 300 in 15 months, and $600 m 18 months, in what time should he pay the whole sum at once t In this and simUar questions, the work may be somewhat shortened by counting no time for the first payment, and deductmg its time from that of each of the others. Thus : $100X 0== 200 X 7= 1400 300X12= 3600 600X10= 9000 $1200 ) UOOO ( llf, to which add 3 months, and we have for the equated time 14§ months. 3. J. Smith owes R. Evans $1300, of which $700 are to be paid at the end of 3 months, $100 at the end of 4 months, and the balance at the end of 8 months. Required the equated time for the payment of the whole. 4. T. C. Musgrove owes H. W. Field $900, of which $300 are due in four months, $400 in 6 months, and $200 in 9 months ; what is the equated time for the payment of the whole amount! 5. A. & W. McKinlay have in their possession five notes drawn by G. W. Armstrong, all dated 1st January, 1883 ; the first is drawn at 4 months, for $45 ; the second at 8 months, for $120; the third at 10 months for $75; the fourth at 11 months, for $60; and the fifth at 15 months, for $90 : for what length of time must a single note be drawn, dated 1st May, 1883, so that it may fall due at fhe properly equated time ? 6. A gentleman left his son $1500, to be paid as foUows : J in 3 months, J in 4 months, J in 6 months, and the remainder in 8 months ; in what time ought the whole to be paid at once t 7. A merchant bought goods amounting to $6000. He agrees to pay $500 down, $600 in 6 months, $1500 in 9 months, and the remainder in 10 months. In what time ought he to pay the whole in one payment ? 8. A grocer sold 484 bbls. rosin as follows : Feb'y. 6, 35 bbls. @ $3.12^, on 4 months time; March 12, 38 bbls. @ $3.00, on 4 months time; April 12, 411 bbls. @ $2.62i. on 4 months' time. '?i> 182 EQUATION OP PATMENT8. What is the equated time for the payment of the whole f crnATnw, f;^^; 1 109.375X0"L 22 ^^"^'^2 ui. X1.12=114 ^P"^ ^^ 1078.875X2.12=2158 432 1302.26 \ 2770 /2.13 / 1. 30 3.90 In the .bovo example we We Uken the b«gumi„g „f reb„.„ the figure cut off is 5 or more. Thus, in th« -K., , have carried out twice 11. in the l^^ZZ tZlClZH U lt'foTut:T ''' '' '-'" *"' ' ''''- ''''^^ ^^^ num^r" It "T.""' '' '"'' '"^ °°* ^""'^^ 3 an integral number of time, the nearest smaller number that does may be o^ fof "JV ' w *'^ "^^ ^>'« °^-' -^-h must bTe^ther^ a*y8 aa i, and 15 .« J, when more convenient EXERCISES. Its In performing the multiplications and division the cents need not be noticed, except to increase the dollars by 1 when the cents are 50 or more. 9. Purchased goods of J. R. Worthington & Co. at diflferent times, and on various terms of credit, as by the following state ment : — March 1, 1882, a bill of f 675. 25 on 3 montha. July 4, Sept 26, «« Oct. 1, " Jan. 2, 1883, Feb'y. 10, " March 12, " April 15, " 376.18 " i 821.75 " 2 981.26 " 8 144.60 " 3 811.30 " 6 567.70 " 5 369.80 " 4 II 11 What is the equated time for the payment of the whole t oraunov. March 1, 1882—3— 676.25X 3, 1*= 2026 for 3 mos. 22 " 1 day. " —• 4— 876.18X 8, 4= 3008 " 8 mos. 38 " 3 days. 13 " 1 " " —2— 821.75X 8,25= 6576 " 8 moa 656 " 24 days. 27 " 1 «' " —8— 961.25X15, 1=14416 " 16 moa 32 " 1 day. Jan'y. 2,1883—3— 144.60X13, 2= 1885 " 13 mos. Feb'y. 10, "-6—811.30X17,10=13787" 17 mT* 270 " 10 daya March 12, " —6— 667.70 X 17,12=^9656 " 17 mos. " 228 " 12 daya April 15, " —4 — 369.80 X17,16= 6290 " 17 mos. 186 " 16 days. 4727.73 ) 69123 (12—15, TK»t ia, a little more than 12 monthB, 16 days from the Usiiming of ItUrch. 1882, which will be March 16th. 188S. Am. oegummg oi «u«n, July 4, Sept 26, Oct 1, m^im^^w 184 V EQUATION OP PAYMENTS. 3 months' credit on the first bill, and 1 day in March give the time on the first bill ; i months from March to July and 4 months' credit with 4 days in July give the time on the second bill ; 6 months from March to September, and 2 months' credit with 26 days in September give the time on the third bill, &c. To carry out the products,— Ist, multiply the first bill by the months;— for the one day, take J of 68. 2nd, multiply the second bill by the months, throw off the 6 and take the remaining figures of the principal, plus 1, for 3 days,— take J of that for 1 day. 3rd, multiply 822 by 8, for 8 months,— multiply 82 by 8, for 24 days,— take ^ of 82 for 1 day, &c 10. Bought of A. & W. Smith, 1650 barrels of flour, at different times and on various terms of credit, as by the following statement :— May 6th, 160 barrels @ $4.50, on 3 months' credit May 20th, 400 " " 4.76, on 4 " •« July 10th, 500 " " 6.00, on 6 " « August 4th, 600 " " 4.25, on 4 " " What is the equated time for the payment of the whole ? 11. J. R Smith A Co. bought of A. Hamilton & Son 676 barrels of rosin, as follows : — May 3, 62 bbls. @ $2.50, on 6 months. May 10, 100 May 18, 10 May 26, 60 May 26, 346 May 26, 9 2.50, on 6 months. 2.50, as cash. 2.76, on 30 daya 2.50, on 6 months. 2.00, on 6 months. What is the equated time for the payment of the whole ? 12. follows T. B. Jones & Co. sold goods on 3 months' credit, as May 9, a bill of $436.60. i- « 30, July 17, Aug. 28, Sep. 21, Oct. 23, Nov. 30, 75.30. 183.75. 239.18. 82.10. 89.85. 390.67. EXERCISES. 185 When, in equity, ought they to hare received the whole in one sum, and, allowing money worth 6 per cent., what sum ought they to have received at the date of the laat sale 1 13. Bought of T. * E. Kenny, on 6 months' credit, goods as follows : — 1882. January 3, to the amount of 8250.00. February 6, It II II 317.40. March 9, i< 11 II 171.70. April 12, 11 II II 88.12. May 15, CI 11 II 623.50. June 18, II II II 49.04. July 21, II 11 II 73.90. August 24, II II II 218.75. Sept'ber. 27, II II II 8.15. October 30, II II II 55.84. Nov'ber. 29, II II II 398.00. Dec'ber. 11, II 1. II 191.25. Wliat is the equated time of settlement, and allowing interest at 7 per cent, if payment be delayed till February 1st, 1883, how much will then be due 1 AVERAGING ACCOUNTS. When one merchant trades with another, exchanging mer- chandise, or giving and receiving cash, the memorandum of the transactions is called an Account Current. The fixing on a time when the account may be settled by simply paying the balance with- out interest against either party, is called Averaging the Account. Example 1. — A merchant sold goods amounting to 84000 on 8 months' credit. Tho purchaser paid ^ down, and J in 3 months ; what time should be allowed him for the payment of the remainder t $4000 X 8 = 32000 2000 X = 1000 X 3 == 3000 3000 3000 subtract from 32000 1000 ) 29000 ( 29 months= * 2 years, 5 months. # 186 AVERAOINa ACCOUNTS. ^ f4000 for 8 montlM which u thfl wme m the interent of »1 f„r 32000 months paid. Thi. « equal to the mterert of $1 for 3000 months. He hw, therefoT to receive on the remaining flOOO what U equal to the u«> of # for S JTnlhl T^ P*^ ^* »«» "'"nths, which U 29 month., or 2 year., ExAMPLB 2. -A merchant sold W. M. Brown, Esq., goods to he amount of $3051. on a credit of 6 months from Sept. 25th, 1883. October 4, Mr. Brown paid $476 ; Nov. 12, $375 ; Dec 5 fSOO; and on Jan. 2nd, 1884, $200. When, in equity, ought tlie merchant to receive the balance 1 OPIRATIOIC. m. d. Sept. 25, $3051 X 6 25 = Oct 4, 476 X 1 4 = Nov. 12, 375 X 2 12 = Dec. 6, 800 X 3 5 = Jan. 2, 200 X 4 2 = 1851 1200 12) 18306 product for 6 mos. 2440 II II 24 d. 102 II II II II 1 d. 20848 476 1 mo. 48 u II 3 d. 16 II II 1 d. 750 If II 2 mos. 152 li 11 12 d. 2400 11 11 3 mos. 133 II II 5 d. 800 II II 4 mosi. 13 II II 2 d. 4788 160.60 ( 13.38 30 11.40 13 mos. 12 days from the l)eginning of September, 1883, which will be October 12th, 1884. miM. 7 EXAMPLES. 187 The interest on the Pr. side from the beginning of September is equal to the interest of $\ for 20848 months. The interest on the Cr. side from the same date is equal to the interest of $1 for 4788 months, which leaves a difference in favor of the Cr. side of the interest of $\ for 16060 months ; that is, the interest o: the balance, $1200, for the tAjw part of 16060 months, or 13 mos. and more than 1 1 days. Therefore, Mr. Brown is entitled to the use of the balance to October 12th, 1884,-13 months and U -^ days from the beginning of September, 1883. Example 3.— When did the balance of the following account fall due, the merchandise items being on 4 mos. credit? Dr. MACDO»At,D Bros. Or. 1882. May July Sept. 15 20 27 To Mdse., 350 186 431 76 10 73 _ fc.- 188S. Jiine 1883. Febv. Mar. 9 18 8 By Mdse., " Cash, " Mdse., 200 300 290 00 00 00 OPBRATIOK. May 15 — 4 — 350. 1 75 X 4.15 = 1404 175 product fc It < )r 4 mos. ' 15 d. July 20 — 4 — 185. 10 X 6.20 = 1110 62 ct II ' 6 mos. ' 10 d. 61 ■" 10 d. Sept. 27 — 4 — 431. 73 X 8.27 = 3456 387 6655 K 1 II • 8 mos. ' 27 d. 967. 53 June 9 — 4 — 200 X 5.9 = 1000 60 II 1 II ■• 5 mos. » 9 d. Feby. 18 — 300 X 9.18 = 2700 180 II aehcard ft cm the beginning of >fay 1882, which gives August 31, 1881, the time from which interest w to be charged on the balance. The interest on the debit side, from the beginning of May ISSO 13 equal to the interest of |1 for 6655 months, while the interest on the credit side from the same date is equal to the interest of »1 for 8077 months, which gives a difference in favor of the debit side, of the interest of |1 for 1422 montlis, equal to the interest of the balance. $178, for ^\, part of 1422 months, that is o months. From the above examples we may deduce the following : Rule.— /Vocc«i wi*h each mde oftlie account a» in Ee proihtcts of the larger side is greater than the sum of the products of the >niialler side, reckon the time denoted by the quotient forward, but when the opposite of this is the case reckon backward from the date from which all the time has bee^ reckontd. EXERCISES. Find the times at which the balances of the following accountB became due, or subject to interest : — 1- ^- J. S. Pkckham. o May 16, 1882 $724.45 | July 29th, 1882 $486.80. 2- I>r. T. B. Rkagh. • ch-, November 19, 1883 $635. | December 12, 1883 $950. 3 Dr. Jno. T. Lithoow & Co. o. February 24, 1883 $512.25 | June 10, 1882 $309.70. *• Dr. T. J. Golden & Co. Cr March 17, 1883 $145. | January 16, 1883 . . . .$696.'60. EXERCIREB. 189 5. Dr. 8. E Whiston. Or- August 27, 1883 |341. | November, 7, 1883. . . .1247. 6. />. L C. Eaton. Cr. July 20, 1883 $711. ] April 14, 1883 $1260. 7. JJr. Gordon & Keith. Cr. June -24, 1882 $1418. | September 7, 1883 ... .$2346. 8. Dr. Gbo. W. Jonks. Or December 2, 1883. .. .$1040.80. | August 13, 1883.. . .$1112.40. 9. Required the time when the Ulance ^of the following account l)ecame aubject to interest, allowing the merchandise items to have been on 8 months' credit ? Dr. S. T. Hall & Co. Or. 1882. 1 1888. Ma> 1 To MdM., $300 00 Jan. 1 By Cwh, $500 00 July Sept. 7 it « 769 m Feb. 18 " MdM. 481 V6 < 11 11 11 417 2(» Mar. 19 " Ca»h, 760 25 ?5 «< u 287 70 An! May. 1 " Draft, 210 00 Dec. ao « w 671 10 25 " Oa»h, 100 ou 10. When did the balance of the following account f^U due, the merchandise items being on 6 montlis' credit ? Dr. Barnes & Co. O. 1S83. 1 188a May 1 To Md»e., $31*? 40 .Tune 14 By CaBh, $200 00 May 23 It It ' 86 70 July 30 " Mdge., 185 90 June 12 "cashpddt. 106 00 Aug. 10 " Cash, 100 00 July 29 " Mdse., 243 80 21 " Mdse., 68 OU Aug. 4 ft ti 92 10 Sept. 28 46 10 Sept. 18 " Ca«h, SO 00 11. When did the balance of the following account become subject to interest 1 Dr. BbAP.D a VKSNINa Cr. 1882. 1882. Aug. 10 ToMdge.,4n»o8. 286 30 Oct. 13 ByCa.li 400 00 17 It II 2 " 192 fiO 26 150 00 Sept. 21 It tl ^ 4t 256 80 Dec. 15 " Md8e.,2nio8. 345 80 Oct, 13 " Cash, 190 00 30 230 4U Not, 25 30 " MdM., 6 " It 1. 3 It 432 215 20 25 Dee. 18 ft u 2 '^ 68 90 ^_ ^^ 190 AVERAOINO ACCOUNTS. 12. In the following acct., when did the balance becom* due, the merchandise being on 6 months' credit 1 Dr. S. M. Kerr in acct. mth T. E. Jones & Co. Cr. 1883. Jan. < teh. Mar. April May To Mdse., Cash, Mdse., Cash, Mdse., 96 57 80 38 60 15i 42 23 28 177 I 19 I 1883. Jan. April Ay Ar Ml 30 3 22 By Cash, 240 OO 48 I 8» 50 00 13. \ATien, in equity, shoiUd the balance of the followihcr account be paid ? ° Br. 1883. Jan. Feb. Mar. April June July Sept. Dec. 3 31 8 21 10 24 12 1 20 4 27 9 To Cash, Daniel & Boyd. Or. 200 300 75 100 350. 25 40 80 125 268 250 loo 100 |00 1882. I I Sept. 20 By Mdse., 6 mos. Oct. Dec. 1884. Jan. Feb. April June Sept. Dec. 4 6 2 6 4 2 6 6 .'583 321 137 98 53 634 97 84 132 17 00 00 75 98 00 23 00 14 ' arsE ' V ACCOUNTS SALES. An Account Sales is a detailed statement bf the sales, expenses and charges of a consignment. It should show the dates and particulai^ of the sales, the dates and particulars of the charges and the net proceeds and when they are due. The Net Proceeds is the sum to be paid the consignor from the 8ales after aU charge* have been deducted, and is payable at the average date of the whole account. In averaging an account sales, the sales are considered as one side, and the charges the other, the averaging being done the same as in any othei* account. As to when the commission should be considered due, whether at the average date of the sales, or at their average due date, or on the completion of the sales, there may be some ditference of opinion. In the exercises here given this charge is considered due at the date of the last sale when the acct sales is supposed to be made out. The small amount of the commission compared with the sales renders it of little practical moment, which of these dates is taken as its due date. Commission merchants often become interested in the merchan- dise consigned to them for sale, by accepting a certain share, ard selling on joint account of themselves and their consignors. When this is the case the terms on which the consignor becomes responsible for his share should be known, whether payable as cash, on some definite term of credit, or at the average date of the Acct. Sales. Many commission merchants do not average their accounts, some because they do not know how, and others prefer, as affording more profit and less trouble, to retain a percentage for prompt payment, and pay over the net proceeds, or place the same to the Cr. of their consignors on completion of the sales. 1. In the following acct. sales at what date are the net proceeds due as cash, and what sum will settle the same on June 30th, 1883, interest at 7 % 1 butter for acct and risk of E. A. Donkin, Amherst? 192 AVEBAOINO ACCOUNTS. i April Mky Mm-. May 10 14 600 " Butter I *^y» *7« " Bi»on, C«di 2976 " Chee«^J«- , 746 " Butter /**<^y" CHABOES. 13 c. 21c. 12f e. 16 c. 22a Paid freight uid cartage labor re-salting Bacon ....'. Storage and Advertiaing Commiasion @ 2i % oullSTO.'oS '.'.'.'... Net Proceeds due as per ar. (due date m £. & O. E. Halifax, May 14, 188.% R. Fkxon & Oo. sao 106 476 163 28 8 6 46 00 00 16 90 10 BO 00 76 626 00 604 99 640 06 tl870 06 88 •1781 36 2. September 4, 1883. we received from W. Cummings, Brautford Ont, 120 bbls. 1^ Pork and 742 bushel Clover Seed days sight draft for $3450. The foUowing is the Jount sales, mat are the net proceeds and when due, and what is the cash bdance of W. Cumming's account on December 31, 1882- interest at 6 % ? . «-• Aoot Sales of 120 bbla Mess Pork and 742 bush. Clover Seed, foracctand nsk of W. Cummings, Brantfoid, Ont. Sept. Oct Nov. Sept. Oct. Nov. 12 30 18 2 16 25 bbls. Mess Pork ) „„ j 21 no SO bush. Clover Seed [«*<^y« 3.35 lObbl^MelisPoric }»^y aiico 86 bbli^ Mess Pork V y I » TO 12budi.aoverSeed; 6 ^ aW CHARGES. Paid freight and cartage " Insarance on «4500 @'ij'%; Storage and Advertuing. ^. . . . . . Conwn'n. @l}%onS.JM. Net proceeds due as per av, E. ft O. E. Jab. A!"BcaT k Oo. 210 16 7 r-a ACCOUNTS SALES. 193 3. Jan. 2, 1883, received from R Bremner & Co., Charlotte- town, 200 bbls. Pork invoiced @ tl8 per bbl. ; 3760 lbs. cheese @ 10 c. per lb. and 100 firkins butter averaging 80 lbs. each @ 16c. per lb., to be sold on joint account of shippers |, and consignee |, our J of invoice due as cash. Invoice date December 27, 1882. Jan. 21, Cashed B. Bremner & Cc's sight draft payable to their order for $1264.50. Feby. 14, Accepted B. Bremner & Co.'s one month's sight draft favor A. Gunn & Co., Halifax, for |864. Feby. 28, Cashed B. Bremner A Co. 's demand draft for 11174.75. Find average date for payment of the net proceeds, per the following acct sales, the average date for payment of the balance of B. Bremner & Co's acct., and the cash balance of their acct on May 14, 1883. Aoct Sal^S, Merchandise on joint acct. of B. Bremner & Co., Charlotletovra §, and ourselves ^. 1883. J»n. 16 Feb. 9 27 M.U. 7 24 Jan. 2 14 16 24 40 bbls. Pork )« 60 firkiM Butter, 4028 Ibe. J " 60bbls.Pork U-,^ 11601huChee«>r™ • 50 firkinb Butter, 4025 Ibe. 1896 lbs. Cheese 76 bbls. Pork, Cash, 26 bbls. Pork ), 706 Ibfc Cheese r ""'• mos. }' mos. CHARGES. Paid freif^t, ke " cooperage, Ac " Insurance @ H % on 96000 . Storage Comm'n. ® 2^ % on sales 18.76 24 0. 19.37J 13 c. 24 a 14 e. 19.26 19.87i 16 c. Net proceeds of sales J n. p. due B. Bremner & Co., per average. T* A O E Halifax, March 24th, 1883. _ ^( 132 6 11 26 V wm^ 194 ACCOUNTS SALES. STATEMENT. Halifax, March 24th, 1883. Messrs. B. Brbmner & Co., In acct. with T. A. Maclkod & Co. 1882. Jan. Mar. Jan. Feb. o? ?7 ^ l?"- "^ Shipment due Dec. 27, 1882. 24 ' i Net pro. do. " April 19, 1883. Dr. To Cash paid a^ght draft f i264 50 Acceptance, 1 mo., due March 17 8(54 00 Cash, paid sight draft 1174 75 Bal. due B. B. & Co., April 22, 1883 17.51 3955 5707 3303 »2403 67 49 16 25 91 4. December 1, 1882, Received from Messrs. Gillespie, Moffatt & Co., Boston, per str. Canima, to be sold on joint acct. of consignor and consignee each one half, my half due as cash Feb 24, 1883. 27 cases Mackinaw Blankets, 540 pairs @ $3.20, weight 3510 lbs., duty 7^c. per lb. and 20 % ad vol. ; 2 cases Factory Cotton, 987 yds., 1 yd. wide, @ 7|c, duty Ic. per square yard, and 15 °/ ad vol. ; 20 pieces Table Oil Cloth @ $3.70, duty 30 % ; 126 yds W. E. Broad Cloth @ $3.00, weight 284 lbs, duty 7^c.°per lb, and 20 % ad vol. ; 7 bales Cotton Batts @ $6.20, weight 312 lbs duty 2c. per lb. and 15 % a<; val. ' December 5, Cashed their draft for $1200. " 17, Accepted their draft at 30 days' sight for $684. Jan. 14, 1883, Cashed their draft for $500. Make out GiUespie, Moffatt & Co.'s acct. current and interest acct. to March 31, 1883, (interest at 7 %). What is the balance on that date 1 >^ The iyilowing is the account sales ; AVERAGING ACCOUNTS. 195 Acct. Sales. Merchandise on joint acct of Gillespie, Moffatt & Co., Boston, and myself each one half. 1882. Dec. Dec. 14 17 28 Cash. 260 pre. Blankets 4.20 425 yds. Cotton 9 7 pes. Table Oil Cloth 4.60 Note at 6 mog. 140 pre. Blankets' 4.60 54 yds. Broad Cloth 4.20 4 pes. Table Oilcloth 6.00 Cash. 562 yds. Cotton 9 13 pes. Table Oilcloth 4.40 54 yds. Broad Cloth 4.00 Note at 3 mos. 2 hales Cotton Batt*. T.Od 80 pre. BlankeU 6.70 18 yds. Broadcloth 5.00 Cash J, Acct. 30 days g. 60 pre. Blankets 6.75 5 bales Cotton Batts .7.26 • CHARGES. Duties Freight, &c Commission @ 5 % on sales Net proceeds Half n. p. due as per av Halifax, Dec. 28, 1882. G. A. Murdoch, 761 94 12419 00 -4S^?-i^^^.^^^S- RATIO AND PROPORTION. DEFINITIONS. Ratio is the relation which one quantity bears to another of the same kind m respect to magnitude. Thus, the ratio of 2 to 6 is the relation which 2 bears to 6 in respect to the quantity expressed by each, and since 2 is i of 6 this ratio is equal to J. j > Hence the ratio of one number or quantity to another is s^rni '^""*''''* ""^^^'^ ^^ ^^'^'""^ *^' ^"* ^y ^^' of2n'rf9''*'''°'**°^''^''^^*'^°''^'°'^^*"^^2; Ratio is generaUy expressed by the sign : placed between the quantities. Thus 3 : 12 expresses the ratio of 3 to 12 and is equal to J. » « The two numbers or quantities of a ratio are called its Term Coi^Mnr *'™ '' ''"'"^ *^' Antecedent, the second the A Simple Ratio is an expression of the relation of two quantities only, as 7 : 21. A Compound Ratio is a combination of two or more simple ratios as, { ^ j 6, | A compound ratio is reduced to a simple one by multiplication. ^^"^ { 2 i 3 }=6 •• 18. oriX^ =A = 6 : 18. (5:8) Also, j 4 : 5 1=120 : 120, or f X fXf = m = 120 : 120. A Ratio Of EquaUty is one in which the antecedent is eoual tn tne consequeiit, as 7 : 7. BATIO AND PROPORTION. 197 A Ratio of Majority is one in which the antecedent is greater than the consequent, as 12 : 8. A Ratio of Minority is one in which the antecedent is less than the consequent, as 8 : 24. Proportion is an expression of two or more ratios equal to one another. A Proportion or Analogy is an expression of the equality of two ratios. A Simple Proportion expresses the equality of two simple ratios, usually by means of the sign, (::). Thus, 2 : 4:: 7 : 14, which indicates that the ratio of 2 to 4 is aqual to the ratio of 7 to 14, and is read, 2 is to 4 as 7 to 14. The four quantities of a simple proportion are called its terms. The first and fourth terms are called the Extremes ; the second and third, the Means. Ill every proportion the product of the Extremes is equal to the product of the Means. The fourth term is generally known as the Fonrth Pro- portional. To find a fourth proportional, the first three terms being given. Rule. — Multii)ly the second and third terms together, and divide the product by the first. Example.— "What is the fourth proportional to 3, 21 and 101 Multiply the means together,— 21X10=210. Now, since the product of the means is the same as the product of the extremes, the number, 210, is the product of two factors, one of which is 3. Therefore, if 210 be divided by 3, the quotient will be the other extreme, or fourth proportional. 210^-3=70, Ans. EXERCISES. 1. Find the fourth proportional to 5, 15 and 24. 2. Find the fourth proportional to 17, 34 and 19. 3. vVhat is the fourth proportional to 9, 36 and 48 1 4. What is the fourth proportional to 8, 48 and 72 1 Its DEFINITIONS. menever the first term, or any factor of it, is a factor of one of the others, the operation may h, shortened by cancelling. V^.w;!'^ 1 *^' ^^^ '^"''"""' '^^"•' ^^^ fi™t fc«™ i« a factor of Dotn the others : ^ : ^^ :: 72, or, P : 48 :: J^ ® « 9 9 *32 An* 432 ^ns. 5. Find the fourth proportional to 27, 72, 31. 5^^ : ^? :: 31 9 is a factor of the first and second term* 6. Find the fourth proportional to 16, 27, 56. ^J : 27 :: ?? 8 is a factor of the first and third terms. * 7 7. Find the fourth proportional to 14, 21, 32. 8. Find the fourth proportional to 22, 37, 363. 9. What is the fourth proportional to 9, 19, 99. The following principles will be found useful to the learner. In the following, or any other proportion :— 8 : 6::12 : 9. thiJf thT"'"'^' *^' ''"°''*^ '' ^ '^' ^''* "" ^^^ ^°"^^ *^ ^^^ 6 :8::9 : 12. By alternation, tha first is to the third as the second to the fourth, thus, 8 : 12::6 : 9. By compo^tion, the sum of the first and second is to the second as the sum of the third and fourth is to the fourth, thus, 14 : 6:: 21 : 9. By cKldttion, the first is to the sum of the first and second as the third IS to the sum of the third and fourth, thus, 8 : 16:: 12 : 21. By divmon, the difference between the first and second is to the second, as the difference between the third and fourth is to the fourth, thus, 2:6:J3:9. i^^i^SOG^A.T SIMPLE PROPORTION. 199 By convernm, the first is to the difference between the first and Becond, as the third is to the difference between the third and fourth, thus, 8 : 2::12 : 3. By mixing, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference, thus, 14:2::21 :3. SOLUTION OF QUESTIONS BY SIMPLE PROPORTION. Questions to be solved by Simple Proportion contain, or indicate, three terms, two of which are alike, and are to be taken as the terms of one ratio ; and the third is of the same kind as the required answer, and between which and the answer there exists, by the nature of things, the same ratio as between the first two. If 3 barrels of apples cost $7, what wiU be the price of 12 barrels 1 Now, in this question, the two terms, 3 barrels and 12 barrels, are of the same kind,— let them be taken as the terms of a ratio, thus, 3 : 12. Thi8 ratio is evidently equal to that of the price of 3^ barrels, ^7, to the price of 12 barrels, which is the required answer. We may, therefore, state the question in the form of a proportion, the fourth term of which is to be found. Thus, 3 : 12 : ; 7 : the fourth proportional which is obtained by the rule already given. The completed proportion will be — bbls. bbls. f * 3 : 12 :: 7 : 28. By examining the the previous examples of Proportion, it will be seen that whenever the fourth term is greater than the third, the second is greater than the first : and whenever the fourth term is less than the third, the second is less than the first. Therefore, To state questions in Simple Proportion : EuLE.— PZace the term, or quantity which iso/ths same kind as the required answer and may form a ratio with it, in th£ third place.^ Then, when the answer, or fourth term, is to be greater iiaui ihU third 200 EXERCISES. thefir^t; hut when the answer is to be le*^ than the third term rna^ the less of the other two the second term, and the ,jr.ater the 14:36:: $44. 10 36 26460 13230 U)158760($113.40. Ana EXER0I8E8. 1. If 6 barrels of flour cost $32, what will 75 barrels cost t yards? ^"""^ °^ "^"^^ °°'' ^^^' '^''** """"^ ^ P*^*^ ^«^ ^2 3. How much must be paid for 15 tons of coal, if 2 tons can be purchased for $15 f wwm you ur: r;^ ?tSer ^" ^^ ^^-^ ^^^ --^ -^-- bought ^t^'t^ '' '""" ^^^*' ^^ ^ °^ '^« -«-«« -^- - ^ cost^igT^*' """'^ ^ ^'*^ ^"^ * "''*^'° P''°' °^ '=^"*^' ^^ ^ °^ i* 7. If 5 men are required to build a wall in 5 days, how many men will do the same in 2 J days ? Js is^ol ""' '^ '''' '°^ '^ "^'^ °' "°°^' '' *^« -^' «^ 3 9. What is the height of a tree which casts a shadow of 125 feet, if a post 6 feet high throws a shadow of 8 feetl 10. If a train run at the rate of 5 miles in 15^ minutes, how mJ t W^^L'j'r '^ ^*-^° ^"' ^ ^^y^' ^''^^' ^°^ W should a man work for $25 ? o « " ' ■"""■ ''^'"^ ""'"" *" ^ *i*J'Oi iJui. at (lie end ol the fourth V WLLdSiKi- EXERCISES. 201 ii' day he finds it will require 3 -lays more for the men to complete the job. How many additional men must he put on to enable him to finish it in the time agreed upon at first 1 13. A bankrupt owe* $972, and his property, amounting to 1607.50 is distributed among his creditors ; what doea one receive whose claim is $11.34 1 14. WTiat is the value of .15 of a hogshead of lime, @ $2.40 per hogshead. 15. A garrison of 1200 men has provisions for j of a year, how long will the provisions last at the same allowance if the garrison be reinforced by 400 men ? 16. A borrowed of B $745 for 90 days, and would return the the favor by lending B $1341 ; for how long should he lend iti 17. If 495 gallons of wine cost $390, how much will $72 pay fori 18. If a certain quantity of hay lest 112 head of cattle 9 days, how long will the same quantity last 84 head t 19. If 171 men build a house in 168 days, in what time should 108 men build a similar hiuse t 20. How many pounds of tobacco may be bought for $119.50 if 111 lbs. cost $89.62 J t 21. If 110 yds. of cloth cost $18 ; how much will $63 pay fort 22. If 123 yds. muslin cost $205, how much will 61 yds. costt 23. If a man walk 78 miles in 27 hours, 54 minutes, how long would it take him to walk 152 miles at the same rate 1 24. Suppose a man by travelling 10 hours a day, performs a journey in four weeks without trespassing upon the Sabbath, how many weeks would it take him to perform the same journey provided he travel only 8 hours a day, and pay no regard to the Sabbath 1 25. How much may a person spend proportionately in 94 days if he wishes, to save during the year $73.50 out of a salary ol $500 per annum f 26. If 7 watches cost £30 38. 9d., what will be the cost of 3 dozen of the same kind with 25 % duty added 1 27. If 13 dozen hats cost £37 14«., what will be the price of 'i GOZoIl i ^m SIMPLE PROPOnTION. 28. If 3 cwt 3 qw. 14 Iba. of sugar cost «36.50, what will 2 qrn., 2 lbs. coett 29. A wedge of gold weighing 14 lbs. 3 oz, 8 pwt. is valued at £514 4«., what is the value of 6 ot 10 pwt? 30. If the carriage of 3 cwt. 1 qr. 18 lb«. from Liverpool to Halifax cost 6/11, what at the same rate will be the freight for 2 tons 16 cwt 2 qrs. 31. A cubic foot of pure fresh water weighs 1000 oz. avoir- dupois ; find the weight of a vess 1 of water containing 2171 cubic inches, ' 32. A butcher used a false weight, 14} oz. insteatl of 16 oz. for a pound ; of how many lbs. did he defrau.l a cu.stonier who bought what, if it had been properly weighed, would have been 112 Ibe. from him t 33. If a long ton of coal is worth $4.75, what is the value of a short ton (2000 lbs,)? 34. A citizen whose property is assessed at $42500 is taxed $403 75, what should a citizen pay whose property is assessed at ?3600 ? 35. Find the value of 7 tons, 9 cwt, 3 qrs., 20 Ibe. of iron @ 85 shillings per ton. 36. A watch was 10 minutes fast at 12 o'clock (noon) on Monday, and gained at the rate of 3 minutes 10 seconds a day • what was the reading of the watch at a quarter past 10 a. m. on the following Saturday t 37. A was sent with a warrant, and when he had ridden 65 miles B was sent after him to stop the execution, and for every 16 miles thfl.^ A rode B vb^e 21 milas. How far hau each ridden when B overtook At " ' 38. A detective, travelling at the rate of 8 miles per hour chased a culprit, and caught him at the end of 200 miles, but the culpr had a start of 75 miles. At what rate did the latter travel t " 39. A mason engaged in building a wall ascertained at the end of a certain time that the part he had finished bore the same proportion to 3 miles that ^ does 'to 87. How many feet hod he laid ! •• 40. A farmer by his wiU divides his farm- consisting of 97 acres, 3 roods, 6 rods betweei. his two sons so that the share of the VOUnCer is 4 of th« ahara r>f fl,» «1J p v_ ^ J, ~ *' t **' ^-'**-' '_x*a^i, i*.u^Ui*OU 1/1x6 5lAaI6b» COMPOUND 1»R0?0HTI0N. SOS 41. A legacy of |398 is to be divided among three orphant, in jMirts which Hhall be to one another aa the numbers 8, 7, 11. the eldest receiving the largest share. Rwiuired the parts. 42. Divide $5000 among A, B and C, so that B's share may lae one half greater than A's and C's one half greater than B's. 43. Suppose that A starts from M. and walks 4 miles an hour towards N., and at the same time B sUrts from N. and walks towards M. at the rate of 3 miles an hour. M. and N. being distant 432 miles, how far will A have travelled when he meets Bt 44. A certain sum. being divided among two persons, it was found that the less share was § the greater, and the difference of the share was $800. What was the whole sum divided, and what were the shares 1 45. A parcel of land is to be divided into two parts such that one shall be ^ of the other, and the difference of the parts 716 acres. Required the whole, and the parts. 46. In a mixture of copper pnd tin the tin is J the copper, and the difference of the parts is 75 lbs. Required the whole, and the parts. 47. Pure water consists of two gasses, — oxygen and hydrogen ; the hydrogen is about -ft of the oxygen. How many pounds of water will there be when there are 764|f oz. of oxygen more than of hydrogen 1 COMPOUND PROPORTION. Compoand Proportion is used in the solution of questions, each of which involves more than one condition. Example. — If a man walking 12 hours a day can accomplish a journey of 250 miles in 9 days, how many hours a day would he require to walk 400 miles provided he walk at the same rate 10 hours a day 1 In this question there are two conditions, viz., first, that in the one case he travels 12 hours a day, and in the other 10 hours; and, secondly, that the distances are in one case 250 miles, and in the other 400 miles. It may be ^solved by two statements of Simple Proportion. Thus, 10 : 12 : : 9 days ; laS days «nd 2b\} 4UU iu.o uays J i_ 204 COMPOUND PROPORTION". But by a combination of the ratios which express the two conditions, the solution may bo attained by one statement of Compound Proportion. Thus, 10 : 12 ) „ , 250 : 400 I '• ^ ^^^^ ' ^^aV days- Ans, To state the question. Rule.— Ptec the term which is of the same kind as the answer in the third place. Then consider tlie conditions separately, and place the ratio expressing each as in Simple PropoHion. To work out the question. ^ HvLE.— Multiply all the means together for a dividend, and divide it hy the product of the extremes given: the quotient mil he the required extreine, or answer. Note -Whenever it can be done cancel the factors of the divisor against those of the dividend. Example.— If $35.10 pay 27 men for 24 days, how much will pay 16 men for 18 daysl OPIBATIOH. 2 ;?; 2 $ eta. ^y feadingr the question we observe ?^.10 that the answer is to be money, and 11.1 9 as there is only one term of that kind, 3.90^ we cake that for the third term, or 4 the antecedent of the ratio of which the answer is the cjnsequent. Then «15.60. Aug. take two terms of the same kind, as 27 men and 16 men, and observe that «;i5.10 pay for 27 men, and it is evident that a Ugs sum will pay for IC, men not considering the difference of time We therefore i.lace the hsa of these terms, 16, in the second place, and the- greater in the first. Next take the other two terms of the same kind and observe that 835.10 pays for 24 days, and a has sum is required to pay for 18 days, therefore we place the less of these, 18, in the second place, and the greater in the first. To work out : First it is seen that 9 is a factor of 27 and 18. Cancel these terms by 9, and use instead the quotients 3 and 2. In like manner 8 will cancel 24 and 16, leaving the quotients 3 and 2. Then 3 vrill cancel Itself and $35. 10, leaving I and *11.70, and the other 3 will cancel itself and tll.70, leaving 1 and SJi.tlO. This com!)letes the cancelling because the divisor IS reduced to 1. Now multiply the uncancelled quotient of the third term «3.90 by the reniaining other factors of the dividend, and becaus. th«r« to uu divisor this product is the answer . \ EXERCISES. 205 EXERCISES. 1. If I pay 16 men 862.40 for 18 days work, each, how much should I pay 27 men for 10 days work, eachi 2. If 842 keep a family of 8 persons for 16 days, how long at that rate will 8100 keep a family of 6 persons ? 3. If the freight of 10800 lbs. of flour be $16 for 20 miles, how much will it be for 12500 Ib^'. for 100 miles 1 4. If 120 yds. of cafpet, 5 (iuarters wide, cost 860, what should be the price of 36 yds. of the same quality, 7 quarters wide? 5. If 48 men can build a wall 864 feet long, 6 feet high, and 3 feet wide, in 36 days ; how many men will be required to build a wall 36 feet long, 8 feet high, and 4 feet wide, in 4 days 1 6. Suppose that 50 men, working 5 hours a day, can dig in 27 days, 18 cellars which are each 48 feet long, 28 feet wide, and 15 feet deep ; how many days will 50 men require, working 3 hours each day, to dig 24 cellars which are each 36 feet long, 21 feet wide, and 20 feet deep 1 7. If 60 men can build a wall 300 feet long, 8 feet high, and 6 feet thick in 120 days of 8 hours each ; in wliat time would 12 men build a wall 30 feet long, 6 feet high, and 3 feet thick, working 12 hours each day ] 8. If 24 men, in 132 days, of 9 hours each, dig a trench of four degrees of hardness, 337J feet long, 5J feet wide, and 3| feet deep; in how many days, of 11 hours each, will 496 men dig a trench of 7 degrees of hardness, 465 feet long, 3} feet wide, and 2 J feet deepi 9. If 50 men, by working 3 hours each day, can dig, in 45 days, 24 cellars, which are each 36 feet long, 21 feet wide, and 20 feet deep ; how many men .vould be required to dig, in 27 days, working 5 hours each day, 18 cellars, which are each 48 feet long, ^8 feet wide, and 15 feet deept 10. If 9 comiwsitors, in 12 days, working 10 hours each day, can compose 36 sheets of 16 pages to a sheet, 50 lines to a page, and 45 letters in a line ; in how many days, each 1 1 hours long, can 5 conqiositors compose a volunit, consisting of 25 sheets, of 24 pages in a sheet, 44 lines in a pagej and 40 letters in a line? 206 ANALYSIS. 11. If 48 men, in 5 days of 12^ hours each, can flijr a canal 139| yards long, 4 J yards wide, and 2^ yards deep; how many hours per day must 90 men work for 42 days to dig one 491^ yards long, 4| yards wide, and 3J yards deep 1 12. If 112 men can seed 460 acres, Snoods, 8 rods, in 6 days ; how many men will be required to seed 72 acres in 5 days 1 13. If 15 urs of iron, each 6 ft. 6 in. long, 4 in. broad, and 3 in. thick weigh 20 cwt., 3 qrs., 16 lbs. ; how much will 6 bars 4 ft. long, 3 in. broad, and 2 in. thick, weigh 1 14. If the freight by railway of 3 cwt. for 65 miles be $11.25 ; how far should 35^^ cwt. be carried for $18.75? 15. If 126 lbs. of tea cost $56.70; what will 68 lbs. of a different quality cost, 9 lbs. of t^e former being equal in value to 10 lbs. of the lattert 16. If 15 men, working 12 hours a day, can reap 60 acres in 16 days; in what time would 20 boys, working 10 hours a day, reap 98 acres, if 7 men can do as much as 8 hoys in the same time ? QUESTIONS TO BE SOLVED BY ANALYSIQ. Analysis in Arithmetic is the process of solving problems by- steps of reasoning, each of which is so simple as to be self-evident. It therefore re(iuires no rule, but each person must seek to discern the steps of reasoning, and follow them to the required result. ExAMPLa— If 12 lbs. of sugar cost $1.80, what will 7 lbs. coat? 12)$1.80 co.stof 12 lbs. , - f f > IK If 12 lbs. cost $1.80, 1 lb. will cost 1-12 .10 cost 01 I Itx of .,180^ ^jji^h j^ 15 gg^^g. ^^j ;f J j^_ 7 costi 15 cents, 7 lbs. will cost 7 times 15 ■ cents— 41.05. Anfs. $1.05 cost of 7 lbs. 1. If 5 bushels of pease co.st $5.50, what should 19 bushels cost ? 2. If 9 men can perform a certain piece of work in 17 days, how long would it take 4 men to do it t 3. How many pigs, at $2 eacii, must be given tor 7 stieep^ worth $4 a head I EXERCISLo. 207 4. If $100 gain $6 interest in 12 months ; how much would it gain i.i 40 months 1 5. A man bought | of a yard of cloth for $2.80 ; what was the rate per yard 1 6. Suppose I pay $55 for f of an aero of land ; what is that per acre 1 7. If f of a pound of tea cost $1.66§; what will J of a pound cost 1 8. If I of pound cost 23-ft cents ; what will 2^ It's, cost 1 9. If I of a pound cost $| ; what will ^ of a pound costi 10. If $\l pay for IJ stone of flour j for how much will ei payl 11. If 8f yards of silk make a dress, and 9 dresses be made from a pisce containing 80 yards ; what will be the length of the remnant 1 12. What will be the cost of 8 cwt., 3 qrs., 14 lbs. of beef, if 4 cwt. cost $34 1 13. If 4| bushels of apples cost $3^ ; what will be the cost of 7^ bushels t 14. If f of 3| lbs. of tea cost $lf; what will be the cost of 5J lbs. 1 15. If I of a mine cost $2800 ; what is the value of § of it? 16. A is 16 years old, and his age is f times § of his father's age ; how old is liis father ? 17. A and B were playing cards; A lost $10 which was J times i as much as B then had ; and when they commenced § of A's money was equal to f of B's ; how much had each when they l)egan to play 1 18. A man willed to his daughter $560, which was J of } of what he beipieatlied to his son ; and 4 times the son's portion was § the value of the father's estate ; what was the value of the estate 1 , 19. A gentleman spent I of his life in Boston, J of it in Montreal, and the remainder, which was 25 years, in Halifax, at wliat age did lie die? liU. A owns j, and B -j^ of a siiip , As part ;5 vrcnii vC^-Q more than B's ; what is the value of the ship ? -? .^^ f08 ANALYSIS. 'i.v f ) 21. A post stands \ in the mud, \ in the water, and 15 feet ■* above the water ; what is the length of the post ? 22. A grocer lx>ught a firkin of butter containing 56 pounds, -for $11.20, and sold f of it for ^^ ; how much did he get a pound! 23. The head of a fish is 4 feet long, the tail as long as the ^ head and J the length of the body, and the body is aa long as the heati and tail ; what is the length of the fish 1 24. A and B have the same income ^ A saves | of 1 -, by • spending $65 a year more than A, finds himself $25 in d.^i, ai he end of 5 years ; what did B spend each year ? 25. A can do a certain piece of work in 8 days, and B can do •the same in 6 days ; A commenced and worked alone for 3 days, when B assisted him to coqjplete the job j how long did it take them to finish the work ? 26. A and B can build a boat in 18 days, but if C assists them, they can do it in 8 days : how long would it take C to do it alone t 27. A certain pole was 25^ feet high, and during a storm it was broken, when J of what was broken off, equalled § of what remained .' ^ow much was broken oif, and how much remained ? 28. There are 3 pipes leading into a certain cistern ; the first will fill it in 15 minutes, the second in 30 minutes, and the third in one hour ; in what time will they all fill it together ? 29. A cistern has two pipes, one will fill it in 48 miniJtes, and the other will empty it in 72 minutes ; what time will it require to fill the cistern when both are running ! 30. If a mau spends ^ of his time in working, \ in sleeping, T^ff in eating, and 1^ houw each day in reading ; how much time will be left ? 31. A and B can perform a piece of work in 6^ days ; B and C in 6| days ; and A and C in 6 days ; in wliat time would each of them perform the work alone, and how long woidd it take them to do the work together ? 32. If A can do 2 of a certain t>iec9 of work in 4 bnnrs. s.ti^ B can do J of the remainder in 1 hour, and C can finisli it in 20 minutes ; in what time will they do it all working together ? I EXERCISES. 209 ' 33. My tailor informs me that it will take lOJ square yards of cloth to make me a full suit of clothes. The cloth I am al>out to purchase is 1| yards v/ide, anil on sponging- it will shrink ^ in wiiUli and length ; how many yards of this cloth must I purchase for my " new suit ?" -■ 34. A certain tailor in the City of Brooklyn bought 40 yards of broadcloth, 2^ yards wide ; but on sponging, it shrunk in length upon every 2 yards, ^ oi a yard, and in width, 1^ sixteenths upon every 1^ yards. To line this cloth, he bought flannel IJ yards wide, which, when wet, shrunk | the width ou every 10 yards in length, and in wii'th it shrunk | of a sixteenth of a yard; how many yards of flannel had the tailor to buy to line his broadcloth 1 35. Suppose that a wolf was observed to devour a sheep in I of an hour, and a bear in J of an hour ; how long would it take them together to eat what remained of a sheep after the wolf had^ been eating | an hour i 36. Find the fortunes of A, B, C, D, E, and F, -ty knowing that A is V ovih. $20, which is J as much as B and C mre worth, and that C is worth J as much as A and B, and also that if 19 times the sum of A, B and C's fortunes were divided in the pro- portion of f , i and i, it would respectively give | of I^s, J of E's, and ^ of F's fortunes. 37. A and B set out from the same place, and in the same direction. A travels uniformly 18 miles per day, and after 9 dajrs turns and goes back as far as B has travelled dj»inq those 9 days ; he then turns. again, and pursuing hia journey, overtakes B 22J days after the time they first set out. It is required to find the rate at which B uniformly travelled. 38. A hare starts 40 yards before a greyhound, and is not perceived by him until she has been nmning 40 secpnds, she scuds away at the rate of 10 miles an hour, and the dog pursues her at the rate of 18 miles an hour ; how long will the chnse last, and what distance will the hare have run:? 39. A can do » certjiin niece of work in 9 daySj and B can do the same in 12 days; they work together for 3 days, when A is taken sick and leaves, B continues on woAing alone, and after 2 -^^^-^ 210 ANALYSIS. 4 days he is joined by C, and they finish it together in 1 1 days ; how long would C be doing it alone ? 40. A and B start together by railway train from St. John for Moncton, a distance of (say) 100 miles. A goes by freif^ht train, at the rate of 12 miles per hour, and B by mixed train, at the rate of 18 miles per hour, C loaves Moncton for St. John at the same time by express train, which runs at the rate of 22 miles per hour ; how far from St. John will A and B each be when C meeti them 1 41. Required, the sum of the surfaces of 5 boxes, each of which is 5 J feet long, 2^ feet higli, and 3 J feet wide, and also the number of cubic feet contained in each box, — the boxes supposed to be made from inch lumber. 42. If I pay |^ per cor(| for sawing into three pieces wood that is 4 feet long; how much more should I pay, per cord, for sawing into pieces of the same length, wootl that is 8 feet long ? 43. A sets out from Oswego, on a journey, and travels at the ^ rate of 20 miles a day ; 4 days after, B sets out from the same place, and travels the same road, at the rate of 25 miles per day ; how many days before B will overtake A? 44. A farmer having 56^ tons of hay, sold \ of it at $10| per ton, and the remainder at $9.75 per ton; how much did he receive for his hay ? 45. A merchant expended $840 for dry goods, and then had remaining only J J as much money as he had at first ; how much money had he at first \ 46. Divide $1728 among 17 boys and 15 girls, and give each boy -j^j a-s much as a girl ; what sum will each receive ? 47. If A can cut 2 cords of wood in 12 J hours, and B can cut 3 cords in 17^ hours ; how many cords can they together cut in 24 J hours ? 48. A person bought 1000 gallons of spirits for $1500, but 140 gallons having leaked out, at what rate per gallon jnust he sell the remainder so as to make $200 by his bargain % 49. If it require 30 yards of carpet, which is J of a yard wide, to cover a floor; how many yards, which is IJ yards wide, will cover the same floor ? Also what are the dimensionw of the room, X i EXERCISES. 211 «' allowing the -width to he the least possible to permit either piece to he used without waste t 50. If I st'l hay at 81.75 per cwt. ; what sh^ald I give for 9 J tons that I may gain $7 1 51. How many tons of hay, at $16 J per ton, can he bought for $196 J] 52. A gentleman left his son a fortune, ^ of which he spent in 2 months, J of the remainder lasted him 3 months longer, and § of what then remained lasted him 5 months longar, when he had only $895.50 left ; how much did his father leave him 1 53. A farmer having sheep in two different fields, sold J of the number from each field, and had only 102 sheep remaining. Now 12 sheep jumped from the first field into the second; ihen the number remaining io the first field, wi.8 to the number in the second field as 8 to 9 ; how many sheep were there in each field at first? 54. A and B paid $120 for 12 acres of pasture for 8 weeks, with an understanding that A should have the grass that was then on the field, and B what grew during the time they were grazing ; how many oxen, in equity, can each turn into the pasture, and how much should each pay, providing 4 acres of pasture, together with what grew during the time they were grazing, will keep 12 oxen 6 weeks, and in similar manner, 5 acres will keep 35 o?eu 2 weeks 1 i Criyia r^r'T^/ 'Sf PARTNERSHIP. f Partnership is the result of a contract by which two or more parties combine their resources for the purpose of carrying on some business or enterprise for their joint benefit l.-fj'^' Pi^^n* thua asBockted ^re individnaUy cUled i»rtne«, «d ool- leetiveij a Firm, House or Company. An agreement to enter upon a business and share the profits «nd losses constitutes a partnership, and this agreement may be written rr verbal Articles of Copartnership are the written agreement under which the partnership exists. A Secret Partner is one who is actually a pariiner by partici- pation in the profits, but who is not avowed or known as such. A Dormant Partner is one who takes no part in the control of the business of the firm. A Nominal Partner is one who holds himself out to the world as a member of the firm, but who is not so in fact, having no interest in the profits. All such parties are liable to creditors for the debts of the firm they were in every respect regular partners. The Resonrces or Assets are all the property to the extent of its value belonging to the firm, together with the debts owing to the firm by others. The T.lfthilJHaa fV,, either direct or certain, or indirect or contingent uiiu Oyich, aiid are i h\ f^^!!^r^r^=:^^^:rt: - ^^:J-^,— j;^^..^;^^^;^^ DEFINITIONS. 21S Direct Liabilities are those for which the firm is certainly liable. Indirect Liabilities are liabilities of others which the firm has guaranteed, and for which its liability is contingent on the good faith or solvency of others. The Net Capital is the excess of Assets over real liabilities. The Net IlWOlvency is the excess of real liabilities over Assets. NoTI. — The last two definitions do not includ* as liabilities the partners investments. The net capitals of the partneni are liabilities of the firm, and when ascertained and added to the other liabilrties make the total liabilities equal to the assets. The amounts drawn out by the partners are not assets in any other than a oonttructive sense. The Net Gain for any given period is the excess of gains over losses during that period; or it is the amoimt by which the net capital at the end of the period exceeds the net capital at the beginning of the period. The Net Loss for any given period is the excess of looses over gains during that period; or it is the amount by which the net capital at the beginning of the period exceeds the net capital at the end of the period. The share of the net profits which each partner is to receive is generally determined beforehand by agreement, and is equitably in proportion to his entire contribution in money, labor, skill, &c., to *he resources ^nd management of the business, as compared with the total amount of such resources engaged. Example. — A and B were partners sharing gains and losses, A §, B J. A invested $2700, B $1500. At the time of settle- ment the assets and liabilities were as follows : Cash in hand and in bank, $1935.42 ; merchandise, per inventory, $7551.36 ; notes on hand per Bill Book, $2000; various persons owed them $966.24. They owed on their notes $2931.95, and on personal accounts $3978.12. What was the net capital of each partner? *^* PARTNERSHIP. AsSBTS. Zf 11935 42 Personal Accts, Dr. 966 '>4 Total aaseta ^ ^" $12453 02 Liabilities. l^^ Pfy*^^« $2931 95 Personal accte,Cr gg^g jg , Total liabilities [T::^;: $6910 07 Net capital of the firm ^777777 ^'-f^ ,..;:::;;:::;,27oo-oo '""*' ° 1500 00 4200 00 Finn's net gain . . . ^ B;sshareof net gain (J). ..' .'i ;;;;;;;;;:; •«44r65 '' (*> 895 30 1342 95 A;8 investment $2700 00 ±118 Share of net gain ggg jq A's net capital $3595 30 Bs investment «1500 00 Ui8 share of net gain 447 65 ^'^ °^* ^"P^*«^ TTTT 1947 65 Total net capital as above ^5543 95 If the books had been kept by douWe entry the same result would be amved at from the following data and process : _ A and B were partners, sharing gains anc'. losses A *, B i • A invested $2700, B $1500. At the time of settlement the Ledger showed gam on merchandise $2151 33 and 1w nr^-n.^- ■ 4049 TO T V * v-iJi.oo, ana by commissions »^4rf.72. Loss by expense $810, and by interest $242. 10. What was the net capital of each nartner 1 ^^^i^r-{ >^T>^ EXERCISES. SIS Oainb. From merchandise $2181 33 " commissions 243 72 Total gains 2395 05 Lossm. By expenses |810 00 " interest 242 10 Total losses . 1052 10 Finn's net gain 81342 95 B's share of net gain {^) $447 65 A's " " (I) 895 30 1342 95 A's investment $2700 00 His share of net gain 895 30 A's net capital 13595 30 B's investment $1500 00 His share of net gain 447 65 B's net capital 1947 65 Total net capital $5542 95 The Profit and Loss, and partners' accounts are shown in the following skeleton ledger accounts : PROnT AND L08& Expense Interest A't net gain {i B'» " " (J) 810 242 895 447 00 10 30 66 Mdse Commissions 2151 243 33 72 _2395 05 2395 05 A. Balance 1 3596 3595 30 30 Investment Net Gain 2700 895 3595 00 30 80 Balaniee 1947 1947 Investment Net Gain 11600 447 1947 00 65 65 I ^ / tie PARTNERSHIP. EXEROI8E8. ^ 1. W, Smith and R F»an« «,-.- ^ ■ . •hip .h. ^u „a ,i.i,mL"."eri- fa, :. M^'l' " •"?": «t 11295 • cMh ll'lii . * ■* "'"'^'^« • Merchandisa valued 31 a settlement being desired *h J, '^ December merchandise in stoj^r clh .5^37 T '"""' '^ "^ considered good. «3000 Liatil"^ S''^, ^^t't^''^ '^^^^^ •940 and Brown $875 W^tT T' ^"^''^ ^" ^^^^ ont wn »o /o. What was each partner's net capital ? 3. Harvey Miller and Jamoc IVr. -rcr .«. -„,. «» JTor. SootU Cotton Co «90(i • . K„u" ■ . ' '"' "' pe».„.l .cct. »U57.33, „d on n,l» ,Su mft T °k partner's net capital t »' •'-'o. i ». W hat is each loss. Young and Rusin IchT ^o ," i' " "^^ ^ ^'"^ "^* hand 8712 90 • nS^ ^' ^" '^^^'I'^'ng they had cash in B B ft i^n-'- u^' '""^'^^^''y ^*360; bills receivable nlr B. B., ei450./o ; cash on deposit in People's Bank fsAr ^ ehipped to Montreal to be soM n„ f\, * ^'^ ' ^''"^^ .. .M5 , debt. du. .hl^r,^r *rar,Zo'°'' '?•:"'"=' was accrued interest t4i fi7 ^ *«'0"nt8 «2600, on which there *^m, .nd d„, 0.. ^„, c'c Lt.2";;r:i EXERClHES. flT ^ \ 4 1 ^rew out $.'500 ; Frank RuBnell iBTested $3000, and drew out $750. Whiit WM the net capital of each partner at clusing 1 8. A, B and C were pnrtnerH, sharing the f^ins and loaaM «qually. A'a net invfl«trn«nt was |87ft2.13 ; B'g 8860O ; C'a 18500. During th« year the firms gains were, on raerchandia* #8529 ; on stocks and bonds |65G ; on interest 1985.26. The cost of conducting (he business was f2[25. What was each partner's intert-xt iit closing t 6. M and N are partners, M slmring J of the gain or loss, and If l- M invested 115,000 and N $C 000. At the and of a year the rt'sources and liabilities of the concern are as follows : Cash in hand, $2128 ; bills payable, $4000; bills receivable, $3000 ; the firm owes sundry persons $8375 ; there* is due the firm from sundry persons $1€427 ; out ol which $1314.16 is written off aa bad ; rent paid in advance, $375 ; mortgage held by the concern on the property of W. S. Hope, $5000 ; accrued interest on the eame, $150 ; shop furniture valued at $835 ; mdse. in atore $9500; ft''crued interest on firm's note* eutstanding $112. Accrued iiiUrejt on no-o*. ueld by the firm $175. M has drawn out $2465, and N $2075. According to agreement each partner is to receive a salary of $2500. What are the separate interests at the close of the business 1 ^i 7. A, B and C are partners sharing gains and losses as Mlows : •A, A ; B, T^ ; C, ^*^. A invested $3000, and has withdrawn ♦2600 ; B invested $2700, and has withdrawn $1150 ; C invested $2500, and has withdrawn $420. After doing business 14 months C retires. Their assets consist of bills receivable $2937.20; mer- chandise $1970 ; cash $1240.80 ;^125 shares ef the People's Bank stock, par value $20 per share ; cash deposited in the Bank of B. N. A. $1850; store and furniture $3130 ; amount due from W. Smith $360.80; from G. S. Brown $246.40 ; from K R. Thomas ' $97.12. Their liabilities are, due Saml. Harris $1675; W. T. Esson $935 ; outstanding notes $3385.76. The People's Bank stock is valued at 10 % premium, and C oa retiring takes it as part payment What is the balance due C, and what is A's and what \ is B's interest in the business ] ^ 8. M and N have been partners sharing gains and losses, M jil. iiiveeucu %>t\/'j\jf ayi^Ta^xj UiivC rtr -loan 7w^ ■ Ufi^A 218 PARTNERSHIP. i f : X)^ 1^! drew out $2700, average « «<"«« a. if As had been SlOoOO, and B's S9«00 for 1 month, or the same length of time each Helce the proportion as above. 18. A, B and C are associated in trade. A furnished $300 for 6 months ; B $350 for 7 months, and C $400 for 8 months They have J1490 profits to divide. What is the share of each 1 19. A, B and C contract to perform a certain piece of work A employs 40 men for 4^ months ; B 45 men for 3i months, and are *8oO. How much of this belongs to each ? 20. Four men, A, B, C and D, hire a pasture for $27.80 • A puts in 18 sheep for 4 months ; B 24 for 3 month* ; C 22 for 2 months; and D 30 for 3 months ; how much ought each to pay ? 21 On the first day of January A began business with a capital of $760, and on the first of February following he took in B, who invested $540 ; and on the first of June following they took in C, who put into the business $800. At the end of the year they found they had gained $872. How much of this was each man entitled to 1 22. Three merchants, A, B and C, entered into partnership with a joint capital of $5875, A investing his stock for 6 months B his for 8 months, and C his 10 months ; of the profits each partner took an equal share ; how much of the capital did each invest 1 Tlirce persons, A, B and C, do business for 1 year from Jan. 1 and the profits are to be shared in proportion to average investment. A, on starting, invests $4000 ; April 1, withdraws $500; Sept 1 invests $700. B, on starting, invests $3000; April 1, withdraws f «oL ^'^'*' ' '"''''*' ^*^- ^' ""^ «*«'""8' i'l^^sts $2500 ; June 1, $800 more. At the end of the year they have $1500 to divide. fV iliit !H ftfl^l* *^aT*f ?^£ST*C c1-i.-.^^. *? •Jf^lff ■-iW>3l EXERCISES. 221 B SOLUTIOif. 4000X3=12000 — 500 3500X5=17500 +J700 4200X^=16800 3OO0x3= 9000 — 600 2400X5=12000 + 400 2'800X 4=1 1200 46300 2500X5=12500 + 800 3300X7=23100 32200 35600 114100 Then, 114100 : 46300 : : $1500 : $608.68 A. 114100 : 32200 : : $1500 : $423.31 B. ' 114100 : 35600 : : $1500 : $468.01 C. A's investment was eq»ial to $46300 for 1 month, or an average i v ,stment for the year of ^.m^. B's was equal to 8.32200 for 1 month, or an average for the year of .*2(;s;ii C's was equal to 136600 for 1 month, or an .WHrage for the year of 82966§. And the whole investment was equal to 8114100 for 1 month, or an average for the year of 89508J. The proportion may tlien be made tlius, ^^^^ _ ^^^^ _ _ ^^^^ _ 8608.68 A, and so on for the others. But it is clear that 12 times the first and second terms bear the same ratio to one another as the terms themselves, and by taking the average for 1 month instead of for the year fractions are avoided. The first proportion above is therefore to be preferred. / 23. Two merchants, A and B, entered into partnership for ' two years ; A at first furnished $800, and at the end of one year . $500 more ; B furnished at firs!; $1000, at the end of 6 months $500 more J and after they had been in business one year he was /^ compelled to withdraw $600. At the expiration of the partnership their net profits were $2550. How much must A pay B who wiielies to retire from the business '' 24. A, V, and C are partners. A puts in to the concera $4000, but withdraws half of it at the end of 6 months ; B puts in $2500, and adds $500 at the end of 4 months ; C puts in $2800, and at the end of 8 months adds $400. The gain during the year is ?rioui). What is each uuea siiaie » 222 P iRTNERSHIP. 25. A, B and C are in partnership from the 1st of January under the following conditions : A is to manage the business at a salary of $1800 which is to be credited on July 1. He is to receive interest on his salary from the date of credit, and pay interest on sums withdrawn by him @ 6 %. B and C furnish the ca[iital, and are to receive interest therefor at the rate of 6 %. The net gain or loss to be divided equally. B invests, Jan. 1, ^ 810000, May 1, $5000. C invests, Jan. 1, $10C00, July 1, 85000. A draws out Feb'y. 1, $250 ; March 10, $200 ; Juno 15, $500 ;_ Sept. 25, $300 ; Nov. 21, $100. At the end of the year the gain, before the interest on the partners' accounts is reckoned, IS $6384.80. What will be the balance of each partner's acct. when everything is properly entered ? Note. -In reckoning interest ^» aen the time is even months reckon by months ; when not, reckon by daya, 26. Thre»«porl8men go out for a day's fishing. A takes 3 rolls for lunch, B 5, and C takes none. Meeting when all are hungry they take their meal together, A and B charging C 24 cents fer his meal. On the assumption that the food is divided equally, how should A and B divide the 24 cents between themi 27. A and B buy a ship for $40000, A having f interest and ^ B f. Subsequently they sell C a J interest for $18000, and ' agree to retain each J interest. How much of the $18000 belongs to A, and how much to B ? 28. J, K and L are partners, J to have f of the gain or loss, K f and L I Interest is to be reckoned at 7 % on the partners' accounts, and each partner is to receive a salary of $1800 to be credited on July 1. J invested, Jan. 1, $16000, and withdrew during the year $4875, average date Aug. 18. K invested, Jan. 1, $21000, -and withdrew $7224, average date July 10. L invested, y Jan. 1, $6000, and withdrew $2525, average date July 15. Dec.' 31, the merchandise account shows a gain of $18743.16' the interest acct. (before the interest on the partners' accts. is reckoned) again of $496.12; sundry shipment accts. show a net gain of $1572.10. The expense acct. (not counting the partners' salaries) ehovva a loss of $2842.72. What is each partner's interest in the DUoilicsa at uiumug ? I EXERCISES. tss ^ 29. E, F, G and H are partners in business, each to have J of the net gain or loss. The business is carried on for one year, when E and F purchase from G and H their interest in the business, allowing each 8100 for his good will. Upon examination their resources are found to be as follows : Cash in bank $3645 ; cash in hand $1422 , bills receivable $1685 ; a bond and mortgage i5!274C, upon which there is interest accrued $106 ; 5 shares Bank of Montreal stock $1000 (par value); 25 shares "Halifax Banking Go's, stock; merchandise $4125; store and furniture $3500; house and lot $1800 ; span of horses, carria^res, harness, &.C., $495 ; outstanding debts due the firm $4780. Their liabilities .ire, notes payable $6470, upon which interest has accrued $57 ; due on book debts $1560. E invested $5000,^and has drawn out $1200, on which there is interest $32. F invested $4500, and has drawn out'^lOOO, interest $24.50. G invested $4000, and has drawn out $950, interest $12. H invested $3000, and has drawn nothing. In the settlement 10 % discount for bad debts is allowed on book debts due the firm, and on bills receivable. G takes the Bank of Montreal stock at 190, and H takes the Halifax Banking Go's, stock at 108. How much is still due G and H, and what are E and F's net capitals, allowing all the debts to be good! 30. H. C. Wright, \V. S. Samuels and K P. Hall are doing business together— H. C. W. to have J gain or loss ; W. S. S. and E P. H. each J. After doing business one year, W. S. S. and E P. H. retire from the firm. On closing the books and taking stock, the following is found to be the result : Merchandise on hand $3216.50; cash deposited in Bank of Nova Scotia $1627.35; cash in till $134.16; bills receivable $940.60 ; G. Brown owes, on account, $112.40; Thos. A. Bryce $94.12; W. McKee $'13.95; J. Anderson $54.20; 11. H. Hill $43.60, and S. Graham $260.13. They owe on notes not redeemed $1864 ; H, T. Collins, on account,' $i24. 45 ; and W. F. Curtis $79.40. H. C. Wright invested $3200, and has drawn from the business $350. \\" S. Samuels invested $2455, and has drawn $140. E P. Hall invested $2100, and has drawn $2000. A discount of 10 % is to bo allowed on the bills re^ceivable and book accounts' due the firm for bad debts. H. C. Wright takes the aasets and assumes the liabilities. What is the settlement among tue parlueis al liiooolutioii i 224 PARTNERSHIP. 31, I, J, K, L and M were partners 8harin -L^i ^(j, and ii, 1- EXERCISES. 225 i- ^. A is to pay JJl.25 per day for all lost time ; B, $1 ; C, $1.50 ; IJ, $1.75, and E, |1.62^. * At settle'uent it is found that A has Ibst 24 ; B, 19 ; G, 34 ; D, 12 ; and E, 45 days. They receive in payment for their joint work, $2500. "What is each partner's share of this am jtmt according to the above regulations ? , ' 35. A. B. Smith and T. C. Wilson commenced business in partnership January 1. A. B. Smith invested, on commencement, $9000; May 1, $2400; June 1 he drew out $1800; September 1, $2000, and Octolier 1 he invested $800 more. T. C. Wilson invested on commencing, $3000; March 1 he drew out $1600 ; May 1, $1200; June 1, he invested $1500 more, and October 1, $8000 more. At the time of settlement, on December 31, their mercliandise account was — Dr. $32000 ; Cr. $29456 ; balance of merchandise on hand, as per inventory, $10500 ; cash in hand, $4900; bills receivable, $12400; R. Draper owes on acct., $2450. They owe on their notes, $1890, and G. Roe on acct, $840. Tlieir Profit and Loss acct. is— Dr. $866; Cr. $1520. Expense acct. is — Dr. $2420. Commission acct. is — Cr. $2760. Interest acct. is — Dr. $480 ; Cr. $950, besides which interest is to be allowed each partner at 7 % on his investments and charged at the same rpt^ on the amts. withdrawn. Gains and losses to bo shared equally. Work out by both single and double entry methods and give each partner's net capital. 36. A owns a business the good will of which is estimated at $10000, and the stock on hand at $15000. B and C agree to unite with him on the following conditions : B to invest $25000 cash, and C to devote his time to the business for which he is to receive, in addition to his interest, an annual salary of $1000. The capital to be kept intact and no interest to be allowed therefor. The gain or loss to be shared equally among the three partners. At the end of the year the resources, including the good will, book accts., notes, inventories, etc., amount to $66425, and the liabilities to outside parties, to $10500. C has drawn during the year, $2500; B, $1575; A, $2000. What is the balance of each partner's acct. ? 37. A, B and C are partners in business, investing as follows : A, $4000 ; B, $6000 ; C, $8000. The partners are to share the profits and losses lu proportion to their investments. Each ia 226 PARTNERSHIP. entitltMl to compensation for services at the rate of $150 per month, payable at the en.l of each month and not to bear interest In case tliat either party draw a greater amount than shall bo duo him for services, he shall be charged interest upon such overdraft at the rate of 1 % per month for the length of time such overdraft continues. At the end of the year B and C purchase A's interest, and in the payment ther,for it is desired that the remaining partners shall so invest that their interests 8ha 1 be cpiaL It is mutually agreed that, for the purpose of settlement, the "good will" of the business shall be valuo.l at «JUUO. It IS also agreed that a discount of 5 % sliall be allowed upon all uncollected accounts as a fund to meet bad debts and costs of collection. A statement of the business previous to closing shows the following results : Merchandise, horses, waggon and office, fixtures, $9840; cash in hand, $2570; sundry debtors, $17030; sundry creditors, $4050; expense acct. (not including partners' salaries) $2400; ^Jrofit on merchandise sold, $15290 A was paid on acct. of salary, April 1, $450; July 1, $300 • Oct 1, $400. B, March 1, $400; April 1, $150; June 1, $400; Oct 1, $800 ; Dec. 1, $500. C, AprU 1, $600; July 1, $700; Oct 1 $600 ; x\ov. 1, $200. How much must B and C each invest iil purchasing A's interest. And how should the books of the new firm be opened 1 GENERAL AVERAGE. Gteneral Average is a method of eqiiitahly distributing among all parties concerned any loss which has been sustained by one or more of the parties by a necessary and voluntary sacrilico of property for the common safety. It is especially ap[)lied to the adjusting of such loss when happer 'ng at sea where a vessel and contents are saved from destmction by the voluntary sacrifice of a part of her cargo, or by cutting away her masts, rigging, &c. Among the losses which become subjects of general average are the following : 1. Jettison, or the casting overboard of cargo, stores, &c., for the purpose of lightening the ship ; damage to .cargo by the influx of water during jettison ; freight of goods jettisoned. 2. Two-thirds the cost of replacing masts, sails, &c., volun- tarily sacrilieed to save the ship. Note.— When a vessel is on her first voyaRe the whole cost of such repairs is allowed. 3. Damage resulting from running the ship ashore to prevent her sinking if the operation is successful in saving her. 4. Expense of entering port of refuge, cost of discharging and reloading cargo, rent of warehouses, &c., 'fee. 5. Wages of seamen from date of bearing up till ready for sea. Note.— Some of the above charges are allowed as subjects of general average, in some countries, and not in othsrs, the practice not being entirely uniform. The above general heads, however, though capable of great sub- division into particulars, include all or nearly all allowed in any country. The Contributory Interests on which these charges are assessed are, in general terms, the ship, cargo and freight. ^2^ GENERAL AVERAGE. The ship contributes on its full value at the time the loss occurred. The car^o (including the portion sacrificed, if any) contrilmtes on Its market value at the port of destination less frei.d.t and charges. " TJie freight contributes on the full amount earned, less the captain's and crew's wages for the voyage and all incidental expenses. fnr !!"^^'~^" """' Pl"^*' *• '"•^ '" "'''^■•^ i " deducted from the freigh. An Average Adjuster is one whose business it is to adjust and apportion the losses and expenses of general averages. ExAMPLE.-The stoamer Cuf>a left Halifax for Liverpool with a cargo as follows: Shipped ,by A, $7480; by B, $53fir, ■ bv C miS; by D. $11428; by E, $7559. After two day^ out a heavy gale was experienced, and it became necessary for the general safety to throw overboard a part of the cargo, and to put into St. John's for repairs. Repairs were made to the steamer cos mg $1176. The total cost of entering the port of refu<.e including wages, port charges, dockage, &c., was $1498. The value of cargo jettisoned was estimated at $4282, of which $1123.40 belonged to B, and the remainder to E. The steamer was valued at $100000, and the freight, less seamen's wages, was $3450. What was the loss per cent., and the settlement among the parties interested ? SOLUTIOM. Loss FOB General Average. Contributory Interests. Cargo jettisoned $4282 Steamer $100000 Expenses entering port . . 1498 Cargo 4 1 qsq Toi^Iloss ij^ ^''''''' '.'.'. Ji50 Total $144500 e5780-^144500=.04, or 4 %, loss per cent. ■ EXKKCISES. 2J9 APrORTIONIIBXT. Steamer'8 ahnre of loss, 4 % of «100000=|4000 Freight's " " 4% of 3450= VM ^.g " «« 4 % of 7480= 299.20 jj-a .. «• 4 % of 5365= 214.60 ^^'^ .« " 4 % of 9218= 368.72 j)'a » '< 4% of 11428= 457.12 j«.g .. .. 4 % of 7559= 302.36 Total loss, 4 % of ei44500=$5780.00 ADJl'RTHENT. $4138 -$2498=82640 bal. payable by steamev. $1123.40-$214.60=$908.80 bal. payable to B. $3158.60 -$302.36=2856.24 IwL payable to E. Payable by Seceivabiji! by Steamer $2640 B $908.80 ^ 299.20 E 2856.24 C....! 368.72 D 457.12 $3765.04 « $3765.04 EXERCISES. 1. The bark Ocean Queen, on her trip from Philadelphia to Liverpool, was crippled in a storm, in consequence of which, and to save the bark from total loss, a portion of the cargo, afterwards ascertained to be worth $4465.50, was jettisoned, and one mast, costing to replace $595.75, was cut away. The cargo and owner- ship were as follows: A, $3650; B, $6500; C, $2000; D, $550 ; E, $5450 ; F, $8500. Of that thrown overboard there belonged to B $3000, and to F $1465.50. The contributory intere^'sts were, vessel $30,000 ; cargo, as above, and net freight, less seamen's wages, $4150. Required the loss per cent, and the settlement among the parties, concerned. 2. The steamer Persian left Boston for Halifax, laden with 72iO bushels wlnjuL, cOUoiguea n __,^^;,««.l rtf Q,5 f\f»ntfi Dsr 2S0 buaht>l GENERAL AVERAOE. cents per ,...h.,,;:^^f3;;o™:,rr' '^"' "'"^ ■"^"■''-' "^ «o bbk iluur. On estin.nf; *i ' " ^""'''- *=«"'. '""1 1140 tHatt,..,eat::r::::f::,nE^^^ the com at an advanc. of 15 7 Id th « "" :'''""'" "^ '^ ^• contributory i„ter,.st« » /"' ''''"' ** *'' P«'^ '^''J- The ""jiy inieri'sts were, steainor aOfinnn ■ and net freight «.->246.20 WhT T, !r ' '"^'° ''' "'"'^■^' «'^«°. settlement ? " '^ *^^ ?««" ^ent of loss, and the Co.; 9200 bush. corn, valued a rVVr*^ '^ ''"""' ^''"^'^ * Roe; 14.00 bush, oalrley^tf^^^^^^^ Morris VVright & Co 1800 . «' ^ ''"'' ^'^ ^"^'^•' ^'''I'P-' by shipped b/smirh ;Wor n'c ' "'"' ** ^^'^^ ^^ ''^'^ the Gulf of Mexico, it was LnJ ^^'''T '' ' ''"''''' ^'^^« '^ ' flour, 4600 bush.;ats a^d 3 50 Zr^h t"" 7^'""' ^^« ngging were cut away, which cost to "^^4'^ "T ^°' was on her first voyage and w«, ,1 '^f '''=<' J3694. 17. The ship after deducting sei?: Wagls/ndth:; f ^^^^^ ^''' '"^^^^ Reaui^d the I0.SS porce„t..Ld t aett^n:!""' ^" '*'^°- ^^-"^^1^:%:::^^ «„ boar. 117400. and by D. ,$9000 ^A^Lr 'the fr,/ ^ ' ^''''' ^^ C' tered heavy gales, and sustained con.lrah 7 '"* ^'^ •'"^'^"°- the safety of the vessel and . '^"^''^^'-^We damage, so that for were jetfisoned alTtt "-o^^^^^ ^^- ^' ««60.I5 The disbursements of the'lmT IT ''^^ ^^^"''^ ^^^ repaid. Custom house fees pilole f "' ^"""^"^^ ^^^^ «« follows: cargo, wharfage. &c « 40^' R n"'\ 'T"'' ''''''''' ^-^'"-« commission for 'advJndng fundsT? ''w''' ^''f''' ^^«-^' -mea from point of 'deviati^ isS^^T The T-'f", '' oeamens wages ar,d other charges 36624 T. u '^'^*' ^^ at «12000. Adjuster's fee ^100. ' ^atis the' m' "" "^"' the parties interested ? • y^fiat is the settlement among MISCELLANEOUS EXERCISES FOR COMMERCIAL STUDENTS. 1 A men^hant hought 500 bushels wheat, and sold one-half of it at 80 cents per bushel, which was 10 % mow than it cost him, an.l 5 y less than hii asking price. He sold the remanulcr at ' 1 01 7 more, than it cost him. What was the cost per busb-l, what was his asking price, and how much did he gain on the whole t J Mayl 1880, I got my note for $2000 payable in 6 months discounted at a bank at 6 %, and immediately investe.l the proceeds in woo.lland. Nov. 9, I sold the land at an a.lvance of 15 7 receiving i of the price in cash, which I loaned the same day It 6 % interest. For th6 remainder I received a note payable in 1 year,°9 months, and bearing interest at 7 % after Dec 31, 1881 When my note at the bank became due I renewed it for 6 months, and did the same again and again, each for 6 months, and then for three months; when the last renewal became due I collected what was due me, and paid it How much money did I have left? The student wiU also write up all the entries in the Cash Book in proper form, s 3 Five men were partners for 4 years in a business which required the time and attention of only one of them. The profits were to be divided in proportion to average investment. Ihey advanced capital as follows :-A, |60 r-,t first, and ^800 more at at the end of 5 months, and $1500 at the end of a year and 8 months B, $600 at first, and $1800 at the end of 6 months. O, ^400 at first, and $500 every 6 months thereafter. D, $900 at the end of 8 months, and the same sum every 6 months thereafter, fc paid in no money, but managed the business and kept the books, for which he was to receive a salary of $600 per annum, to be credited as ., 1 > 1 Tu« ««<• TM.nfi*-.a a*^. *^be end an investmeul at liio oQ>i oi c-cu jo-i. j.-- "•-•• v— 282 MISCELLANROITS EXERCISES. 'i if iff I ^ of 4 years were 120000 Whaf w^o fk l ■ . JoMR h.is al» inaJe sale, to the val™ of S'S-e « J -.1 , paiJ I364.16 a.d J„„„ »239.I4 fo, expel, 1 1 ) T year J„u« ha, on hand good, worth Co, ,, ll ""' "' "" woHh ,3U.«.. The peLd foniliL"^:!'":'': Se ^n and .hat money n.n,t p^ between tho partner, to « e - e^h^hern,. w.U.„« to keep t^e ,.o„d,, in hi, po„e»ion at the Z. cash, * 15. The agent received cash for liquor sold Sno^ in He paid for liquor boueht flSQ-i? • t. .u . ' ^^•^•^•^•*0 sundry ex^ens s SOQ V ' ? ' *"'"" *''"^''"«'^' ^^OO • indnlf^t >. ', ' ''''' '"^*''^' ^2^^' h<^ delivered to mdl^t persons by order of the town, liquor to the amount of moO. Upon taking stock at the end of the year the linuor hand amounted to «616.50. Did the town gr;ts^Tv the agency, and how much; has the agent any money iLlL' "r ^iiriT ' '' "^^ ^" ^-" - - --- - -: from Ju1v l1'' ""'^T V'' "'''''' '' *^« -d «f ' months from July 13 ; on August 9, A received $62 in advance as- mrf payment, and on September 5. S45 more; and on Oc toC 3^ B w.hes to tender such a sum a.s will, together with tl payL L^ already inade. extend the time of payment forty day Wd" how much must he tender ? ^ loiwara , aveL '!'500 lb! '' "llf ^ '"'"' '" "^° '°« ^^^^^ ^^ -tton, i . ^.3 a^an at OH days from MISCELLANEOUS EXERCISES. 233 N N. January 1 for an amount sufficient to pay for the cotton, charges and commission, includinj^ ftlao 2 per cent, discount on the draft. On receipt of the invoice, I insure for the amount of the draft plus 10 per cent.; I pay 1^ per cent, premium on the amount insured, and from the premium is discounted IJ per cent, for casli. On arrival of the cotton I pay | of a cent per pound for freight, and 5 per cent, primage to the captain on the freight money, and also 4 cents per bale for wharfage. I sell it on the wharf, January 20, at $1 per bale profit, and agree to take in payment the note of tlie purchaser for 6 months from January 20. What amount would be received on the note when discounted at a bank on the same day at 7 per cent 1 8. I have purchased for cash, ])er the order of J. P. Fowler, 70 lx)xeH of bacon, containing on an average 400 lbs. each, @ 13^ cents per lb., and 140 firkins butter, in all 8312 lbs. @ 17A cent.'* per lb., on commission @ 2^ %, and paid shipping and other exjienses in cash $13.40. I wish to draw on J. P. Fowler a*, sight in full settlement of my account, and I shall have to sell the draft at I % discount. Reijuired the face of the draft, and all the journal entries. 9. J. A. Jones, of Halifax, owes W. A. Murray & Co., of Washington, $1742.75, Iming net proceeds of a consignment of tobacco sold for them, and Simpson & Co., cf Washington, at the .same time owe J. A. Jones' $2000 payable in Washington. J. A. Jones . is to remit W. A. Murray & Co. the proceeds of their cpnsignment, and he does so by a draft on Simpson & Co. Now if drafts on Washington are at 2 % .premium, what would be J. A. Jones's journal entry on making the remittance ? Also what would be his journal entry if similar exchange were at 2 % discount 1 10. A. Cummings, of London, Lng'^nd, owes me a certain sum payable there, and I owe Chas. Massey, of the same place, $1985.42, being proceeds of a consignment of broa'^cloth sold for him here. I remit Cliaa. Massey, by his order, in full of acct., together with $21.12 interest, my lull of exchange at 60 days sight, on A. Cummings. Give my journal entry, the buying price of sterling exchange l>eing 109J? 11, On May 1, I jiurchased for cash 380 bbls. mess pork @ $27, .'iO ]WiT bbl. on cnjiunission (S' 2i °/, .ind .<5binned Ross. Wina-ia (fe Co., commission merchants, IJaltimore, by arrangeuient, to be sold r 234 MISCELLANEOUS EXERCISES. 'S 1 KM I 1 J- ■'* [ \ ou joint account of them and myself, each one half. Paid sliippin.' expenses $7.40. July 7, I irc-ived from Ross, Winans .1- Co." anaect. sales, .showinj,' lialf the net jwoeeeds 1,. he $5319.79 duo as per avera-e, Aug 12, and they advise me to draw ou tliem pay- ahlc at that date in full of acct., mcluding interest @ 7 %. What should be the face of the draft if it cost i % to cash it, °and what journal entries should he made for the whole l)usines.s ? 12. On Sept. 27, I received from James Watson, Leed.s, En<'., a consife. ment of 1243 yds. black l)roadcloth, invoiced at 13 6 plr yard, to l^e sold on joint a-ct. of consignor and myself, each on(> half, my half to 1)e as casli, — invoice dated Sept. 16. Oct. 5, 1 sold R. Duncan for casli 207 yds. @ $3.75; Oct. 24, Jas. Ora'nt on 3 months' credit, 317 yds. @ $3.90; Nov. 18, E. G. Congdon on his note at 4 months, 400 yds @ $3.95 ; Dec. 12, J. A. Davis for lialf cash, and acct. at 1 month for balance, the remainder at $3.85. Charge for stora-e, advertising, &c., $13.40, and commis- sion and guarantee 5 %. When were the net proceeds due as cash ; what was the average time of Jas. Watson's acct., and what would be the face of a sterling bill, dated Dec. 15, at 60 days after date, remitted Jas. \A'atson to Ijalance acct. purchased at 108|, interest being allowed at 7 % ? Ahso give journal entries for the business transacted. 13. March 10, I shipped per steamer Caspian and consigned to Samuel Vestry, Liverpool, Eng., to be sokl on joint acct. of con- signee and consignor, each on(i half, (consignee's half to be on 4 nionths), 27,894 lbs. cheese, worth 11 cts. per pound. Paid ship- ping expenses $18.30, and insurance on above valuation plus 10 % @ 11 %.^ May 19, I received from Samuel Vestry an acct! sales showing ludf net proceeds to be £298 14s. lOd., due as per average^Aiig 21. May 28, 1 drew on Samuel Vestry, at tlie mimber of days after date that it took to make the bill fall due at the properlreipiated time of liis acct., and sold tlie bill at 109^. Retpiired the number of days I drew the bill at, its face, and the journal entrie.s. 14. J. II. Smith, S. North and E. Wills, coiuuienced business together as partnei-s under the name and style of J. H. Smith & Co., on January 1st, 1882, with the following ettects : mei-eliandise, $7844 ; cash, $5000 ; .store and furniture, $3984 ; l)ills receivable, iiuoii.ijO; of this amount there belonged to J. !{. Smith, as MISCELLANEOUS EXERCISES. 235 caiutal, $8000 ; S. North, $6000 ; E. Wills, $4560.50. The iii-m iLssumod the liahility of K. ■Wills, which was a note for $425.80 ; This note was pai.l on March 10th. The loss or gain was to be shared equally by the partners, but interest at the rate of 7 per Cent, per annum was to be allowed on investments, and charged on amounts witlidrawn. J. H. Smith was to manage the business on a salary of $1000 a year, payalJe lialf-yearly (the time of th(! other partners not being re(|uired in the business). March 14, S. North drew cash, $300; K Wills, $200 ; April 19, J. H. Smith drew $500 ; S. North, $100. On May 1, they admitted Geo. Smith as a partner, under the original agreement, with a cash capital of $4000. The books not being closed, he paid eacli partner for a particii^ation in the prohts to this time $450, which they invested in the luisiness. May 14, J. H. Smith drew $160; May 24, E. Wills, $100; June 12, S. North, $250, and J. H. Smith, $200; July 1, E. Wills $300, and S. Nortli, $450; July 21, E. Wills $180. July 31, E. Wills retired from the partner- ship, the firm allowing him $500 for his profits and good- will in the business, which amount, together with his capital, was paid in cash. Oct. 14, George Smith drew, $340; J. H. Smith, $725. November 1, with the consent of the firm, S. North dis- posed of his right, title, and interest in the business to J. K. White, who was aihnitted a partner under the original agreement. J. K. White allowed S. North $600 for his share of the profits to date, and his good-will in the business. J. K. White not receiv- ing funds anticipated, was unable to pay S. North but $1500, the firm therefore assumed the balance as a liability. Decemlser 10, received from J. K. White, and paid over to S. North, the full amount due him (S. N) to date. December 31, the books were closed, and the following ett'ects were on hand :— Mdse, $1 1943.75 ; cash, $2110.12 ; bills receivable, $6400 ; store and furniture, $3850 ; personal accounts Dr. $14987.50; personal accounts Cr. $10711; bills payable unredeemeil, $4000. Wliat has bocn the net gain or los.s, the net capital of each jiartner at the end of the year, and what were the double entry journal i-ntries on con. mencing business, when Geo. Smith was admitted, when E. Wills retired, when S. North sold his interest and right to J. K. White, for J. H. Smith's salary, and the interest due from, and to, each partner, and the balance sheet at the end of li.' jfeai » ANSWERS. 1. *2308. 2. IB1335. 3. .'525. 4. $1116. 5. 1758. $123.06 $2332. 102206. 9. 13961. 10. 12057. 11. 2943. 12. $142. 13. 285594. U. 1875. 6. 7. 8. Pheliminary Exercises, pages 1 15- 162. 29. 156. 43 16. 1008. 30. 95ct«. 17. 245. 31. 189. 18. 37375. 32. $537. 19. 39262. 33. 144. 20. 56940. 34. I47^j 21. 21000 lbs. 35. 17079' 22. $435. 36. 35 cts.' 23. 5123. . 37. $892.50. 49 24. 4893. 38. 720. 50 25. 256198. 39. 35. 26. 84239|. 40. 128 27. 24404fe. 41. 16 cts. 28. $4. 42. $22.05 1. 5, 7 -t 3, 5, 3. 3, 7, 4. 2, 2, 5. 2, 3, 6. 3, 3, 44. 45. 46. 47. 48. 51. 52. 53. 54. 55. 300000 lbs. 56. $5.75. to 4. $19.60; $526.50 $5.25. $4.88. $437.50; $2625; $136500. 1230. $845. $1039350. $2075.75. 1440. 22 milea $537.75. 32 cts. 5 31 3,3,7,7 3, 11 19 Prime Factors, page 10. 7. 2, 3, 5, 7 8. 2,3,5,7. 11 9. 2, 2, 2. 2 "^ «> lij 19. $7.97ij 20. 20261 J; i i-y 1 !» 2 ay 1- u 2. 20 3. 21 1. I? 2. 1,V 4- U 5. 5] 6. 13.'. "• n?' 8. A 9. 1^ 1. Division of KnAcTiox.s. Case I, page 22. 5- tV 9. ^- 4 k 10. 7. A 11. J^. rV 12. ,., Caae II, page 22. 1 -, 13. .t 5 m .'A 14. .Vy .1 1' J 15. h\, 4. 39 5. 37.\ G, 63 7. 84. 8. 21 H 9. 198 Case III, pages 23, 24. 10. II. 12. 13. 1 1 2.\ 21 1^ 14. IV 15. 2^, 16. l]j 17. li 19. i? 20. U 21. J 22. U 23. ]J 24 "• 25 1 2 26 1 •-• 27. if Case IV, page 25. 10. 550? 11. 264iJ 12. 145| 28, Hi 29. 3 J 30. 2\ 31. J, 32. 8 1 33. iJ 34. 18 35. U- 30. ^^, 1583^ 2. 546JI 3. 976.-) 735 f 4. (! .i 1 T 1 1 .. 1 -■'1554 G. lOOj^V 7. 46 A 8. 723,ij 9- G8vV. ANSWERS. SS9 Case V, pngc 25. 1. 094^7, G. i^iV. 2_ GH,\ 7. GliJ 3. 16.51iJ 8. IGlflJ 4. 16G8i*r 9. SG^Hr 5. 2G8'f 10. 483^ Least Common Denominator, page 27. 1. 2. 3. US, iVs, iet A- \h^'i i8, i8. U- i.\ G. 7. 8. BiVj ft o', Bo J3?,. ^58. 25S. StS 4. 5. U- it. W V^8. HS, iVo. .Ya 9. 10. iVfi, !i8, T}iT Addition of Fractions, Page 28. 1. 2 6. \l 11. 4tV 2. 2A 7. m 12. fij 3. li 8. ^-h 13. lO^i 4. 1t\ 9. Ui! 14. nu .5. n 10. 2^,^ 1.'). ^Ot\ IG. 21:,V 17. ^ 18. 4. A 19. r)9il 20. 12i«^ Subtraction op Fractions, jiages 2',>, 30. 1. 1"T 2. i 3. A 4. .\5f T). 11 35 6. ^^ 7. e 8. ^0 9. 7,V 10. j5 12. ^ 23, 76H 13. 2i 24. 82H 14. G,^,T 25. 3r.9M 15. 525g 2G. 352iV IG. H 27. 2G7ii 17. H 28. mi 18. m 29. I'GTb 19. 711 30. $34 1 20. m 31. A 21. 243H 32. 7A 11. im oo. t40 ANSWERS. Dbcimal Fraction8, pag3 32. 1. Two-tenths. 2. Four-hundrecUhs 'l n„n i j , thirty-eight thousandths. 4. Four thousand fi l^""?"f '"'^ thirty-one ten-thousandths 5 ZnltlTu /" T'^'''^ ""^ 6. Sixhundredthousandhs. 7 Stt'h . '\^'^-''^- tliousandths. ft V ^'"^ V ^'g*"* thousand and four ton- nousandths. 8. Pour thousand and ten ten-thousandths. 9 Iwenty-one thousand and forty-two hundred-thousa"2 h. 10 Wteen nulhonth. H. One „.i,rion seven hundred ad forty ^r thousand one hundred and ninety-six ten .illior.ths. P E g t thousand n.ne hundred and eighty ten-nullionths. 1 3. Fort; ■ght. and seven thousand eight hundred and four ten-thousandths H. L,ghty.three. and eighty-four ten-thousands. 1.5. 7 hun dred and twenty-one, and eighteen thousand and six hid d" thousandth.^ 16. Three hundred and forty-five 'd t^^* milhonths. 17. Xine hnn.1pp,l „. i • -^^ ";^' ''"^ eighteen and niuetv-nine mU io,thr 18 O "".' ""^ '""' ^""^'^^^ I Pages 32 and 33. 1. -5 2. -22 3. -087 4. -0056 5. -0304 6. 7. 8. 9. 10. •5347 •000088 808-008008 •10057 121.121101 11. -0007007 12. 120000072101 13. •600607 14. 27905 045004 15. 9700000000453168 Page 34. ' -52 13. -3 8. 53125 14. -6 9. -47916+ 15. -5 10. -714285+ 16. -8* 11. -3125 17. -63 6. -4375 19 ^R 1. •6 2. •75 3. •5 4. •375 6. •625 19. •gie 20. -42857 i 21. •461538. 1 r» m.^ ANSWEUS. 241 Page 35. ]. \ 10. ■» 1 -• 4 11. H '-'0. /., 3. ,' 12. . 1 :i J It 21. i 4. i 13. ^\'-i •-'•-'■ U 5. ,\f 14. m 23. il, 0. i 15. ^% 24. }.l 7. ,';r 16. A 25. :,'« 8. n 17. H V 26. fl^ 9. 16 5?, ft 18. I ''7 i"***^ uu ITION AND SUDTKACTION OF Dklimaijs, pagt'S 3G aiid 3 1. G913-3477 10. 12-775 20. ■0099 2 84589734 1-J. 10-6780371: ■> 21. 1 0-001 S 3. 390374625 13. 38-885 22. -356 4. 25-563375 14. 4-887 23. -95 5. 7300-429 15. 11-2632 24. -2.38857142 6. 4039496 16. 10-3029 25. 1251 7. 800.2272.38 17. 102.00169 26. 4-9225 • 8. 920-1754 18. •0092 9. 2-52')8f 19. -0476 t ^lULTlPLICATION OK DECIMALS, page 38. 1. 2_ 3. 4. 5. -8636 -05824 18 -0015 6-4 6. 7. 8. 9. 10. 18-58922 11. -000064 -00000114 12. -001478741 472-619 13. -020736 •0441 14. 40-10416 28 15. 63-0416 16. -552 17. 1-55295 18. 1-95 19. 2-390i5 20. 5-0923076 Page 39. 1. 3. 45 -7 17050 4. 5. 6. 62 5 4866-6 48333-3 7. $486-66:^ 10. 8. $6750. 11. 9. S1737-50 Page 39. 48GG66G66ii 671428-571428 1. G44-1 2. 1-3365 4. 1806 7. 24075 5. 449-025 8. -08 10. 247-5 ^:-~;.'.V 3. 199-62." G. 48-75 242 ▲ NSWEKS. Divislux OK Dbcimals, pages 40 and 41. 1. 70 9. -005 17. 17-57 2. 42 10. 092268 18. 3875. 3. 313 11. 450 19. -3 4. 7191 12. -004485+ 20. 1237 5. 1122 13. 9706-36 21. -00007 G. 440 14. 1035-1042857i 22. 718-022884- 7. 63-445 15. 955-305 8. 0084 16. 88-252887-1- 1. 34:] -55 4. •083£ 7. 7 cents. 2. -57 75 5. •000075 3. 1-444755 6. -0586372 Keductiox OF J)>:nomi.\ate Numubiw, Paj, es 56, 57, 58. 1. 6144 17. 144000 33. 3267 49. 633 .\ 50. 144' 2. 78235 18. 1615 34. 18585600 3. 18240 19. 1842 35. 69984 51. 30 i. 26781 20. 144000 36. 480 52. 151^ 5. 30778 21. 31948 37. 4015967 044 53. 544 ti. 882 22. 168 38. 128000 54. 826 7. 27300 23. 1500 39. 40000 55. 2576 (<. 47825 24. 8330 40. 270 56. 684113] 9. 16000 25. 1020 41. 14760000 57. 20781756 10. 17730 26. 2240 42. 559872 58. 1248009 11. 7700 27. 220 43. 724032 59. 172225 12. 194428 28. 248160 44. 600 60. 210290 13. 576000 29. 997057 45. 1500 61. 2400 14. 2734 30. 20259,1 46. 702 62. 250 15. 31022 31. 253004 47. 180 63. 181 16. 8773. 32. 900 Payes 48. 400 59 and 60. 64. 184 1. £12. 12.S 7. 273 2. £325. 19« 7i I 8. 478-25 3. 19 9. 16 4. £27 17s 11" a 10. £17 7s 3d 5. £128 4s 10<1 11. 3 torn, 17 cwt. G, ISs 4^(i 12. 759 lb. 7 02 . 12 dr. ANSWEUS. i;». 18 39. 4 14. 24 cwt. l.ir. 18 Ik 40. 27 15. 13 tOllH 16 cwt. 3 i\v. 26 11.. 41. 147 a. 6 wj. ch. 16. 4 tons, 7 cwt 73 11). 42. 12 17. 25 43. 419 18. 6 lb. 8 oz. 15 pwt. 44. 75 19. 3 oz. 16 pwt. 18 Kr. 45. 15 20. 25 46. 21 gal. 3 qrt. 1 pt. '-' R. 21. 5 11). 6 oz. 4 dr. 1 scr. 8Kr. 47. 216 oo WW. 7 48. 480 'J3. 25 49. 760 24. 245 50. 120 25. 17 51. 25 26. 7 52. 126 27. 40 53. 17 28. 47 54. 12 bush. 3pk. 5 qrt 29. 15iu. r tf. .35ril. 3ytLlft.7in 55. 40 bush. 1 pk. .30. 3 ni. 6 f. 27 rtl. 4 yd , 56. 1873 31. 31 mil es, 50 cliains, 4 link. i 57. 240 d. 12h. 42 m. 36 8 32. Hi 12 58. 2 y. 136 d. 161 .9 ni. 33. 59. 47" 50' 25" 34. 6 GO . 58° 24' 50" 35 , 54 61 . 50 36 3 62 m 37 . 1 sq. m. 37 i sq. rJ. 20 sq. ya 38 . 20 [6»q.ft 112 sq. in. 243 Miscellaneous Exercises, pp. 60-64. 12. 13. 14. 15. 1. 5671 2. 15763 .3. 7 t. 7 cwt. 96 lb. 4. £55 7s. Id. .'). 95 t. 10 cwt. 75 lb. 16. 128. 6d. 6. 103654 7. 16 R. 31590 9, 17350 10. 76 a. 1 r. 35 sq. rd. 19 sq. yds. 21, n. 640000 [2 sq. ft liy aq. in. 22 99 m. 6 f. 29 rd. 3 y.l. ft. 102 [6 in. 62 A 1400O Ji" 17. 18. 19. 8s. 9d. 17s. 6d. 138. 4d. 20. 56 ii cwt, GGj Id. 244 .'■•5. -2 ((. H X 111. ■2L S 1)/. •-'.'). •■>/. 'JO. 883 •27. iJ 28. ? 29. i 30. (4 31. 0'* 'V2 7 4 III) 33. /•I 34. .■^.T 3o. 8 36. 5 M 37. » 38. u 39. jj 40. ■' 41. -li} 42. iVo 4.3. ,ii 44. 111 4.1 iB 40. fi?;^;} 47. 5 48. l^g 49. f:\ .")0. 17.S. Gel. rn. 128. C(l. r)2. 17s. 4ja .53. lis. 7id NSWKRS. TjI. Gs, 8(1. .')."». 1 38. 4.1. .'ifi. 8s. 4.1. .')7. lorwt. 9311). 11 oz. 3^.1r r)S. 17 lb. 12.)7.. 8.1r. 59. 14 oz. 5 dr. GO. 8 oz. 2 pwt. Gl. 19 pwt. 12){ gr. G2. G (Ir. sf.r. 19 if f,'r. G3. 2 oz. Odr. 2scr. 18-512 gr. G4. 9s. GJ. G.5. 775 lb. ()G. G.l .1. G7. G8 11). 7 oz. ^ ilr. GS. •2937') G!». ■^irt 70. •70875 71. •0025 72. •840625 73. •04375 74. •00729 IG 7."). •45 70. •Oi) 77. •9875 7S. •04583 79. •160 80. •09GS75 81. •375 82. •115625 8.3. •242245370 Additiox of Denominatk Nlmukrs, pp. 64, 65, GO. £368 19«. l^d. £452 13s. 11(1 £515 2s. 10,R £44 1 5a. 9.1 ;). 6. 7. 8. 00 cwt 2 qr. 23 lb. 34 t. 1 7 cwt, qr. 7 lb. 1 7 t. 8 cwt. 82 lb. 89 lb. 10 oz. 2 dr. ANSWERS. 245 U. 77 lb. 8 oz. 20. 'Js. 41.1. 10. U8 1h. 4oz. (hlr. Iwcr. 4yr. 21. 9s. ;4. 0. 7. 8. 9. 10. 11. 12. 13. 14. £590 158. Gd. 17 t. 18 cwt. 40 lb. 1245 n. 7 f. 30 rd. 489 a. 2 roods, 25 rd. 15" 24' 19' 3907 d. 8 11. 38 m. 5 5 h. 41 ni. 39 .<. 7 m. 10 d. 9 in. 29 d. 7 h. 43 ni. 5.') s. 37=^ 50' 14" 8 s. C>\ d. 5 cwt. I .|r. 18 Ih. 5 cwt. 2 qr. 10 11). 1,5. £14 10s. 8d 10. £7 3.S. 9^d. 17. £94 Is. 22d. 18. £0 lis. lO^d. 19. 7 cwt. 44 J lb. 20. 8 oz. 10 i)wt. ^T. 21. Iqrt. O^p, 22. 4s. It.'jd. 23. 3s. 8^.1. 24. 3s. lOd. 25. 14s. 5-28d. 20. 12 cwt. 93 lb. 2 oz. 12 dr. 27. 2 ([rt. I pt. 2 fjills. 28. 11 cwt. 3 qr. 24 lb. Mli.tii'i.ication ok Denominate XuMnKHs, pp. G9, 70, 71. 1. £193 15s. 4 Ad. 2. £704 13s. 9':,M. ,3. £1771 5,-*. 3(1. 4. 29 t. 6 cwt, 45 lb. 5. lOG lb. 6 oz. 1 i dr. 0. 51 lb. 9 oz, 11 pwt. 3 i;r. 7. 40 lb. 2 oz.'O dr. 1 scr, 5 gr 8. 47 m. 3 f. 9 93 b. 2pk, 3qrt, 10, 22 h, G in, 48 .s. 1 1, 50 b. 30 m, 25 s, 12, 24 b, 42 m. 20 s, 1,3. £280 .3s, 9d. 14. £905 17s. 4id. 1.5. £1431 10s. "lOfd. IG, 1504 t. 19 cwt. 24 lb. 246 ANSWERS. 17. 643 cwt. ;$ qr. 24 11). IS. 1779 yd. Oft. 6 in. 19. 3;{32 il.. 3 oz. 4 dr. 20. 8 t. 7 cwt. 9 lb. 21. 96 a. 90 >»[. id. 22. 96 h. 24 m. 10 s. 23. 6G9 j,'al. 2 (irt. 24. 49 t. cwt. 20 lb. Division op Denohinate Numbers, pp. 71, 72, 73. /. 8. 9. 10. 11. 12. £95 7 lOi ^ £115 isi^f £192 IJ 2 t. 6 cwt. 38 lb. 13 lb. 7oz. 2 dr. 8 lb. 11 oz. 2pwt. 7 1 cwt. 3 qr. 20 lb. £3 19 oj £8 8 U £12 Io'b] ,J,- 18 t. 12 cwt Gl lb. 49 lb. 11 oz. 12 LT. sr. 13, 14. 15, 16. 17. 18. 19. 20. 21. 22. 23. 24. 1 t. 3 cwt 41 lb. 5 oz. 8 pwt 8 gr. 15 b. 7^ qrt 9 h. 40 m. 2 b. 2 pk. 5.\^ qrt 15 t cwt 3 qr. 14 lb. 32258 lb. oz. 15 pwt ll;^f gr. 9 cwt 3qr. 14 lb. 5 lb. 11 oz. 18 pwt .TjS^gr. 17 t 14 cwt 3qr. 18 lb. 14 oz. 12 111. 3 f. 19 rd. 24 a. 8 1* sq. cli. 1. n •■?( 3. $2 4. $2.50 5. $1.32t«;. G. 81.50 The Cental, p. 74. 1. 44i cts. 2. $4.80 3. 87.20 4. $1.26 Longitude and Time, pp. 77, 78. 1. 3 h. 1 ni. 24 8. 2. 1 h. 47 m. 16 s. 3. 9 m. 4 *■ 9. 4. 7 h. 45 m. 44 s. A. M. 5. 11 li. 31 111. 56 8. A. M. G. h. 3 111. 28 3. P. M. 7. Oh. 21 m. 8s. P. M. 8. 2 h. 26 lu. 1. 2° 9' 2. 4° '^' 3. GG- W. 4. 73° 44' W. 5. 83° 55' E. G. 130° 4.5' W ANSWERS. Aliquot Tarts, pp. 80 , 81. 1. 83ct8. 35. £1 Os. 5d. 68. £1 17s. 6d 2. $1.69 36. £0 188. 4 id. 69. £24 7s. 6d. 3. $1.13 37. £1 lis. lOAd. 70. £19 lOs. 4. $5.iO 38. £0 13s. 4id. 71. £55 28. 6d. 5, $4.25 39. £1 3s. 4id. 72. £48 6. $4.81 40. £2 lis. 4id. 73. £680 Is. 3d. 7. $0.89 41. £2 16s. 9jd. 74. £381 5s. 8. $0.42 42. £3 2s. lojd. 75. £316 2s. 6d. 9. $0.74 43. £3 2s. 7Jd. 76. £637 6s. 3d. 10. $0.95 ■'A. £4 12s. 5id. 77. £119 12s. 6d. 11. $1.09 45. £' 1 1s. 2id. 78. £483 17s. 6d. 1-2. $0.77 4G. £0 'Js. 8l± 79. £35 6s. 5d. 1... $1.01 47 £0 7s. IW. 80. £218 10s. 14. $5.40 48. £3 3s. SJd. 81. £697 Os. 6d. 15. $5.43 49. £2 lOs. l|d. 82. £63 18s. 9d. 10. $13.81 50. £3 12s. 2Jd. 83. £88. 17. $9.69 51. £180 84. £34 4s. Od. 18. $7.56 52. £109 85. £102 19s. 19. $3.39 53. £435 80. £178 Os. 8d. 20. $2.26 54. £17 12s. Gd. 87. £36 5s. 21. $1.75 55. £24 15s. 88. £132 3s. 9d. 22. $4.50 56. £765 89. £141 23. $8.44 57. £1610 90. £448 Us. 10 24. $9.30 58. £1.**" '3s. 4d. 91. £1 5s. 7^d. 25. $13.30 59. £2 9 Is. 3d. 92. £1 Is. 2^d. 26. $15.38 60. £lti4 13s. 4d. 93. $12.76 27. $24.04 61. £236 13s. 4d. 94. $9.47 28. $2.27 62. £236 10s. 95. $12.60 29. $9.78 63. £5.50 96. $3.65 31 $7.81 04. £105 97. .«6.16 • 31. $24.48 05. £43 2^. 6d. 98. $4.34 3l». $6.22 06. £26 OS. 99. $6.44 33. $10.12 67. £84. 7s. Od. 100. $1.92 34. $20.40 AYO ANSWKRS rBR'JEST.\GB, pp. So, 86, 87 1. 37.80 21. .$250 41. 15% 42. 1 .L % •2. 37.80 1'2. $760.40 3. 4.->.(i2.1 4. 317.76 2:1 $961..5G 24. 321.05 J /o 44. 70 V .">. ?34.i'.-)6 25. 97 /j 45. 7,1 7 6. 8129.33^ 26. 16.50.45 - /o 46. 75 % 47. 5 7 7. $8.64 27. 2460.20 8. $14.62," 9. $1520 ' 28. $17.40 29. $460.50 49. 25. V 7 10. $291.93 30. $450 2 /o 50. i % 51. * 7 11. 336.60 31. ,3600 12. 3120 13. $812.50 32. $85 33. $640.80 5 /o 52. ;": 7 53. $203 14. $131.25 34. 1200 54. .$34.40 15. $16,317 3.5. #1200 5.5. $1,300 16. 789.75 17. $625 18. $789 36. 36000 37. 6% 38. 17M % 57. 2H % 58. 15 % 19. $325 39. 10^/ 59. $109.37.i 20. $15 40. 11% 60. 5311 rEUCEXTACiE, pp. 88, 89, 90. 61. $77.5.75 76. $12.50 91. 12^% 92. 1'^/ 62. $484.42 77. .$840 63. $869.32 78. $84.45 ^^4 3 93. 423 64. $1386.18 79. 1800 94. 684 6.5. 254.61 80. $4.44 J 95. 42 66. 546.75 81. 20% 96. 1191 67. 46.08 82. 5y^ 97. 422.4 68. 638.40 83. 10% 98. .$328.95 69. 240.90 84. Sh% 99. $350.58 70. $4.86.;j «5. h% 100. $177.18J 101. 240 71. $725 ^6- i% 72. 800 ^'- i% 102. 325 73. 25 SH. 80% 10;5. 600 74. 540 89. 87 /o 104. .$382.20 75. 600 on 1 °/ , « -. '""■■ i/ci iUi>. if2000 i AXSWERS. 106. 85339.0211 118 n % 130. §171.50 107. §80 119 1^^ % 131. 34i% 108. SIO 120. m % 132. i%i)rein 109. §256.12 121 H% 133. .§040.10 110. §960 122 $720 134. 11 % 111. 5 % 123. §167.76 135. ler/o 112. 6% 124 §1620 136. 5% 113. 25 % 125 $110 137. $82800 114. 40% 126 $6500 138. $47.00 115. 12i% 127 13i% 139. 41 % 110. 33.^% 128 $3.50 140. 20% 117. 30% 129 . 50 % 141. $2493.35 Pages 92, 93, 94, 95. 1. 25-2 26. 780 51. $609.30 2. 4«3 27. 170 52. $564.48 3. 344 5 28. 140 53. §425.25 4. $150.80 29. 195 54. $4.59i 5. §680.40 30. 108 55. 2010 6. $12612.30 31. 192-5 56. 1203 7. $4807.216 32. $344.40 57. $1682.10 8. §565. 49A 33. §61.25 58. §480.30 9. §1635 34. $9.80 59. $1903.80 10. 528 35. 648 60. $226.69 11. 1178 36. 614-56 61. §1084.05 12. §2.94 37. 10295 62. $465.39 13. §40.89 38. §2154.60 63. §88i60 14. $1.38 39. $2,183 64. $776.10 15. §1547 40. §■7072 6.5. §494.94 16. §882.70 41. $15,996 66. $5.36 17. §581.25 42. §3116 67. $4.90 18. §456.37 43. §1302.71 68. §5253.90 19. 480 44. §2220 09. §4.80i^ 20. 2590 45. 88'5 70. $4. 83 J 21. 1080 40. 2940 71. $4.90 22. $2600 47. 3020-0 72. $4.87J 23. §951). 14 48. $10.50 73. $4.83| 24. $706.05 49. $281.25 74. $4.87f 2.5, S!12L]2.V 50. $41.40 75. $2005.50 249 zou answer;s. 76. *3385.8U 82. $1749 88. $248.10 77. $124.37] 83. $2312.50 89. $90 78. 81)') 7. go' 84. $8062.50 90. $1100.50 7'J. $74.85 85. 470 91. $14.40 80. ,$83.89! 86. 1200 92. $109.37^ 81. $674.90 87. 4500 Interest I., p. 98. 1. B-ir, 5. $10.53 9. $62.69 '2. $1.75 6. $-54 10. $41.23 3. $8.40 7. $23.75 4. $-18 8. $57.03 IL • 1. $-83 5. $4.35 9. $527.47 2. §199.50 6. $147.08 10. $152.19 3. $204 7. $297.08 11. $371.72 4. $86.34 8. $385.90 TTT. 12. $688.86 1. $25.90 7. $87.50 13. $91.09 2. $13 68 8. 826.25 14. $79.86 3. $9.26 9. $72.34 15. $19.10 4. $8.87 10. $107.25 16. $17.57 5. .$110.18 11. $20.34 ■47. $448.48 6. $65.65 12. $156.95 Page 99. 1'8 $83.85 10. $4.10 25. $29.0l> 31. .$853.50 20. $52.39 26. $31.10 32. $2481.24 21. $14.98 27. $1.44 33. $204.22 22. $1.53 28. $12.01 34. $13. 1 'J 23. $37.20 29. $242.64 35. $69.65 24. $4.14 / 30. $44.79 IV. Pajjc 101 36. $197.09 1. $2,466 5. .$8,582 9. $4.14.^1 2. $2.65.') 6. $2,693 10. $36,405 3. $1,166 7. $-288 11. $2,764 4. $6,673 8. 814.475 12. $3,945 ANSWKUS. 251 Payes 103 and 104. 13. .?3.9r) 31. $1.45 49. $5.5G 14. i?r).39 32. 82.32 50. $8.28 Vk $-29 33. .$2.69 51. 823.18 10. i$-82 34. 8-91 52. 82.39 17. ?-84 .35. $8.91 53. $81.75 18. $-94 3G. 83.74 54. 833.GO 19. $88.04 37. $-80 55. $203.35 20. .*2.72 38. $3.8G 5G. 83G.78 21. 8-17 39. 840.77 .57. 81.35 22. #8.14 40. $2.40 58. $12.70 23. $-53 41. 81.5G 59. 845.55 24. i?'47 42. $1G.87 GO. $2.18 2.^ .S29.31 43. 81.40 01. $3.73 2G. ei5..Tl 44. 81.39 G2 819 27. 897.73 4.5. 857.11 G3. $-98 28. 84. G2 4G. 82.42 04. $10.02 29. $83.33 47. $5.38 G.5. $37.94 .30. $-45 48. 81.91 ^ V. Page 105. GO. $19.50 1. SCO .5. ig871.31 9. $1000 2, 840 G. .8225 10. 829827.90 3. 8204 7. $480 11. $4210.04 4. 812107.84 8. .83228.33,\ VI. Page lOG. 12. >^4G25.01 1. $2700 5. 8G32 9. $248.25 2. $148..')0 G. $1200 10. 81110 3. 87r>0 7. 8387.40 11. .$980.40 4. 8595.28 8. $G00 VII. 12. 84000 1. 5 5. 9i 9. 8 2. 12 0. 7 10. 8' 3. 8 7. n 11. 8 4. 10 8. 7 12. % 252 ANSWKRS. VIII. Page 107. 1. 3 years 5. 3 in. 18 d. 9. 187 f) 2| years 6. 2 y. 1 ni. 24 d. 10. 10 y. 8 ni. 3. 4 y 8m. 10 d. 7. 84 11. 3.3 y. 4 in. 4. 8 ni. 20 d. 8. G5 12. Se.jt. 1G;82 Accounts Currext, pp. Ill and 112. 1. $416.85 3. SC.09.17 5. .324.59 2. $658.74 4. 61259.85 6. 653.71 Discount and Presknt Worth, pp. 113 and 114. 1 $200 7. $576.46 13. $1029.13 2 $80 8. $545.45 14. Casli, by $2 3 $126.30 9. $600 15. $22587.66 4 $813.01 10. $450 16. $865.38 5. $11538.40 11. $"')34.98 17. $706.54 G. $3905.83 12. $1000 18. $1201.92 Compound Interest, p 116. 1. $85.87 10. $931.78 19. $4383.91 2. $78.65 11. $1390.15 20. $2665.84 3. $59.55 12. $562.75 21. $14033.97 4. $194.25 13. $695.56 22. $138.14 5. $1021.03 14. $1104.48 23. $238.66 6. $1418.52 15. $559.74 24. $138.02 7. $1804.36 16. $941.50 25. $1012.83 8. $2302.03 17. $3195.83 9. $2846.62 18. $1603.57 Page 118. 1. $l.'-..i0 5. $120 9. $3247.90 v $10000 G. $233 10. $447. 9r. 3. $1600 7, $2194.17 4. .>5000 8. $1110.53 Annuities, p. 120. 1. $7908.48 3. $60321.01 5. $487834.71* $47727. 10 4. 0*2063.70 G. Js4745.b4 ANSWERS. Page 121. 1. 2. 3. 4. 5. $34408.26 8172920.33 845639.81 84120.38 83037.15 6. 7. 8. 9. 10. $9954 8306.60 83060.29 87257.06 813710.99 11. 12. 13. .850000 81^:66.665 811693.59 253 r.ANK Discount, pp. 129, 130, 131. $10.70 ; 8689.30 10. 811.10 ; 8988.90 1, 2. $10.93 ; 8444.87 3. 811. -"'l ; 81188.49 4. $9.81 ; 8629.44 5. 813.92 ; 8496.08 6. 81.33; 8127.17 7. 82.^*0 ; 8290.38 8. 8336 ; 8423.64 9. 8-61 ; 896.14 11. 81481.85 12. 8333.20 13. 84.34 14. 82.85 I.'). 8475.54 16. 8708.53 17. 844t^.20 1. .8380.95 2. 8777.43 3. 8809. 03 4. $719.72 Pp. 132 and 133. 5. $619.03 9. 8284.06 6. 8557.21 10. 8300.71 7. 8934.83 8. 8380.83 Paktul Payments, pp. 135, 136, 137, 138, 139. Ex. 8363.70 4. 8615.03 8. 8151. .54 1. 8259.43 5. 8102.03 9. 898.14 2. 8251.08 6. 81235.32 10. 8144.59 3. $520.81 7. 858.13 , Commission and Brokerage, pp. 142, 143, 144. 1. $46.89 2. 810.50 3. 811.25 4. 8100000 5. $3111.25 6. 83920.63 7.1:351% 8. 8950 ; $38 y. 8760 ; $19 10. 840 11. 84568.27 12. 12i % 13. 15 % 14. £25 183. lOd. 15. £38 14s. 7d. 16. 5 % 17. 3072; $11.52 lo. $1(1:0. yr' 19. 83103.13 20. S80.80 21. 7000 22. 15070|; $83.47 •2.3. 8103.64 24. 828800 25. 89955.50 26. 186005 I Tr- 254 ANSWEUS. SnXKS AND ]5oND.S, J)]!. 148 to 152. 1 . >!108 ■) $220 3 88G2.50 4 Sir)42 5 837.^)0 6. !?")340 7. .?78.5.40 8. •Sr)474.92 9. *34.120 10. $1200 11. *333G 11 82488.50 13. 8l2.-)25 14. $12.55.-) 15. .^470 IG. $4400 17. 84025 18. 8322.50 19. 81237..50 20. 82018.75 •21. $1005.26 22. 8404.31 23. $3190.04 24. 816140.15 25. $21.25 2G. 27. 28 29. 30. 31. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 4.3. 44. 45. 46. 47. 48, $125 873.44 86.5.55 $12.92 $24000 ; $37.50 3i%; $36.40 , $75000 7500 83985.25 21 65 $5000 $5000 ' 85 100 $250 $560 About 5f % 6 % 1)oii(]s by ,2. of 1 7 « % " ' $821.25 ; $41.25 $771.37.1 ''il.69 56. 57. 58. 59. 60. 40. .^GO 50. $5880 51. 5% 52. 25% 53. 33^% 54. 60% 55. 1.20 1.33] I.07f 824 828 1 11(^1 $78 61. $75 62. 93 J 63. $12832.01 64. L...st $194.66 G5. $153.75; Los.s $240.20 66. ^3.3.75; $4500 67. $12G.88; Loss $253.96 69. $7.5;2.',;,$,5437..50 70. $32000 LvHUiuNCE, pp. 154 and 155. 1. $70.40 7. $405 1 3. 45 cents 2. SI 305 ^- H % 14. $6500 3. $1900 9- i^(r % 15. 40 4. ,826.25 10. $2.5.20 16. £28 Is. 9]d 5. $36 11. $3200 17. $62.63 6. 84: /./:> 12. 89000: .S4250 ANSWERS. TUOFIT AM) Ltiss, \>\i. 150, 157, 158, 15'J, 160. 1. .*7H.10 21. 2;. 41. 0' •_'. .*S. .").") 22. $20 42. 7t{cts. 3. .*5.tO 23, $120 4.3. 24 ^ J 4. !i?19.50 24. $5 44. $3.65 5. .«36 2.5. $3.25 45. $7.50 gain 0. .*90 20. $1.50 4(). 42 J 7. .«3.90 27. $608 47. 405 s. .*r)370 28. $1350 48. $6. Hi 9. $6.30 29. 3.3Jt 49. Lost $270 10. m:.y3\ 30. 4 % loHs 5a $5 11. SI .3.44 i;acl 31. 12i%«ain 51. Gains 6] % 1-J. 15 32. 32i % 52. IH 13. G 33. 4 % loss 5.3. $700 14. 25 34. 16 % loss I63 / 15. 15 3.5. 35 "^ $122.. 50 IG. 20 3(5. 13,V $17.50 17. 25 37. $1.32] 54. 4 18. im 38. 12A 55. 5§ 19. 12^ 39. $7. TO 56. 2^ 20. 17i 40. $1540 1 ;ANK1!LI'T( V uu Insoi-vencv, i>. 161. 1. Div. GOc. 1 -.11 0/ 0. 21c. A. i?240 $995.96 A. $226.80 15. $210 5. m % 15. $178.50 C. $360 LuiKlon, $11616 C. $361.20 2. 37c. CUasgow, $9504 ]). $331.80 P.. .«296 New York, $9028.80 K. $203.70 C. $185 :Montreal, $8448 1). $407 Toronto, $2323. 20 E. $222 Halifax, $2217.60 3. 47J % $608.95 1) J.MKSTie KXCHANOK, pp. 163, 161, 165. 1. .■i<3003.75 4. .$8435.53 7. $954.23 2. «46 11.50 5. $1884.88 8. $.5875.87 255 •1 ?.•{ 7 7 1.03 1«. !?2493.75 1. $98 2. .*305 3. $231 4. 334.10 5. $i 139 1.25 6. 8380.73 7. $514,925 8. $818,283 9. $25.3.475 10. $22,417 11. $71,833 12. $197,733 13. $325.89 14. $80.63 15. $323.91 16. $644.86 17. $406.93 18. $1856.96 19. $5.50 20. $2.12 Taxes 1. $123.23 2. $2895 3. $315 4. $233.50 5. $664.75 6. S223.82 7. $65.40 8. $23 9. $496.55 ANSWERS. 17. $2867.83 18. .^.'i 7 4 7. 6 6 19. $3921.57 20. .^3620 21. Si 824 22. !?,S728 23. $2725 24. .$865.40 2.5. $l9Ht;.o:> 26. $2789.03 27. $966.20 28. .$3861.54 29. $21.08 .$8453.93 FOUKION i;.\'(HAN(!E, pj.. 168 to 172. 21. $15.'). 35 22. $282.78 23. $95.03 24. $162.44 25. $11,305.77 26. $343.64 27. .$933.19 28. $1021.68 29. $1982.67 30. $275.89 31. .$418.86 32. $3568.08 33. $2378.04 34. .$2550.65 3.5. $930.09 36. $150.3.74 37. ,£205 19.S. .38. $244.44^ 39. $8960 40. $466,67 41. $6164.85 42. £170 9s. 2i.l. 43. 109 44. 109 1 4.5. .$.3034.68 46. $5996.35 47. 19A 48. 5.22A- 49. 1794"9,60 f. 50. $15.38.53 51. .$.3.26 52. .$2312.17 53. Lose $2.34 54. $11.96 55. £1482 16.S. 9d. 56. 1083^ roubles 57. $17160.19 58. .£17 10s.; $85.46 59. Via Fiance by $15. 6 9 60. £2016 iLs. ;4a. AND Duties, pp. 174, 175, 176, 177, 178. 10. $1182 13. $311.40; 11. $25.01; nearly 07 ^ nearly 26i«j % U. 41; $.-,13.56;' 12. $65.68 ;^ 1st lot. 28.55 % 2n(l(lo. 34.12 % 3nl do. 28.55% 4tli do. 23.2 %° Average 26.86 % 40.133; $1.39; $2.46; $3.98. ■*.*.. i,- Vi" t ANSWKUS. m E* 258 ANHWKRS. il. S6iil\ ;«12l/3 ; 43. •J4(;^ miles 4G. Wliok', i:)0 ; eiOO^:, 44. S400U ; $1GUU ; tin, 37A ; 42. A, *1(»A2.«3t'b ; #2400 coi)i.cr,' 112J I!, ;?irj78.y4JJ; 45. 1700; 537; 1253 47. G2A C, $2368. 42ii^ Compound Phopoution, pp. 205, 20G. 1. $58.50 7. 15 days 13. 2 cwt. 2 qr. 8 lb •) 50jJ'j days 8. 5 A 14. •Ji'j miles 3. >!y2.5'J y. 50 15. 827.54 4. «25.2U 10. 16 16. 26-88 days. 5. 32 11. 3U\ G. 45 12. 21 Analysis, pp. 206 to 211. !] 1. *20.90 24. $425 40. A, 35yV milts ; •> 38i days 25. 2} days li, 45 miles 3. 14 26. 14f days 41. 369 J supertic'l ft; 4. $•20 27. 12 feet broken oil; 33J cubic feet 5. J3.20 13 J " remained 42. 22^ cents G. $88 28. 8 m. 34? s. 43. 16 7. «1.55§ 29. 2 h. 24 m. 44. $580.54 8. 77/, cents 30. 3 hours 45. $3430 9. 39? cents ?1. A, 10 days; 46. Each girl, $66^f ; 10. Wf St. I), 12 days; each boy, $42^i^ 11. l\ yds. C, 15 days; 47. «tW 12. $75.44 together in 4 days. 48. $1.97|| . 13. m 32. 1 J hours 49. 18; Hi by 14* ft. 14. $14.12^ 33. 6T»l;r 50. $329 15. $4200 34. n,v 51. nil 16. 36 years 35. 10/j minutes 52. $4477.50 17. A,"$45;B,$40 36. A, $20; 53. 80 in the 1st, 18. $13440 B, $55 ; 56 in the 2nd 19. 60 years C, $25 ; 54. A, 18 o.xen, 20. 115600 D,E&F each $1200 and pay $72 21. 36 feet 37. 10 miles per hour 1), 12 oxen. 22. 20 cents 38. 60jV8ec.;490yas. and pay $48. 33. 32 feet 39. 12 d.iv.s ( r "Tfl^- ANSWERS. 2'>{) PARTNBnSfil G. 7. 8. 9. 10. 11. 12. 13. 14. 15. IG. 17, 18 J!l2lfi..30rach .John .Smith'H ?l 034.0.') (iio. IJrown's $1491.0.") Millt-r'-s 12204.01 J M.uininx's $2094.11 J Dnvis's 14.^95.30 YounR's $1800.18 Russell's $2110.18 A's $1U.''1.38 IJ's $11279,75 C'h $11179.75 M'.s $17531.03 N's $0257.21 Kill. dtieC, $815.52 A's interest, $2350.90 r.'s interest, $2004.14 M's $3848.50 N's $4901.50 $0198.50 A, $1800; I?. $1500; C, $2100 ; I), $:^400 Th« capUin, $980 ; the nmte, $420 ; each sailor, $70 A, $400 ; B, $320 ; C, $520 ; D, $360 A, $1400; B, $1000; C, $800 ; D, $950 ; E, $1187.50 ;F, $1002.50 L, $2000 ; M, $3000 ; N, $2500 A's $400 ; B's $850 ; C'a $750 ; D's $1000 A, $8.32 ; B, $7.04 ; C, $4.48 , A, CO ft. ; B, 80 ft. ;C, 100 ft . A'«$360; B's $480; O's $640 pp. 19. 216 to 225. 20. 21. 00 24. 25. 20. 27. 28. 29, 30 31. 32 33. A, $340 ; B, $297..50 ; (', $212..50 A, on.l H, each $7.20 ; C, $4.40 ; D. $9 A, $384.93; B, $250.71 ; C, $236.30 A, $2500 ; B, $1875 ; C, $1500 • $2190 A's $015.97 ; B's $.581.75; C's $002.28 A's $2007.42; B's .«17408.C9: C's $17358.09 A, 3 cents ; B, 21 cents A, $15750 ; B, $2250 J's $17909.29 ; K's $20795.45 ; L, $7039.92 Dno G, $2420.25 ; due H, $3742.25 E's net cap., $5173.50 Ps net cap., $4881 Samuels receives $2097.32 Hall pays back $117.09 I'a $4060.31; J's $2823 18; K'8$4095.05; L's$l320.38; M's $4183.23 A's gain, $368.43 ; B's, $330.20 ;C's, $278.06; ITs, $243.31 B. is to pay in $464.80 ; ^. » '• " $1521.94 ; A. is to receive $1143.43 D. " " " $843.31 P. Ran ton pays A. W. Smitli $9.58J, and James Walker 83J cents i 'IjGi 260 ANSWERS. 34. A's 8374.12; L's $250.41 ; 37. B. $5009.42 : C's $487.83; D's 6787.24; E's $600.40 3.5. Smith's $13296.95^; Wilson's $14223.04| 36. A'8$16666.66|; B's $27091.6G§ ; C's.«2166.66iJ C. $1791.80 Mdse.,il'c., Dr., $9840; Cash, Dr., §2570; Sundry Drs., $17030; To Sundry Crs., $4050; " B, Cr., $12695 ; " C, Cr., $12695. . General Average, pp, 229, 230. 1. 8 7 ; Vessel pays $2333.50 3. 231 %; Ship pays $7960.83 A pays $292 B receives $2480 C pays $160 D " $44 E " $436 F receives $785.50 2. ^'Z^, Str. pays $6516 A receives !$ 1182.26 -'B " $667.25 C " $4666.50 4. a 2 /o > •1. W. Roe pays $1610 Dunn, Lloyd & Co. re- ceive $1895.83 Morris, Wright & Co. receive $430 Smith & Worth re- ceive $7245 Ship receives $1818 A pays $292.50 B " $337.50 II « C " $783 D " $405 M18OELLANEOU.S Exercises for Commercial Students. 1. Cost 72t\ cents; asking prico 84-,^ cents ; whole gain $40.91 2. $153.37 3. A, $5743.12 ;B, $6855.06; C,$8303.8G;D,$12214.48; E, $4243.48 4. Net gain, $3242.64 ; Smith should pay Jones $2379.12 5. Loss $103.20; Agent owes town cash $7.40 T). $lil.2i 7. $28017.73 8. $5478.01 J. P. Fowler, pr., $5450.62 Casii Cr., $5S18 Com. Cr., $^2.62 Cash Dr., $54150,62 J. P. Fowler, Cft, $5450.62 9. W. A. I^Iurray & Co., Dr., $1742.75 Simpson & Co., Cr., $1708.58 Exchange, Cr., $34.17. W. A. Murray & Co., Dr., $1742.75 Exchange, Dr., $35.57. Simpson & Co., Cr., $1778.32. ^It*"^ 1 AKSWER8. 261 10. Interest, Dr., $21.12 July Chaa. Ma«8ey,Cr., 121.12 Chas. Masaey, Dr., $2006.54 A. Cumimngs, Cr., £411 78. 3J=2006.54 11. Fac« of draft, $10798.67: May 1. Shipment in Co. with Rom, Winans & Co., Dr., $5359.33 Ross, Winans & Co., Dr., $5359.32 Cash, Cr., $10457.40 Commission, Cr., $261.25 12. 7. Ro88, Winans & Co., Dr., $5319.79 Shipment in Co. with Rosa, Winans & Ca, Cr., $5319.79 When the draft was drawn, Ross, Winans & Co., Dr., $105.86 Interest, Cr. $105.86 Jash, Dr., $10771.67 Exchange, Dr., $13.30 Ross, Winans & Co., Cr., $10784.97 January 21 ; Nov. 23 ; £906 Ss. 5Jd. 13. 60: £620 188. 7^d. March 10. Shipment in Co. with S. Vestry, Dr., $1564.42; Samuel Vestry, Dr., 4 mos., $1564.41 ; Mdse., Cr., $3068.34 ; Cash, Cr., $60.49. May 19. Samuel Vestry, Dr., £298 14s. 10d.=$1450.56 Shipment in Co. with S. Vestry, Cr*, $1450 56 May. 28. Cash, Dk., $3014.97 ; Samuel Vestry, Cr., $1564.41 Samuel Vestry, Cr., £298 Us. 10d.=$1450.5G 14. Net gain, $6677.7'. On commencing business, Jan. 1, Mdse., Dr., $7844 Cash, Dr., $5000 Store, &c., Dr., $3984 Bills Rec, Dr., 51732.50 J. H. Smith, Cr., $8000 S. North, Cr., $6000 E. Wills, Cr., $4560.50 E. Wills, Dr., $425.80 Bills Pay., Cr., $425.80 When Geo. Smith was admitted. May 1, Cash, Dr., $5350 Geo. Smith, Cr., $4000 J. H. Smith, Cr., $450 S. North, Cr., $450 E. Wills, Cr., $450 262 ANSWKRs. When E. Interest, Dr., $194.10 K. Wills, Cr., $194.10 K. Wills, Dr., $20.38 Interest, Cr., $20.38 When S. North Interest, Dr., 8365.75 S. North, Cr., $365.75 S. North, Dr., $34.40 Interest, Cr., $34.40 •S. North, Dr., $5681.35 Additional Interest, Dr., $851.63 J. H. Smith, Cr., $598.50 Ceo. Smith, Cr., $186.67 J. K. White, Cr., $66.46 Wills retired, June 30, Profit and Loss, Dr., $500 Iv Wills, Cr., $500 E. Wiils, Dr., $4478.42 Cash, Cr., $4478.42 3old to J. K. White, Nov. 1, 'I. K. White, Ci , $5681.35 June 30. Expense, Dr., $500 J. H. Smith, Cr., $500 Dec. 31. Expense, Dr., $500 J. H. Smith, Cr., $500 interest entries, Dec. 31. J. H. Smith, Dr. $50.23 Geo. Smith, Dr., $5.09 Interest, Cr., $55.32 t Balance Sheet, Dec. 31. ^Wse $11943 75 Cash 2110 12 Bills Kec 6400 00 Store and Furniture, 3850 00 Per. Accts., Dr. 14987 50 $39291 37 Per. Accts., Cr $10711 00 f^'llsPay 4000 00 J. H. Smith (net cap.) 10539 17 •1. K. White (net cap.) 7973 71 j Geo. Smith (net cap.) 6067 49 '-;» $39291 37 'A %