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Les diagrammes suivants illustrent la mdthode. 1 2 3 4 5 6 I s^ IMP .lEU TH] "Vac Th NEW AND CONCISE SYSTEM OF ARITHMETIC, CALCULATED TO FACILITATE THE IMPROVEMEIST OF YOUTH IN UPPER CANADA. Published by Subscription, UNDER THE PATRONAGE OF HIS EXCELLENCY, SIR JOHN COLBORNE, K. C. B. .lEUr. GOVERNOR OF THTlTMriN^E Ol^PPER CANADA, &C. [na^^l Tbc Honourable and VelRaale* THE ARCHDEACON OF YORK, THE REV. DR. HARRIS, PRINCIPAL OF THE COLLEGE^ &C| Bt WILLIAM PHILLIPS, ""^ackerof Writing, Arithmetic, Geo^rajhiy, S^c in Ladies Schools, and in private Families, The advantajre of fracti^vis i« so great that f dare affirna t, a person who js well nc<; jjiinted with them, wi!l, in many uses, perform as many Culculatious as four or five who aro ^°'- Dr. Hut ton. ■ii •ji YORK : PRINTED FOR EASTW GOD AND SIUNNER, PAPER MAKERS, a I //i'^ m *iECOMMENDATIOIf. York, Zlst May, 1832. Sometime, ago Mr. Phillips left with me, a copy of a lort Treatise on Arithmetic, of which I think highly, as roceeding upon a clear and simple principle, easy of com- rehension, and am of opinion, that with a very few alter- tions to adapt it to the business! of the countrj', it might ^ith great advantage be introduced into the Common Ichools in the Province. JOHN STRACHAN. The Author has made the alterations suggested by hii [onoucable and Venerable Patron. I H i t ■ PISEFACE. Many Excellent works hnve been ptihlished ►n the Science of Arithmeiic ; but ir appeus tt> (he Author, that a Treatise calculnted to initiate ^outh into that branch of the Science which is [nwuediately applicable to business, would be still desideratum; with this view lie has endeavour- ^ed to arrange the present system in as concise nu easy a form as possible, consistent wkli D(-f- jpicuily— to divest it of whats^«rvei^'/m4#^^^^^ to perplex the youthful niind^&^^ff&rrFTf^ ►peration upon one genera[r''|^(y|f)1e, whici/ rs" 10 scFentifically founded as to elicit the spontane- ous efforts of the pupils, to establish the judg^ ^iient, to exercise the imagination, and to assist Ihe memory. Hereby, the pupil with iuimense- ly less figures, with the greatesi desTpatcii, and With the most perfect accuracy, will be frmhied, in Incomparably less time thnn by ..nv other sys- tem, to perform the most intricate calcidations ;and the generality of commerciHl romputrHJoni a by the mental jmoers alone :) thus the tuv'n ^^.>-' ••-^s^.i^- ( t cxpeditioiis and practical application oTtlioorefiv eal arithmetic is made, to whatever purpose its aid may be called for in business ; being assur- ed, that to the busy tradesman, whose piincipal | desire is to know tlie value of a given quantity at a given ratio, the more expeditiously the o- peration is performed the more acceptable it will prove. Algebra is founded upon Vulgar Fractions, which is the basis of the system now presented | to the public ; therefore the Author presumes it will bo found equallj^ advantageous to those who are intended for matliematical pursuits. The experience the Author has had in Ladies Seminaries of the first respectability enables him to judge of the capacity of the fair sex, and he is confident from the attention and docility of young ladies, in general, that he will be justi- fied in presenting to them the above system, which was primarly intended for their use* Yorh, IT, C, 1st Jtflf/, 1833. AXEW- T Arithmetic js the art of computing by num- bers, and all its operations are performed by in- creasing or decreasing given quantities ; addition or multiplication being the increasing term ; sub-, [traction or division the decreasing: term — thus. Increasing Ta /.- 2 -f 2 = 4, 4 + 4 r= 8, 2X2=4, 4X2=8, = 16 = 16 16 — 8 = 16 -V- 2 = Decreasing Terms. 8, 8 — 4 = 4, 4 8, 8 ~- 2 = 4, 4 2 ==^2 2 = 2 Digits or figures, are marks by wiiich num- )ers are expressed, and are the nine following, iz : I one, 2 two, 3 three, 4 four, 5 five, 6 six, [T seven, 8 eight, 9 nine ; to which we may add he cypher or nought, which is of no value when taken by itself, but being annexed to the •ight hand of a digit increase it tenfold — thus, j50 signifies fifty. / f ... M I 8 A NEW SYSTKM An Intejrpr is any whole quantity or number, as 1, 2, 3, 23, 754, &i'. ^ , A fraction or broken number is an impression for any assignable part or parts of an intogpi — tbus, *tt or f of a pound are assignable parts g for l5 shillings. Compound numbers are such as consist of in- tegers and fractional parts — tbus, 54£ 13s. 4(1. or 54 f £, • Numeration informs us in what manner we are to express and accommodate numbers to th^| various purposes of business, it consists princi- pally, of Addition, Subtraction, Multiplication and Division, to which the following tables arc subservient. Arithmetical Characters, Tables, Sfc. AR1THM1 TICAL CHARACTERS- 4- Plus, or more, the sign of Addition. , _ Minus, or less " ' Subtraction.^ X Multiplied by " Muhiplieation; - Divided by " Division. = Equal tc " Equahiy. : Is lo ) ! ! So is V Sitrns of proportion. • To ) " WJ-9i.j:^S)i^Xl OF ARITHMETIC. d or number, ira Dress ion 1 ;nable parts )nsist of in- manner we ibers to the 1 sists princi--^ Liltiplication ^ g tables arc ERS. Idition. btractioh.^ iltiplieation; visu)n. ualiiy. o V3 -a fl .i: G « o C3 GO CO CO CO CO CO i*^ wo vo lo wo in ^ ^ o •O O 'O o o O O 'O • •N • w\ *«% ^^ •r* •c* •cs t^ t^ i^ r^ I— t - N- ^'^ 00 oo ^ ^ cc C^, :>. C^ Ci a, r>< G^ GS{ CO CO NEW SYSTEM OF ARITHMETIC. 11 I ku Mmi l^ A NKW SYSTEM t MONEY. Farthings. Pence. ShiUiug s. qr. d. s. d. S. £ &. 4 make 1 1 2 mak el 20 1 Liiake 1 5 .. ij 20 1 8 30 B ■ 1 10 6 .. H 24 2 40 • k 2 7 .. If 30 2 6 50 ■ ■ 2 10 8 .. 2 36 3 GO ■ ■ 3 9 .- 2i 40 3 4 70 ■ • 3 10 10 .. 24 48 4 80 ■ ■ 4 11 .. 2f 50 4 2 90 • ■ 4 10 12 .. 3 60 5 100 ■ ■ 5 Q 13 .. H 70 5 10 110 ■ • 5 10 14 • . M 72 6 120 • ■ 6 iliiJitfk-,.^->/'" Ht^ojV 8Q 6 8 130 • • 6 10 84 7 I-^IO • • 7 WF?^. 90 7 6 ! 150 ■ • 7 10 18 .. 4J 96 S ! 160 • a 8 19 .. 4S 100 8 4 170 ■> ■ 8 10 20 .. 5 108 9 i 180 1 ■ • 9 21 .. 5i 110 9 2 190 ■ • 9 10 22 .. 5 A 120 10 200 » ■ 10 23 ,. 5| 130 10 10 300 N.- 15 24 .. 6 132 11 j 400 ■ • 20 25 .. 6J 140 11 8 i 500 1 ■ ■ 25 48 .. Is 144 12 ! 600 • ■ 30 9G0 ..20s 1240 20 ' 1000 • ■ .50 NOTF.- -L. Rt andft for Pound? J (frr Jtn libra being 1 the Latin for pound ■')':.^ for s hiUin^r.s, ( fro 2 Yn polidi) ; 0. for pencw. ft' :.. J fifru \ 1 I \ ami -\ .. foi ^ /• Ai.: r luriiiiiijK IC lUiugs. £ ^. ake 1 1 10 2 2 10 3 3 10 4 4 10 5 5 10 . 6 6 10 . 7 7 10 . 8 8 10 . 9 . 9 10 . 10 ■w . 15 • 20 . 25 . 30 . .50 1) Ig the Latin . tor |ienc«. f\^ to mills, ^^ to cents, M 10 dimes, ^ 100 cents, 10 dollars, fiV ARITHMETIC. FEDERAL MOiVEY. make 1 cent, marked m. for mill. J dime, 1 dollar, ,. 1 dollar, . . l» cts. for cents, d. for dimo, $ for dollar, Tv«^,, -pu- u .L -^^ .""*^" ' •• E. for Eagle. ?^0TK.- i h.s Character $ placed before a number, show^ .t o express Federal money. The ea^^le is a gold ciin, the .iollar and dime are silver coins, the cent is a copper coL the mill IS -imaginary. ^^ri^er com, 1 eaorle, TJlOV WEIGHT. 24 Grains make 1 20 Pennyweights .. il2 Ounces 1 1 1 24 480 5760 dwt. 1 20 240 pennyweight ounce pounds Marked . dwt. lb. oz. 1 12 1 6 Drams A(\ Ounces 128 Pounds 4 Quarters or 1121b. . 20 Hundred weijihr AVOIRDUPOIS WEIGHT*^ ^^^' - %^^- Marked, dr. ounce oz; pound lb, quarter qr. hundred weight cwt. make 1 1 1 1 1 ton dr. 16 256 7168 28672 573440 ton oz. 1 16 448 1792 .^5840 lb. 1 28 112 2240 qr. 1 4 SO cwt. 1 Ion, 20 1 iii^ ^Ihif 14 A NEW SYSTEM APOTHECARIES WEIGHT. ^0 Grains make 1 scruple *3 Scruples .. ^ ^''''^ 8 Drams . . 1 <>""^«, 12 Ounces .. ^ P^"^^ grs. 20 60 480 5760 sc. 1 3 24 288 dr. 1 S 96 oz. 1 lb. 12 1 Marked. . g»- - sc. s dr. 12 oz. 3 lb. ■% 6 -. 5^ 4 40 8 • 3 M^ J ^ 69.^ II • 1 f WOOL WEIGHT. 7 Pounds make 1 cloVR 2 Cloves or 2 Stone 14lb • • 1 stone 1 tod 6i Tods 2 Weys 1 wey 1 sack 12 Sacks 1 lasi lb. c1. 7 i St. 15 2 1 tod 28 4 2 1 w. 182 25 13 6J 1 SB. «»/:.i •»<> 'J a 13 2 1 -C/VJ'« Marked. cl.| St. I t. w. 8.1 la. la. 4368 624 312 156 24 12 3- i9( 171 fi^^Sifc. t)F AHITHMETIC. 15 LON(J MEASURK. Marked. I R P-<^ -»^ ». w - - - RIj irked. Dar. gr* ^M sc. 9 S Biirl'^y corns ma ike 1 incli in. d^- I 12 Inches foot fr. oz. 1 3 Feet yard yd. lb. 1 6 Foet fathom fa. ■ 5J Yards rood, pool, or pel ch p. ■ ■ 4" Pools chain ch. I 40 Pools furlong fur^ ■ 8 Furlongs mile m. I 3 Miies league lea. 1 f;0 Geographical ^ or > 69^ Statute miks) .. I decrree deg. 1 imJ Marked.! 1 ^M be. in. 3 1 fr. % 36 12 1 vd. St.! 108 36 3 1 P- * ^'1 594 198 I6i 54 1 fur. ^^ 1 32760 7920 660 220 40 1 m. la J 190080 63360 t >2S0 4760 320 8 I CUBIT OR SOLID MEASURE. In. 1728 Inches make 1 saliil foot. 27 Feet ., 1 yard, 40 Feet of rough timber \ ^^ i ton or load, ^i) t oet huvvn timlitT I 16 A NEW StS'TEJVI «UUARE OR SUPERFICIAL MEASURE. Marke make 1. foot ft* .. 1 yard yd. 1 square of flooring 1 rod of brick work 144 9 100 272-: 30^ 16 40 4 4840 30 640 Inches Feet Feet Feet Yards iPools Pools Roods Yards Acres Acres 1 1 1 1 1 1 1 pool chain rood acre acre yard mile ch. r'd. A, • • m. m. 144 1296 39204 1568160 6272040 ft. 1 9 2724 10899 43560 yd. 1 301 1210 4840 P- 1 40 160 r'd. 1 4 SURVEYING CHAIN. 7ff Inches make 25 Links or 5j yards 4 Pis. 100 Iks. or 22 yds. 10 Chains 8- Furlongs or 80 Chains 10 Square Chains ieu 1 1 1 1 1 1 a. 1 link pole chain furlong mile Marked. Ik. acre r-ii- • _ V. Mains in 1 ^1- iUli^lii an Acre. J uiiu one iii ..I ■ #-1 ^lo ch. fur. m. maks ©F ARITKMRTir, 17 J RE. 1 Marked, | ft. vd. orii^ ' work P- ch. r'd. A- 1 CLOTH MEASURE. Marked. 2i Indies mtike 1 nai I n. 4 N^iils 3 Q-Kiriors 4 QiatUMS 5 QMarirrs 6 Quarters 1 qdartrr of a yard ^ \( 1 FUMiiisli ell " 1 y\\vi\ 1 Ei)jjlish ell 1 French in. n. H 1 qr. Si) IG 4 1 vr;rd 27 12 3 1 Flem. oil 45 20 5 1 En'^T. eU 54 24 6 1 Fr. ell F. E, 1. v< E. E. Fr. E. WINE MEASURE. Ma rkcd. ■ 4 OiMs make 1 pint I 2 Pints 1 quart ^^^^1 4 Q larts 1 g.dlon m ^^^^^1 10 (iilltins 1 nnclior nnk. ■ 42 Cj,ill.)ns 1 tierce H 2 Tierce 1 punrliPon pun. H 63 Gallons 1 iiogsliead ithd. ■ 2 [loirslieads .. 1 pipe or butt P* ■ 5 Pipes 1 ton too 18 A NEW SYSTEM pts. C]t. 2 1 gals. 8 4 1 tie. 336 168 42 1 hhd. 504 252 63 Ij 1 pun. • 672 336 84 2*" U 1 1 ton 1008 504 126 3 2"^ ll 1 201G lOOS 252 6 4 3 2 1 OLD MEASURE. IMPERIAL MEASURE. GaL qt. pt. gill, 100 pts. 10 Gallons equal 8 1 2 .58 or 1 anchor 3 13 3 13 1 18 Gallons 42 Gallons 63 Gallons 84 Gallons 126 Gallons 252 Gallons 14 34 52 69 104 209 3 3 3 1 1 1 1 1 1 3 3 o O .87 .70 .55 .40 .11 c>0 or 1 1 1 1 1 1 runlet tierce hhd. pun. pipe tun ■ ALE AND BEER MEASURE. pint quart gallon firkin kilderkin barrel hogshead puncheon 4 Gills rua ko 1 2 Pints . 1 4 Quarts . 1 9 Gallons . 1 2 Firkins . 1 2 Kilderkins . . 1 li Barrel . 1 2 Barrels . 1 2 Hogsheads . . 1 2 Pipes . . 1 Marked, pt. qt. gal. fir. kil. barl. hhd. pun. pipe or butt djdc. ton ton. \^ Ot ARITHMETIC. Id OtS. 2 qt. rals 1 1 ton 1 anchor runlet tierce hhd. pun. pipe tun Marked, pt. qt. gal. fir. kil. barl. hhd. pun. t DJDC. ton. 144 18 'S8 144 ^6 4 1 kil. 2 1 barrl Q 432 2]Q 54 Jihd. 576 388 6 3 U 1 72 854 432 108 12 6 J butt. 2 1 • OLD .MEASURE. i^jpcraAL y.zAsvuE. gal. qt.pt. gill 100 ptJ MS 9 Gallons equal 9 10 .91 18 1 1 .82 36 2 3 .64 54 3 1 1 .45 73 1 3 .27 109 3 2 .91 DRv^ MEASURE. ^S GxU'j S6 Gallons 54 Gallons 72 G:; lions .08 Gallons •- 1 4 Gills njakc 1 2 Pints 2 Quarts Potil es 2 Gallons 4 Pecks 4 Bushels 2 Cooms 4 Quarters 5 Chaldrons 2 Wevs pint qiiurt 1 pottle 1 gallon 1 peck 1 bushel 1 cocm 1 quarter i chald 1 wey 1 last ron fi^'kin 1 kil. 1 barrel 1 Jihd. 1 pun. 1 ton Blfirked. pt. qt. pot. gal. peck. bus. cooni. qr. chald. wey. ii w A Nr.w nr^TfM jots. gal. 1 pk. 16 0) 1 bus. 64 8 4 1 coon). 256 32 16 4 1 qr. 512 64 32 9 2 1 w. 2560 320 160 40 10 5 1 la. 5120 640 320 80 20 10 2 1 TIMEc Marked '"«i sec. i 60 Seconds xiiake 1 minutQ m. yM 60 Minutes • (< 1 liour b. i-.::S 24 Hours ■ ■ 1 day d. 7 Days ■ • 1 week \v. T* -f.^^ 4 Weeks • ■ 1 nioiUh mili. '■'s^^ 12 Calendar er 365 day mtlis ) s6h. J 1 vear '" vr. Sec. jn. 60 1 h. 3600 60 1 a. fto 86400 1440 24 1 w. ^0 604800 10080 16S 7 1 in. -$0 2419200 4Q320 672 ; 28 4 1 yr. 51557600 525950 8766 36 H 52 13 1 I ^ Every fourth year has one day added , an d is cal- ' "'99 led L wm 100 Years make 1 Ccnturv^ OF ARtTHMKTltf, ai la. Marked SOC. m. b. d. • w. mil). To know the Daf/a in each Month. Four months have thirty days we fiuJ, To fev'n are thirty-one a^sign'd; April iu Sprinnr the first we view, fa Summer Juno in lovely hue^ September also is one more, And dull November makes the four : ^ But 'tis cold February ^8 fate, To bo complete in twenty-eight, ' Save that in leap year, (one in four,) This mouth contains just one day more. . The Quarter Days are L^cly-Jay 25th of March Midsinnmor-da}' 24th of JunQ ]V1ichnelmas«day, 29th of September Christmas-day 25lh of Doconiber 1 4 9 in. 1 yr, 13 1 ASTRONOMICAL MOTION. •60 Seconds make 1 minute Marie od ^0 Minutes ^^0 Degrees §2 Siirns 1 degree ® 1 signs of the Zodiac 8 1 great eirclo of ditto, and is cal- I ^■l i i: Ticelve Signs cf the Zodiac. f 2! O H *^ J Pi 05 O CJ H 5^ I I I L SPRING. Aries, the Ram, .. , . . Taurus, tho Bull Geaiini, tlio Twins,.. SUMMER. Cancer, the Crab..-. Lf*o, tha Lien « Virgo, the Virgin. . . o AUTUMN. Libra, the Salance. . . Scorpio, the Scorpion. Sagittariur, the Archer WINTER Capricorn^?, tiie Goat.. Aquarius, tlio Water-benrrr Pisces, the Fiihcs FRACi'IONAL TABLES. 1 Farthln^- is :| of a P^nny -^ • • g" « ■ 3 ■ ••■••• M « ■ 1 Penny is -V of a Shillings 2 i i 4 * 41 Ji ^ o i -rV- s T b ■^m n ^^ fs -iT^^^H a. nji i 4' • • -ri%«««itiMKt .it liac. Olr ARITHMETIC. 13S • • • ■ • • ■ • • a • T b n a. /wv M ^y killings 6 Pence is ^ of a SltiUin 7i 8 9 10 lOj 11 12 -T^- I s 1 2 1 2 ff* «-• or 1 sbillln^ 3f Pence is -^V of a Pound, 7J 8 10 ~§ 4 8 4 U 1 Shilling is -5V of a Fount!. 13 __ -.-!_ 1 3 1 4 t 8 2 2 6 8 3 4 4 5 6 8 T 6 i -rs i • '• nt 24 A svAV «>\S'rf:M V ■ • « 2 (I 5 9 Shillings is -A,- of a Pound, 10 11 12 12 6 13 13 4 14 15 16 17 17 18 19 20 I 5 .17. • • • a « ■ ■ « ■ • • • 50 cento is 2j 20 12} 6J 5 'J t 5 i l^- or one PounJ. of a dollar, • • * TllOV. 2 Grai».r. is nV of a penny wcigiil. S 4 6 S 12^ ■ ■ G 1< .jt« f)f AumiMmTu; '^.» 1 tiwt. i>i 1 ♦> gr 8 . 16 ± I of an Ounce 5 10 S Ui I Ounce is 1 '^ of a PoUijrI. 12 dwt. ^ ■■ •. •-tf • • • • a ■ • • AVOlRDLPOfSt: 1 () "nco js .1 H of a Poiuul. •> • m 3\ 4 Pounds is -^V of a (luartor, or 28lbs, 14 * « • a • • I ■ • ■ • • • • ■ ■ « ft- V 1 it ■tm *^^ A NEW SYSTEM 2^j Pounds is -iV of 2 quarters or 16 lbs. 4 7 8 14 28 i ± 7 1 i 1 4 X 7 7 Pounds is iV of a hundred weight. 8 14 16 56 1 cwt. is 1 1 qr. •uV of a ton. 1 6 4 5 10 1 4 8 • » 1 u i i CLOTU aiEASURE. Nail is -^V of a Yard. i or 2 quarters J INTEREST TAULE. B. d.f. J or 5 per cent, is Oj 1 in the £. 10 1 I i la • «, ■ H i • • • • • a • a OF ARITMiMETIC. tJ7 or 16 lbs. INTEREST TARLE-Coutinued. je d. in r 1 per cent: is 2\ '\ ij 3 1* n i / If 4 i- . 2 43 i weight. . 2i n 6 ■^4 ... 6^ f . • 3 7 t SJ 7f i , . 3^ 84 f 3S 9 f 4 . . . , n i / "« 4 J .... 10 1 % 4.} 10,? i -. 4f 5 .... 1 6 I 2i i • 1 4^ i ■ a Yard. 8 9 1 7 i 1 9} 1 10 2 12j 2 6 u» 3 17^ :< G ^0 ..., 4 he JS. 25 30 5 6 ■ ■ • • • ■ • • 30 . . . , 10 the jC I i Mr ^< Tabic of MhceAlancGii^ Arilclcs, 56 *•■*•••••■•■«•« o* A barrel of potashcis. ^ 200 A fnklii of butter Is A . . of soap. . . . A A A A A of anchovies o f can f.l les 120 of so.ip 256 of raisins ,. 112 of butter „ 2^' 1 A A A A A A 14 P, 5 A foiber of load is 19j' hundred woigiit. .2184 stone of iron -., of butcher's meat of «>I;;ss - of hemp of cheese ., i() gaHon of oil. . . 1 7,1 A faqgot of steel l2o" A peck of s;:U ^4 A bushed of salt , 5(i VI Articles. ,1 dozen. 12 Dozt-n ..•.!. I gross. 20 Articles.... 1 score. \ Score. 1 common hundred. ^^ Score 1 orcat hundred. ^4 olieets,, .......I quirt) of paper. 20 Quires \ ream. - Roams 1 huuHl?. J> Do/., skins p irclnnuti} . I iioll. .\ J^Ul ' I'' \\^\\\\ '%\k :Ics. Ids, 56 6i "^m • ■ • • • a « • • • • • « • • • • • « • > • • ■ • • • P, 5 32 1(> it 1.20 14 5(> hundred. drcd. pnpor. NOTATION. .Notation is the ait of expmssiiig' liiunbcrs l)V guros, and tc.:u:hcs to read or write anv sum or dumber rcquiied. . Writo in figtires the following numbers: Twcnty-stjvcn. Two hundred and ninc^ty-oigbt. Seven hnndred and sixt v-*':rro. I iirco thousand four hiujihed and five. Twenty-five thousand seven hundred and fjf- fy-lwo. * One hundred and ihirry-scven thousand, four Ittindred and t wc^nl y-nine. Four millions, eight hundred and sixtv-fjvo thousand, five hundred and fourteen. Twenty-nine millions, tljree hundred and twenty-four tiiousand, six hundred and tweniv- llinp. Ei-hl Inindred nm] twenty-four millions, two .hundr(.'d and foriy-ihrco ihuusa.id, nine hundred aiid eiiihtv-seven. Seven liundrcd end fifiy-four millions, two- hnntlred and sevenly-four thous^and, six hun-^ are d and seventy thi'e(\ Write in words at length \\ic. foIlowinc>- num- bers : 34 69 103 yzoA ^5071 215G75<> 32572464 4t' i» A NZ^ SYSTESf ADDITION. Addition teaches to collect into one sum, or to. tal, several niimbGrs of the same denomination. EXAMPLES. 82512 74523 42861 53124 21402 54287 31042 15134 87654 64325 63251 12861 65432 54261 42783 296435 22S571 240446 476-198 3S4856 575476 858427 576828 2567^2 345368 246542 343274 465482 682673 575476 623428 722346 256782 ,232698 232782 343274 734S7623 82998763 84987654 43284783 23765436 87236875 24687329 87349235 35976329 72358927 98984687 64136897 67243884 85239496 33297973 79847263 87238643 12315634 , *r AraTFrMt sum, or to* nomination. 561 287 554 361 783 I 446 476 7^2 274 476 / O^ 274 }S7654 236875 976329 136897 297973 315634 76843792 43417612 67308784 4S976139 ^4643675 70385723 56320523 54335004 7G:)4328 54342347 n294606 63976542 JS9074234 74526488 7262540 224253 ^5730216 5430256 7653024 8,^24204 65798432 46078024 7262540 2342153 65430215 76302416 764523 42346740 54023647 14323624 76432940 43284324 736-45327 65432432 23456789 75421407 7864324 43654326 43246 64320043 53243200 65320402 4230046 2323624 67598325 434270 432v)9542 6534203 742302 876S5997 42308046 7236243 434270 5439552 65342083 '^- :u 403120.14 23443270 43204024 6234203 523430 45032302 53204272 65420743 34325436 40352042 33420043 50603228 37832565 84064232 46030626 42340476 7652355 39567836 90892347 842650 70814764 56430282 75643213 42347476 6652345 87089234 83265 7084764 32 A NEW SYSTEM SUBTRACTION. Subtraction teaches to deduct or subtract a less number from a greater of the same? deno- mination, whereby the remainder or difference is found. EXAMPLES. From 7613456 948765381 731426871 Take 2347892 578631497 377631268 Remainder 5265564 370133884 353795603 Proof 7613456 948765381 731426871 576504320 312321234 876980608 141213065 760054367 213561213 '■ i^ 657345134 252176581 827658974 245371892 957894761 682763457 % subtract a no de no- difference CF AIUTlIMETir, ^^9S7i):)4S • 7(i06547:>3 ii2jQ789l2 254S?"0317 ^3 42S7^3L4$ 31426S71 r763l268 )37956()3 51426871 ()473 14879 316321568 598761492 3423679S4 958276134 720324189 •:-^. 74876354S63S402670303 1 460785^^ 3 278.361325434501234542232132821 5432187652532212304546700000000 ;n42l67 171316543216778289172345 S4 A NLW SVSTEM ri! MULTIFIJCATION. Multiplication is n compendious metliod of peilbrming addition, teaching to find the amount of the greater of two given numbers repeated as often as there are units in the less. The number to ho repented is called the muU tiplicand: the number expressing how often the rrrjlliplicand is to be repeated, is called the mr* tiplier ; and the number produced is called ti product, or answer. uh he fJASE r. EXAMPLE. 47654S321 multiplicand 2 multiplier 95309oG42 product Multiplicand Multi( 231042S52532 2 468104261428 3 102897142634 4 42694 104226 L 5 509270860274 6 987654321234 T 144869104212 8 Product 261042785409 :>40926S5426l 10 *>r ARITHMETIC. S5 Alultlpiicand 437820491276 542907123645 939876421027 Multiplier Product 12 12 CA5I5 !!. Whrn the nuiltiplicr is more ilian 12 and less than 20 nudtiply by tlio unit figure in ilie multi- plier, lult.iing to the product iho back figure ia the muUiplicand to the one you muiiiplicd. . EXAMPLE. 542789246S91 Multiplicand 13 Multiplier 7056260209583 Prodact Multiplicand Multiplier 654270654212 u 594206142123 15 124670924352 16 426704260142 17 542096512312 18 426012423504 19 5426014231'26 19 Product 9159789158968 8913092131S45 1994734789632 7253972422414 9757737221616 Or\r\ AC\ o/?/-i A ^a >^/Z 10309427039394 39 A NEW SYSTEM CASE III. When liio niullijjlier is the piocluct of two or more numbers in the multiplication tabic, mul- tiply successively by each number, and the last product will bo the answer required. ^ EXAMPLE. 5420643 58 «■ 4 X 6=-24 2168257^32 - - 6 92 ier 130095445 Multiplicand MuJtipl Product 437094285 32 13987017120 760425513 42 31937871546 870354261 ' 56 M8739838616 925401326 64 59225684864 542670329 72^ 39072263688- 624506274 81 50585008194 785462501 84 65978850084 862435871 96 82793843616 432014936 121 52273807256 f^ ^\ A /-^ /^ ••• f^ •* <-W JU4oO/2i;> 144 72618879392 513742867 1728 8^7747674176 or AUITIIIVTETia.. 37 CASE IV. When tlio multiplier consists of sereral fi- [gares, multiply separately by each ol' the f/riivos, iif ciphers intervene, otnit them, and pl.jc .■ tlia [unit lii^jure of each product under its corres()ond- ing figure in the multiplier, and the sum oT these [paitial products will be the product requirc^t;.. EXAMPLE. 24230612452 Mulliplicnnd 23 Multiplier 72691S3735G 484(3.1.22 1904 Pro^l. required 1 357304086396 Multiplicand Multiplier 56013542634 37 15270253612 43 9270426514 65 5740642390S 76 64212346573 93 1246092544 257 5642709431 549 1234567S9 1342 42786581 63452 . 54306712 72564 560254389 . 40026 459624137 602004 2 642042571 4200706 26 42802754 570040.:^ 2 Pj'OdlTCt 2072:01077458 656620905316 602577723410 4362888217008 6292809964154 32024';7o3803 31^97847477619 16567P010S3S 2714094137612 394071224956S !2242 1742174114 2766^ 55689705 .^:8- 97Xr;208O255125 4399303291537-0 H $s A ntW .SYSTEM CASE V When there are ciphers at tho right of one or both numbers, proceed as before, omitting the ciphers, at the right of the product, phice as many ciphers ds are annexed to both numbers. EXAMPLE. ■ artii 1 1 254361400 iMultiplicand 423000 Muhiplier 7630842(3000 508722S 10174456 10759487220000 Product Multiplicand 52714230 6435720 3452640 753264000 789254400 560254389 459624137 642042571 42802754 47892541 542603^4 Multiplier 542100 8435000 6452(^0 5462704 7831200 40026 602004 4200706 5700 105 4250006 42700^5 Product 2746411383000 542S529.S2()000 2SO:S323328000 11485,525280000 618080907280000 224247421741 14 276695568970543 2697032080255126 243993032915273 203543586605246 2316928239172570 k'm. OF ARITHMHTIC. DIVISION. S9 CASE 1. Division is a comnondious method of perform- ing subtraction, loaclnn^Lij lo find how many times one nun^her is coniained in anoilier of iho SJjnii^ (icnominiilion. The number to bo divided is caHed the divi- dend : the niiniher by which we are to divi(hi is caUed the divisor : the number produced is call- ed the product, quoti(*nt, or answer, and if ther» be any number over, it is called the rcmuider. Divisor Dividend 2)732045630 S()G022840 Product 2 7320456gO Proof Divided Divisor 724943r)81 4 395420157 5 4928743G3 G 567'80I239 7 6204SI934 H 572SG0341 9 654302178 10 S23521457 11 108605482 12 Product 1 ' ■ [ 1 1 .J 40 A NEW SYSTEM sli CASE ir. When the divisor is the product of two or iDore numb .rs in the multiplication table, divide succes.v'^/oly by each number, and if there be ^ny remainder from any division except the first, midtiply it by ii.o precedinjr divisors, and add to tho product thy preceding r;i;iiainder. EXAMi'LU. ( 3j84327084 15 < I 5)28109228 3 Divided D 843;?7 6849 .563482634 486348276 843263243 48 3268 420 432684794 ' 487357647 824268475 684327684 763246843 32C:3r2645 ivisor 15 24 S6 48 54 Q>3 64 72 34 96 108 132 )218456 Product 56218456 23478445 13509674 17567984 8949415 686r,012 8962888 99o\H^7 7128S3 7067100 2476307 3 X o^9 Remainder < » t> 11 10 ^^ 4 15 49 4 43 121 CASE III, Wlien tho divisc;' wxceeds 12 and h not a composite number : find liuw manv iimG<^ tfi^ dX^ OP AniTHMBTIC. 41 two or , divide be ^ny e first, id add lainder ? 1 > L ) i visor is contained in tlie highest figures mtke di- vidend, by finding the greatest product of the divisor niultij)lied by a single figure, that is con- tained in those figures ; subtract this product from tiiem, and place tho number of tines in tho qu )tient ; thru to the remainder bring down tho next highest figure in the dividend, and find how often the divisor is contained in it ; place this figure in the quotient, subtract the product, and so proceed through all tho remaining figures hi the dividend. EXAMPLE. s Divisor Dividend Product 13)234536(18041 + 8 13 13 J 04 234536 Proof 104 5S 52 not A to 18 3 Reniai^Nder. ut 42. A NEW SYSTEM Dividend 4278345798 3d6427D'^S4 2542058749 e92 1 654873 32.)0o4578 472945G3744S <^^J791 ^745076 4997434SGJ843 19794GSG30(;02 499G33S299S75 645S9742G21755 Divisor i/ 19 2o 37 lOG 1G4 31GS 3974 'J Z..» xZ 4 or • t ' ") 1234025 Product 25lGo7399 187593G51 97770721 IO5090G72 30GGG45 1299301201 210847457 1257532G78 6126034 ' 1370G857 ^2315271 CA:^E IV, "VVIien the oivioor lias a cipher or cipliers at the riglit hand of it, separate theui [roni tho di- visor, also cat of]' as many pjucts on the rif,4jt of the dividend, then divide the figures reniainin072 )6^J5 201 '457 678 034 857 271 ors at iio di- ^'ht of fiinin<>: or ARITHMETIC. 4o '1 Divideiul Divisor . Product 65406752 100 3 J 00 210989 13 6326S762570O 3900 162227596 5042683910 2630 1917370 123268956493S0 42060 29307883 643851974480500 4567200 140973019 47946,S746845000 4635000 103444174 405134068053312360 87675^10 46)2084357 235975384600583760 435126780 5 42314092 COMPOUND ADDITION. Addition of Money, Weii,4its, Measures, iScc, teaches to add sundry sums or nimibois together having divers denominations. MOiNEy. EXAMPLE. £ s. d. £ 5. d & \) 25 6 u 6 3 G 67 17 6 7 4 8. J. 76 7 1 9 5 85 9 14 (vj 55 7 J 1 13 7 77 !; 7 3 18 4:1 93 15 ^:f 5 13 S:^ 75 16 9 9 16 17 i- R 3 *» 4 43 44 A NEW SYSTEM 457 19 6i 547 19 9 498 17 OJ 700 6 s" 629 19 6i 900 6 6 352 19 6 357 15 5^ 896 4 7 680 15 3 649 5 7 672 18 1^ 395 19 7 423 2 8 532 14 5f 274 16 6 792 9 5^ 960 6 7« 11 279 675 698 667 407 564 709 279 248 «. rf. 16 9J 18 53 14 9 C 2f 17 4 19 9? 8 6 7 9 14 4 £. s. d^. 346 16 rf 360 J2 4 209 9 9 776 16 6 467 7 8J 467 9 73 953 K) 5 645 39 H 797 10 c>k 6 o 7 8 6 rf ©I' AK ITtt-MIiTlC. £. s. d. ^. a. d. 457 17 7 187 19 6 26i 18 8 146 15 6 296 18 3^ 106 17 7 :3S4 12 6 236 18 H 547 12 4 429 17 10 270 10 3 387 17 7 320 19 4.^ 140 10 6 387 15 10 443 13 4 387 12 7 584 19 10 ir# FEDEil AL MONEY. • Eagles. dol. dim. cents. milfs d. 4576 7 5 4 9 n S963 8 2 3 6 4 6734 3 4 3 2 9 5878 4 8 9 7 6 9 7 5 Si 1342 « 5 4 7^ 2546 I $ 5 3 5 7234 i#M 9 6 7 8f 1 '^J75 IS f 5 8 1 ■T 46 A NEW SYSTEM TRoy WEIGH r. ©7.. dwts. g'*- oz. dwts. §»•• 9 10 18 10 18 20 8 18 7 11 17 18 10 19 8 7 14 19 11 12 22 8 9 4 10 7 7 5 19 19 7 8 16 9 8 ^7 4 14 16 8 15 15 O 17 7 9 9 10 7 18 20 5 18 16 ^ 111 lbs. oz. dwt. 20 10 IS 15 11 12 27 7 17 18 11 10 14 10 19 19 • 4 -i^ 18 5 17 26 9 18 10 19 lbs. oz. dwt. 25 11 12 14 9 IS 16 7 3 56 10 10 19 11 17 23 b 18 26 10 10 24 8 12 li 7 12 OF ARITUJir/ru. 47 AVOIRDUPOISE WEIGHT. lbs. OZ. dr. lbs. oz. dr. 15 13 14 20 14 12 13 15 12 18 15 14 24 12 10 25 14 13 5 7 9 26 12 10 23 10 7 20 2 13 25 3 15 25 14 12 24 12 14 23 12 13 17 14 12 27 13 9 12 10 15 24 13 12 m cwt. qr. lbs. ton cwt. qr 19 a 20 kj>j 18 2 17 t 14 29 19 1 14 t 12 18 6 3 17 1 4 25 18 2 15 t 17 Sf) 10 1 14 f 18 39 19 2 13 19 48 14 17 % 24 49 2 2 13 i 23 50 2 1 4$ A NEW SYSTEM ArOTHECARIEG WEKU] [T. r. sc. g^'- OZ. dr. sec 6 2 18 10 6 7 1 14 9 S 1 5 19 § 7 2 6 1 14 9^ 2 5 2 16 U i <5> Mi 4 1 19 10 4 7 18 7 7 ,1 4 2 19 7 t « lbs. ox. dr. lbs. oz. dr. 20 1 7 It 10 7 24 % 6 23 6 6 17 % 5 ' 26 9 7 24 f 3 If g 4 18 6 7 23 11 6 25 10 6 26 10 7 26 9 7 15 9 27 9 5 28 7 7 19 8 7 17 9 6 r>r AHiTHiMr/nc 49 Vv'OOL WEIGHT. St. c]. lb. t. 1 (3 5 1 1 5 4 1 3 6 1 1 5 3 1 3 2 1 G 4 1 1 2 5 1 1 3 1 1 4 1 St. 1 1 J 1 1 1 cl. 1 1 1 J 1 1 1 J* dr. 7 6 r 4 6 7 r 7 ) 6 t. St. cl. 4 1 1 6 I 5 3 1 6 1 2 1 1 1 1 1 1 •J 1 Id. sa. w 21 9 1 18 9 10 1 8 1 3 7 I 29 8 1 19 7 8 6 27 9 1 i », 1 t i / Iji i i»l! 50 A NKV. SYSTEM - CLOTH M!:AS('ii^:. vds. *ir. n. vcis. qr. n. 15 2 O \9 2 2 18 3 2 17 3 17 2 3 20 2 1 24 1 27 3 1 27 3 3 26 3 29 2 3 2f) 1 21 .3 3 3 1 3 2 46 9 AG 1 i 17 1 15 3 3 E, f: 73 4 65 5 39 1 2 '^^i /O"-* 2 3 55 6 33 3 98 7 II {{ r n. ni. fur. P- I en. ni. fm 3 24 7 26 37 2 7 2 27 6 30 31 1 6 30 4 18 42 2 5 1 4C 3 35 52 6 2 52 5 23 4(] 4 3 46 7 34 64 2" 5 1 50 3 62 57 2 1 S 42 5 28 76 1 1 23 6 22 33 6 t lit It ' i' 'If I i, i OZ 47 A NEW f5yS'rL:vl SQUAUE MEASURE. 26 46 27 54 3 S3 56 r>7 78 2 30 84 24 85 S S3 95 37 99 • • a ■ 38 r ■ a a. 51 o. 60 2 38 57 3 35 48 2 38 59 29 64 3 24 63 2 36 34 39 67 « ■ • " 3 1 • > • 33 ■ • • • • • *r- a. r. P- 52 1 27 62 9 18 29 3 19 40 I » 29 34 74 9 i*^/ o 41 38 2 24 32 24 a. r. P- 24 2 27 36 3 rs 44 28 54 2 34 6j 1 2(i 74 36 17 32 45 28 29 30 OF ARlTH/dETIC 5« Yun. 47 57 62 54 57 54 62 43 17 /^•i O 12 i7 7 16 6 ^i WiXr: MEASURE 3 <7> f) ^^, run, I.) :li 4-1 K' r* O / 4 o/ 42 ffj 2 f» 39 86 28 n ^'O O .'.1 3 «7 T*^ hhd. gal. j)t5 56 43 58 49 61 16 71 47 84 37 63 42 98 24 89 64 47 8 2 X\\x\%. hbd. gal 5! 48 27 28 24 38 42 57 29 1 38 20 30 14 52 3 29 i;y 1 ■ r G2 63 46 o 41 40 42 49 r:v\ svstj::*! AV.E tij.d BEEPt JJEASLilli 11 r 2 'nl 6 6 .14 29 r>6 3S AS 29 33 49 ^: t fir. 2 TT irai 8 ii hlid. gal. qts. 72 43 54 64 72 28 36 29 23 20 o hl)(!. gal, 55 23 G3 14 69 24 70 28 67 29 49 32 qti 2 3 o 28 23 2 48 18 48 38 60 28 2 18 32 fM«« • a • 2 48 37 • t . • ■ « • « ■ • I k fl J V a « « a a or ARITilMET *X-.. ^o lil. DRV MEASURE, p. qr. ]r* 7 > > 38 ^» 4S ;1 1 /J4 4 57 7 60 38 ■^ / « tT 49 48 6 24 39 34 49 3S 3/' 36 90 88 bn. 6 5 rr / (. 4 O 3 O 3 .3 3 r 1' til. bii. P- ch. b-. P- 71 3 S7 18 1 76 ("» SS or, 2 64 25 80 so 88 18 4 82 32 8 98 CO 36 30 86 :v: 76 r> 3 38 S) 77 2o 33 21 3 78 38 47 • • a 1 23 • * « S9 • • • I 9 3 B ■ ■ •• ■ » i > • • • « • • • • • • • 1 1 a • a « • « • A Wnmt 56 A NJGW SYSTEM TIME. h. m# (« d. h. in. 48 53 49 54 7 42 54 38 43 56 13 44 62 49 37 67 8 38 83 20 47 58 19 49 60 48 50 70 () 40 72 40 44 70 20 38 44 38 48 49 4 39 64 36 38 30 19 30 81 30 37 52 18 59 W. d. li. 47 6 14 49 6 17 48 16 57 6 17 46 5 8 53 4 8 44 3 17 59 18 58 2 23 mth. w. d. 46 2 5 45 3 6 40 1 37 2 5 38 4 40 2 3 4G 6 43 3 5 37 3 6 CF ARITHMETIG. 57 MOTION • m. 91 9»» m. ♦» )«t 49 34 34 45 18 24 45 42 56 57 34 10 60 57 49 24 42 28 53 15 24 37 22 3 55 16 57 19 57 10 CO 33 38 20 12 2 33 37 39 36 42 10 34 40 40 29 32 50 46 44 44 35 m m tm 14 25 a a • • s. 33 45 76 57 97 36 89 90 G5 S'9 i:8 16 20 20 26 27 8 rr?. 50 58 59 56 58 58 59 55 4J n. flf'fr. m. 65 18 53 36 27 39 37 14 40 36 23 44 55 14 44 GG 15 48 76 3 46 60 4 33 44 15 35 ■ a « M N •Jo A NEW SYSTEM COMPOUND SUBTRACTION. r;jbtrp,::;:,n of Monoy, V/ei;:hts, Meastires, SzQ., toaclio?, to doc! not <>no sum or quantity f.on) nnuiiaT; ono or both of tlie quuntiiies bc^- in«- of (.^''S^rent ('onominn.tions. .13 18 15 EI'ArjPES. 42 6 1 • V> a, a 14 cJ • • • X • • •> .9 r> :> f« « « < » • — < u; o 4 '--l £ p. 4 5.') 17 8 4? 4 Sf^ 5 42 13 14 19 9 10 ~4r 4\ 4 3 .C i:,4 86 12 10 r?. 104 6 :236 148 1() 14 63 • • a <* OF ARirniMETIO. 50 2j7 s. 17 17 d. 3 £ 439 147 s. 10 19 d. 1 4> £ s. d. £ s. d. 443 18 4t 454 14 1 263 14 1 105 10 n -- FEDERAL MO.'^CY. E^elosf d(3l. dim, cents mils 6734 S 4 3 2 5876 4 8 9 7 K^ CO A Nz^y srsTE.'^ TUOY vViEiGHl' OZ. tlwt. J?r. 26 18 ^21 2i 14 18 oz. di^'! 41 14 17 18 n. f 15 14 ^ >« « « ■ .« a # • r ^ OZ. dvvt, 10 18 o 'W Jb. 45 OK, 9 J vvf„ 14 17 ^-f-' R fl • a ■ •«••«•••■«« AVOIRDUPOIS WEiCIIT. OZ. 10 12 ur. 8 lb. cz. dr/. 26 .-to G 18 10 14 ••«•««•«« ••••••»f»»»»#t CF AniTiiMr/rrc- 61 «wt. qr. lb. lO?J cwt. qr. 1-^ 3 7 48 4 1 • • • • 1 • • f • J 14 • ■ • a '23 • a a 12 9 A • « • 1 3 • • • ■ ^m9m»tp»mmmm m m ^ * 12 3 APO'i'iJEC tl 1 1 AIIU OS V/ElGI CZ. \) r'jt 1 I . (jr. 6 5 SC. • * • • m m m m • • » a m • m lb, 10 6 # • a 035. G 7 dr. 1 lb. 15 4 07. 4 3 dr 3 4 % #'''^ ll 62 la. 21 18 9 A NEW SYSTEM V\GOL WEIGHT. \v 3(3 o s:i. 8 w. h. ST. w. 54 3 1 27 11 1 in. 76 67 sn. 9 4 1 • • • • • M • ■ < • a • • I CLOTH MEASURE. ■ yrls. qr. n. qr. n. 38 2 3 64 1 3 S4 3 2 15 3 2 1 OF ARITirMETIC. EE qr. n. Fr.E qr. n. 50 2 3 34 3 2 20 3 3 SO 3 3 03 .-._ LO^JG measltj:. fr. in. ^)^»r. Vffs. fr. in. S6 4 2 40 2 6 28 5 2 34 1 7 ni. uir. p. I. m. fur. 12 6 37 7G 2 7 9 4 28 43 1 4 - i 11 ' 1 I 64 A ISEVr S VST KM a. S9 15 • • • • r. 1 2 • a > ■ LAND ME P- 20 17 A>SURE. a. 40 S6 P- 2 P- 15 16 * a. r. P 10 4 5 I T a. r# V' 54 15 ■ * • • 1 18 « * « • - I 50 2 1 4 3 J'T, IT 12 14 15 Cjt. 1 3 ■ hhd. 62 58 • • ■ • 45 57 • ■ ■ ■ < OF . qt. 2 2 AniTlIMETlC. i.hd. GO 54 13 25 • qt. 2 65 i / ALE AND BEER MEASURE, bnrl. fir. gal. bail. fir. 20 2 5 34 3 18 3 f • 27 2 ^al. 5 3 4 if t t. . hful. gnl. qt. 26 14 I 18 15 2 63 32 1 23 4(3 I p ? lA i M 24 12 o DRY MK.\^rnr. «. ^\.4 o 14 >u. 70 10 b n. 1 If!, 47 10 10 14 • • « ••••••• • • • • « w llm i 1 Sft. 76 43 22 28 m. 54 18 •••••• • « mm. 62 18 34 5 m. 51 ::8 • ■ • • • •••••• OF AiirrnMETit. w. d. h. mth. w. d. P' - d4 6 21 62 o S 4 23 5 14 34 3 5 3 ft; II • ■ P 7 »* »»♦ 11 «• 72 14 52 43 22 58 • ••••«•••••• m. »» »»» m. »» m 51 28 32 37 33 24 # • • < S7 44 1 • • • 18 ■ • • < 57 ■■••■< 40 t • • • - m. 34 21 10 42 12 tt#ff §• •■■«■■• 11 *■ ' 6? M I REDUCTION. Reduction is the chnnging of numbers Aom one name or denomination to another retainin(r the samo value, and is (Dorformed by multiplica^ tion and division. Groat names are brougiit in- to sm;dl, hy mulliplying by as many of the next less as made one of ilio ^rreater, adding to the prodiict the parts of the less name, if tlic num. ber to be reduced be a compound one ; and small names are brought into great by dividing by as many of the less as make one of the next greater. MONEY, s. cl. 14 1 into pence. An3. GiG9 pence. EXARIPLE. s. d. Reduce 05 £. 25 50 314 12 14 1 Ans. 6169 Pence. Reduce 17 Reduce 346 s. 6 1 m d. r>^ into farthinirs. Ans. 16573 firthin^. 8j into farthings. Ans. 33248 Ifarthinjr*. v»ij iiiiu iuruiuigs. Acc;. 537587 fr.rtliingi. 'i's ft om :?taining Itiplica- Jgiit in- Uq next to the c n tim- id smiiil g by as ';reuter. pence, things. tliiogft. OF ARITHMETIC. Rtiduoe 6169 pc^ncc into j^ounds. Ans. 25 Reduce 16373 fartl^jinc^s into pounrls. Ans.. 17 Reduce? 3324^1 farllnn^rs into pojinds. Ans. 346 Reduce 337C>S7 fartliings into pounds. Ans. 351 69 ^'. (1. 14 I 5 3i G <^J \3 02 TROY WEIGHT. Reduce 37lbs. into grains. Ans. 213120 jrrnins. Reduce olhs, lOoz. 7dw't,'?. oias into grains. Ans. 22253 grniria. Redure lolbs. Tvoz. 8d\v}s. ^liirs. info i:rj»ins. Ans. J0(>75o gr.iin.^. Reduce 59 lb:-5. 13d\vts. 5 j:rs, into izrulns. Ar.s. r.40157 grains. Reduce 2U3120 rrains into lbs. Ans'. 57lbs. Reduce 22253 cjriins into lbs. Ans. oil)s. K'oz. 7d\vts. 5grs. Reduce 106759 grnins into pounds. Ans. ISlbs. 607. ^^C\\\\. -Igrs. r-- --••-..•- *- T'-' ' *' f W** •«»♦»-• p*st-j- •----« An«. 591'?'^. l.>dwl«!. 5j;ri, U'- (lit if 4 NSW sy.STEM mm^ Ilediice R-odiicG Reduce He il 11 CG Rcdr.cc Reduce Reduce Roduce ArvOTHECAUIES WEIGHT. IJlhs, into scruples. Ans. 4S96 scrnpk's. 27lt)s. 7oz. 2Jrs. l?c. 2.>r'^. ir^to frr;rn?;, A::'^. 150022 ijr.iin^. 15lbs. 9oz. 6. Irs. 2;^c. J2'r. inlo t^B! I m Rcduco Scvvt. 27ibs. Icz. into oimrcs. Alls. 147C90ZS. RcJiice Ocwt. 5]bs. into cz?. Ans. 1G203 ozR. Rcduco 35tcn?:. I7c\vt. Tqr. 23]b£. 7(>/. 13dr5. into dranis. \rs. 20571005 d Kim's. :rii pk'S. .^r» •n-n?;. irr aitis. '.rr .'iin?. ^' • g' ains. 1 1- T ! , , c. 2grs. .1 ^ fr r <: 4* S^rrs. j3 ozr. :i Redi'cr; l^joions. 12cv;t. 2qrs. 8ll.;s. 4u^. Gdvs. i-ito (]r.;rn?. An?. 04082738 draniy. Reduce 1 ''i769 cz. into cwt?. Ans. Scv.'t. 27lb:^» l^'^.. Rcfjucci lG'203 oz. iato cuts. Ai-s. 9 cv.-{. 5lbs. Ileflnce 20571 035 ' 8403275S di^. isito -on?^. Anji. i'l-j u»ns. 12c\v{, 2qrs. 8il)s. 4nz. (Idrs. Tl:o nsi]:.l jiliowmu'c* ny;'Zo. Ne:ir or tn'l \vrhyn\ i:^; ili. i which rem »iiis ',\i\r\' the allovv.mcc.^s r^it^ dcduclcd. Gross \vf't;:Ijt r2r\vf. I4:l^s. t;iro icwt. 2qrs, ISibs, rcquii<:'6in 3cwt. n^quired tlie net? ^ Ans. 50cwf. Iqr. 24i^Ibs. Gross weight x:8cwr. 2qrs. tnro ISIbs. per cwf trett -^T^^ofrms. insert, required the net! ns. 22cwt. 3qrs. I2fibs. [{G{ 14lbs, '^.XIl s. (reft 14lbs. 13Ibs 7^1 bs. per IS. us. per -J5 )S. I 3" por qnired 2511 )S, s. pnr uired 4jlbs. r cwt. ci the OF ARITHMETIC 7f? Ujoss weight :3c wt. :?qrs. 7il>.<. tare 3 libs, per cwt. trvM /„ cloHf^lbs. in :?cwt. rc- qiiired tiie net | An.«. l(>c\vt. fqr. 22^1bs. VVOOr. WEIGHT. Reduce 21 Lasts in wevs, Rod Ans. 4S4 we vs. uce 184 Lasts, 7 sacks jnto vveys. Reduce 1 tods into pounds. Reduce 5 tods J St. Icl. into KGduro ^S I Wevs into lasis, Ans. 4430 Mreys. Ans. 112 pounds. pounds. Ans. I6l pounds. Ans. 21 last. R odtieo 1 i;;0 wevs into lasts. Ans. 184 lasts, 7 sacks^ Reduce 112 pounds in tods. Reduro 161 pounds into tods. Ans. 4 todi Ans, 5 tods 1st. 5cl. CJ.OTll MEASURE. Uoduce (S2yds. 2qrs. Inail into nails. Ans. 1001 nails. Reductj 3 iFl. F.. 2qis. 3nls. into naib Ans. 1010 nails. Reduce 40K.F.. /.(ps. 2nl«. into nails. Vns. SI 4 nails N r il I m ? tML 74 Red A NBW SiY8f(.M u«e 50Fr. E. 4qr«. into nails. Reduce lOOlnls into yards. Ans. 1216 n-dih „ , Ans. 62yds. 2qrs. Inl. K'^^^jr^ 1019nls. into FJ. E. ^ Ans. S4F!. E. 2qrs. 3nls. ■ -'s 3l4nls. into E. E. .., . ^ A"s. 40E.E. Sqrs. 2nls. it<>fiuce 12l6nls. into Fr. E. Ans. 50Fr. E. 4qrs. LONG MEASURE. Reduce 7 miles into barley-corns. Ans. 1330560 barley-corn. Reduce tiTS miles into inches. r, , _, -^^"s. 17297280 inches. J^?,duce 50 leagues into inches, Ans. 9504000 inches. Reduce 25020 miles into barlev-cornrs Ans. 4755801600 barley-corns. Reduce 1330560 barley-corns into miles. •n , ,_ Ans. 7 miles. Reduce 17297280 inches into miles. Reduce 9.U4000 inches into league*. Reduce ^rn.Qoi^.^ . • ^"^- ^^ ^^^S:"^*- - -.- ..uJiOv.0 Marley-corns into miles. Ans. 25020 mlhs. Redii Redii Redu Redt B,edu Rcdu Redu' Redu< Redu< Redui Redu< r Redm< 3 6 nails, rs. Inl. 5. 3nls. s. 2nls. . 4qrs. '-corn. nchcs. nches. corns. miles. niles. igues. Qiles. or ARITHMETIC. 75 SQUARE MEASURE. Reduce 27 acres into poles. Ans. 4320 poles. Reduce 484 aores into poles. Ans. 77440 poles. Reduce 27 acres, Iro. 32 poles into poles. Ans. 4392 poles. Reduce 4321 acres. 3ro. 34 poles into polos. Ans. 691514 polos. Produce 4320 poles into acres. Ans. 27 acrss. Reduce 77440 poles into acres. Ans. 484 »crc ■ Reduce 4392 poles into acres. Ans. 27 acres, 3ro. 32 polos. Reduce 691514 poles into acres. Ans. 4321 acres 3ro. 34 poirs, WINE MEASURE. Reduce 19hlid;s into pints. Ans. 9576 pints. Reduce 5 tons into gallons. Ans. 1260 gallons. Reduce 13 tons 1 pipe llihd. 17ga!s. 2qts. inio pints. Ans. 27860 pint>\ Rcdmce 46 tons ihlidi. 45 gnlis. Ipint into pints. An«, 94609 plnti. I I V l!U h ' P. V li-n f. ■'. ti-^ 7H A NKW SYSTKM Retiuce 9j70 pints into hiid-s. Ans. 19 ijogbhuatli^ KeJucG 1260 galls, into tonij. Ans. 3 toijb. Ruduce 27860 pints into Ions. Ans. 13 tons 1pp. ihhd, l?gals. 2qts'. Reduce 94609 pints into tons. I R^du Ans. 46 tons. 3hlids. 4;)gal. Ipr. ALE AND BEi:ii MEASUHtT. Reduce 10 barrels of ale into pints. Ans. 2880 pintsr. Reduce ISlihds. of ale into gallons. Ans. 702 gallons. Reduce 30 hhds. of beer into pints. Ans. 12960 pints. Reduce 242 hhds of beer into pints. - Ans. 104544 pints. Reduce 2880 pints of ale into barrels. Ans. 10 barrels. Reduce 702 gallons of ale into hhds. Ans. 13 hogsheads. Reduce 12960 pints of beer into hogsheads. Ans. 30 hogsheads. Kfedwce 104544 pints oi' beer into hogshe-ads. Ans. 2 J2 hogsheads. al. Ipr. ) pintsf. gallons. 3 pint.s. 4 pints. Jarre Isf. sheads. ids. slieads. shc'rids:. slieads. or ARITHMETIC. DRY MEASURE. 17 Reduces 128 quarters of corn into pecks. A is. 4096 pecks. Reduce 2 lasts. J wey 3 qrs. 2bus 3pks. into gals. Ans. 1814 galloins. Reduce 20 chaldrons of coal into pecks. Ans. 2880 pecks. Reduce 124 chaldrons of coal into pecks. Ans. 17856 p^cks. Reduce 4096 [)ecks of corn into quarters, Ans. 128 quarters. Reduce 1814 gallons of corn into lasts. Ans. !2 lasts, 1 wey, 3qrs. 2bus.' and 3pks. Reduce 2880 pecks of coal into chaldrons. Ans. 20 chaldrons. Reduce 17856 pecks of coal into chaldrons. Ans. 124 chaldrons. TLME. Reduce 29 days, 12hours, 45 min. into seconds. Ans. 2551500 seconds. Reduce 87 days 23hrs. 15niio. 30 seconds into seconds. An. 7600530 seconds. Reduce 224 davs, l6hr. 49min. 15 seconds ia- to sGCondss Ans. 19414155 seconds. : n2 I it * i r« A -VCW SYSTEM fir jr Reduce 365 days 6hr^, IVito ^e^^orids. Ans. 3K->^7600, Reduce l'551IOO seconds into daya. Ans. '29 dav<, i^'lui. 4C>iniiu Reduce 7600530 .seconds into dav.s» Ans. 87days, SShr-s. 15n'.in. 30 seconds. Reduce 19414155 seconds into days. Ans. 224 days, l6hrs. 49niin. 15 seconds. Reduce 31557600 seconds into days. Ans. 365 Jlivs, 6 lioins. MOTION. Reduce Z degrees 4 nun. 15secc into seconds, Ans. 11055 seconds. Reduce 6deg^ 2l)inin, into seconds. Ans. 23340 seconds. Reduce lldeg. 51 min. into seconds. Ans. 42600. Reduce 4 signs 2ldeg. 20niin. ISs-ec. into sees. Ans. 50S81S seccyiids Reduce 11055sec. into des^^rees, Ans. oiS{.\yg,^ 4niin. 15sec. Reduce 23340 seconds into degress. Ans. 6de2:. 29niin. Reduce 42660 seconds into degrees. Ans. lldeg. 51n)in. Reduce ^08318 seconds info signs. Ans. 4 signs 21deg, 20min. ISscc. HF AKITHMIf^?r. t^ ^7600, conJs. 1)01! r-!;. )n(,ls. iconds, b26GO. J sees. 15sec. Wnun, >ln)in. 18scc. FRACTIONS. Fractiu!iii :uo t^?i[M<. ssioiis lor iiuy :i»*il^r.aai^J« ];uit or piirts or' an integer, tluiii, •|-S' or ^ aro;}t< r)OLin(] aro assii^rsablo parts toir 15 fibiUings^**- Tiie fi^iiuct above tlio 11 in; is ofilled tlio nuiflL^p- tofy i\nd that below tho denoniiuMlor. , Tb.n (Jo.'ion-jiiiator shows how m^.riy part* f5f« rotitaiiied in the inle^er or whole nui))!}er, ao'r! ihtJ ninnyrator bljows how nniny of thosi> ;«arts afu (le.sianated by tho iVaction. Fi" fictions arc eiilicr proper, iiupropiT, coro- pou nd or mixed. A propcM' 01 .siiri|)lo iVaclion is when the uu- inorator is less thiiii the deiionjiuator, a^ J, §, ^, if? At /. 'V J iX^ <-- . An improper fraction is when the numerator exceeds the denominator, as §, f , W^, Sec A coniponiul iVaction is the fraction of a frac- tion, as i of § of Jil, is (Vs. 8d. A niixf.'d iiiiniber is that which is composed of a whole number and a fraction, as 4 J, 12f , &c. CASE I. To reduce a whole nnniber to the form of a fraction, place 1 under it for a deaominator. EXAMPLE Reduce 1 to tlio form of a fraction : Reduce 4 to the form of a fraction: Reduce 7 to the form of a iVaction : Reduce 12 to the form of a fraction ; -} answer, -{- aiiDwer. ■f answer. iinswer. f 1 ■^ M 80 A NE^V SYSTEM C\fiL II, To reduce a whole ntjmbcr to a iVaction of a given denominator. Miihiply the whole num- ber by tho given denominator, and under the product place the denomindtor. Reduce 6 into a fraction whoso denominator shall be 4: 6x4=^/ answer. Reduce 8 into a fraction whose denominator shall be 5 : ^f answer. Reduce 9 into a fraction whos^ denominator shall be 7 : ^^^■ answer. Reduce 10 into a fraction whose denominator shall be 12 : ■^'2'- answer. n CASE iir. To reduce a mixed number to an improper frac- tion, multiply ihe whole nu/nher by the denomi- nator ot the fraction, and to the product add the numerator, for a new numerator which place over the denoaiifjator. or AniTiiJMiijMc. 81 ri of a nuni- ier tlie inalor iinatyr lluduco :2!l ^^ ^" improper Iracrioii : Hoduce 14^ to cVA ijuproper fraction: '^8 '* answer. llcdiico 79'^(i to an improper fraction: s li"^ answer. Kiidiice ()o7'-i^i, to an inipropor fraction : '* '! on 7 * -firj '^- answer. JlyduGo 784?^ { to an injpropejr fraction : "'^'Vi"^"^' ^insiver. ver. inator ver. inator ver. r frac- nomi- Id the place CASE IV. To reduce an improp^^r fraction to its proper tujrn.s, di\i(ie the numerator by the denominator. EXAMPLE. lleduce V"' to its proper terms : 42-r-5--J answer. Reduce ^"^y*^ to its proper number: GOT'l) answer, lleduce ^^;V^ to its proper terms : 637 "iS answer, lluduco H«^^ to its proper terms : ()4jiJi answer. Ktjdiice "'^^ ' to il« pi ojK'r forms : 17 '^yi answer. I'- \ W$^ lid 82 A NEW SYSTEM CASE V. To reduce fractions to a common dttnomimt- ti)r, inuitiply each ninrierator into ail tho d«- nominators except its own, for a now numerator, then mnliiply all tho denominators fo. a common denominator. tiie rei then tl which minatf] EXAMPLE. Reduce § «fc i to a common denominator : 5x9-15 4x8=-cJ:2 H" H answer. 8X9--72 Reduce | sfc | to common denominator : ik ^ 1^ answer. Reduce i|, ^j tfc ;j to a common denomitiator : iSV> ~i^iV &^ i^Kj" answer. Reduce ^, § t*b 12 to a common denominator : ih of ^ ^1?^ answer. CASE VI. To reduce a fraction to its lowest lornr^s, divido t!io tJ'rms of the jriven fraction hy any » ^uiiber which will divide both without v. remainri«jr, a»jd these producls again in the same munner, tiil ii appear that there is no number greater than I which will divide tije»i) ; in which case the frac- tion is said to bo in its lowest term ; or divide the denominator of tiie fraciion bv tbo numera- tor, and if any remain, divide lliu K^^t divisor by f>F AltlTHMETlG ji*S imiiut- Mator, turn OH \he lemniiKler continually, till notliing romain, lor : yer. *ver. tiator : nator : divide r, a>id till ii Iran 2 frac- divido 1 mora- then the hist d ill be lie i:isf divisor will do a common nioasjue which will divide both the nnmoralor .md deno- minator of the given fraction into its lowest terms. EXAxMPLK. Reduce ^j-| to its lowest ferrns. ^it -f-12'^ f|~-6-=§ answer. or 114)216(1 143 72) 14^(2 JH -4-72^1 answ<*r 144 Reduce Reduce Reduce Reduce Rtdace Reduc Reduce Hi to its lowest term : 'i answer. §H to its lowest terms: ci answer, ill toils lowe.rv icrms : i answer. 'ifi to Its lowest terms : "tV answer. •~t^3^5V to i«^ 'owest terms : ~aV answer, mi to its i ""est terms : f^ answer. >^ ir> itc> lowest terms : f^f answer. M 111 i. i I r<,{ K <^KW .■•VSTKU To jediici^ a r<>n){>ouncl IVdotion lo a sldglr one, multiply all ibe numerators together for a now numorator, 'di\d all the denominators togc- iher for a now denominator; or, wiien any two fcrni? of tho fraction wi!l divido by the same nuiDoer, it may bo done, and the products used iustoad of them. Reduce n ')^ '} of -A, to a single fraction : ~T^i^ answer. Reduce i;- ' n of g to a single iVaction : J answer. Hoduce i Ox § of 4 to a single fraction : -}%- answer. Rcduco Y 0^ ?. 0^' ' i''" ^0 a single fi action : yV answer. Reduce ^i of H of A to a single traction : --/>• answer. RedMc^ i of g of f of r» to a single fracJ'op^ UrCi 7 i , T 1 t-U*.. lied tion of Red Jiff] a mile Red an acr Re(] hof!sh( 1 ^ CASE Villi. To reduce any given jiuantity io trlie fraction of any j:;realer denomination retaining tho same value, reduce the eivou quantity to the lowest (errn mentioned for a numerator, then reduce tti? inteirral part to tnp snmp Icrni. which j^larc nndieV' ihy nunvpratoi'^ will or the fraei »n ro«pjire(i. Rgc barrel Re.- chaldr ^n" OF AUi'i'li^iL- i f;;. V > -j^ ~{--S=:f|- answer. JlrJuce l6:s. to tiK) j'i action of a poiintl : licCxcQ ". c::. 4:l\vt5«. \o i\v^ fi-aclioii of lb. Troy : f; aiuv;'or. Ilc:];»co Ofirs. ;> lbs. To:':. i^Vdi'^. to t!ic fiiic- tion of a cwt. "5 answer. Reduce iqrs. Tjnuih,lo ibe fi-aclion of ayrirci: , V answer. R<"r]r:ce 6 fuiloDTs. l6 nole^, to the fraction of a niilij : V insw'or. RoJmco J roods, r^C) porclies io tlie fiaction of an acre : l answer. Rfiducc 45 gallons of wine to the fraction of an hof^sbcad : ^ answer. RGdiice 30 gaUons of boer to the fraction of a barrel : tl answer. Rod'.xo 24 bushels of coals to the fiaction of a chaldron : § nnsvvor. fk J^f) A SV.W «VJer, and divide by ihe denominator. EXAMPLE. Reduce f of a shilling- to iis proper quantity : :■, X \'2 -tr: 3(.) -r- 4 r^f)d. answc!'. Reduce \ of ;i potind to its proper quantity : li>3. answer. Rj'dure •; of a pound Troy to i!s proper quan- tity : . Toz. -^dvyts. an:swer. Reduce \ of a Inindred weight to its proper quantity : 3»qrs. M lbs. 1 oz. 121^ drs. r^nswer. Reduce "% of a yard to its pro|)er quantity : 2 qrs. If nail, answer. Reduce \ ^i A mile to its proper quantity : 6 fur. ](> poles, answer. Reduce \ of an acre to its {proper quantity : 3 roods, 20 perch»s, answer. 1^ IV ; i\ e liar- iver. ) frac- intUv : wer. ititv : wer. ' qua II- wer. proper wer. tv : wer. ilv : wer. :it\ : wer. OF AIUTHMliTlt. ^'^ Uockicc V oi'«^Ji hogaheiid of wine to Us proper tiuantiry : ^ 45 gallons, answer. Roduco ;: of a barrel of 'ocor to Its proper (iium- 30 gallons, answer. Rod lice :}' of a chaldron of coals to its pro- per qnanlitv : " , 24 biisuels, answer. Reduce 'y of a month to its proper quantity: 1 week, 4days, 4\ hours, answer. Reduce i\l of a degree to its proper qiu\nti- tv ; 4 minutes, 50 seconds, answer. ADDITION OF FRACTIONS. Reduce all the given fractors to simple ones ot the same integer and denominator (if not so al- ready) then the sum of the numerator beiiig made a numerator to the common denominaior, irives the fractional nmnber recpaired, which may be further reduced as the ca:ie will adnrsi. FXAMPLE. Add j and -^ tonjether : 2 X 4 :=8, 3 X 3 =1} + S =: [, 3X4 \l or 1 aiHiwer. Aihl : «nd 'i tn o t ail Add I cf a weok, i oi' a u.i}-, aiK SU3TP. ACTIO?! OF F-t ACTIONS. Pi'on^ro the lV:ic:i(>ns tjs •]:«-erted i:i ii^.^'i* i^--5, t!"n s-'his-M't ciH' ni!i>jer.iU'v iVoni thn o!!:cr, and the (nlKr(?nco written ahovo the? comn^^!) dono- ininalor, will givi3 the IVaction r{.?qaiicd. From ?r tako s- cnny. old. a^i^^^cr. F rom ? ci' a nound take J of a shilling. •^ ' i4s, -Id. ^ a'iswer. From - of a pound Troy lL.k. J of an onnc Got.. lOdwls. i6, .'2 be. .'inb:\re?r. rrom V of a chiildroii take | of a busljol. 23 bushels, 2 pecka, aii::;vver. Frojii 7 weeks \:\\u^ [) - . v days. 5 weeks, 4 day, 7 iioiirs, 12 niinules, answer. IMULTIPLICATIOM OF FRACTIONS. Prepare tiie given numbers if they require it, then multiply the numerators together for a now nnrnerator. and ihe denominators for a new denor. aator. EXAIVIPLE. Multiply I by ,V 4 X 6^ 5 X 10~ Multiply J by -i. Multiply I hy i. Multiply I by ~',\- Multiply 36g by 245. Multiply 420| by 32|. Multiply is- by :f of f. Multiply 4f by f. iJ answer. t answer. J answer, ■fif' answer. 907 -i%- answer, o/lu -Y(r answer. -/(T answer. S| answer. • * 'S. ys, answer. ACTIONS. they roquiro ogeiher for u )rs for a new or AnTrnMiiTic, f^l f answer^ ^ answer, ^ answer. - answer. - answer. ■ answer. i answer. Mitltpily 3- by ;, Mukipiv '] of 6 bv ■(■ MuUipl}^ 6\ by H. ''i^ answer. ,V answer. iV answer. II answer. I anivver. I answer. 'Divide }^ by ^: * DiviJeil^-by g: Divide o.s4 -/.r by 12 i : 3 1 ".^f" answer. Divide !) i- by 3 ^ : J answer. • Divide 'h l^}' ^^ i • i answer. Divide 20 I by 14 | : 1 [^f answer. Divide J by I of f of ^ : J an^Vr'ffr. !ii m. % n. /,. m IMAGE EVALUATION TEST TARGET (MT-3) 1.0 !.! |50 '"^" •^ 140 Ui In 22 1 2.0 1.8 Photographic Sciences Corporation // *•/ / '^ i/.x 1.25 1.4 1.6 4 6" ► c>> 13 WIST MAIN STRUT WiBSTER.N.Y. 14580 (716) •73-4503 ^"^ ^ ' !^ n A NEW UYS'J^EM PROPORTIONAL ARITHMETIC. Proportional or general arithmetic teaches to find an equivalent to any given quantity at a gi- Tea ratio. CASE I. State the question, that is, place the three gi- ven numbers in a straight line, making the term I of supposition, which is of ihe same kind as the term of demand, the fust number; that whicii the term of supposition is said to equal, the se- cond ; and the term of demand, the third. Re- duce llie given numbers into an imf)roper frac- tion, invert tfie first term, bring all the terms in- to a single fraction, then divide the numerator by the denominator, and the remainder will be the answer, which reduced into pounds, shilings, and pence, if required. Proof, reverse the question, or if the price be aliquot parts, divide the quantity by the aliquot part or parts: or if the quantity bo component parts, mulfiplv the price by the component parts, and you will obtain the proof or answer required. EXAMFLB. Snppoc.i 1 lb. cost a farthing, what will 2476 bs. amount to at the same rate ? i i ^,^^ r= ii^Y = 51 + 7 = £2 Us 7d answer. Suppose 1 lb. costSd. what will C540 lbs. a- mount to at the sanrie rate t i h ^Y^ = ^V^ = iei36 5». answer. OF ARITHMETie, 9S nc. jaclifjs to at a gU three gi- Iie t(?rm id Hs iha at which the se- d. Re- •er frac- ?rnis iri- meratoi will be shilings, Tse the I, divide s : or if ply the 1 obtain II 2476 answer, lbs. a- Tcr. Siip^iosc 7 cAvls. 1 qr. cost £2G 10s. 4d. what will 43 cwl. 2 qrs. amount to? cwt. qis. £ s. d. cwt. qrs. 7 1 26 JO 4 43 2 4 6 2 V invorted •i 9 Term of Suppositi^K. 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 'I'crin (if Equality. d. 2h iAQ 2 V 3 Term of Deraaiid. 4834 4274 9658 1253 6540 1472 2674 • 987 9864 2436 3524 4697 8420 2f500 1487 8670 2594 4265 J:<749 2380 Terttt sought, or Amount. £ 5 8 20 ^ 20 6 13 37 71 20 33 48 96 28 20 100 40 71 154 4^ s. 18 2 18 9 2 18 8 18 6 18 9 15 14 Term of 1 I .1 1 1 1 1 1 1 .1. 1 1 1 t CF AF.iTIlMETlC. 97 Teim of iLquaiity. X £. (1. Tern* of 10 1!? 12 13 14 G 15 1 i 15 17 19 5 18 c> >•> 7 15 15 3 1 6 5 5 3 13 4 6 9 12 17 1 7 1 15 16 33 3 5 6 12 12 7 7i 6a 7 6 * 1 4'A 4 8 S 4 3 32 9 4 4^ 4 Tt:rm sought, or Amount. 2386 3345 1209 2510 4325 3 UO 7153 2710 4613 3210 7965 2157 2175 2517 4261 2573 4726 6134 4876 9564 2150 14 17 23§ 25 34S 119^ 2007 760 8. 53i 32203 17.S78 21941 38282 23 2 6 182 21 S6 10 13 8 5 16 16 18 6 1 (i. 1752 S 6 1835 8 9 S6l8 15 2511 1^ 6280 7 2602 14 7 5900 15 11 6189 5 7^ 16925 12 6 5 1 09 7 10 J 6022 74 9462 6 14 17754 3 4 15652 8 4 44 1 09 6 8 4 9 6 33 1 4 Hi 9 ii HI II ' ft ^^ A NEW SYSTEM K^ Term of Term of Term ( }( l 'erm i =IAUffht ^Hj Suppositiou. Kqua lity. Demand. or amount. £ s. d. £ s. d. 9 4 64 29 17 4 2 14 3;: (yji 177 14 8f 1 3 15 6'r 73" 275 13 oi 1 14 9J 81 140 IS l^i 8 7 4i 96 803 8 5 6 5 104 J 556 6J IHii 1 1 19 Si: ll6i 231 3 7 20 16 Or. 121 2516 18 6i j^Hii ;}_ 2 4 Sr 127'i 281 13 ^'^i 1 25 14 2h^ 144 3702 6 15 3 17 6 1 5 2 24 10.3 10 1 4 6 3 H '59 103 17 7 1 1 15 2i ■ 74f 107 4 6 1 1 8 8- ■1 ^■^ 54 5 1 12 11.1 m ^^'^ 95 15 Of I 1 2 1 m ^°H 133 17 10 1 1 5 H ■ ' 132 554 8 1 4 4 B 177 432 16 8 1 2 8 10| 218 636 8 3 1 2 18 4 246 684 8 4 1 2 15 7^ ■p"^- : m 705 7 9 1 7 4 M - ■^.M^'^t43 12 8 1 17 8| ■I 502^. 8S2 12 4 1 13 2 ^^^^^Hj 647 ' 948 17 9 1 9 - 3? ■' $46 1008 9 3 1 3 10 ■ 1129 1265 10 10 1 2 H 2 15 26 16 9 o/ d. 4 8S Gi 7 Si <^ 3 2* 1 2i 10| 4 4 8| 2 10 54 oy A turn:. ir.Tic. >'i Term of Ter m of Trrm of rerni fouiiht. s?uppositioii. Equality. DcJiand. or amouat. f ■ Jj S. d. .-c S. d. S 18 34 10 4 ." 4 - W 32 7 12 §: 1 It 7 72 20 3 7 s i § 3G 17 i 1 4 96 14 8 9 5 12 72 44 IG 14 9 12 75 51 8 G3- 27 18 14 GCy 43 12 8 54 6 G 8 18 8 G (3 9 1 5 9 81 8 18 10. V 10 1 2 1 90 109 2 G i 2 1 4 11. 09 66 12 G 14 12 5 0^ 108 42 10 G 15 5 18 li • £ s. (3. £ P. f1. 9 15 26 15 2 18 $ 10 4 34 7 12 m 19 4 20 3 72 1 13 7 6 3 6 6 7 17 2 36 43 12 8 ^ G3 18 14 27^ 18 8 B G G ^^^W^ 14 8 9G 1 4 ^ 4^^^'^ 5 12 9 ri IG ^.■ 109 2 6 90 14 11 12 12 5 J 4 :-'G 12 G 99 4? 10 (> lOS 5 IN 1 A 1 5 Ji 7 100 A NEW SYSTEM 5 • '' ^^-^ Wj"^ • 'O O^ GO i-- O CO ■O o ^2 . cr^ »n 1-t GO (N a-, S .-s W »-( 00 GO .CO %C> O O GO O^ Ch ^ C/D O ^'^ €■>? O C C^ O CO rH C-J O^ t>- CO ^ u O O O C-^ O O «?--3"£ooo«o^Gs ° a j::: ^ r-n ^ El r^ i? N O C) CO t- o o j:2 Oi O Oi O i^ 'T H^ G^ GO GO C^ J^' G^ (-1 * "2 00 C^ !M CO !fl O GO C-.^ • tH CO CO GO c^ o r-i '^H ^ >< ^^H ^ .tj iH £^ "^ o rH r-^ o 'O o >^^H ^ c: '^H J" ^ H ^»'^ o O f-< o GO »c^ GO o o o o o o ^^^^B ^H £ -M o o o o O -H ^^■fl *^ "^ r-^ !^B "Wk > ^ v' GvJ G-0 o T-l C I- ^^^■i - 3 O .■^ X ^^■H^ 'B -^ o o GO o ^ o . al^Hi •"^ GO O O G^ -^ O^ Ci G^ ?-« liio '^' '^ o G^ >n 'sO tH Oi O ^ ?0 G^ O^ C-O G^ IW '^GOOO'^O cOOO *- O GO GO iH i"^ CO G^ G1 qr CO rs O t- G^i I- -TS J- G? O O rH >►» r-" G^ t*:, K) *)F AfllTIIME'riC. 1 01 ■An "^7. ^v. O ~f tsS cj« Qi to ^ t>3 K) to O CU Vj cr. ^' O '>C — O C« 4ii. <-i' f-* 4i, O O O GO o o o -1 M OS OO O O S" cr* O O O O W (/i 00 ^^ ^ i'j O r^ <^-' O Y^ ^^ r. ■-« OO OO CO »0 r— • !3 4u O ^^-s O O cr ^ o HH K) O O O O ' '< ' cr^ O O O C 1,^ 03 ^S C^ o ^^ oo VO ^ ^ C^ r- 00 O hi> 4:^ a> OO i-» O ^^ O oa 00 ^4) i:^ VI 4^ C^ ft Cl 00 -.1 g- 03 K) •» ^ c: ^ c p: 'o -a - V z "^ v-i C « ^ ^ .= ^ s C) -, .^ W v_ r«» "W •^ ,,«, -»-< ^ ^ ^ . >. . fl ~i*i ^^ — (^ -* *, < O -, ^ W ^ _^ ca . — — cj — *— JT? — ' - »^ C» -J -►^ Ci^ ii c c/: ^ .— u .ir ^ ~ ?3 cju t: ^: -r i^ 'O o c o ^ o o g - - <:« 2 . "^ h- O O O O 'iO "^ C^? jr- '^ 5J "^ 'O 10 00 cTi — c*. i> ^ 'O C^ CO ^< •xj 000000000 . ^* 000000000 •~ S O O O O O O O CN O ?^ rH rH rH rH ^.t O VO O O •TTCOOOOO'^OO ?: ro s/^ O O O O O CO O O <^ -o 00 rt< o >r5 O O O '^ »-0 H Ci ^ -: '-^ '^ o b- ^c c/o .rj C-? o "^ H-^ CJ Ci iTi C--5 'n^ M^ O C7i G^< p; ^ a; ;H o = _.. *-<*-•. '^ c ^ -> t: :•« '/> ■: >.-::; — t: •-" r: — - cjj ra Q, *-< r— « -J- *-' 3 • M« _ ■— "^ •« »- '-> u c ^' . 5 -^ »-" ^ IZ *- --s *•"• • •* «, rr; »-• •■^ ■^ *" bi3 •— -* O ^ o cr CO -^ "^ >,-.,* 0000 C; 0000 Q •♦— W* ^ ^ t^OOO'-HOOr-tr-iO Hy^'^^'N^iriOOoOO'* '^ g'^OOOOOOOOO E'^ cr:OOOOOOQOO U. ■ >.^ \,„,/ '^^^ 1 : I — ! >*!»' • — ' ■'■"• • SBP' S . ^ o O o o o OF AUlTHMETtC. \\)A CO n* O O n "^ c*^? T. t^ '^ D O O o o o O CN O O O O Tj* o o CO o O t-H o ^ >-o •n> c^? O O CTi G^« o o o rH rH O O O ^ O O O Q O O t-* 5+5 C/2 tr. d O boo O !• c t-T a o » t»i i-i M ifo 1-* o o o H- o ;2 o ^^ 5 O 3 ^2 3 •OOOOCOOS« i£. =^ § -• o o o c o o o p- § "^ ;^ ^* "-1 — • O O l^O i'S 03 -T O O ^ O Ci -o o o o o i^ l:^ t^ J p *- -J c o « g^3 Ci O -a- • "^ ffi r? 5 o 3 O " ^■^ ^ S+s O CTi CO ,. , CD Ct) IMn* fWiW ^w> o <-« o^ ^ *^ ^ "^ 5 5 Cft ftj 3 o o o ^- 00 o o : D- T .^-i W M i-» K) >- to 00 h-* to \ UO -- o O O . w _ o s O o o p- o O o ^ O O O 3 -• • 3 o O O j< • C^ CTi ^ . ■ u< oa O O ^^ "-*• * '-: "^ V-* 03 3 o o "-! :" 3 ^ K) CO 'O c- r5 ^ -f + + 104 .c M o JU A - -T c> ^ --r 'f O "^ ^C' C -^ ->• "^ . -^ v> -^ p. i^ -1^ o ^ V •^ '■■ ' C*. '^' '^^ ':i '^y^ '*»' v»y 'C O '^ ^ c5 g g '^ '/^ fM*- •■^ o ^ w C c o O O Ci r e 0) ■'^C00000'2> r- 2= ^:j o S ? S "" 2 9 • K vKilJiW !.('((! ta^ '^ f'*^ -"^ '^ ,**^ '~> ^ ir ir" '-' "— ^■- ■'-' *^ ■•^ Vi^ v«x <«y C, (^ c- o o o o o -r- '^ :i, . o o c '5 ;^ ^2 O O :^ O ^ § "^ ^» ^' ~^ c CT; o o :: J^ "^ o v« C-. c. o o ^ ^'* C»J c/; rrr 3 '-^ ^O ^--» jfc. --i /^ ^^ "^' ^' O 0« C>. CT; J'^ o o lo c § o o o ^ 5? :73 o o o c o o o VJ cooooooo-:^ 05 '.j Q, to 'O i^ b 5 ? ^— ,— ^- -I. J ^1 p^ j^ ,^, . "^2 C «; o« o c: X X O •' C 5. 'O ^ 3 O -,» « p- r :t- u— -■. »^.i-, -a » l*-! r> rq ,■"5 -5 ^ 5' '^< ■-^ ^ V, — •-^i — V, C '•'' ^ =; o 3 O ~ "* '^ 2 '•; o "^ ^ "^ c (^ C5 .y UD • *• a!" MM* • •^ •* 3 ««k -3 2l O 2J 3 a. f/1 s" ;: en •f. MM * % 10» I DHjf •i m I 10(3 I' £3 « Q- C o o s O o • 1-4 CO S as c o V) A NEW SVSTEM 4J . -ijmH''' Ki"«f :ci'-r-''-f j3 . -^ O t^ i^ O CO r-i '^cr o 2 ^* O c^ico o CO O o S- . 00 CO 00 Ci C^j O >o ^ ^ . -; ^ ^ o o vo r-. ri^ H ^ ^ C^ t^ G-J O ^ CO a; , e o o o o o o o -o «S OooOOCi"^ i - S 2 W rM rH rH E^ o . o o "o o I - 1- 'X '— ^ ti> CO Tf Cf O «-- Ci lO vo ^ CT) C^l »r.. t- j.- ^ Z E:^ o ;^. y^ HX CCtT (TT- T- •"• /) a; 3 E- ^ o o r>0 ^ gnDOOOOOCO o '^ 13 '5J cwOCOOOOO r^S! 0000000 l!i I «i'' ARiTHMKi'IC 1 07 I jI O <.^ C? "* *"• • O O O O :::- -"^ Ol O'. '^K ^ 0< Oi^ O O O O O O ^ :i o o o o o o 3 '^ »-* t-i •«* uj I-. ^ ^ ;:f^ o o o — o o «.^-~ H <^ Co <— CO ;j^ CI • -:^ o ►— » .- [/; ^ o o o« o o o • :-;• o o o o o o r- g '^- ^ 05 i— -^3 Cm Cx ^- J^ -^ ^wwA -- •'«* tMf = ':' 4. C3 CO Ct *-• 5^ r- ^' ~ '^ f5 ;? ^ r^ ";: s*. m '^ fA ^ 't i: 3 X «, •—r CJ ^ :^ 1; -s =^ ^ ^ - ^^ -. B r- ^- 5* 0) X — r- 3 C^ Q ,3 (/> — 3 O il -^ =3 ? ;:t rs 3 1? C £ CO ,''' O 3 cr c^ 11 1^! .1 ! f a II IL! en A N'tlW SYSTEM ^' ^ —I O I-* vU 1— w^. '■^ ^ »- r-' •- re' ^ - O — i—e CL. - ^C — c: ^ c= o S ^« ^ 15 ^ - ?:^ g -75 :^ *- ta s- o o • r-. ^-^ y> ^-1 . ZZ r^ *— "^ "^ ^' -^ »^ . ^-, k- ♦-» .4>M .^L, ^, -^ JO o ■- •' ^ c j::: ^ j: j- — T C ^ _ "^ ^ wW *^ ,.*» ^^ r-; S o -z: — :; •" o ^ cr, i- ci ^ 'J5 "•;::: ra c ^, ^ '^ C^ -^^ ii '■3 u rt '^ D •—• (i;i — t/) C j:^ ^ "" ■" ^-^ 2 «5 S ^ :e a ^ -T '■^ ^- > -^ •^ = •'-' cj ^ -^ o ^ 0? i> O C y . tr* O r~ — ' — -< — «J «_,♦-.;:; *-> h- 1 ^ c: .. = ^ *~ — *r Cu •» ri *• _ i c^ ® Cv> ^'"J C^ ^i O b^ • C O O O o &> S r-* O ^ C C. h- ; GO CO -f Tf i,^ i^i ^ O O O O O *^1 cr3 O O O O O .^ C O O ^ l^ "^5 o c o 'O o. •^ r-1 l^ ^' o o o o o £^ a:ocooo hy ^ »0 ^O m O O u- >, o ^ 5 ii •- ^ . a "a O >.. ^ -^ - r; • »*r 3 ^* o o o o o oo o o o -^ O O O O Q <^^ o o o o o r-t r-1 rH iH tH ■m- AKITfBlETIC. 1#« €ASE IX. Exchange is the receiving er paying any sum owing in one country in the money of another. The par of exchange is that fixed and intrin- sic value of the money of one country compared with that of anotlior. The course of exchange is a fluctuating price, varying from the par of exchange. Monies of exchanoje are of several kinds ; viz. current, banco, specie, paper, &,c. : all of which may considerably vary in their relative value, either by agio or discount. Accounts are kept in Ireland, America, .and the West Indies, in pounds, shillings, and pence, as in England. In Ireland the difference is a!5 12 to 13. In Jamaica as 5 to 7. Halifax Cur- rency is as 9 to 10 in favor of England, to which is added a premium of from 5 to 12 per cent, upon Specie and Bills of Exchange. Term of Term of Term of {^uppositioa. Equality. Demaud. Slerlin £ 100 100 100 100 10<3 Irish. £ 106 110 Jainaica. 135 150 16(^ £ 750 375 212 760 6«0 Sterling-. s. 15 12 18 d. 5 !) Term sought or Amount. Iritk. £ s. d, 795 .413 6 G Jamaica. 287 lOtl 10S9 11 H / ■ Pit I"! a 110 A NEW SVSTEIVI Skrlmg'. Hah fax. Sterling. £ £ £ 9 10 27 90 100 100 Halifax. Stcrlhig. Halifacc. £ £ £ 10 9 30 100 90 111 Hiilijtix. £ «' 24 1350 2523 reas. £- s. d. 3G56 875 360 4 n 528 714 ly 11 f Accounts are kept ia Holland, Flanders, and Germany by .on,e in pounds, slu hng^ and land and llanders is disnnuu...M. . "^ ;- " of Flourish, excb.ingo trom 33s. Od to .0.. Flomisii per pound sterling, subject to Aigo po ;3 to 6 per cent current. 1 1 1 1 1 1 s. 14 J3 d. () 8 700 842 314 s. 5 .5 d, £ s. lliM) 14 U) 15 52^ W) d. 4Jl 1 12 iJuelds. Guelders. 105 100 A NEW SYSTEM Guelders St. 2982 2840 104 100 110 12 106 6 0-f Arbitration of exchanges is, in making pa}'- ments from one country to another, through the monies of several countries, to find the most ad- vantageons way to effect it. The arbitrated price is that found by a circu- lar course, and when this dilSers from the direct course, the difference shows the advantage or disadvantage of a circular remittance or ex- change. Ex. 1st. If the course of exchange between Paris and London be 24 francs per £ sterling, and hetween London and Lisbon 50 pence per milrea, and between Lisbon and Paris 525 reas per crown, what will be the arbitrated price between Lisbon and London ? Lon. d. Pa. f. Lis. rees. 10 X 40 2402, 33 IOOOO05 400 24o 525s>5 21.^ 7 d. = 571 Ans. Note. — The arbitrated price being required be- tween London and Lisbon, and the ponce ster- ling being the variable number, it is made th« K>hu)k t-irm, which equals 1 milrea, or 1000 roa«, 6 + ig pay- }gh the )ost ad- 1 circw- e direct lage or or ex- iris and let ween a, and crown, Lisbon Ana. ired be- CO ster* Eide ihtfi )0 roa«, OF ARITlirvIETiC. 115 'uid "^25 reus equal 1 crown, wbicii, to save adjust- ment is fxi)ressed in francs ; and 24 francs equal j7, o'r :40 pence sterling. The result gives As tlic direct course of exchange helweort London and Lisbon is but 50^/. per milera, it is evidi'nt tiint the circular exchange is in favour of Lishop, and aeninst London, at the rate of 71//. p7r milrea. Upon thii principle the advantages in arbitration of exchanges are discovered. Ex. 2nd. From the course of exchange betwcn the se- veral places given in Ex. 1, find the arbitrated price between Paris and LondoHo Pa. f. reas. Lon. d. 8 X 24 4O5 1.000,5 240, « 102 . . =r 27t Answer. in Os 5|< 5252 r. -^0,0 2ln. 7 NoTK.— Tins ,^„^.,. _,„.. circular exchange gives 27f fnncs and as the direct coursais but 24 francs it must be in lavour ot i^u»uw..^ « Paris, 5f francs per £ sterling. m (. ?H Hi A NEW SVSTEM Ex. 3rcl. From the course of exchange between the se- veral places given in Ex. 1, find tlie abitratcd price between Lisbon and Paris, recs. Lon. d. Pa. f. 200 X 242 4 IOOO5 240, e 3 =^ 5q() Lis. rees. Answer. * 50,0 242 4 This circular exchange gives 75 rees per crown in favour of Paris, and against Lisbon. CASE X. Loss and Gain is the discovering what is gain- ed or lost in buying or selling of goods, and in- structs merchants, &c. hov/ to raise or fall (ho price of their commodities so as to gain or lose so much per cent. Supposition. Term of ^H 'HI £ s. d. ■■ flP loo HH 1? 100 ^^^^Ib Hh ' '' ' 1 4 ^^^I^H ^^B i^i 13 4 ^H ifti 10 __l_l r^^S^I j 10 100 I^^^^^bB ^^^Bi' * 100 — ^B^;" 10 ■ ft) 100 B ■!' Term of Equality. £> s. d. 500 1 S 100 16 ICO 125 112 1 110 90 115 1 1/} ICO 3 6*^ 100 2 6 i. erm 01 Demand. £> s. d. 13 5 10 13 6 8 Term euugbt or amount. 1 1 100 £ 560 125 120 112 1 1 1 12 s. d. 16 9i 10 10 13 8f 10 0^ 7 S w ill the se- iitratcd nsvver. boi per I. «^- lin- nrl i/i- bll the or oso guugbt s. d. 16 9i- 10 10 13 9 10 7 S OF AlilTHMLTIC. iir» CASE XI. Singlo Feilowsiilp tenches to divide any ^Iv- en number into any assigned number of parts which shall be proportional to so many other proposed numbers. Make the sum of the num- bers to which the required parts must be propor- tioned, the term of supjiosiiion ; the quantify ^to he divided, the term of equality ; and each of (ho given numbers or sharf;s, si'paraiely, the term ot demand ; and each amount will ^;ive the respec- tive parts, or answer re([uired ; or m;.k(; one pound t\n) term of demand, the product will give the rate in the pound, whi.'h multiply by each person's share, will give the amount due to each. Tvv'O merchants make a joint stock of lOOOZ. W. put in 300/. and S. 700/. they clear iCO/. what is tlie gain in the pound, and what is each person's share ? In the pound Ss. 2jd, J W's. share 48/.— S's. 112/. Ans. A bankrupt whose effu'cts produce 340/. owes A. 120/. B. 140/. C. 200/. and D. 2G0/. what will it produce in the pound, and what is each man's dividend 1 In the pound 9s. 5^d. l- A's share 56/. 13s. 4d.— B's 661. 2s. 2.^d.— C's94/.8s. lO^d.— D's 122/. 15s. 6U. Ans. tA !• i. llG A r^K;v SV^iTKM Tin'oe j}ers;)ns mnko a joint stock, I). jkIviim- cos 15CvO/. F. 900?. -And 11. 600Z. ihoy gain 609/. wluit is oacl] man's s!i":\? 1 D. gaii-jc: 300Z.—F. ISO/.-rll. 120/. A trpjU smnn becoming bankr-jpt owf^s to Ii. 520/. K. ()S0/. nnd to N. SOO/. his cfrticls arc worth 920/. find s per yard, tmi I « ili^Mi li^*< A Ni:Vi Si a TEA! CASE XIV. inHiv< Equulion of Pnymciits h ilia finding a tinia, when if a sum of niont^y bo p;;itl which is oqual lo tiic^. siKij of several others diia i\i {jinbrent limes, sa th:it no loss will bo sustained by either party. I'liO iDethod used by mercantile men, t'ljougli not exactly correct, yet suiriv^iently so lor most (|.i]eslions that occur in business, is to multiply each piynioiit by the time -ii which it is du<.', then divide liu; sum of the products by the sum of the p.jyments, and tl:e (luolicnt will be the time required. A debt of 190/. is to be jiiid as follows, vi/. 50/. at () moot lis, 6()/. at 7 montiis, and 80/. at 10 montSi'^;, wint is ih.e equaled tiuie for the pay- ments of llie whole i A iswoi' 8 moiitlis. A debt of 200/. is to bo equal ucrent either llOllgll most uitiply i (.iu<;, e sma JG the 'iO/. at ihs. 1 00/. it r«- t it. be ihs. s, WA, St at <> /hole .'* illis. Coiijpoi'.nil Proponion toachrsto rrsclvc such fjucstions as roquiro two or moro slatinus by fIhi- }>lc proportion ; makolhctorm of equality, \vhirh is of tlie samo kind as iho answer, tiie mitidK} term onlv ; muliiplv the corrosponilins: U^nv.r, to- f^ether, then make the term of supposiuon, hie iirst term ; the term of •..•quality, tl.e second ; and tho term of demnnd, the tliird ; and the a- mount will be tlie an^^wer required : or mnkt^ tlie increasing terms, the numerators, and (ho de- creasing terms, the flenoi-ninators, llien proceerl as in proportional arithmetic, and the result will G:ivc the answer. If 100 men in G d.-jys, of 10 hour rr.rl), can diii a trench 200 yards loniL^s 3 wid'.^ 'cuul 2 deej), in how many days of 8 hours lonjr, v»ill 180 men dig atrencii of SGO yards long, '4 wide, 3 dee[). 10 10 100 10 3X5 2, lOo 3u0i,o ^i 3, ■--\:) Ans, 200 , 20io 22 o O 2'2 180 1 8 84 23 Suppose 100?. in one year gain 5/. intnest, what will be tho interest of 700/. for 7 years? Answer 2u2/. 10s. If 27s. be tho wages of 4 men for 7 day?, what will be the wages of 14 men for ton days. Answer 6!, ir»s. r! li ■ill ^^ if I , r ,. i ,.,.j*' VM) A NEW SrsTEM What is liio interest of 340/. lor '2h years at 4^ per cent, por annum. Ansu'cr SSI, 5s. U the pay of 72 soldiers bo 192/ for tS weeks, how much will pay 27 soldiers tor 24 weeks ? Answer 36L l( the carrin^e of IScwts. Iqr. for 72 miles be 2/. 10s. Gtl. what will be the carriage of 7cwts. 3qrs. for 112 miles ? • Answer 2/. 5. ll^d. If 9 sturlents spend 10?. |- in 18 aays, how much will 20 students spend in 30 days ? Answer 39/. 18s. 4d. If 1 pay 10s. 4d. for the carriage of 5^^ cwls. 20 miles, what must I pay for the carriage of 17^ cwis. 7^ miles. Answer Is. 8jd. If the carriage of Icwt. 20 miles be 6Jd, liai will t mount to t what will the carriage of cwts. 100 miles a- A I .»„ /:i J OF AniriiMr:T 10 ^ bombusins 36 . 20 ** 58 10 *' 75 1- |i!|: ; lf'5 Jti!j:ii Uf*. 122 A NEW SYSTKM York, U. C. iSth April, I8:i3. 2Ai\ James Vavoscr, liougijl of William Pouol. ^>0 pieces of l)0{»ilja?;eUs at 25s. C;], ]irr pi'ico 12 15 4 2 44. ItOiubcizins ;it 7 f>v'i" piecr. plfun di-il\\ ♦>;u:lj 'JO vtls ,-it 9>s per }'(]; C'hi.uni oTyHs. i.'ach 'U j4:>. luo.tci cloili csu.'h Sdyd--^. 28y. per vJ. Dlt.»:oiuU 2^ per cent. £:VJO 16 85 York, i;. C, l^Oilj April, 133:^. 1^1 r. Syivt'stor, Don^Iit of Tiiiiotliv Piior. DZ. dwt. ^!:r. A sihrr waiter weijirlilng 23 4 Oat 5s. 10. p.oz, A silver tankard wciiihiniclO 3 6 6 2(1. A silver teapot and lanvp SO 5 12 7 3 ^ do7,. silver plates weigfw3 11 5 6 1 Jj iU>7. silver tnblo ) ^^ „ 10 6 spoons weiL'hnig ) 3 ;€r>6 1c. 4.i K 4 Jibs. 42j!b:^ Tiiibs I— * > 1 1 * ii'bs 9 l>.iv 1 J y? 7 11 11 ^ CF AlMinMI'/iMC. tl^ York, \^ . C i i5 <.^ o . OIK, i^ . V . >jv*i;j v'prii, Ml. 'Viionvds \V(:>5. :2.">ii>s. (ioubki lefitx^d siiunr Is. i.> . i^:i:^i 5.S. 9 J. li»' = . -1<1, York, i;, C. .:U1 Aniil, 1^^?^, Mr. \Vblij<'i'l 17s. nut ^^alls ii)(i. gujn iVrtiblc Is. 2v). sass:4r:;s -i?']. £su 1 (>i t b ^ k: ^H 124 A SEW tiYii'VEM DECIMAL FRACTIOrif^. Decimal Fractions represent the ;)nrts of any intoorral quantity divided into dccnpic, or ten- fojd ])roportion. ADDITION OF DECIMALS. Write the {)roposod numbers under each oth- er, according to the value of their places, which niny be done by pLxing the separnting points ex- actly under each other, then add as in whole nun.hers, placing a decimal point in tiic sum exactly below the other points. ^m » 7-421 1*275 2-75 9- ^H mk 4-165 •on 1^426 40'2f, ^B fl :}'27G •024 9-i 1-44 ^H '^p S-147 ~ ] -042 •192 6003 B ■ 1-52 L 7-964 3-G •256 •237 6^ 4-2S ^S H 4'6'39 5-641 •542 2 '.•5 4 ^H B J -706 •4 •117 ■■^iH Hnigi 4-.^'?f? |-?M -r ;1-4^s! •F AuirriMnrir. li^^ SI BTllACTiON Oi-' DICCIMAL.-'. i \ .1 ] - • of any )r icn- h oil]. wliicli II ts ex- wiiolo 10 sum 9- 1-44 )003 4-2S 2'S4 FMuce the decimals lo be subtrficted as iJiriu-r- cd in addi(ion, then subtract as in wbolo iiuin- 'jcr:^, placing the dccinidl points as bcibie. From (35 •21. Fake 3-1-12 m ^ rii 7-65 1 5-154 i-ooo 4 276 1-925 '7oi 1-2:) 4 G 000 2-71:5 •719 •995 1-964 From 5 1 Mi Take S7-6S xMULTIPLICATlON OF DFCIMALS. Muliinlv tlie decinials as if ilicv WfTt? wliulo numbers, and from the product cut oH'as many decimal places as there are in both fractors ; if there are not so many [>laces, perfix ci()hers to "- -iply the defect. Multiply 79'S47 by 23 15 1836*58305j answer. Multiply •G;347S by '8204 : •520773512, -mbwcr. Multiply -3040825 by 23'4 7-12957050 answHr, '"-'Jnly 1234'5(;7^i9 by 478-216243 •^90390^1808423727 »■ / n '! 1-2(5 A MvW »\S?fEM «ASE I. To conltact l!;e operation, so as (o reUiln s© many deci.n.d places in the product, ns may be tjjougiir necessary; transpose all t!ie figures of tiie muhiplier, viz. let tho units place stand to th(3 lofr li jnd, then nvikc the units place pf the transposed niuitiplier stand under the pl.ico of the midiiplicand, whose decimal place you in- tend to niaiii in the product : proceed as in coijimoo niidiipliciuion', always having regard to ihi} increase of tiiat figuro on the rijjt Inind of the figure that stands over your multipdier, car- rying 1 from^ to 15; 2 from 15 lo 25, 6lc. making use of no more places of your multipli- er than those which stand even wilh your multi- plicand to the left hand. Multiply -5046825 by 2S-4 reserving two dcci- nial places in the product : 7*12, answer^ Multiply -248264 by 725234 reserving 6 fi- gnres, 5 figures, and 4 figures u: the product respectively : •1S0049, -18005, and -ISCO, answer. Multiply 1234-56789 hy 478-216243 reserving Onlv the intp>o"/ir« In til© r»»«rt/4iw># . 50OSS7\ answer* ©r AJ"*lTl:IMET{€. 1^7 lay be ires of nd to pf tl)e a CO of [)U in- ns in :n\d to jnd of •, car- ilt'jpli- multi- dcci- swciv 6 fi- oduct swer. rving swer* Proceed as if iht^y were wliole niimbors, and from the rig']( iiand of the qriotient point off as nirioy pliiccs for decimal?, as the decimal pla- ces exceed those of the divisor, if there are not so manv, snpplv the defect hy peifixing ciphers. Divide 85643-325000 hy'-S'il : 13549.094, answer. Divide 234'70525 by 64-25 : 3 65 3, answer. Divide -1.727537 by -162 : 5-3S739, answer. CAST. II. To contract th.c up(^r.:jtion so as to retain so rn;iny decisu d pl;\ce3 i»» Uie quoii.'nt as may bo lii,)u-di{ nec<'ssarv. Find (is direcU'd above) wha^phici' of di cimai or inti^^ors ihe first Hiruro of th(^ qiotit-ni will possess, consi(UM- Iiow n)any (i 'urcs will serve the j)res<'r)t purpose, then take as^ mmv of the hd\ Ikuu! fi-u.-s of ihe divisor as arc eqnd to the required nnmher of pdacesin the quoticni ; i.« dividinir, point one nP ReJwGe I8iv. \Q the decimal oi' ;i pound. '9, fini^wer. Reduce iGs. 9d, to the (lecitnul of a pomul. •83, ravowcr. RlhUico 19s. jj-d. to the doclmal of n poup.d. •97291G. ans'.vcr. Reduce o ouncos to the dcclir.al of n lb. Troy. •G(>(), answer. Reduce 6 dwts. to the decinu-.l oi' a lb. T^03^ •025, answer. Reduce 14 lbs. to the deciiiial of a cwt. •125, answer. Reduce 6 onnces to the decimal of a lb. a- voirdupois: •375, answer. Reduce 9.2* inches to the decimal of a yard : •2()3, answer. Reduce 52 days to the decimal of a year : •i424G5, answer. CA??r: in. To find th.e value of a decin^al fraction of an integer :--Midtip!y th.e given decimal by the ])art's of the next inferior denonjinator, cutting oft' an equal number of decimals f^-oni tlse pro- duct : then muhiply the remainder by the next interior denomination, tlius i)roceed lill you huvs krG'.^;;ht it Ui its lowest part? of the intco;eT, g I ' i n . i JJ0 1^*^^ A NEW sv.sti:m What is tlic value of •68464 of a jiouihI : 13s. S^d. -|-, :in;i\vcr. What is the vahie of '775 of a {3oi)nd : 153. 6(1. anawor. What is the value of '0125 of a pound Troy : SiUvts., answcj-. WHiat Is t!io value of '625 of a hundred weigh i: 2 qrs. 14lb., answer. W' hat is the vr hie of -125 of a hundred wcdght. 14lhs., ansiwor. Wliat is the value of -375 of a pouiui avolr- difpois : 6 ounces answer. What is the value of -005 of a day: 7 li.'iijiucs, answer. PROPORTIONAL ARITIiMETIC By Dccl'mahJ Rcdiico any of the convenient examples in proponional Arilhiuetic to decimals, then slate the question, liiultiply the second and lliird ternis^iooeiiier, and divide by tiie tirst, and yoq will c/btairi tiie answer reqi^iied. WF ARrrilMLTff. EXAMPLK. i:U If ono vard of clo:!i cost ]r>s. tvluit will 35 yards aiuount to at the same rate t £26 js., answer. ,'if 3d 35 375 225 26-25 20 5 -CO DUODECII^IAI.5?. tiuodcclmals, or Cross-Mal!ij>lication, is ihd method used by artificers to ascertain the mea- sin't'jpjont and vakio of their materials and work, according to the custom of their respective oc- cupations; the dimensions are generally taken in foot, inches, and parts. — Under the midiipli- cand write the correspondent denominations of the niultiplier. multiply each term in the niulii- »-vT 1 rt 'i »■» /-I I-i r« »v I ii i-^ « !•» nf ilMlil tliQ I /■jtsT Off ]\yr jtl/J fwpf' in the multiplier, placing each result under its respoctive term, ohserving to carry an unit from every 12 from each lower denomination to its 4 I 1 M VM A XEW SVSTKM next superior: proceed in Uie t^nmc lyianner wiili the inches and j)aris, solfino- the result of each term, one place more to the right harjd, ai^d the Sinn of the whole will he the product requir- eJ. Muliiply 3 lent,, 4 inches by 5 feet, 3 inches : 43 feet, 9 inches, answer. Multiply 8 fe^t. 5 inclies, hy 4 feel, 7 in- dies : 38 feet, G inches, 11 part's, answer. • ]MuItii)iy 1' fret, 6 inches, by 8 thct, 5 inches: 103 fi'O:, 2 inche^^, () [)ari?, answer. Mult-i])ly 9 ih^^t, 8 inche:-^, hy 7 feet, 6 inches : 72 feet, G inches, answer. iMultii)Iy 7 i^ct, 6 inches, hy 5 feet 9 incbej?. 43 I'eef, 1 inch, G pruts, nn^^wer. iMuI:ij)ly 73 feet, 7 inches, by 9 feet 8 inches: 750 i'i^ot, 7 inciies, 8 parts, answer. Multiply 26 feet, 4 inches, by l':l ieet 7 inches : 331 fct't, 4 inches, 4pnr:3, answer. Muliiply 45 fr et, 6 inches, by 38 feet, 7 inches : 1755 fcotf 6 inche?, 6 parts, answer. Multiply 126 fed, 6 inches, by 121 feet, 3 Inches 15333 i\:ct^ 1 inch, 6 part?, answer. Multiply 87 feet, 5 inches, by 35 feet, 8 inches: 3117 feet, 10 inches, 4 parts answer. Multiply 764 i'vf^t, 5 inches, by 192 feet 4 inches. 147022 feet, 9 inches, 8 parts, answer. Multiply 7 ft. 5 in. 5 pts. by I ft. 7 in. 6 pts : ii feet, 9 indies 9 parts-, 4. G. answer. • r ARiTUMK'nC. inn MuUijily n i>. <> in. G pis. by 7 ft. -^in. 4pls/ 02 feet, 1 inch, II parts, 8 answer. Mahiply 4 fr. 10 in. 6 pts. by 2ft. 4 in. 8 pts. 11 f(;ct, 7 iiicbes, 9 parts, answer. Multiply 7 ft. 8 in. G pts. by 7 feet. 2 in. 8 pis. 55 fi3ct, 8 iuclicsO parts, 8. ansiver. Multinlv 3 ft. 6 in. 3 pts. by 2 ft. 4 in. 6 pts. * *^8 feet, 4 inches, 4 parts, 1. 9- answer. IMuUiplv 87 U, 3 in. 5 pts. by 18 ft. 1 in. 6 pts. 1580 foot, incbes, 5 parts. 1. o. answer, 1. I! -0 Redaction of Currencies is changing the mo- ney or currency of one state or country to that of another. Ist. To chnn^e English money, into Halifax Currency : Add i to tho Sterling given. To change Halifax Currency into English Money : Deduct ^\ 2nd. To cli;.ngo English Money, the dollar being 43. 6d ; into Federal Money. Multiply the pounds and decimals of a pound by 40 and divide by 9. To change Federal Money to English, reverse the operation. To Change Canada and Nova-Scotia cur- rency, tho dollar being 5s. or i of a pound. Multiply the sum in pounds and decimals by 4, for Federal Money, and to reduce it to the sc^mo currency again divide by 4, tho answer ...:n uir, .^r^.ii^ifc. iirirl /^iTiniAlft of a no^nd. I ^ M IM A NEW SYSTEM ^0 change New-England, Virginia, Kentiickf awd '^ennesee currency to Federal Mone>, the ' ' g 6 shillings, or -^~ of a pound * ^e shillings, pence, &-c, to the de- annex the same to the pounds dollar Red lu, >ir? uce I cimal of a pounu pou an d divide bv -3, l*!'^ quotienl will be the an- <» three decimal figures- New Bnsland, swer in. cents, if there n To change Federal MoDe"/ to New liingland. -&c. currency ,s , Multiply ibe given sum by S the product will be the answer iy) p'Junds and decimals Oi ^ pound Mnth may he reduced to shillings, pei;c*^ a^f* farthings by inspectipn, or by multiplying i.y the number of parts in each denomination. To change i^t3w-York, North-Carolina, and Ohio currency, ihe dollar being 8 shillings or 4 tenths. Proceed as directed for New England curren- cy, using 4 instead o^ 3 for a divisor and multi^ plior. To change New-Jersi^y, Pennsylvania, Dela- ware, and Maryland currency to federal mo- ney, the dollar being 7s. 6d. or g of a pound. Divide the given sum in pounds and decimals of a pound by f , that is, multiply by 8 and di- vide by 3. To change federal money to Pennsylvania, &c. cijrrency ? Mjilliply the sum by 3 and divide by 8, the whole numbers will bo pounds ; the decimal^ must be reduced to skilling??, ^c. I or AniTH.MBtld 1^3 To chnnge S. Carolina and Georgia ciirrcncy tho dollar being 4s, 8d. Divide byi'i or mnltiply by 30 and divide by 7 to change it to federal money. To chang 1 • lif I I . i^3 1 iy 2i X -^H « .fc ., Ill ^ iM A NE^ SrS'lElVt Sterling. £ 20 SO 40 50 60 70 «0 90 100 200: 300 400 k>0. 4> 800 900 1000 22 23 44 55 66 77 88 100 111 222 333 444 ^55 666 '777 888 1000 1111 13 15 17 2 Nalifax. a 4 i 6 8 11 13 15 17 2 4 6 8 11 Hi 8 ' 4 9i4 8 4 2H N. B, — Is. ster- ling passes current- ly in Upper Cana- da for Is. 2(]. Hali- lax ; a crown for 5s. 9d. or 5s lOcl. ; a sovereign for;Ci Ss 9(1., or'^l 4s Ha- lifax, according to the deniund for Specie. IIENTAL CALCULATION. The n)ost obvious method of finding the val- ue of, any number of articles is to multiply tho price t)y tho quantity : or of findinpf the price of ene by dividing the cost of any number by \\\% Aunnf it V OP ARITHMETIC. I3t The cost of a crjven number of articles may bo found, by reckoning the cost of tba given niim- bor at prices, ensy to be calculated mentnlly, which togfjthcr makft tho given price, an«!. and 37 pcnco 3.S. Id. which added together tiiake i^l. Is. 7d. iho answer. If any denomination of money be called a higher, or lower den')mination, it will be the samo as multiplying or divi.ling by tlie number of times the less denomination is contained .*^v> the grof'ler; tlio application of this remark ^^ly^ll (jroady assist the mental calculator, and en^Stti him to form rules, simplo, concise, and accuralo. EXAMPLE. To multiply farthing? by 4. c^ll them pence. Tomu'tipiy " by 4«, call tlioin slnlliugs. To multiply '* by 9 i'), call tliciu peuuJt*. To multiply ponce by 12, call Ww.it sljiUings, and each farlhiD'j; -i p«»ct% ' ^ '.■*.■. %• ,; To mulliply " by 2(0, crWktneTft.pound?. To inulnpiy shil'inr^ by 20, calnhcm poinud^s, a ?is pence omJ! 10 sliilii!..;.*:, thrcc-pcnci) 5 shillings, artdft pGtt" nv 1 shillii.'^ niid B iiciiCt'. * X. u^. 21if' reverse of the above rnhs willMe as follows^: by 4, c:ilj thtni fr»^iiig^. by 43, call the .a farthii^;^. by 20, call tlum ebilUu^iy, To divide pen no Tc divide sbilii'i^^s To divide pound'? iS^c. 6. .( »2 &e, }i I (wjiii^ I8S A KBIT STS^TEM or- ne MultiplKat? on and division ofnumbcri may frequently bu performed by multiplying or divid- ing by a number greater oi^ less than the one re- quired, and then adding or subtracting a prop— tional part of the product. , , i. Example.— By multiplying by 70, nnd addi one-trnflj oflho product, a result will be obtam- ed equ'ii to multiplying by 77 : for ^f- + h of The amount of any number of tenths mf>y be found, by mulnplying by the number of tenths and rejecting ihf^ uniis fiiMire. Example.— What is 4-lOihs of 47 t 47 X 4 = 188. Answer, nearly J 9. To find the value per dozen, at so much for on©. RULE I. A« many pence so many shillings. EXAMPLES, s. d. Atf?d 2 At3d 3 AtSjd 3 ^ So much for one, bow much per Score. RULE If. As many puncu su iiianj niiuiiiJgs, !3i«« tm%s »o many pence. ©F AmTnWETlC. n^ re- EXAMPLES. 3d. each. Si SXSd s. d. 3 2 5 So much for ono, how much per Gioss. RULE iir. As many pence, twelve liuics so many shillings. EXAMPLES. Ad. each* 9. d. . At4(l.Xl2s 48 At5d.Xl2s 60 So much per lb. how :>inrh the Hundred Weight of 112 lbs. RULE IV. As many pence, nine times so ninny siiiliings, and so many groats as Pence. EXAMPLES. Sr/. per, lb. SX9^ 27 8X4d 1 £18 i 140 A NEW SYSTEM So much for one, how much per hinulred of six score, or 120. llULE V. As mant pence, ten times so many shillings. EXAMPLES. 2d. each, s. d. At2a.xio. 20 At3tracl «nc day'rf pay. 1^ H r- 11 •/ 11« A NEW SYSTEM EXAMPLES, 3t7. ptr Day, how much per Year. Three Pounds. ... Three halt* guineas 1 U 6 Yearly income £4 11 6 * The above is for Leap Year, 3d. jyer Day, The pounds Three half guineas 11 6 4 116 .wv*^^.-,. (S^t •*^i; %4. Subract o.ic day's pay. .0 £4 11 3 Lot the Pupil work from one Penny to Twenty ShHlings. To find the Yearly Income at so much per week. RULE X. As many shillings twice as many pounds, and twelve limes as many shillings. EXAMPLE. 35. per Week £ s. (!. ..V.O C> 3X12., 1 ^ ^ ^ £r 1^ ^ if ^P AnrnrMKTic* I4;i mv^mitnUon Saijlr, OR A TAKLE DESIGNED TO EXERCISE THE TUHLS • d. 3 5 IS TflMtipIicatioii aiid in Money. 12 11 13 11 10 12 11 10 9 12 11 10 9 12 31 9 8 7 11 10 9 8 U 10 10 10 9 9 9 9 8 8 8 8 8 # 7 7 7 7 7 6 6 6 132 121 120 110 100 108 99 90 81 98 88 80 72 64 84 77 70 63 56 rj . J 54 AQ f. £ s. d, d, s, d. /. d. ==144 i 144 = 7 6 6 6 132 121 120 110 100 108 99 90 81 93 88 80 72 64 84 77 70 63 56 49 66 60 54 48 5 5 4 4 4 4 4 4 rj 3 4 3 3 3 o 2 3 3 2 2 4 12 1 10 8 19 10 1. 10 8 12 4 4 17 10 3 16 9 6 14 8 141 = 132 121 120 110 ICO 108 9D 90 81 96 88 80 72 64 84 77 70 63 56 49 66 60 64 48 12 11 1^ 1 10 9 2 8 4 9 8 3 7 6 6 9 8 7 4 6 8 6 5 4 7 6 5 5 10 5 3 4 8 4 I 5 6 5 4 6 4 123 121 120 110 100 108 99 90 81 96 83 80 72 64 84 77 70 63 56 49 66 60 54 48 I I 144=3S 33 , i SOf.-"^-^*^-- { 30 . 27 24 2-2 2()i 24 oo 20 18 16 21 19i 17^ 15^ 14 121 16^ 15 12 A 144 .4 m:w system dec. 1 CONTENTS '^^,.,*if<' I n^ t fVC> L^l 0> Aritli;vjeiicul Characters, Tables, ck:c. :sotauon d'lit ion, Mul Paoie. . 8 ,. 29 . . 30 , . 32 ( 1 ' ; licalion 39 /Jo Division Coaipound jvddiiion Compoinul Subtraction 58 63 79 0:2 leductioi'i 1 Fra icuons ' report ion a 1 Arithmetic n voices. ..^-., 1 91 jt. .'^ J. D D K 1 l^ i It ecniKi uodecimals, ction.... X 24 veauctions o r c uirencic >'» 131 133 Menial Calculations.. ISCi M 4 AsF FIN13. ,/ %■ Pa(se. A-" a • • • 29 30 * a a ■ 32 .14 • • • • 39 * • • • 58 6f^ ft * « « 79 191 19,4 • ■ • * a 131 / a • • • 133 » m * » 13^ ■f