IMAGE EVALUATION TEST TARGET (MY-3) 1.0 1.1 1^12.8 ■ 50 '"^™ 2.5 22 2.0 1.8 L25 114 III 1.6 ^ ^ PhotDgraphic Sciences Corporation \ ^o ^\ ?0 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 C^ ^s ^^1^^ f^ £ "% :\ CIHM/ICMH Microfiche Series. CIHIVI/ICIVIH Collection de microfiches. Canadian Institute ?or Historical Microreproductions / Institut Canadian de microreproductions historiques ■msmTit Technical and Bibliographic Notes/Notes techniques et bibliographiques The Institute has attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographically unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, are checked below. L'institut a microfilm^ le meilleur exemplaire qu'il lui a 4t6 possible de se procurer. Les details de cet exemplaire qui sont peut-Atre uniques du point de vue bibliographique, qui peuvent modifier une image reproduite, ou qui peuvent exiger une modification dans la mithode normale de filmage sont indiquAs ci-dessous. Coloured covers/ Couverture de couleur — Coloured pages/ Pages de couleur Covers damaged/ Couverture endommagie Pages damaged/ Pages endommagdes Covers restored and/or laminated/ Couverture restaur^e et/ou pelliculAe — — Pages restored and/or laminated/ Pages restaurdes et/ou peliicul6es Cover title missing/ Le titre de couverture manque 1/ Pages discoloured, stained or foxed/ Pages ddcolordes, tachet^es ou piqudes Coloured maps/ Cartes giographiques en couleur Pages detached/ Pages d6tach6es Coloured inic (i.e. other than blue or black)/ Encre de couleur (i.e. autre que bleue ou noire) / Showthrough/ Transparence Coloured plates and/or illustrations/ Planches et/ou illustrations en couleur -r Quality of print varies/ Qualitd in^gale de I'impression Bound with other material/ Reli6 avec d'autres documents ^"•' Includes supplementary material/ Comprend du materiel suppldmentaire v/ Tight binding nr>ay cause shadows or distortion along interior margin/ La re liure serrde peut causer de I'ombre ou de la Only edition available/ Seule Edition disponible distortion le long de la marge intirieure Pages wholly or partially obscured by errata slips, tissues, etc., have been refilmed to 1 s T v« N di ei b< ri! re m D D Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut que certaines pages blanches ajout^es lors d'une restauration apparaissent dans le texte, mais, lorsque cela 6tait possible, ces pages n'ont pas 6t6 fiim^es. Additional comments:/ Commentaires suppldmentaires; ensure the best possible image/ Les pages totalement ou partieliement obscurcies par un feuillet d'errata, une pelure, etc., ont 6x6 film6es 6 nouveau de fagon 6 obtenir la meilleure image possible. This item is filmed at the reduction ratio checked below/ Ce document est film6 au taux de reduction indiqui ci-dessous. 10X 14X 18X 22X 26X 30X y 12X 16X 20X 24X 28X 32X The copy filmed here has been reproduced thanks to the generosity of: Library of the Pubiic Archives of Canada L'exempiaire fiimd fut reproduit grAce A ia gAnArositt de: La bibliothdque des Archives pubiiques du Canada The images appearing here are the best quality possible considering the condition and legibility of the original copy and in keeping with the filming contract specifications. Les images suivantes ont 4t6 reproduites avec le plus grand soin. compte tenu de la condition et de la nettetA de rexemplaire film6. et en conformity avec les conditions du contrat de filmage. Original copies in printed paper covers are filmed beginning with the front cover and ending on the last page with a printed or illustrated impres- sion, or the back cover when appropriate. All other original copies are filmed beginning on the first page with a printed or illustrated impres- sion, and ending on the last page with a printed or illustrated impression. Les exemplaires originaux dont la couverture en papier est imprimie sont film6s en commen^ant par le premier plat et en terminant soit par la derniire page qui comporte une empreinte d'impression ou d'illustration. soit par le second plat, salon le cas. Tous ies autres exemplaires originaux sont filmiis en commenpant par la premiere page qui comporte une empreinte d'impression ou d'illustration et en terminant par la derniire page qui comporte une telle empreinte. The last recorded frame on each microfiche shall contain the symbol —»- (meaning "CON- TINUED"), or the symbol y (meaning "END"), whichever applies. Un des symboles suivants apparaltra sur la dernidre image de cheque microfiche, selon le cas: le symbols — ► signifie "A SUIVRE ", le symbols y signifie "FIN". IVIaps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc.. peuvent dtre filmte it des taux de reduction diffdrents. Lorsque le document est trop grand pour dtre reproduit en un seul clich6, il est filmd d partir de Tangle supdrieur gauche, de gauche d droite, et de haut en has, en prenant le nombre d'images ndcessaire. Les diagrammes suivents illustrent la mithode. 1 2 3 1 2 3 4 5 6 SERIES OF J^^ATIO^TAL SCHOOL BOOKS y,' ■,^. T^ ■^z ' " i\- ,^;..y;^> , • jjj^.- ■ ■4ic].'^^:'-^i; ; ' mi 1 ?1 ^^ t^< r^< nirm: > A' -^■.: OP 'i^^^^y :->:-.' ^^ „■"■ FOR ■ * " # • , , f»-" 1,. ■ ■ ■ ' > ®l)c l^sc of i5(t)ool0; •- '^. ..-i ---^ -•^"f.. .i:-' --Jr '" .'r* .\'- nvA^^... >-,>..f :;■>>*..'' 'S^iiii.', >- ^" . f ', .'» t ■ . *" .-. •*-.■■ :■ . , ^\.^>*M^-^'i-'^., ;*:.-^.--,v' , .n. .. 1^ - • . •, ,- . ■;> ..:i.. <, '^. ■-„ - ■.^, -- ■;- .^ ■ REVISED EDITION, ADAPTED TO THE NEW DECIICAL !;r; CDRREXCY OF CANADA. •^ v'^"."'-'^ -v^'^.f^ ;''v ■■<•'■ vi" •' ■■'.-: r*>^ • Ty r-^ - ' •* ■ ^f :ft'v;:l-/ ;-^ t r n t 6';;^ v 'vy^;:;:^^'" Published by robert Mcphail •National School Book Depot, 66, King-St., Eaw. ^^c'wSt;^'-:' I860 Entered, according to the Act of Uio ProviDciHl Parliumeut, in the year one thousaod eight hundred and Hixty, by RonRRT McPhah., in 1I)« Office of the Registrar of the Province of Canada. in4 a) / ^/ PREFACE. TN adapting this well known Treatise to the Deci- mal Currency, neither expense nor pains have been spared to make it worthy of universjil patroo- «ge. The assistance of a gcntleniaa has been «ccnred, who brings to the work, besides the qualifi^ cation of a Trnctical Accountant, a long expcrieucf as a successful Teacher. As much as possible of tii^ •Id Book has been retained entire, bnt all the Com- mercial Rules have been considerably enlarged, and geveral important ones have been added. The arrangement,^ also, is more methodical, and as a whole, the book, a^; now presented, is perhaps one of the most complete elementary Treatises ever published oa this Coutinent. THE PUBLISHER. CONTENTS. ARITHMETICAL TABLES. V\QK. Afl'ViUon Tablo 1 Miiltiplicafioii Tubit'.... 2 Pence Tablo H Signs used ill Arithmetic. 4 Honey Tuble 4 Wciftbts and Measures., Nunn-nvtion Table Uoniaii Notation Table of Aliquot Parte. ft 8 8 70 AIllTIIMETlO. Ntimeratlon 8 Notation 9 Simple Addition 10 Subtraction 11 Mixed Qut'Htiona 18 Simple Multiplication... T.> Division 23 Fkactio.vs — dofinitioua. . 27 Decimal Fractions 28 Addition 28 Subtraction 21) Multiplication... 29 Division 30 . Rediictloa 31 Decimal Currency 33 Vulgar Fnictiiins 35 ■ Prime Numb<*ra. . 35 Common Mea."ure. .3(> Common Multiple 37 Canctdlation 38 «- R«'duclion 40 Addition 43 Subtraction 43 Multiplication... 44 Division 45 Reduction cont'd 45 Promiscuous Exer 49 Addition oC Money 50 Subtraction of Money. ... 61 Multiplication of Money. 52 Diviaioii oi" Money 54 Rednciion of Money 67 of Halifax Cy. to $ and c-<'nts. . . . , 69 W.iorjits and Measures., . 6i Praciice 70 Tare jind Tret 72 Hills (»f Parcels 76 8impl<,' Proportioh 76 Compound Proportion... 81 Partitive Proportion, or Fellowship 89 Compound i'artitive Pro- portion 68 Medial Proportion, orAl- li};ation S9 CoiiJ<»ined Proportion. ... 93 Perc(Mitage, or Profit and Loss... 95 Simple Interest 98 Commission. Brokerage, Insurnnc<'. Stocks, &C..100 Componnd Interest 102 Dii^count 103 Barter 106 Involution 107 Evolution 107 Square I'oot 107 Cube Hoot 108 Dnodeeimal Mnltiplicat'n 110 Mental Arithmetic 113 Answers to the QuestioBsllJ 2 2 3 - 3 - 3 - 3 — 3 — 3 — 3 — 3 — 5 ~ 3 — ARITHMETICAL TABLES. ADDITION TAnr.E. FaOE. ^res... I .... 8 .... 8 'arts. . 70 .... 67 Py- to .... 69 ires. . . 6t .... 70 .... 72 .... 76 .... 76 on. . . 81 )n, or 89 e Pro- 88 orAl- 8« n 93 it and 95 98 erago, Ac 100 102 , 103 106 107 107 107 108 cat'nllO 113 StiOQ£ll7 and 1 are 3 — 2—4 — 3 — 5 — 4 — f, — 5 — 7 — 6 — 8 — 7—9 — 8—10 — 9—11 — 10— 12 — n— 111 and and 6 and 6 — 6 — 6 — 12 — 1 arc 2 — 3 — 4 — 5 — G~ 7 — 8 — 9 — lo- ll— 12 — 1 are o 3 — 4 — 6 — 6 ~ 7 — 8 — 9 — lo- ll— 12 — 1 are 2 — 3 — 4 — 14 4 5 (I 7 8 9 10 11 12 13 14 15 5 G 7 8 9 10 11 12 13 14 15 1() (i 7 8 9 5 II I id 5 5 5 5 5 5 arc (i — 7 — 8 — 9 — lo- ll — 12 — 1 2 are l> Ulltl (i — (I — (I ~ () — (» — (; — G — G — G — G — (; — 7 nrul 7 — 7 — 4 — 7 — 5 - G — 7 — 8 — 9 — 10 — n - 1-; 1 ure 2 — 3 — 4 — 5 — •> — 4 __ 5 — (i — 7 — 8 — 9 — lo- ll - 12 - 1 arc 2 — 3~ t — 7 — 7 -- 7 — 7 — 7 — 7 — 8 and 8 — 8 — 8 — 8 — 8 — 8 — 8 — G 7 8 10 11 12 13 14 15 IG 17 I 8 9 10 11 12 13 14 15 IG 17 18 8 9 10 11 12 13 14 15 IG 17 IS 19 9 10 11 12 13 14 15 16 8 and 8 — 8 — 8 — !> and 9 — 9 — 9 — 9 — 9 — 9 — 9 — 9 — and 9 !) 1 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 2 and 2 2 — 2 2 — 2 — 2 — '> 2 — 2 — 2 9 9 are lo- ll — 12 — 1 are 2 — 3 — 4 — 5 — 6 — r» 1 8 — 9 — lo- ll — 12— are — 4 — 5 — 6 — 7 — 8 — 9 — lo- ll— 12 — 1 are 2 — 3 — 4 — 5 — G — 7 — 8 — 9— . lo- ll — 12 — 17 18 19 20 10 11 12 13 14 15 16 17 18 19 20 21 12 13 14 l!i 16 17 18 19 20 21 22 23 13 14 15 16 17 18 19 20 21 22 23 24 I* iRiTlIMKTICAl. TABLKS. MULT11»LICATI0N TAP.LK. Tw'icd 3 times 4 tinv'S 5 timcH tiraca 7 i\mc9 1 are 2 1 arii I) 1 : iro 4 1 art • 5 1 are 1 arc 7 2—4 2 -- i; •> 8 K) 2 12 2 — 14 3 f) 3 — 1) 3 — 12 o 15 :{ — 18 3 21 4 - 8 4 — 12 4 Hi 1 _-. 20 4 — 21 4 - 28 n — 10 5 — i:. .') - 20 5 — 25 5 - - 30 5 — 35 a — 12 - 18 i) - 21 (5 , - 30 - - 30 42 ; r ~ 14 7 — 21 7 — 28 7 • 35 7 ^.. 12 7 - 49 1 n ~ 16 8 — 24 8 32 8 - 40 8 — 48 8 - 5U 1 ^ 18 !) 27 9 30 9 — 45 9 — 54 9 — 03 10 - 20 JO y) 10 - 40 10 0!? 10 - 00 10 — 70 n — 22 11 :v.i 11 44 11 — 55 11 — (u; 11 77 Vi 24 J2 - :ju 12 - 48 12 - 00 i 12 ■- 72 12 - 81 « • 1 8 times 1 aro 8 J) time s 10 times $ 11 times 12 times 1 are 9 1 - - 10 1 11 1 n j 2 - Ki 2 ~ 18 2 - - 20 2 22 2 24 3 — 24 3 — 27 3 - . 30 3 — 33 3 — 3fr 4 — 32 4 — 3(1 4 - - 40 4 44 4 — 4t 5 40 C) — 45 5 ~ - 50 5 — 55 5 CO — 48 r, ~ 54 () - - 00 — 00 G 72 7 — 5(i 7 - ()3 7 - - 70 7 — 77 7 84 « — (;4 8 — 72 8 -~ - 80 8 — 88 8 - 96 •) — 72 9 — 81 9 - - 90 9 — 99 9 108 iO — 80 10 90 10 - 100 10 110 10 — 120 U 88 11 — 90 11 ~ ■ 110 11 121 11 — 132 12 - 9(; 12 1 08 12 — ■ 120 12 132 12 — 144 EXTENDED MULTIPLICATION TABLE. io.vB 26 39 62 65 78 01 14 tiinps *2 ar« 28 — 104 i 8 — 4'2 f)6 70 84 98 112 15 tiiiu'9 '2 nre 30 3 4 5 6 7 8 45 flO 75 ■(M> 105 12<» 16 times I 17 times '2 iire [il '2 are 34 . , il7 9 — 1-26 9 -- I >o 24 25 26 27 28 29 30 ai 32 -^ 13 14 ♦«. 149 iiOO i40 «(»<» 400 480 oOO hOO 700 :'2o 800 fiOO «60 1006 1100 12M 9 — 1C2 . 9 171 ARITHMETIC AI, TABLB8. FENCE TABLE. time* are 7 -- li — 21 — 2« - as — 42 — 41) - 5U — (i3 — 70 — 77 — 81 times - 1* — 24 - 3© - 48 - CO - 72 - 84 - 9() - 108 - 120 - 132 - Ui — 57 - 7« 95 114 13.1 15Q 171 4. S. d. d. s. d. d. 8. d. d. «. d. 12 Hre 1 35 aro 2 11 57 ai'o 4 9 79 ar« 4 7 »:{ — 1 1 3(1 -■ 3 58 — 4 10 80 — 6 t 14 — 1 2 37 — 3 1 59 — 4 11 81 — 6 t 15 — 1 3 38 — 3 2 00 — 5 82 - 6 If 16 ^- 1 4 3(» — 3 3 61 — 5 1 83 — 6 11 17 — 1 5 40 — 3 4 02 5 2 84 — 7 f 18 — 1 « 11 — 3 5 (:3 — 6 3 85 — 7 1 10 — 1 7 12 — 3 (1 04 6 4 80 — 7 2 I'O — I 8 13 — 3 7 ' 05 5 6 87 — 7 3 21 ~ 1 !i 44 — 3 8 00 — 5 6 88 — 7 4 22 — 1 10 45 — 3 9 07 5 7 89 — 7 6 2?: — 1 11 40 - 3 10 08 6 8 90 — 7 fi H — 2 47 — 3 11 09 — 5 9 91 — 7 7 25 — 1 48 -- 4 70 5 10 92 — 7 8 26 2 2 40 — 4 1 71 — 6 11 93 ~ 7 » 27 2 3 ! 50 - 4 2 72 94 — 7 10 28 2 4 51 — 4 3 73 - a 1 95 — 7 11 29 — 2 5 52 — 4 4 1 74 — 2 90 — 80 30 — 2 G 53 - 4 5 75 3 97 8 1 ai — 2 7 54 ~ 4 6 1 70 ~ 6 4 98 8 2 32 2 8 55 ~ 4 7 i 77 - 6 5 99 — 88 S3 — 2 56 4 8 i 78 6 100 — 8 4 Si 2 10' 1 • EXTENDED PENCE TABLt it £. *. d. d. £ n. d. d £ s. d. d. £. ».d. \49 arc 11 8 nnoaro 5 8 4 2500 arc 1 8 4 3700 aro 1 5 8 4 iiOO — Iti 8 1400 — 5 10 S •jr>0(> _ 10 IR 8 3S00 - 15 10 8 i40 — 1 1140 — 6 •j(UO — 11 oH iO — 16 8 U0(» ~ 1 5 lf)00 — 6 .'. 2700 — 11 6 a.Hio — 16 6 400 — 1 13 4 H'OO — 6 !3 4 2800 — 11 13 4 4000 — 16 13 4 480 -. 2 lr.S(» -- 7 V8S0 -- 12 4080 — 17 600 — 2 1 8 1700 — 7 1 8 -2000 — 12 18 4200 — 17 10 *iOO — 2 10 U 1800 — 7 10 aofiO -- 12 10 4300 — 17 18 4 700 — 2 IS 4 1900 — 7 18 4 a 100 — 12 18 4 4320 — 18 T'^O — 3 19-20 -- 8 3120 — 13 4400 — 18 6 8 SOO ~ 3 6 H 'i'lOO — 8 C 8 3J00 — 13 6 8 1500 — 18 16 900 — 3 15 ViOO — 8 l.i 3300 — 13 If) 4560 — 19 «I60 — 4 2ir,o — 9 ;^3fiO — 14 4700 — 19 11 8 1006 — 4 3 4 2-200 — 9 3 4 a400 _ 14 3 4 4800 ~ 20 IWO — 4 11 8 -2300 — 11 8 3f,00 — 14 11 8 4900 — 20 8 4 1200 — 6 . 2100 — ; 10 3C00 — 15 5000 — 20 10 8 %■ IRITnUETICAL TAUrEfl. SIGNS USED IN ArwITIIMKTlC. 4- namfid plus, pi^uifioa Addition, as 4 f-*J equal 6. — named minus, sijjnilics Stihtruction. as 5—2 equal 8. X multipliod by, Hiji;iiili('a Miillipiiculiun, as 1x2 equal S. 4- divided by. sigiiilics Division, us 10-i-2 cquul 5. s= equal to, sigiiilios Kcjuiiiity, uh 2-f-l=(). ' • so JH i signith's Proportitni iix 1 : 2 : : H : fi. • to I '^^^^^' l^K^'i''-''* '^''^' ^''*i'* >'^'ad, as 1 is to 2 so Is 3 ♦>« i %/ marks the Squan? root, as s/ I =2. ^ maiks the Cube- root, as ^ b =:2, I MOXKY. i farthings = 1 pr^nny I'J piMico = 1 I'liilling 20 shillings = 1 pound 21 Khillings = 1 guini'a £ denote? pounds, .>. shillings, and (/. pcnco. ^ one fiu'lhing. or oni' quarter of any thing. ^ a halfpenny, or a half of any thing. I three farlhiags, or three quarters of any thinf AYOiKuuroia wkkiht. 16 drams (dr) = 1 ounce 10 ounces = 1 pound 28 pound;^ = 1 quart" r 4 quarters or 112 lb. = 1 hundred weight 20 hundred weight --^ 1 ton marked oz. lb. qr. cwL T. 14 pounds make one Rtone, and 8 Ntono 1 hundrerl weight. Tlitji weipT t 1*3 nfpd f«»r br«»n«f ftod Rcil bj Avuu(Jup(ii.s vieij^cht. marked. icr. dr. ox. lb. 1.0X0 MKASUUK. J tbinf iark«4 oz. lb. qr. cwL T. lit. 12 liiirs 12 iiichc:* H fi'C't iO p(,'rcli(s 8 3 Rifirked. in. A yd. per. = 1 inch. =s 1 loot, = 1 yard, =:= 1 p('r(!h, = 1 CurloDg, fur. = 1 mil**, m/. = 1 IcP.gllC, l ^ 3()0 dogr' cs = thu earth's circumference. lurlongH An Inch i^; fluppost-a to h« P(\w\\ to tin en bailcy-rnrnH in Icnf(th v'flreu y.\rt!« Irisli tqii.vl ca\c j;«-i('Ii, Klovrn miles Irish are equal to :'nurt»«Q milt's English. 4 inches m.Lt- ouc baad, lueil in motiswAng CLOTil MKASURK. 24 inches = 1 nail, 4 naiU = i quarter, 4 quarters = 1 yiud, marked. n/. qr, yd. The Flemish ell is three-qnarterfl of a yard, the English eS it ftw fv'Murkrd of a yard, aud the I'roach ell aix-quarteru of a yar4. ARITHilETICAL TABLES. SQUARE OR LAKD MEASURE. 144 square inches 9 Rquare feet 304 square yards 40 eqnare perches 4 roods 640 acres = 1 square foot = 1 square yard, = 1 square perch, = 1 rood, = 1 acre, sq. ft. tq.'ifd. tq per, rd. ae, sq. mile. = 1 square mile, In Ireland 49 square yards make 1 squ.re pole or perch. The nqtiart «f »nv number is obtaineil by multiply in;j it bv itdtlf, 12 multiplksi b/ 12 — IM, the square of \L CURIC, OR FOLID MKASVllE. 1728 cubic inches 27 cubic feet 40 cubic feet of rough timber, or 50 cubic feet of bcwii timber 42 cubic feet r= 1 cubic foot = 1 cubic yard = 1 ton, or load r=: 1 toUOfshippiRf A cube is a solid figiiro, .•••••milnr lo marked. 60 seconds {ate.) =r 1 mlnate min. CO ralnutes ' ' — 1 hour hr. 24 hours == 1 day da. 7 days = 1 week wk. 12 inonthP, or 1 • 52 weeks and 1 day, or > = 1 year yr. 8G5 days ) ./▼e-j fourth Tt'?.r contains SGC u.-va, aud i.s called leap year. DAYS IX EACH MONTH. Thirty days liatli September, April, Juno, and Noviiinbor ; All the re.st have thirty-one February twenty-eight alone, But in Leap Year twenty-nine. DITIJ^IOXS OF TUB CII?.CLK. 1. The g^ lel. quari«r, :ubic incheji. Act of rar- Y differed n tains 32, I ad of alt 3f wine iA viHrlce^. <0 seconds" — 1 minute min. or 80 minutes = I degree deg. or • 80 degrees 1 sign S. 12 signs = I circle of the zodiac c. QUANTITIKS. znaiheiji 12 articles = I dozen dox, 20 articles = 1 Bcore sc. 144 articles = 1 grof?s gr- 24 fiheels pap^^v = 1 quire qr. 20 quiies = 1 ream rm ARITHMETICAL TABLES &C. i: I, I NUMERATION TABLE. 1 Units. 21 Trns. ,321 Hundreds. 4 , 321 Thoiisaiida. 54 , 321 X. of TlioiisandR. 654 , 321 C. of Tliousauds. 7 . (>54 , 321 Millions. 87 . (154 , 321 X. of Millions. 9S7 , (154 . 321 C. of Millions. 1 , ().S7 . (;5l . 321 M. of Millions. 21 , 9H7 . (151 . ;;-:l X. M. of Millions 321 . 9.S7 . (^54 , 321 C. M. of Millioiis 4. 321 , Db7 . {)54 , 321 Billion^. M. 1000 rvOMA.\ NOTATION'. I). C. h. X. 600 lUO 50 10 V. 5 i ■^ ii t-.: .1 EXERCISKS IN NU M F. I L\1 ION. R.'ad, or write down in words the nuftiotrs si[:,AlJ'.€. 7, 8, 9, 0. 10. 11, 14, 1(). 19. 20. '12, 18, 17. 200, 420, 007. 98(1. 473. 217. 3-;4. 2. H. 4. 0. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. IC. 17. 18. 912, 874, 78;{. (150. 202, (KH, 40(>0. 1010. 2700. 7o:>o. 0r.7, 2M000(10, 4101010. 2001000, 110214*?. 40000000, 29002(187, 50020017. 1070020. 941208707. 207002007, 401107080. 290020870, 710020010, 270(iO:)0.5(). 1402300740, 3400700010. 4023001497. 7042003714, 5079007900, 1704070000. 81402,300012, 40007087081. 9408042 13fi0. 14023041201. 20800002001, 40002000202. Sl070G020ti204, 24002G10U201, 5yoyU012t"020. EXERCISES IN NOTATION. i i fV^J,fd V^ )20. Express in Figures the following JVumhert. \. Six, — seven, — nine. — citilit. — fivo. — ten, — twelve,— fourteen, — sixteen. — eightetu. — twenty, — nineteen. 2. Seventy-fonr, — twenty-six. — thirty-one. — forty-nine,— ftfty-ciglit. — sixty-two. — seventy-six. — sev< nty-seven, — nine- ty-sevenf — eighty-tour. — tirty-Ii\e. — nini'ty-nine. 3. One hundred. — one linndred and four. — two hundred and forty-four. — six hundred and ninety-one, — seven hun- dred and fifty. — nine hundit-d and nine, — nine hundred and ninety-nine, — eight liundrcd and two. 4. Four ihousand.^ — tour thousand two hundred, — five thousand three htmdred and li!ty-t'A0. — six tlitjusand Reveu hundred and five, — seven thou ;u; 7 8 9 12 21 23 14 21 4t 11 12 24 35 34 23 23 24 35 43 75 97 H 57 82 92 130 1G2 4\ 84 2G 37 42 28 24 24 42 25 56 1^9 JS6 63 59 74 85 Al BIUTLE Mimjiojx, VI P (2) (3) (^ 412 243 623 854 ; ic numbcf 346 427 325 678 146 67« 236 675 423 i t5) (6) (7') (8) lu 1 2fi4 450 647 856 207 3fi8 407 , 653 479 752 679 865 627 824 8G5 636 276 '894 1 4, and udcj ■■' ■ aud 3 make of the 12. tlius, 1 and m (10) (11) (12) . down tin* ^ 246 457 47 8 . 78 60S 602 70 * 604 92 68 926 40 400 720 47 6 4 7 78 79 ^ ^ 12 (13) (14) (15) ' (16) 5129 4268 3687 2407 4 7142 2426 4215 798 ft 9687 4276 708 46 9 4312 8507 9362 7083 8687 2390 9G 679 ^« • «r 23 97 (17) (18) (19 (20) 5126 2427 5036 780 162 1472 768 784 5708 6826 9412 6070 1070 28 9687 893 85 687 ^9 2764 4026 7507 5368 Al 4279 475 687 759 I • •■• i2 SIMPLE ADDITION. 1 !i m \\ (21) (22) (2n) (24) 42«74 24786 4s7(;s 4G537 3412(1 fif.Sia 8(;270 64263 687(>8 2(5879 4(187 43986 28(142 4:1(153 578 6079 657(;8 (58754 4n()(;o 81 74387 50287 187()^ hundndand eighty, an«l in amdh' r foiir iiuiuirid and four, how many apples were there in tlie four l»asket>^ ? 39. I gave John 12 apple.y. .lames 15. I'atrick 20, and 1 bad Btill 25 remaining ; bow many apples bad 1 ;U liist ? I I i r SIMPLE ADniTION. 13 (24> 54263 431)86 6079 81 641 D8076 nake? 70? G5 make? lake ? nd 742(5. -BOG. 826. 807. -4276. k. x^y-l.h^f^e, aud and five Ihoa- eit^hi. — drcd and nine,— r nmonnt $2048,-- n ono of \i\d iuur, 10, una 1 40. In ft school wh'vM T visitod lately, thore were six classes ; In tlu livM \',\ '.rn \v»m(.» 2:> l>ovs, in tliu st^cond 18, in the third '^2. iti tiic fourth 27. in tlif tilth 56, and in the gixth 48 ; can you tell me how many boys there were ia the school ? 41. A man walkcid 2'^ mllfs on Mondiy. iM on Tuesday, 46 on Wednesday, 'M on Thursday, on Friday being unable to walk, he procured a liorsc. and ro«b* 41 miles, and com- pleted his jonrn(;y on Saturday, having trav18, on horses $487, on fiheep $964, on cows $I8!>. on laboring utensils $209 ; how much did he lay out altogether? 45. In a house there were nine windows in front, and each window had twelve panes of glass. In the n-ar there were iix windows, and each of these windows had nine panel of glass ; how many panes of glass were there in all the windows ? 46. A fruitoror bought six chests of oranges. Tn the firai ehest there wer.- 468 oranges ; in the second 679 ; in the third 804 ; in the fourth 979 ; in the tillli 1042 ; In the lixth 1709 ; how many oranges were lli'Te in all the chests? 47. A linen draper sold 4(5 yards of clotli on Monday; 78 on Tuesday ; 65 on Wednesday ; Jhe same quantity on Thurs- day ; 64 on Friday ; and 97 on Saturday ; how many yards of cloth did he sell during the week? 48. A grocer received for goods sold on Monday $4 ; oa Tuesday $6; on Wednesday $10; on Thursday $9; on Friday $13 ; and on Saturday as much as he ha801 19G97 27(101 (24) 110201 2GU «> 20009 (2?,) 741()'>()>^81 61 (2;")) 148120718 2781)01896 17 syOG8l 1 74198648 (2(;) 8612G4981 (27) 921 0024 C (2ft) 181-01041 248000989 198007049 89890122 16 SIMPLK SUBTRACTION. il I ,1 'I 2J). 7 liR'if; 121741- 30. 8llii!)sl7K]l2 81. hliOl lOOlOlH 32. 4-5170! iCMi-H:- ?ui. <;i42i4(.^<7i;4s- 34. 41UUU0JUU()M- 427084(142814 7148!H;412. On an apple tvov there were 1(15 apples, the wind blew olf two dozen aiul a half : how many were left ? 40. A draper bought 4780 yards of cloth, and sold 3987 yards ; how many yards has he unsold ? 47. What sum added to sixty-five thousand seven hun- dred and ninety-six. will make one million four hundred and fifty-two thousand three hundred arid thirteen? 48. 1 was born iu the year 1828 ; how old shall I be in the year 1830 ? i SIMPLK SUBTRACTIOJi. It fulir hnn- id lilty-ODC ion?aiKl axul Liid seven, le liunflred ui-aiid seven hundred anJ -nine ? bas received les, of thcs< r H92 ; hovi f these onlj e '127 boys there in tU horn Ix'ing a nainlng? es. tlie wind left ? hd sold 3987 seven hun- 01 J r hundred en ? shall I be in i 40. Ireland is about 300 miles in l-'^npfth. and 170 mi^ in breadth ; how much greater is the length than tno fcreadth? fiO. r?en Nevis, in Scotland, the hif?)! 'st monntain in the British IsliindM, is 4:550 f ct above tlic level of the sea ; the lumrnit of MairiU'ouddy's Flceks. tin,' hifrhest point in Ireland, is 3(110; what is the ditfeninco in height between these two mountains? 51 . Th" Shannon, the larpfost river in the British Isles, has ft cours<; ol'aliont 170 rnili*»s. The Ania/on in Sonth America, has a course of uimut 3000 miles. What is the difFereuce in length of* their conrse? 62. The d'ameter of the Sun is about 88:52 K) miles; thai of the Earth atjont 7012 ; what is tiio dilference in the diame- ter of tlie Sun and Earth? 63 The surface of tht* «'arth is nearly 200 millionR of fiqiiare miles, of this it is protnit)!*' tliat )iO millions are land; how many rnor*' sfpiare miles of water tlian of land are there in the eartli's surface? 54. The population of Lomlon in 18^1. was 1,770.506. The popnhition of l>ul)lin is about 20:).(i.")2 ; how many more people are there in London than in Dubliu ? 55. Mont Blanc, in Switzerland, is the higho.'?t mountain io Europe, beiiig l^.tiBO feet almve the level of the sea. Chim- borazo. the highest mountain in America, is ab«)nt 21,000 feet in height. W'hat is the ditiereuce in height betvveea these two mountains? 5(). Coals were discovered at Newcastle. A. D. 1234 ; hoit long is it from that time till the year 1830? 57. Since convicts were first sent to Botany Bay, it is now, ?iz.. 1830, about 42 years; in what year were convicts first •cut? 58. Sir Isaac Newton was born A. D. 1G42. and died 1727 j bow old was he when h(; died ? 5f). Petersl)urgh was founded by P' ter the Groat, A. D, 1703 ; how bmg is it from that tinje till the year 1836? do. The art of printing was tru>covered about the yeai H49 ; how long is it from that time to the year 183G? i 19 II SIMPLE ADDITION AND SUBTRACTION. MlXi:n QUESTION^?. 1. Tom had *J'"I mail)!' s ; 1h» pivr ••! lo Jiimcs, 75 to Wil- liam, and 42 to John ; how many Imd he Iclt? 2. A mprohani had I'iiiH yardu ofcUUh. on Monday he w>W IIG yardP. on Tuesday 97. on \Vrdn«Hh»y liJJi. on tlnirHdajr 108, on Fritlay .'U!4, on Saturday 1!)7 ; how uiuch cloth had ^«! reinauiing? 8. Three rcp-'inontM wont to ImttK* ; In tjio flrst there wore 908 BoUlicr?'. In the second 7<;0. and ir Ihe thii8 miles to irnke ; th« first ilay he walked 12 miles, the seeond !<'• mii' h. i,e third ol alics, the lonrlh 27 miles ; how nuich '. r ht \\Mi ho to go? 5 Three vessrl« sailed to Am'MJea wiih em!jr'*J»r ts ; in the •rr.t vessel there were 12i) in n. W wcuncn. ami 41^ children ; io tbc fiecond vessel there W( re 08 men. !^7 wonun, and 2tf •bil^rcn ; In tlie third vosjsel there were 4'{ men. 2/ women, and 8 chiPre'i. Iti the first vessel three persons Oied ; ia I^Q second tvo were wa-hed overht)ard ; the Ihird vtEscl wat wrecked rnd uM on board pvji.shed ; how uuiuy got taSe if Aincrlea? 6. A little l^;(T.»nt to iho Zoolo/rleal Gardens to 80« th« ftuimalp ; he la'o lu ^ hat on the ^n'onnd. which coniwne4 2()4 nuts ; while h\r- .'itent'on was en^mired. the nnukoy •tole 27 of his lans ; w'sle he was pursniuji: the monkey, a squirrel made orf *ruU 't> more ; how many had be .'«- naJDiug? 7. The popnlalion of (JorJ- N nlont 108.000 : of Belfast, 65.000; of Liverpool. bJd.dOO; of Glasgow, 203.000; by kow much does the population M London «'xneed all thcBd eitie.s, the population d' it beiuit, ^,7« '»e'>^><» 'n the year 183H 8. Received on 'T. »u' "'. 17^ ^ "^ aw if (« Tuesday $19(> ; received on '' (..n'stijiy $l?t!)' j^ai ' rv, t """^ Thura* ^ay $402; ree- ived on Friday $(I87 . p.'it' av>i^ oiv Satur- day $398 ; what money hud 1 still remuuiiuR ? 1* 'J! make 24, but ♦ :ike notice that you are to place the 4 of the 21 din.'ctly undi.r that figure of the multiplier by which you are multiplying. Proceed in the pamv manner with the (igiire 3 of the multiplier, logether the products obtained. 13704 0852 570^ 10278 inim Then add Multiply G1S7 by2:;0. 2:;0 194{;iO 52974 1192010 43. Mult. 98176 by 042 44. 758 45. — 205 4(). — 49(5 47. 857 48. — 43(J8 49. ___ 7.S9G 50. — 3 Go 4 Multiply 6487 by 203. 203 51. 52. 53. 5t. 55. 5(). 57. 58. 19 in I 129740 131G8()1 Mult. 65839 by 058 — 627 — 3<)S — 426 — . 701 — 8743 — 6007 — 9864 59. Multiply r-xty-four thousand eight hundred and fifty two, by nine hundred and eighty-seveu. 60. Multiply four hundrtui and fifty-eight thousand six hundred and ninety -four, by eight thousand and seventy-six. 61. Multiply nine hundred and eig!ity-six thousand seven hundred and forty, by four hundred and nine. 62. There are 8766 hours in the year ; hov/ many hours are there in 20 years? 63. A grocer sells goods to tho amount of $56 per week ; liow much does he sell during the vear? 64. In a flock oi 643 .dieep ; hov; many feet were there! f I I &L 22 SIMPLE MULTIPLICATION. 65. Suppose the ^age of a book to contain 49 lines, and each line 47 letters ; bow many letters does the whole page contain? 66. In 264 dozen of wine, how many hottlea are there? 67. A gentleman dying gave orders in his will that his fcr- tune shnnld be equally (livided among his five children} eikcSi received §648; how much money did he leave? 68. Suppose that there were in the parish 896 houses, and that eacli house in the parish contained live persons ; what would be the population of that parish ? 60. A father has live children, their food and clothing costs him two pence each per day ; how many pence does the fcupport of the children come to in the y< ar ? 70. There Mere in a garden eight trees, and upon each tree there were 268 apples, how many apples were there upon all the trees? 71. There were 4768 geese plucked, and 17 quills got from each goose ; how many quills were got from all ? 72. There were 27 desks to be made for the school, and each desk required 29 nails ; how many nails were required for all the desks? 73. In a school, there were six windows in the boys' room, and four in the girls' room ; in each window there were eight panes of glass ; how many panes of glass were there in all? 74. I knew two boys, one of them was lazy and lay in bed lill nine, the other was an active little fellow who rose every iMorning at six. how many hours did the active boy gain in a year that the other lost ? 75. How often does a clock strike in a year at the rate of 156 times a day ? 76. How many pins may a boy point in 6 days who works 8 hours a day, and points 16.000 pins in an hour? 77. A gentleman bought an estate containing 6,968 acres, at the rate of $26 per acre ; how much did he pay for the estate ? 78. How many miles will a person travel in 34 years, sup- posing he travels 9 miles per day, and there are 365 dti/d iA the year? # 23 I lines, and vbole page there? that his f^r- Idren ] e^cli houses, and sous ; what 3th inj^ costs ce does the ^1 3n each tree J le upon all ^^ lis got from school, and .^ ire required | boys' room, /I [} were eight | here in all? | d lay in bed -l rose every t loy gain in a \ 1 the rate of s who works ; 6,908 acres, pay for tho 4 years, sup ! 3ii5 ^uyd lA SIMPT.K DIVISION. Division is tlie method of finding how often ona uufnber is contained in another. Cask I. — When the Divisor does not exceed 12. Divide 252 by <;. Rtri.K WITH ExAMFLK. — Put tho nnmbf^rs down n>,nr^ iiccordiujjj to the aniu'Xf'd exatnplo. Find how often * the fip:ur«' by wliich you are (o divid \ viz. ♦> is T^ coiitain(Ml iu the first, or first and second (ij^urt'S ; thus, i] in 2. th* re are none, tlien (> in 25 : th t 10 u u n it: n m Case. II. — When the Divhor i> a Composile number. Divide G7S9 by 28. two 4)(;78D 7)1 (-"1)7 remniiis 1 212 remains .M RuLK WITH Example. — The factors that produce 23. are 4 and 7 ; 28 divide then by 4 and by 7 as in the example. The quotient foinid is 242, but with two rcnniinders. viz.. 3 ;ind 1. To obtain the complete remainder, multiply the tirsf divisor, viz. 4. by the last remainder, viz. 3, and to the product add the first remainder, viz. 1 ; — thiu--, 4X3-f-l=I3 the true remainder. 54 72 1 08 \:vi Hi 40. 426'! 78 41. 743(187 42. 96S718 43. 6748(17 44. ^43007 46. 426156 16 46. 368745 18 47. 246876 24 48. 784978 27 49. 20-l()76 36 50. 43H876 49 61. 49G876 TO 54. snirLF. mvisii^.v. ^ (14) 687G400 or 12G0()02 68023 by 5 It* r) — 0. «) • - 10 — II — u e nnnihei-. 89 1)7 re in III 119 \ 2 remains ."i C^iJts III. — W'Acn /?//e Divisor contains several JiQUreJi, Divido4317C9 by 528. 528)i:U7,C9(S17quoUenl. J 22 4 528 40S9 ofi'JG oDS rt-maliider. IvOLK WITH EXAMPI.K.* — Put (?i»\va the Slim in this lonn. Con- sider whether ih^ divisor, viz. n2S, ia contaiiicd in th«; lirst three ti;iitres of the dividend, viz. 431 ; v»Hi Fee ^t once tluit, it is not; iiiark oft' then four liffiires, viz. 4.517. Yon are now to find iiow often ;V.\S IP. contiiiiifd in 4:517 ; for this {.lirpose lind liow often the tirst ti>(>ire of the divisor, viz. 5, i.^ con- tained in the tir^t two (ignre:- of tht' u'vu]«Mid. viz. 43. It is ivMUitrtined 8 times : put the 8 on the oppusiif .-"mIp of the divi- lilcnd from the - 72 '- 1 ()9> !_ 1 32 •- \U yL Divide 7423G by 42 43 44 45 ,>3. 54. .>5. 5(). Divide 7423G by 46 67. 689 58. 799 59. 410 * TltiM is r.allier a difliciilt R»ile to understarnV and I think jout feRclu'C coiil''. explain it to von, by iti«>ans of a black board and a bli Jt-S' cbiilk niiicli better than 1 C!»n liojio to do by jtny wiilton e'S|,1iinft ?if.n ; y«t„ if jcu pa/ atientiou, I (shall do my letit to niiikc you tudtr i I m § I I I 26 SllirLK DIVISION. Sijt ml E "t T,l Divule 8710:i by (111 7(1. 8I278(^ ,,*, 7« :;i2 ;);i;s-i:f „ *, ;)4«) :.K I 78. 4..0i07ii „ *, 4:;b 7i)H 7!). (Mli;S7!) * ()1K 2i(; Hi). iiK(;ii»7() 1 * 1 bO« ;5r)7 M. 2^7o;'H7 Go7(! r.IH .Sk 4i)7::s;)-IS «! ., 4L'78 7;;{; S"). 71i;>'(ill — i— 2. SCI •MS .sd. 8.-.7 vSS. 7s(!n'^(i —1— 7110 ri-ji ^\). .3()i»2(;(i2 8(»au •KKl !)(). 402i*2(il 9 MOO 2. 63. (M. ()r>. C(). 67. 68. 69. 70. 71. 72. 73. 74, 75. 92. Divido six millions P(>von hniwlrod aiHl ninety-four Ihoiisanfl. by lour liumlied and eighty thoaTaad six huudred and nine. 93. Divide £79ni8 mnonjif 271 porsons. 94. What is the ninth ol' ,C(;t);^7 ? 95. A sliip sailed in I'onr weeks 12(;2 miles ; how much is that per day ? 96. If a ve^^pel contains (IIS rrallons of water, how long will it take to discharge it all, at the rate of 18 gallons au hour ? 97. The popnlaiion of Irchind is about eiiiht millions, and Ihere are ubout ;il)0.(() sipiare miles of huri'aee ; liow many persons to each iiiilc '.' OS. The fiittn is iilioiit '.)'.) millions of miles distant from th«? enn ; how manv days would a liorso i;ji<(> jn y aciiing tlio sun, supposing he went at the rate of la miles per day ? 99. The r;iys of li;;!)! eome IVom the sun to the earlh in ^ minutes, or 1!'") seennds ; at what rale does light move per eecond, the distance IVom the sun to the earth being 9517.0000 miles ? 100. Th(» cireu!iir<"*(>noe of th(* earth is a>)or(t 2.'0(^0 miles : Ijow long would a man take to v.':ilk round it at the rate of 27 miles per day ? sont oth( thir T tlie liiiis llUlll T into BJIOU by t apph cqiia A ratoi A meru A and or J A tioii A writi 6 ma 10 tl by n (lenoi by tl 27 78 4 lib 1107 ln07 7410 DOOO 4o00 linety-four IX liuudred >w mucb is how long gLiUons an ill ion?, and liow many lit from the ins the sun, - V r • carlh in ^^^ t move per ;1.»5 178000 "000 miles : 10 rate of 27 I FRACTIONS. A FuACTTOx is a part of anytliing, and is reprc- sonteil l)V two iininhtTS, one above the line and tlio otl)er below it : thus, |, J, |, — read cue-half, two- thirds, threc*foiirths. The fijrure above the line is called the rrdmerator y the tiji^iire below the line is called the denombuitor ^ thus, ill the fraction J, rend four-fifths ; the 4 is the numerator and tlie 5 is the denominator. The denominator marks the number of equal parts into wliich the wh^olo is divided ; the numerator kIiows the number of those intended to be expressed by the fraction : thus, if I say that I have f of an apple, 1 mean that the apple was divided into three equal })arts, and that I have two of these parts. A Proper Fraction is that which has its nume- rator less than its denominator, as ^, |, 4- Ax Improper Fraction is that which has its wm- nQV'Aiov greater than its denominator, as J, J, |. A CoMPOuxD Fraction is a fraction of a fraction, and is expressed by two or more fractions, as f of |, or \ of f of f . A Mixed Nump,er Is a whole number with a frac- tion annexed, as 2|-, 4|, ICJ. Any whole number may be made a fraction of by writiui^ a 1 under it for a denominator : for example, 6 nniy be made a fi'action of by writinj^ it thus |-, or 10 thus »j-*. The vjdue of a fraction is not altered by multiplying^ or dividinjj: both the numerator and (lenomiuator, provided botli be multiplied or divided by the same number. 1 w ;t; 'I :i M 2S DECIMAL FRACI'IOXS. A Decimal Fraction is a frattlon whose de- nominator is 10, 100, 1000, tVc, or a unit with as many ciphers annexed to it as thrio arc figures in the numerator. Thus, j^, Z/^,-, f'jVc, ^''^' decimal frac- tions, nnd are usually written in this manner : .5, .25, .325, the denominators being omitted ; biit a point is })laced on the h^ft liand to distinguish Acm from integers. In reading them the first is called 5-tenths, the second 25-hundredths, and tlic thircj o25-thousaudths. When tliere are not so many figures in the numO" rator as tliere are ciphers in the denominator, ai many ci|.)hers as arc necessary must be prefixed : thus' rs =-03 and j^^o -^.OO'S. Ciphers on the left hand of a decimal decreast iis value ten-fold : thus, 5 is 5-tentlis ; .05 is 5-huii- dredtlis, and .005 is 5-thousandths. Ciphers on tho right do not alter the value, for .5, .50, .500 are the same as y\. j^^\, fVA. ^^^^ these are of equal value. bo ADDITION. Rule. — Place the nnnibrrs to be added r-o that the decimal points be directly under eacli other, and add a? in Simple Ad- dition. Insert the point in the answer directly under the othei points. Add together the following numl.'crs : — (1) (2) (3) 2.13 48.27 820.71 .426 9.042 2.006 21.2 712.417 84.213 7.03 41.007 217.072 C40.072 .9G2 9.341 It ihp plio Are of t DECIMAL FRACTIONS. 29 4. Add 4 231, 72.G2, 920.7i. .0;J74, 37C.05. 5. 723.812, 91.0006, 2.0251, 3724.7, .00007. 6. 37.214, .73(1. 7213.01, 123.47t), 21.0743. 7. 800.273, 498.0009, .290, .0071, 42»l0.008. f. 320.492, .23U87, 970.00C 9.08G, 41.7(i2. SUBTRACTION. Rui.K. — Place Ihe numbers us in Addition ; subtract as in Simple Nun)b(M'?>. and insert the point undor the other points 1. From 72.378 take 4.8G1 2. 9.007 .902 3. 41.217 7.0i)(;8 4. 29S.012 .9999 i. K-IO.OOl 170.98 Ck From 279.71 2 take 97.0076 7. 72.0070 1.973 8. 900.005 89.1171 !). 243.21 .9G4213 0. 4ti2.00()8 134.791 MULTII'LICATION. Rum:.— A5"r;in<,'e the I'actors, and multiply a.", in Wliolt* t^nmbcrs. Iteckun the nnnjbcr of decimals in both factors, «n;l point o!l' as many from the li.^ht of ihe product. When the nnnibor of fit^nreB in th(! proilnct »?! not so many as (he Bnml)er of deciniah in both factors, as many ciph(;r3 as may be n('ces.^ary to make up thu d-.'nci' nc-y must be placed at th« left of the product. Multiply 7.4 by M'i. 7.4 .35 370 Multiply .045 by .03 .045 .03 .00135 lu the above example there -^Jy'jQ are five dcclraal plac«!8 in the I factors, and only three figures In the above example there ! in the product ; thf.'refore two •ro three decimal places in | ciphers are placed at the left the multiplicand and mnlti- of the product to make the plier ; therefore three fijjnres are pointed off from the right of thL' product. number of decimal places in the product equal to those in th'j factors. k. W W m f 30 1 ii iti u } DECIMAL FK.VCTIOXa. 1. UuU; .27 by .27 7. Mult. 2300.7 2. 4.21 3.11 8. 704.23 S. 97.04 80.03 !). .780 4. .4102 .1004 10. 4.802 6. .700 .800 11. 200 03 6/ .871) 10 12. .00070 • DIVISION. by 18.003 i .0007 100 .75 .002 1000 tllKlC! ' n.'i III ;; riphi RuLR. — Dlvido as in Whole Niimbcrs. Poini off as niaiiy decimal places in the quotient, as the dividend has nioro Hum the divisor : if necessary place ciphers to the left of the quotient. If (he divipor has more fijjiires than the dividend, i\Cn\ ciphers to the right of the dividend. When there is a n'mainder the quotient may be carried to any degree of exactness, Oy annexing ciphtrs to th* ren:iainder. 4 Divide 4.7614 by 3.8. 3.8)4.7014(1.253 la this case the decimals in the dividend exccvM' those in ttie divisor by three ; three fig- ares are therefore marked oil' in the quotient. 1. Divide 0.74 by 2.34 2. .490 .278 JV 7.6 .734 4. 7.23 4.00 5. .024 .001 6.t 29.0 10 Divide .7041 by 4?.. 42).704'1(.0182 In this case die decimal!^ in the dividend exceed those Id the divisor by four ; a cipher is therefore prefixed in the quo- tient to make four diciuial places. 7. Divide 721.1 by 38.07 8. 82.03 9.000J 9. 7.(i24 2.001 10. .6213 24121 11. 31 .1210S9 12. 3408.9 lOOO i If nre h'>gi each «hft • Tn order to mnlliply a dccimn! hy 10, rtrnove the point one figur* to the right; if by 100 remove it two.plllC(^^, and so on. f To divide by 10. 100, &c., reitiove the decimal place of tlie dtvidead •s maoy plttced to llie Irft as there ace ciphers. Id i 1 rile I I :RCIMAL Fll CTli'NS. 91 )0.7 by 18.003; 1.23 .0007 U> 100 !r,2 .75 ► 03 .002 07 G 1000 nt off Jis many h-nd liaa nioro I (ho left of the dividend, add may be carried liphtrs to Ui« ;ii by 42. (.018U lIig decimals in xci'cd tho? reduce nvmlwrs of a fotvcr (hnomiiiatiun to the decimal of a hiij;hir. jluLK. — Write thr {jjivon numbors. if more tlian one. direcLlf niidcT <'ach olhvT, bc-^iiiriinjjf with tlic b)\vcsl. and divide by «fl many of tin- lowur as nialcu ont; of th(3 higher, aauexiug !r.iphoi's if ni'ccs,-;ary. Rodiico 12.V. 'U. to Ihe dcci- R(duco ICv. «./? to the d»- ii^j:innincima1 of a cwt; 6'. Reduce 4 feet 3 inches, to tlie decnnal of a yard. 7. Reduce 2t) min. 31 sec. to the decimal of a week. 8. Reduce 5 furlongs 3 pol(>s, to the ueclinal of a mile, \). Reduce Aid. to the decimal of a guinea. 10. Reduce .') dwt. 12 grs. to the decimal of an ounco. 11. Reduce 2 roods 12 perches, to the decimal of an acre, 12. Reduce 17 yards., 1 foot, G inche.?, to the decimal of a r.ile. t 19 I>rXiMAT. KKA^.TlONdl. i I In m To find the vuliit of a tfccimai. JliTt.K. — ^Fiiltiply tli(» (lt!clmul l»y iva niuny of tlin nnxl \owf.i dcnoininiUioii us inako one of the f^lvop dniuiuiiiutiou. Point off, from tlio product, us many (h'cimiii phlc^^s i\h are in the ProciMMl tlnis t(] the Iclt of tho poini «iven decimal. Proci! The fi^urcH on dccima!. H( Iow(!rtt tlonomination. itH uro thu vuluu of iht What is the value of .427 of Ik pouud ? .427 20 8.0 4« *6.4«0 4 What is the value ot 243 cf a day ? .243 .24 6.832 (0 i'XVi'lO (iO ^liifi. i hn<. 4'J iii'n. 6/5 ».ri. 1. What is the value of .7C:U/.? 2. What Ib (ho value of ..'IlliV.? 5. What h the value of .007(!/.? 4. WHiat is the value of .701 cwt.? 6. What is the value of .l»;)(t Ihs. avolrdupoIiiT 6. "What is the value of .007 ton? 7. What is the value of .7:J2 shillinj^? 8. What is the value of ,071) crown ? 9. What is the value of .0218 day? 10. What is the value of .40() yard ? 11. What is the value of .079(1 mile? 12. What is the value of .7.32 lb. troy? 13. What is the value of .9^^7 oz. avoirdupois? 14 What is the value of .087 oz. troy? 10 What ifi the value of .779 llw. avoirdupoia? I '! ■] i pi. 83 DECIMAL CUllUENCY. The coins now circulating In CauuJii, are : 100 cents = 1 fiO cc'HtH = A 25 cents =: J 20 ctMits =3 1 ID c<'iits = 1 6 cunts =r IJ 3 coiUh = 1^ ptMlliV. 1 cunt =r= ^ piMMiy, dollar. (lollur. dollar. Hirtllin^. ITalifLix Currcncj. BixHt'ii'jo, P'.'llC'^ It nearly, uoarlj. The Units of the United St rites monry im* : Mills. C: iitn. IJ'i:i"S. 7WA/r.T. and Kagh^ 10 mill:} rt:: 1 OtMlt. 10 Of'iii.s = 1 tli.'nc. JO (linicp or 100 centH, = 1 dolliu'. 10 i.\ duilarn. The dononiinations commonly ir-iod in bnsiness are dollan and cents, thns (54 (•afj:lrs. 5 dollars, W dinu's. 7 o<'nts. 5 nilllf^ are more hiinplv written and read a,■^ (I lo dollars. Ii7^ cent?. The Rui.K for workin;:^ in the D"cimal Cnrrency is th<» same as in Decimul Fractions. \\\ Addition and Subtractiojt he careliil to arran^(! the deeimal points niuh-r »'Heh other, then add or subtract, as the case may be. as in the Binipl* Rules. In MuKiplicalion and Division work as in the simple Ru]r««^ point oil" the (h'cimals ; then. wIkmi the rrholf sum is com- pleted, throw away all the decimals hut the two on the right iftnd of the point ; the fii^nn'S on the left side of the poiat will be dollars, and the two on the right will be cents. EXERCISES. 1. Find the Pum of $100.72.\. $2").0'>. and $110.49. 2. What sum should be paid for a hat at $5.87^, a y**H »t $3,181, and a pair of shoe:? at $2 (.2] ? I M i II i SB m W k I u DECIMAL CUKRENCY. 3. Find tho sum to be paiil for a lot of grocfrios at $13.37^, a qiuirtur of buef iit $7, a barrel of llcur at SLiiO^, aad a lot of butter at $2 Oiij. 4. How iniieii sliould be paid for a quire of pnpcr at 25 cents, % bottle of ink at 12^ centi'. a dozt-n of books at $1,184, J^nd a bunch of quills at 374 coats. 5. Sold a barrel of suoO, 510 and 090. Bv resolvinpr each iuto its prime factors bv the last rnle. W we fisid ');n' 330 — - 2X3X5 X 11 510 — 2X3X5 X 17 390 = 2X3X5 X 13 rbe Factors common to the three ^iven numbers are 2, 3. and 5. The product of 2 and 3, 2 and 5. and 3 and 2 are also common measures, and 2x3x5 = 30 is the groate«t tommon measure. 1. Find tlie greatest comraon measure of 252, 180, 28^ 2. " " " 120, 141, ](;?? 3. « " " 210, 3.3(5, 432 1 " •• ** 392, 604, oCO 604, 5(i7, (130 33(), 688, 756 288, 480, 672 4C0, 1035, 1150 620, 1116, 1488 42, 210. 12r that contains each of them a number of times ; ;';:i^), 13 Ls the. least common multiple of 3 auiJ 5. Tc find the Least Common Multiple. • it LK. -Set the numbers in a line, find divide two or more <*'{ tiiem by any common measure. Set the quotients and the lithiioidid numbers in a lino and divide as bcfon;. uJitil no i.vo numbers in the lo'.vost line can be divideci. Multiply the iliv-fiorii and tlie nnmt>ers in th" lowest line toijether, for tht least common multiple of the pjiven numbers. ExAMeLK. — Find the least Coiomon iMultiple of 7, 13, 2% \Z, 2i\. 18 and G. Thus, 7)7 .10. "n 13" 28 .42 2f). 18 6 C)l 13)1 4 4 f) ~1 2() 2B 18 3 6 1 2)1 1 4 1 2 3 1 1 1 2 1 1 3 1 ■^L'jri 7X^>Xl"X2XiX3=!i5r)2 the least common multiple) dial is. fj5o2 is the smallest number that ia divisible by all fiiV given numbers. i. Find the loost common raaUiplo of 4, 7, 9 and 2\ 3, 9, 12 and la 4, G, 8 and 10 6, 4, 12 and 20 8, 7. 10 and 14 6, (), 10 and 24 6, 10, 13 and 24 2, 7, 13 aud 15 fi, 7, 2 and 17 11, 4, 5 and n 1. 10. (< (( a II (t (I 4t n »t (( ({ (v (1 U u u u t* u a ti << 41 u M t {"■! « VtTLGAR FRACTIONS. ON CANCELLATION. CancolIaMon is a method of shortcnini]^ ArillimtjtlcAl operations by omittiii!^ or (laiicelling common factors, and arises out of two priiic![)Ie8: First. — Tho cancelling of a factor ia any number is equi- Talent to dividing by that factor. Second. — If the dividend and divisor b(>= 4X0 and I8::=2x0, thi'U arrange the factors of 18 under those of .')(», thus ftfter canc'lling the common factor 9, it will only remain to divide 4 by 2. 30 2'X^ ExAMPr.E.— Divide G0xl"X'2CX'>G by 13Xl28x3JXoO Arrange them thus — <^0 X J/7 X ^^ 7 X $^ 7 xt X xn 8 X U x^ X 30 8 Proceed thus — 1?> will divide 20 twice, cancel both, and plat?* th(» 2 over the 2<>. This 2 will divide .'VI seventeen timejt. cancel both, and plac' the 17 under the 81. This 17 will cancel the 17 in the dividend. 20 will divide (50 twice, cancel both and place the 2 ovrr the (iO. This 2 will divide 128 sixty-four times, cancel both, arid plact; tho ('A urider the 12vS. Then (54 and r)(5 are each divisibh? by 8 ; 5t5-~8=7, cancel 6(5 and place 7 over it ; and (Sl-j-8=8, cancel G4, uud place the 8 under it. There are now only 7 left in the dividend and 8 in the divisor ; therefore 3 is the answer. It will be generally found convenient to arrange the dividend oa the right side of a vortical line, and the divisor on the left. VULGAR FRACTION'S. 30 tlimotic'fti I factors, cr is eqiii- flivided hy 1. 18 2 X^ 8 . and pltw«» ,een timen. lis 17 will ice. caned divide 128 cr the 12v«. =7, cancel , uud plac»? e dividen> the required answer. Note." .V careful explanation of the process of cancellation by the teach'T. at this 8i,a;;e, will save much future trouble, and greatly int<'i--'st lh(j pupil. The followinu: examples ap- pear mort! ]-[2X9]]X[l2f30]by[5X8]X[2X9] X [104-17]. n. Find the quotient of 210x141X10 divided by 175X 66X27. I ^i f ii^t; I! .ii'li' I ll tim ; P I if ' I'j 'V > 1 M id VULGAi; i'RAOriO.VS. REDUCTION. G\ier -iG j to au iniprn^)er fraction. 6 2;i0x3=:3^,'' Rofluofe the following mixed uumber.T to their equivalew iwiproper fractions : '*• 4 J 7 TOB 2 8 3H4:i 7 :j <^ 2 t T> 4 3 10 8 7 ♦•) 3 4 f 4 06 8 15. 7i IG. 8} 17. 174 18. IDJ 19. 27^ 20. C47,^^ 21. 3(i0|; 22. 9703,5 %\. H42ij 24. 084} 5 25. 976,2^ 20. 843 jVr 27. G87^Vf 28. 709,'.J» 29. 807^1}. Ill TUI-GAR FRACTIONS — REDUCTION. 41 I Cask III.— Ta reduce a compound fraction to a simplt fraction. RuLK. — Mnlti])1y to*oiher all the nnmorators for a numera^ tor, and nil tlio denominators for a denoiuinator. ExAMPLK.— Roduco the compound 2xOX.'5 3X"7X1 fraction § of Jj of 5 to a simple frac- -^j^ZlZ T~'ri ^^*^' tiou. Rednco tho following compound fractions to their eqniTa lent simple ones : — 35. ^l of 5 of ^ of 13 30. 3 n^ 2 of ? 31. 7 3 '6 ' • f i S • • in 32. 5 17 1 ft •21 33. 4 !) tf • • IT 1 1 ' • 12 34. 7 «_ i T • ■ i li .. 7 36. 1 2 1 7 • • 1 8 53 . . 19; ^7 t 1 17 135 ..24 O 1 , 2 1 • • 3 6 • • ^l 38. If • • 2!) ^8 .. 32 30. 7 T5 • • 1 3 21 3 1 . . 27| Case IV. — To reduce a fraction to its lowest term.n, Rni.E. — Divide the numerator and d^'nominator by any nnnv- hor that will measure them ; that is. that will divide them without a remainder. Do the same with the quotients as lonjf rf« any number can be found to divide them. Reduce JfJ to it3 lowest terms. Divide the fractions and \be quotients by the fig- ures placed above them. (2) (2) (.3) (2) (2) 14 4 7 3 ;if. ^2 fi _ 2 4 5 — r '2 6 3^ 2 i 5 " Ans. Or, If a nnrabor be wished for that may brinff the fraction t» its lowest terms at once, divide the greater term by the lej??, and the divisor by the remainder; and so on. dividing each divisor by the last remainder till nothing n^niains. The last livisor is the numb<'r by which, if the numerator and deno- minator of the fraction be divided, the lowest terra will h$ obtained. m ilr i. u f. 43 VULGAR FILVCTIONS— RKDUCTIOX. iiii. J !5 ' Reduce ^4^ to its lowest ternH. The denoniinai^or of the fraction heiiip^ 14i)2'J0«l •h;; 114(1 !)6 jrreattM*. it is (li\ itl e divided \>y Ihc icinaiinlci'. 9(1 ; the re- niaindiT. 4S. is now to divide the foinuT divipoi'. '.)(». Thi' Iuki divisor. 48. is the iMiinlK-r by which, if tlie innncrator and dononiinator biMlivid'd. the lowest term will be oblaiu'.Ml : thus, 'iy).;^;^, ■^= l> as in former exnmplo. 48)00(2 Reduce the following' numbers to the lowest terms : 40. 41. 42. 43. 4iL 2 1 -2 4»i I Iff 1 in 1 60 44. 45. 40. 47. 74 af.is 48. 7C.4 41). f)4 4 1 1 ''1 6 50. 82 5 VO2O 51. t :.'4A 2 "? » ' :<4 4 "> .". '.} S > 4 ti :t 1 offi" Case Y.- To reduce fractions to a rommou (ituomlnator Rule. — Multiply each numerator by all the denom'npiton except its aim. for a new nuini-rator ; ami multiply all th denominators to and 7 tlis' deno- 8X-^X7= fi8 a nu minators ol' the other fractions. 4x;>X;")= CO ) Mark, that it is m.t multiplied JO<"ox v=T05 com. denom by its own denominator. 3. The same is done to the other numerators. The answer then U 7 V »! :< 79 5' Tos- co '«r. Reduce the following fractious to others having a common leuominutor. 52. 53. 54. 55. 2 3 41 5 7 ^■> 8' ^_ JL TP 13' J 3 I ! 18' ?3' and and and and 11;. 1 T e;A 17 in 15 n-nA 13 • 2l" 26' 4 2' ""^ TV 4'i „„fl 27 and 57. 58 21 1 a 4 1' srr : I _;? !' 4 10 BT' 26 i'r ^o i ' nq Kis 7J0 7»''J .^,1 <^^' 45 i' 5^2f'0^ j' *"^ ■BfTr H.I i -■ YULGAR FRACTIONS. 43 lamina for ADDITION. RirLF!. — Reduce compoiunl fractions to simple fractions, and mixed numbers to improper fnictions. Tlavinjrdone (his, \)T\iv/ ttu'm to a common «lin<»tuinator. Add ull the numera- lorH tojjethcr. imO , luce, undtT tl)e result, the common de- nominator. If tlie answer be an improper fraction, bring it to a mixed number. Add together the followin;:; fractions, -3, j, and 4^. Ht'vo the mixed number 41 is 2x'^X-= first brouglit to the improper ;'>x'!X-= Invctlou !|, and then all ili" frac- Ox'^X-''^^ lions an* brought to a comtnon nuraeratorf denominator. Therefore H -f i^ -f 4. 0. '^X''X2= :iO com. denoni y^P =5J^j; sum required. Add togetlier the following fractions and mixed numbers. 7. f of ';-i-A-\-^ of 3 8. 2 I r? I 4 5T-5 I >» 4 11 111 8 7 11 ;iii4 I ?r» IT I i 1 1^ I 1^ 1 2 I _B _L.li_i_ I 1 4 1 3 i^ '2 ;< "^ i "J 1^ :'. ^ 2 1_1_4 1171 i-''3 %2 T^5:j i^eo I 2 3 ^+Aof {?+^of5| 0. Yl of 7i|of ^+^'of H 10. q+ilof2^-f-;|ofG| 11. {;of^;;ofi7i-h*ofi2 12. l^H>f^^+^iof8;} fS lumeratop SUBTRACTION. a common RuLW. — Reduce the fractions to common denominatorj?, as in Addition. Find the ditfrrence of the numeratois, under which write the common denomiiuitor. From {% take *. Here the fractions are first 12 X brought to a common denomina- tor, tiien the (lO taken from 84, and the common denominator K-ritten under tl)e difference. numeratom 7= 84 4 X\r>=z 60 l5X 7 105 com. denom. Therefore ^^^ 6 1 u5 _ S4 the answer. W ' i 44 VXM.OAll FRACTIOXS. a. •' ?''i *• "What is the diff"onMico lietut'on Mif rollowln"; fractions? i. o 3. 4. 4 I i 7 3 i 3 I 7, I 3 .'J. fl I It I 7 5. U - - ,°« 0. 07 -51 7. -'8 - 8. 0^- _ \ 10. 9 1 f I I if 11. 1(5:) ~ ir^ 12. 70; - J of r.) MULTIPLICATION. RcLB. — Reduco tho mlxoor fi'jictiom, tills has been e numeratoi er lor its d« DIVISION. RuT.K. — Proparo tim fructiona as in miilU plication ; thor iavcrt the diviaur ixiid prococd as in multiplication. Divide ^ by J. 'ij-r-S inverted tlius 4x5=20 7x3=21 I. Divide 2. 3. 4. 5. C. V by 1 ! i i 21 80 tV U J ii 3 iff \2 4f 1 B 56 1 4 9 1 7. 8. 9. 10. n. 12. Divide ii^ by ^4 8 5 T 11 iof7 11(),V iof5} § of ^ by i of g RF.DlJCTrON, CoNTLVUKD. CVsK Y[. — y*? reduce fnictiont from one dcnom'mation to aiiOiker. 3 rtf 7 .:_ !4 S '-'^ * — '24 •=3!|f Tim fraction tJ*- tiplif^d, pro ; reduced if! ons. X f of -3 X i of y«^ X 15 of 1\ rX liofOj R[;i,n. — If from a lo'.vor namr" to a liiijlior, multiply the dcnotainator, as in rtsluctioti of wholo numbers. If from a liio:!ior natnc! to a lower, multiply the 'numerator as ia rciiuotion of whole numbers. Reduce | of a farthing to the fraction of a pound. Here the denoniiriator is multi- o 2 nlie.l, as it is to be brought to a ~^,^.^^o(\ ^«^ higher name. 3XiXl2X20==28bO Reduce f of a pound to tlie fraction of a penny. Hero the numerator is multiplied, as ^X20X 1L=72Q it is to be brought to a lower name. 6 6 i;^ i 16 VCI,GAR F^.ACTI()^^S - nKIU'CTION*. 1. Rod HOC 2. IloJuoo 3. K 01 luce 4. lloduco 5. R«uiiicc 0. Jioduco 7. Kuduce 8. Reduce 9. Reduce 10. Reduce i) of a r.utliinj]; to lli»^ rimtion of a pound, * of a |»')und to llu^ fi'aiMiou of ii penny. I of a sliiiiln^ to I ill' fraction of a jjjuinea. ^ of a rtliillin;^ to tijc fraction of a farthing' I of a fartliinij: to the fnu^tion of a crown ,^„ of a day to I lie fraclioji (tf a week. I of a week to llio fraction of an liour. ^ of a nail to the fraction of a yard. I of a cwt. to the fiaction of a dram. I of a yard to the I'raction of a niilo. in' Case Yir. — 7\; cxprfisfi nnif f:^ivf'n fffntnli'ti/ a.t n /taction uf\ another quantUf/, coufiidc/cd as an integer. Rcr('i)c<' ; the pence in the iiilcger. 210, is made the drnoniinator, and the pence in Uic oiher quaatily is made the numerator : the fraction. I (I u of /. •JO n L'lO a pou nd. ip. when l>rou"rht to its then ino. 2 4 (1 ' 13 12 itid Ans. lowest terms, equal to 3 of a pound. 11. Reduce 145. M, to the fraction of a pound. 12. R'duce 17s. \d. to the fiactioii of a pound. 13. Reduce 5.9. ^\d. to the fraction of a pound. 14. lieduce 17."?. 9t/. to the fraction of a penny. 15. Reduce O.v. 74^. to the fraction of a farthing. 16. Reduce 7 hours 21 minutes to the fraction of a day. (I pctuinl, jtouny. a j2;uinoa. II larlhin;; a crown week. liour. anl. Irani, [iiilo. VULfl.VU rUACTIONS.— RKnUCTIO.V. 4t 17. HotliiCL' 7 11h. .") (Iranw to t!»o fraction of a cut. IM. Il'.'iliico 8 c'.vt. 2 qr.s. 1 1 Ihri. to tlio fraction of Xj Oanoe. ID. Ilctliicfj .'» lbs. 1) u/. to (lio fraction of a .Ivvt. ji). iVifluoo 1<) iioui's l;j miiuit'.'S to the fraetloi. A '■, il".y. C.vn VIII. ~7\) find Ute vJuc of a fra'Uii.n. l!i i,K.— RoT tiiti (li'MorniiMtor : nMl;ic(» Hk? riMiiaiiu'.'M', if uuy, It ) ih-' ir:xt loT,'(.'r naino, and divide aj^aia, and iio on tr) tlw jlo'A'i'JiL naiiu!. What is tho valuo (^f \ of a j.<)ui)d siteillng ? Hto tli'» nnnKTiitor. 7, is rniill;])lird l\v 20, 7 //•a(,'^/*»N <>/ Hto liiinii: it to liic ih'.\t, iidV-ri.)!' iiaia •, I lOv. 1:0 |Tli'' 1 IOn. art; (lis idt'd l»y S.\\iii(!l! ;riv<'.-; I7.v. and 8)1 !(• 4 wf a PMiiaiiul r : the I is in;illip!it'd hy I'J, -^j t'l hriD'j: it to tli" ii".\t iiiCcrior nam!'. '18,'/. ; it " •^vr. lation ; tbfiii id tho olbtT s. rf. 13 4 12 1 i'i^ -I Ans. I. 1. J. 1 of a day. t llicn r ;is may be neces- sary. Point oii* as many dreimal }ilaces in tlie quotient as there were ciphers ann(!xed to the numerator. Reduce \ to a Dcclmnl. 2)10 .5 the answer. 1, Reduce Mo a decimal. 2. 3. 4. 5. 5. \ 7 "8 X a 5 V I Reduce 'l to a dccitnal. 4);;oo o .75 the answer. 7. Ik'duce ,"g- to a decimal I 8. 9. 10. 11. 12. I 1 rt 1 1 3 » 4 2 1 Ca.sf. X. — To Reduce a Deciiuul to a Vuh^ar I'Vaction. Rui.K. — Arnke the given deciin;vl ihe numerator, and place und.'i- it. for a diMioiniiiator. a unit with as manj tjiphors as there are li.i^ures in the decimal. Reduce .5 to a mil g(U' fraction '^^ the answer. 1. Reduce .25 to a vulgar fr. 2. — .025 — 5. _ .375 — 4. — .005 — 5. — .01 — Reduce .078 to a vulgar frao^ yJHy the answer. G. Reduce .001 to a vulgar f i 7. — .41 — 8. — .021 -- 0. _ .007 — 10. — .019 — 12. 13. 14. 15. v:>. 17. \ of a 18. 19, 1 '2~, 1 3.; I'y VULGAR FRACTIOXS. 49 I Decimal PROMISCUOUS EXERCISES. If the fi'acLioMs are of (linVront donoininutlans. it will tx» necessary to hv\n>/^ t.h mu to ihc Hiuno iiuine befaic ihvy are ntlded or KubtracLid. a decimitI>B mixed nunjber r Fraction. 1. What arc the facloys of 39, GG. 72, 84. GP., 18. 35, nd48'? 2. Find the frrcatcd common nipasuro of 84 and 5G. o. Give the lead coinm;)n r:iulti[ile of 0, 8. 15, and 21. 4. What is the qant-LM.l of lGxl8x24x42, divided bv :x8x3Gx48? ). Ch;in<,!,o ih'i impr.jpcr fraclions *"''^", ^| 4 ;' -7 into 0. Chan^li t>f '/ of 30 8. Reduce ?n, ."'i and I!'i:! to their lowest terms. 4 .1 •> ;. I C:?!)" Ij. Reduce 4' 1 ■>.' WW 1 ;? t o a common ucnominator. 10. Add i of a ton to /'., of a cvvt 11. F rom 7' o )f 2 t; ike I o 12. i\Iultiply 2', of :; by 70. 13. Divide | of 14. Reduce i of i 1 ./ C) to a vulgar f. a owt. to a frat'tion of a dram. 15. Reduce 8 houro oO minutes to tiie fnietion of a da,y IG. What is the Y.iliie of 1' of a pound avoirdupois? 17. What is the dirt'orcnce between ^ (4' a lejg>ie. ajvd I of a mile ? 18. Mow much is 8 times ]l of a yard ? 19. Find tlHMv.ult of [104-4]— [r)-f3]x[17-3]x[Gx 7 ] di \ ided by 8 X <*' X 7 X 28. i of ' of •! of I of 20. Reduce the C!)m[)ound fraction 3i; by C iincc Ihiti on. 21, How much is 8 times !| of a pound avoirdnpoi»' 11 ■I „■!?> I .3 50 COMPOUND ADDITION. IvULE WFTir KXAMI'LK. — PlaCO pounds Ulltlt;!' pOUllJn, bllil- Ung.s under shillings, and poiict^ undor ponce. Add {.ha larthin;j;s, and di\ ide by i ; ibf quolicut £ .v. d, in ponc(N the remainder is f';irllnnjj;s and must, bo (iJ 12 fjj put under farthings. A(hl the pence with tlio 8(i 15 C.J la.-sl quotient, and divid(^ by 12 ; the quotient is 14 1(5 f).! sliillin^.s, the remainder i.s pence, and mu.-t be 'M 17 !'4 'o-^) put under pence. A0 IS 4, >7 11 Zkt i: C:^ Vl 42 11 lO.V (1) £ .s. 43 10 05 13 84 12 !)2 11 41 10 d. 4 >> 1 (■>) .£ Of) 72 i:j 10 72 s. 12 17 8 14 12 4 7i ^1 (3) 12 10 4^ 10 4 oi 04 17 2^ 43 12 tJ ('j; £ s. d. 30 13 4i 12 8 Oj 11 19 lol 17 14 ^;f 28 12 Oi- 7. I boii.Tht o"o<)ds r<)r wiiich 1 piiid £!!)>> 10,s. 0*/. ; I paid for pr*eking O.v. 8f/,. for case hi.v. (i<7., lor cordage \s. Of/.. for portei' ago 4.V., fur IVoight £1 1 1,-?. ()^/., for waggon carriage 13,9., for booking 9(/. What was the entire cost (d' the goods? 8. The expi'U'-es of building a liOU'H> was: architect £108, bricklayer £t7t!2, mason £2111 1 0.s. OJ., carjx'nter £27(18 Ms, \)d.. plumber £h')';) 1 I.s.. painter a!id glazier £l;UO lo.>i. H^f/., jKipcr-liangcr £213 18.v. Id. Wiiat did the house cost? •J. A housekeeper paid fur lea £2 \us. 7t/..conee £2 75. S.^t/., sugar £3 14s. ()./.. beef £2 Us. ikl.. nuilton £1 17. (*'>, 14 IB (A :i4 17 H :oi 2 ^\ !ut, as i« .<. d. 1(> 4^ 4 ()i 17 2^ 12 7i 5. d. i:j \h 8 n- 19 10.^ 14 ^;i 12 (5i- ; I paid for .for portoi' go lu."?., I'ur :)ds ? litcct £108, ntcr £-i7(;8 UO ITjA-aiJ., cost '.' £,'l's.^d., 7.S., bam 9.'«. How inucb COMPOUND SUBTRACTION. From £VA Vis. O.]//. take £27 18s. 8^.7. Ul'LR wttii ExAMi'i.K.-- Place the smaller ftiiinlKT under the greater as in Simple Sub- t-acLioii. Then, IJ larthinos from 2 fartbings, laiHiot; add 4 iartbinfj^H (= 1 penny,) to the 2. and 3 farthings from (!, there remain 3, I'lace the '\ under the farthings. Add 1 to ilie 8 : then i) pence from (1 [)ence, cannot, add 12 pence i=_; 1 shilling) to the (], then l> from 18. there remain 9, put [he 9 pence, under the pence. Add 1 to the 18, then V) shillings from 12 cannot; add 20 shillings (= 1 pound) to th<' 12. thcPi 19 from 32, there remain 13, place the 13 under llio hlilliing-s. Curry 1 to the 7 and proceed as in Simple Sub- iirfCllun. EXERCISES. ■ * n * £ s. iJ. -> f ()4 12 t>^ t 27 18 sf 36 13 0^ M £ .lyin<:j Iho fiirtlilngs by 7 ; tlni.'*, 7 times \ are o}i, .set down }, iviid carry .> to th(? p(Mice. 7 tiiiU'S 4d. are 2.^. •'//.. and '.kl. curried are 2,v. Id. ; set down 7 undi r the pence iiLul carry 2. 7 times 12 are 81. and 2 OiPTi(>d iro 8()S., v.'hich is equal to £1 (Is. ; bet 'loAii the (J under the s]iillin,L?H, atid c:irry -i. 7 limes G are 42 and 4 carried make £i'6. riace it under the pounds £ ."c. d. £ . lens, a.nd the units lou,-cther for tlie required answer. For thousands muUi]*ly by 3 tens, and pro- ceed in the Kame manuLr. 43 2 cxa 10 431"' 5 4 172.) 8G 5 12 18 9 £ f. d. 5. Mult. (14 K; 7^ by < 8G J 3 -1.1 ('9 1 G 8. _ (M8 H; 7' ^>( 7 li 1. 10. G58 13 7 GS 241) 478 11. Mult 4(>7 1; 14. IG. G75 r)G3 807 !)8 42 1824 a 9 .1. d. 15 8| 1 !y G47 4^ GOS 12 O^i 78.-» 14 ^ ficMJ 13 8 J 87 16 7i 45 J .5. d. i G 3X^ 10 J 2 0X2 10 1' 5 \ .) U G 5 2 18 9 ?I COiirOUND MULTIPLICATIOJ^. b% Cash III. — To Midtljily hy parts. Multiply 45. Shd. by 4^. If Uio part 1)0 4. take a quarter of the multlplicaiKl. If the ri\rt 1)0 h. take a lialf of tlio nr.jUiplicaiid. If the part by |, itikc half aiiil a quarter of the niultiplicaiHl, or divide the multiplicaud by the under fiijr.rt^of the fraction, and multiply the pro- duct by the upi)i'r n!-!:uro. Add the quotie-it fJuis oblaliU'd to tiie jM'od;:;;t obtained by 18 10 4 8k 4 iTiultiplyin;^' the iniilliplicai'.d by the whole iiuiiibfr iti tlie Muilliplior. Thlb latter v.'ay ai..!>lioB to aiiv fraelionai part. ^ half of lop Uue 1 1 2V £ d. !7. MulL 4 2 (•» 18. — 7 1' 7.^ l.i. ~ 28 V.) 8 0. 87 1 9. 21. — 87 t 12 in f.> ■ i'i'i 1 c 9. 12 11, £ 23. Mult. 7 8 0,1 h 21. — 4 10 3i 25. — 48 17 Ci — 50 14 11 — 70(1 i;i 4k — 80 I 10 0[ y »')( »"!',> ^^). 87} 94^ 20. What do 7;; I'o- of tea come to at bs. o.jfi. per lb.? "0. What do 4 lbs. of butter come to at Is. \d. per lb.? 4. Patrlcd: earu.s \s. Vkl. per day, what does that come* to hi ») da c'J :!2. IjouQ:ht llr" toiis o!" h-.iy at £3 IT.s-. C^d. per ton ; how much did they coaie to? X). A gctitlernan i^'perid 9 £1 7.v. GJ. pf^r day •, how much (I'X'ri he .'^pvuid in a year? oL A f;i;-mer paid iu r'^nt £it() IC.s. G(/. every year; how much did he pay the laudh.ird iu the course of 2j3 y^iirs? ;>5. A carpenter received lis. Qd. per week ; v/hat did his uMXOs auiouut to in a year? 8G. V.'iuit is th.» value of 5G8^- ounces of gold, ,'alucd ai I £3 105. (Id. per ounce ? H7. Sold 8 oxen, and gained upon each £2 llr. 7^d. ; Low I much did I gain? ij ■SX .1 54 COMrOUXD DIVISION. Case I. — When the Diin.'ior dots not exceed 12. Divide £8 12.v. 7.]/M)y G. Rdlk ^yrTlI Example. — Procoed lliiiv, in 6)8 12 7^ 8 once and 2 o\er, sot down tin? 1 I'.inlcr tho 8, and carry 40.v. for the 2/. to tlie 12; Ukmi (5 in 52, 8 times and 4 over, set down I lie 8 and carry A^d. for the •!*'. to ilie 7 ; then (I in 55, 9 times and 1 over set down the \) and carry 1 farthinp;? tg ibo farLbing, 1 a;^ -o <», in (i uuce ; f-ct down \. 1 8 9J 2) 71 16 8: \) 70 12 2| £'S1 8 4 1 £ ., 9 19 0. 50(;o 7l- 10 20 JO. 8(;87 18 1 1 \ 11 21. 11. 4711 11 7'. VI 12. DlvMo £25 10 8^-2 .C .«?. d. 98 11 7:V liy ; 47 i;j CV 8 (17 1!) 8(J4 1 71 ■I 587 M 10.} ;{ii 7 11} ..'000 v^ 8i;8i 11 7010 18 0} :;(i7l 2 lU 87<;2 17 o![ V, r • I 23. A tradesman ]i;ul ia the siwinj^c'' "bank 9(7. IC.s. fiJ ; tbis sum bo bad saved iii 5 vear.s ; bow much did he tiuve on an average each year ? 21. Ten men rented u Iiousl at ?''/. 11^. 8'/. ; bow iniifhls bad each to pay ? 25. A faiher left 42o/. ICv. CJ. to b- divhled cnjially wiaoriii liis ei^ht children : bow mneb Ml-i.U.\D lil VISION. 55 • ' 2''. noii;;lit nino «lo/v'ti boiUtB of wliic, for 'aIiIoIi 1 pu'ul 1:'/. Ms. \)d. ; wlial did I pay per dozcii? 2f). Nino vessds Irnpoiicd goods, valued at 79G87/. IO5. ; what was the avcriigo value of each cargo ? Cask II. — IVhcn the Divisor exceeds 12. Dlvid'^ £0i 75. 8^ri. by 47. RuT.E iTiTii Example. — Divide the pounds as in pimple long division. Mul- tiply the rtntainder, 17. by 20, adding to it the shihii.gs, 7. l)i\ide again as in simple divit^ion. Multiply the reniaiiidcT, IS, by 12, adding to it the pence, 8. 1)1- Tide aguht as in simp!" division ; iriuUiply the rvraaiiider, ?A], by j, adding to it the farthings and divide as bcfcro. Tiio qno- li'nt tin-n is 1/. l.s. \'\iL with niainder. 5 of a ve- £ s. A1)U 7 47 17 20 d. 47}o47(7 329 "T8 12 47)224(4 1_88 4 47^14(i(i5 141 it (■ o remain '. ; how inuf'hi nuallv aiRoniL 81. 32. 37. :i8. Divide 47 78 487 798 080 0^27 70G3 4317 s. Hi lo 10 17 t 14 1(5 4). Hi 8'l hy 28 37 14(1 31;;") 478 042 80(5 718 30. 40. 41. 42. 4 a. 44. 4-). 4(ir ; iiud r ^(^ i 0] , n4. 7:; j n.'». '•17.'', ;''('). M)4 I ;>/ ' ' > ) i re ^i,^^^ (;{ 17 (u hyv. 1 "" ' • •> I i -x *^ 0;i CM ^: 780 0^ 78! [^07 10 10 J 841 l'7y 17 Gi[ DOi 5'). A fanvcr niii. a r::rm ai T;;:/. K'^- Ctl. per annnn! lit) wishes to l:iy j, rent : hov»" inucl; nv.i^L ':■■ ;;;.\c culi wc k li ''\' ly u(rgo town ilicre v.-i r ' 4": ' c}i!!dr(Mi edttrutcr by T/O tcaeberfa ; bow !!!;i!iy inij'i'- 0:1 un avorj|i,-:; to t'Ui.> toacher ^ 02. A inrni'.ifr.c'uv. r y';'.'! 1 in \\\ •sh \^vi\ ?ACL Vs. receive ? were .;i.! wvrS.tiui; L.llcl 1 (I : \.i U,]i !1 fil Go. Tiiere. are about r'i<:lit hundred liiiiiior.:- of people the world, und it !.•< tl-oii^ht that as n.aiiy die i:i o2 yean Uiw many .ti<. *)t. If ."^0 m; J on an av'.')'at;-e in a \''ar ■ (li<' in a year. I.. '.v D.anv d!o in aii Lour, there being 87'J5 lioiir.^ in a yar? ('.". A ])r!ze of 7l';"7/. r;,v. Or/, is to he divided equal') among 500 fr^ailorn ; v.hal. is ee.eli n);in"s ."-liare? 00. A frentleman hv<} an optnic of ']j{;8 acrep. for Avhich her'. c»'ived pvr a!.num ^'7U/. IC.v. 8c/.: how much v.- as it let for p;r acre ? 57 ■j r llEDTJCTIOX. Reduction is tlio brin'/inp; of one (.Icnomination U AuytLicr wiUiout altering its viilue. O.-JL -4 5 51 V4 Si > 0^ 7c^!. 1 10.V 811 %'i icr nnuuni , K Cask I. — ^o bring from a h(,s:,her to a lower* Rui.K WITH ExAMiT.K. — Miiltinlv l)y as £3 limit V of tlio Ic^s us nrakf oir' of I lie p:vt';il(-r. 20 TliU3 to brinpf li/. to sln!liiin;s. miililply 2 by 20, l'-:causo there nre 20a'. i;i a pound. iOs Case II. — To Z^r/..'^ a lotccr to a higher. IluLK WITH Ex\MPi,i':.- -Div:'!*' ny as many »T tiio leps us niukc one ol" the gr'Mlei-, Tims (o briiij^ 40 shiiiin.u'-' to ixiuiids. (ii; idc by 20, l)ccAU5;'j there are 20 Hhilliii'.;,^* in u ^^oir.id. Bring £1 9s. fJ.V/. to iliriLIng?, Multiply the 4 by 20. and add (!) > H.v. ir) the proJuc', thJBwill givi! tlie nninb"!' ; !' -I 'MingH, H''9. Multiply then l)y 12 .\d(lin;>- pence, tills will give tlie number of ptuce ; 107i in 12/. 7*. Ctld.'! 1. In 2ul/. [)s. KW. how many pence? :;. Reduco 3(11/. H.v. 9l<{. lu I'luUiingH. 4. In 217/. ]2s. ny, hovv many IralCpcnco? 5. Uow many ptuco are tlioro in 2iG gaincas? 0. In 2'.i8 crown;'. l:ov»' nuuiy farthing? ? 7. Ri'dnce r-}(i48 j^ixponccs to rarUiinga. 8. In 42708 farlhin.:;^,; Iiow many pence? 9. How many ])Ounils ar.; tlicrc in (;7S00 fhiillng*;? 10. In 'liO.STiJ liu'ihijms. liow manv ponnihs? 11. lIow many (]i;ni:'.<.'a^ are JherL' in 3->789 shillings? 12. In CSV94 nr;:iM\ lio', manv crown?* 13. IIow ma;\v fonvp; net:; ar as? Uing p' eccc* inds? 9 • i2 gull >vnfl ? Reduce the following amounts to their equivalents in Peel- mal Currency. 81. £4 7.9. 8Ar/. 41. £3 t;5. hU 32. G 5 42 42. 4 7 8 33. 7 8 p;^ 43. 2 G 34 31. 6 4 21 44. 5 8 ii^ 35. 3 7 H 45. 4 7 ^ 36. 6 4 H 4G. 3 7 n 37. o 6 4^ 47. 6 3 n 38. 5 7 8 48. 3 7 84 39. 3 G 44 49. 8 9 Ci 40. 4 7 a 60. 3 C H ii- Ht; W' ml 60 WEIGHTS ANT) MKASUUCS. EXERCIS ES. AVOIUDUrOIS WEIGHT. ADDITION • twt. 4 2 6 S qrs. 2 3 1 2 lbs. VI 14 7 24 (1) avt. qrs. 7 3 8 1 4 2 8 1 lbs. 10 11) 27 13 qrs. I 2 3 •> (2) /.';.^ It 24 13 17 oe. 12 1') 7 13 17 2 1 SUUTRACTIOX. etvt. IG 12 qrs. 2 3 lbs. 12 24 LVt. qrs. 17 1 10 2 lbs. 10 27 qrr. 1) 11 A'-. 22 20 0*. 12 li 'A 2 10 tV)t. 4 qrs. IG 4 MT^TirtJCATlOX. G 2 IS 7 qrs. 2 23 09. 12 9 19 2 8 (twt. 3 lbs. 8 DIVIHfOX (7) act. qrs. G)14 2 • Ihn. 17 qrs. l))IS) lbs. n Mr. 6 2 12 9. A tobacronis'-- r«ir»oivo(l K» ewt. 2 qrR. 2r> lbs. of lohr-rcv nd sold 12 ewt. 3 t£is. 20 loa. ; how much luw lie uuisyld ? 'P' WniGIITS AND MKASUKES. 61 10. A brewor boni^ht Ilvo l>a<^? of hops ; No. 1, wcif^boil I cwt. 2 qrs. 14 lb. ; No 2, wci.^'linl 1 cwt. ;i q^^^. 21 lb. ; No. 3, wti^Iit'tl 1 cwt. 1 (jr. 27 II). ; No. -I, wci^-Vii'-d 1 cwt. .'5 qi'H. 2'j 1 I.; No. f), woigbud 2 cwt. 2 qrs. 25 lb. ; what wna tho weight of i\w whole? 11. A p:roc."r sol J l,ho first year ho \\\i^ In l)iisia''.s3, Hi cwt. T (jr.s. 2() lb. 14 oz. of.«n<^ar; th'j thud year ho wa.s in liu.siiirss, li" sold 8 tiiiioi3 as much ; how muc.'i il;d hu s-dl iii the third )''i\r? 12. 7']lr?!it ho?:^:h"ads contained 108 cwt. 3 qrs. 20 lb. of ^iij^ar ; how much did each contain ? Ill A plantation prodnctMl the first year PJG cwt. !!^ qr«. 1*1 lbs. of .sugar ; Lh'j second y<'ar 4715 cwt. 1 qr. 9 lbs. 1.5 oz. ; flic third year cwt. 3 qr."?. 13 oz. ; tli'j lirtli year 737 cwt. 2 (jrs. 13 Ib.s. 10 oz, 13 drama ; how much .sugar was produced on the piantution in Ihcao five years? 14. A grocer bon.jyht 3 Idids. of funfar. each containlr ^; i C'.vt. I qr. 13 Ib.-^. Tliu lirst month lie sold 2 cwt. 3 qrs. It lb. 13 oz.; the second month lie sold 2 cwt. 2 cjrs. 14 c .. lOdrams; tlio third month he Fold 3 cwt. 1 qr. 11 lbs. 15 iraris; how much has he on hand ? 15. What is tlio we!p;ht of 8(1 hhds. of tobacco, each hhd. Weighing 5 cwt. 3 qrs. 14 lbs. 13 oz.? in. Eleven pieces of iron weighed 4 tons, IG cwt. 3 qra. ; how much did each piece weigh? 17. Ten packs of potatoes weighed 10 cvt. 3 qrs. 13 lbs. 11 oz. ; what was the v.'eight of "ucii .«ack? 18. How many parci'ls, each containing 4.^ lbs. can be madt? out of 2 cwt. 2 qrs. 23 lbs.? 10. If 3G bagr] of cotton weighed 41) c ^t. 3 qrs. 13 lbs., bow much did one weigh? 20. How many hogsheads of. sup;ir, each containing 13 cwt. 2 qrs. 14 lbs,, may be put on 1»oard a ship of 324 tons bur- den? 21. St. Paul's bell in London weighs 5 tons, 2 cwt. 1 qr. 22 lbs.; by how mucli does t!ie great bell of xMoscow exceed it, which weighs 198 tons, 2 cwt. 1 qr. ? '1-' - f- if!'.. At' i :, J 1- •; 'i 1 ";i ^ ,1*! J f3 WEIGHTS AND MEASURES. TROY WEIGUT. ML'LTl PLICATION. (22) (2o; lbs. oz. diet. Ihs. yx. dwt. oz. £/t<>^ /^v.V. 18 G lA 4 2t a 12 8 43 5 M 9 71 lbs. ;)17 •) I lli dwt. U 17 DIVISION. (24) /Z'.'?. oz. dtl t HZ. 1)G7 8 17 7)13 (25) dwt. Ill 22 '*%« 2(5. A silvcrsmltb madn tlireo dozen spoons, •«'t'igli!n<;- 5 lb. oz. 8 dwt. ; a tea-pot, \Yei;j,hing ;» Hi. 2 oz. 1(1 dwt. KJ grs. ; two puir Sjilvcr candh'.-tieks, wci^hii!;; i lb. oz. 17 dwt. ; a dozen silver forks. \\oip;hi:ig 1 ll>. 8 oz. 10 dwt. 22 grs. ; what was the weight of all ihci arlicks? 27. Three dozen silver table spooiirs wcliilied 5 lb. 9 oz. ! dwt.,>\hile three dozen silver tvMSjiootis weighed only 1 lb. J uz. IG dwt. ]H gr.s. ; what vras the dilL-rencc in weight? 28. Sold eight silver tt-a-poL-;. each weighing 3 lb. 9 oz. ]S dwt. 13 o ^v^. ; how nuich did liivy a!! weigh V 29. A silversmith received 3t'. lb. 8 cz. 11 dwt. IG gr.?. of Bilver to make 12 tankards; what would the weight of each tankard be ? 30. What is the weight of 3G ingots of silver, each ingot wt'igbing 2 lb. 10 oz. 15 dwt.? 31. 2 lb. 4 oz. 9 dwt. of gol. 9 oz. 1? 1 <; ji^rs. of t of CUCh ach Lugot rhat did il weighing . ml. fur. per. fur. (3'>^ pi r. y^/. per. (36) /^ 4 6 20 10 1 IG 2 1 1 7 6 ,M5 25 2 10 4 12 4 2 2 37. A mnn rode 35 miles. 2 fiirlon^-s;. 31 ptM'cbos; v/alknd 5} miles, G rin'lori;:^s. 25 perches. 2 yuids; tli'Mi rode agtiin 42 miles, 7 rurloiigs. 4 yards ; llieii walked ;!_i;-ain 15 mile?, 4 iuiloiigp, 38 perches, 3 yards; uhat wus the leiigth of hi:? j'juruoy ? 1)S. A traveller walkcil on Moiiilay .'>2 tnlles, 5 riirlon;j:s ; on Tmrday he walked 27 liiihs. 7 lurloiiU'^. 3") perches 5 how Uiiich did ui;3 journey of .Moiuiay exceed that of Tuesday? TiO. A mail e-nieh travelled at the I'e.to of 7 miles, 5 furlonf^s. 2-< \) rehe.s. p v honv ; how fur would it g'o in twelve hoLir.'i? 40 A surveyor who had 10 miles. 7 roods. 30 perches, of r-'ae. to keep in repair, appointed 12 m n to the work ; Avhut leiiu'lli of road had each to attend to? •11. A man travell-d in nine days 150 miles, {furlong, IS perches, ',\ yards ; how much did he tiavel per day on uu hvci'a / * 3 9 yds. 4')25 qrs. PIVIFION. (44) f/'/.s. (^r.f. 7j/."f. yd^. li)3() (ir>) qrs. 3 1 6 1 8J 40. A Ifiilor 1)oi.!;;lit four pieces of cloth ; In the first lhrr mIs. ; in th,- Rccond. Wd yih. 2 qrs. 1 n!. in the third, o2 vd,-;. ;! (jrs. 3 al^. ; iii the lourth, 47 yals. 3 qrs 2 nls. ; how much hi vAl ? 47. A tiiilor. f.-nm n piece of clot!; oonlairi'ii.^ 37 yds. .'> qrs 2 Ills., cut oil' 13 yds. ;.) qrs. 2 nls. ; h;.«>v much remained? 43. A dozen wcavrs wove, cacli. of) yds. 3 qrs. 3 nls. of cloth; ho'A' much was woven by the whole? 40. In nine pi^cf'? of cloth ci' cqnol l(M!.!::[th, there -were 1^7 yds. 2 qrs. 3 nl<. ; how much in each piece ? 50. A piece ofclolli at 7.9. (>/. per yard, cost 17/. 12.?. CJ. ; low many yarda v. ere there in it? 51. What is tlie difl'crenoe in len- urlng 23 yds. 2 qrs. 2 nls.? 52. How many Puits of clothes can bo made from a plocf> containing 31* yds. 2 qrs. 3 nls, ; each suit requiring 3 yds. 1 qr. 2 nls. ? WEIGHTS AND MEASURES. 65 ! I SQUARE AND LAND MEASURE. i3) ►-5. 2 h/9. 3 9 ADDITIOX. (5:v) etc. rd. per. ac. /•//. p/^r 32 •6 Hi 46 3 27 16 2 21 12 2 10 7G 1 13 61 34 24 2 27 46 3 17 (54) ai\ rd. per. 37 2 12 ^l 3 21 C2 1 17 47 2 34 liO 37 '» SUBTP. ACTION. rs. li!s. 3 first th"r« qvs. 1 III. y roods, 12 porclufs ; in the second 7 acres. 2 roods ; in tho iJiird 9 acres and 13 perches : in tho foarLh 5 acres, 2 roods, Iv) perches. How much in all ? 58. A (armer sowed with whrnt. a flidd containing IS acres, 2 roodn, 25 perches ; and another with oats, containing 19 aores, 3 roods, 34 perches. How liuich larger was cue field than the other? 59. Eight men cut down a field of hay ; cacli man cut 3 acres, 2 rood:?, 27 perches. How much was mown? 60. Twelve men ploughed a field containing 16 acres, 3 roods, 35 perche'S. IIow much did each plough ? 61. In a field containing 211 acres, 3 roods. IG perches; 170 acres, 2 rooiis, 23 perches wen> sown with wheat; the re- mainder of (he field was sown wiih barley ; how much was town wiih barley ? 62. llonght !)() acres, 3 roo(l<. 17 p Tches of land, for which I pay 1701/. ; what did I pay lor it per perch ? 66 WEIGHTS AND MEASURES. MEASUIIK OF CAPACITY. WUCni'MCATfOX ( 7 8 23 3 2 qrs. huf^h. pk. 2^9 7 2 ()7. Sold to oi:o DIVISION. (05) O-r.;-. biisli. pk. r/;,-?. bush. jih. iU;\ll 1::^ ii".^. G bus! pcCu? to O.IlOlluM 5S qr?. 4 bu>Ii<'ls. 2 p 'cks ; to aiHiLlHT tO qrs. G bash{>ls ; arid to aiiothcr i)8 ki all ? burl)-. o \K ckj^ : liow much did 1 Bell (18. Lent a pt^rsoii -10 qr?.. 2 biuhcls. 1 prck. I have re- how much docf 1 . •> 1 o , O peci coivod from hiiti Wl qr^. I> bushc be still owo inoV CO. John has 21 qrs. 3 1)nsh('ls. 2 pecks; but Tom has I^ lini'. p as much ; how nniih has ho ? 70. I received 218 qr.s. G bushels. 3 pecks, and gave away a sixth part of it ; how much did 1 <.';ive away? 71. What quantity of beer v ill bo c onf-uni ed in a year, at Hie rate of 2 gallouH, 3 quarts, 1 pint p( r day 72. One cafdv contained T.\ gallons, 3 quarts, 1 pint [ another 37 [gallons, 2 quarts, 3 gills ; how much more did the one coi>- tain than the other ? 73. Nine fitdds produc d each on an average 2i loads, 4 quarters, 7 bushels, 3 p cks ; how much was the produc(3 of the uiuo iields? 74. In 27 '/arrels th.ere was on an avorag * la each, 20 gal- tons, 3 quarts, 1 pint ; hovr much in all V fs/i. ph. 5 2 8 7 2 to o.notlHM did 1 sell I liavc re- much docf Dm lias H a year, at f • another ie one coii- 21- loiids, 4 ■ducy of the c-V, 20 gal- i WEIGHTS AND MEASURES. TIME. M ADDITIOX. (75) (7G) >/;•*. U'/i-."?. dt/f:. 7/rs. whs. dys. dys. Iirs. mi7t 21 fi 3 27 110 4 'd') 17 c 12 Ifi 5 4:\ 12 4 24 18 14 41 24 4 7t 43 (1 52 12 5 32 la G 27 18 .') C4 13 110 SUIITKACTIOX. (77) (78) t/r.s'. irhs. Jt,'S. V^-'. tvhs. dys. di/s. hrs. m/« 43 4 2 :i2 3 4 47 12 10 24 « 5 IG 7 6 17 20 40 18 49 4 70, The bricklayers wore enj;a,ired about a house 23 weeks, 4 days, and S hours ; the ciirpentcrs, 14 weeks, G "days, and II hours ; Ihe p;iir.toi'3. 12 wook?. 5 days, 7 hours, and 34 minutes ; the upholsterer. 5 weeks. 10 hours, and 42 minutes ; how lonjT were those dilfereat workmen en,'>:a(ired about the '.10 use ? SO. Two vci-sels sailed for America ; one of them was 9 weeks, G days, aiid 11 hours on the voyage ; the other got to America in 7 wee!;s, 5 days, and 10 hours ; how much les8 !':ne did the cue go in than the other? PI. I can go to !'„ certain town by the railvvuy in 9 hours, 2.") minutes, and 30 s^ccosids ; it wouKl take me, at least, five times as long to go by the st:vge coach ; how long would the coach take ? ft2. There are 805 days. 5 hours, 48 nvnutes, 57 seconds. ill a Kolar year ; how much is there in a twelfth of it? 83. Row many seconds has a )>oy lived, who is 11 years old? H +'> If ts WEICniS AND MKASURES. it REDUCTION. AVOIRDUPOIS WKICIIT. 1. In 7 cwt. 2 qr:'. 14 lbs. ; how nuiiiy pdunflH? 2. Ill 3 qrs 13 lbs. 12 oz. ; how luuiiy ounces? 3. How many pou-uls are !hcio in M'J7 (./..? 4. Bought 24 bagp of hops, <\}ch w gTaii;^ of gold dust; how r.iuny ounces 8. In a silver siiuff-box weif»hin;' 10 oz. lH dwt. ; how grams many 0, How many silver tablo spoons, oacM wApJunn; 4 oz. 16 dwt., can b« mud*.! out oi' 2 Iba. 8 oz. 13 dwt, ol" silver? la xdvo What quantity of gold will it r(Hjuir(» to make gold ornaments, each weighing i oz. IS dwt. 12 gr. ? II. A gentleman sent a silver tanl^tinl (o a Hilversmith, and ordered him to makfi it into spoons, caeh to weigh 2 oz. 12 dwt. ; how many spoons did he made, the tankard weigh- ing 4 lbs. 7 oz. ? 12. In 4 lbs. ArOTnECARIKS WKIGIIT. 8 OZ. 4 drams, 2 scr. ; liow many grains? 13. In 2487 grains, how many ounces? 14. In 7 ounces, 5 drams, 3 scruples ; how innny Rcmplrs? 15. A patient is required to take daily ' "lams, 2 scruples of bark : how long will 7 lbs. of b»ark i; 'lu? t. 2 qrs. 13 9 cea? how many \rf 4 oz. 16 .ver? [iko twelvo K ? ilvrrpmitli, •('i«;h 2 oz. lid weigh- •iiins? 2 ecruplcs WEIGHTS AN'D MEASURES. — REDUCTION. 69 1,0X0 MlOASrUK. 1(). Ill 7G miles, (i fiirlong-i ; how rn;iny perches? 17. In '179(>8 iucbes ; how miiiiy yards? 18. From Dublin to Livorpo'jl is about 38 leagues ; how ;;i,nv vurds is it? 10. From Diiblta to Cork is aboii^. 130 miles; how ol'lon iT I 's a co.ieh-wli'U'l turn ^^)Ui!d b(;i,wetMi the two places, tlic ■ ';\3iiiuferoiice of tli ; wheel bSuv^ 12 feet? L'O. Frorii Diihliii to Belfast is iil)0!it 90 miles ; how often ■<()•:« a coach -whe^'l invn round between the two places, tbo ij.caaifereuce of the wheel being 12 feet? CLOTH MKASUIi;]. 2!. In 'lib yar;].-!, liow m-iny nails? 2.''. In ■178*] nails, how manv yards? 2:5 From a ]);ec.: of !i;i;;!i co:it;^in;ng 2 ! En.alish ells, hovf .'ijiiy Tshirls can be mile. e,ich nii} lirin,^ 3,] yariKi ? 'il. Hiiw many .^nits m\j be male from 2(5 yds. 2 qrs. each »,i'( roaUining .3,] y.irils? Mia.-riJK or ("M, i'Acrrv. 2'). It;. 24 gallons, 2 fin.ii-L--, 1 pint : iiow many pints? 2'!. In 4;»;-7 pints; how nuuiy f!:t{!!)ns? 27. In 2t lo;i(l-i, G bn.^hcls, ;> j^ecks ; how many pecks? 2i How many bushels are tliere in 179G pecks? 2!), In a lK;]j!'/".id of wine contaiuliig 'j3 gallon-!, bow many jiilc. are tiiere ? TIME. 30. In (i weeks, 3 d'lys, 11 hodrs ; how many hours are ^acre ? 31. Jn 74G07 minuses: how many days? ;»2. Hi- nanr \ni!;utes h.is a boy lived, who is 10 ycar.s And C \ L-ks old? 3V A clock otrikes I5;i time?, during the day j how often iior* It htr '.ke ill G years ? I, -T' ^.:«.. ..:m^M^ '* 10 niACTlCE. PracJlce, is an easy mothocl of app]yin<]f the rule^ f>f Arithmetic to que^jtious which occur ia trade ami business. All Aliquot Part of a miinl)er is an e^iad part ; lu'uce, if a niiniljcr ))0 divincii by an aliquot part, tho CiMutient will be an integral nuiuber. TABI.K OF ALIQUOT PARTS. l'artriot'lirl:Part8ori:ii Parts of [Parts of liPartsof u Year. CTS. GO =r I'M I t>^>j == 3 25 = h 20 = -» it lOl i l^V == 8 ^i — 1 8 s. il. I Shil]in<;.l V'^^' Month 7} 10 ;= ^ pence. j (> = ^ jf^«//'S. I •2 ()' 15 - 5 i .» .1 4 0=3 i I 3 p, 4 1 I o 2 0=^ 18=' 1 '.> 1,2 = i 7.} = \ •f^.! mn. I 3 = — VI KxAMPT.E. — What is the cost of 37G yards of cloth at $1.75 =1| dollars pnr yard? At 1 dollar per yard it won'd oost .... S^JO 00 at 50 ecu's. ~ $.\ per yard, it womM Cf)?t . . 188 00 at 25 cents, = $,^ per yard, it would cofit . . 94 O'.i Total cost . . . $C58 00 ITenco at $1.75, = $U dollars, :)7(; yards will cost $058, 1. What is tho cost of lOG yards of cotton at 9 pence, = i| Bldlling, per yard? 2. What is tho cost of 425 yards of tape at Hd. (=^.th at $ I .75 $?JC> 00 188 0(1 94 oa $G58 00 cost $f .58. 9 pence 1 — ' PRACTICE, 71 pir yn.rd? . per yard* r>. At 12,] cnnt;-?, = $g per yard, what will be the cost of 47')G vai'ds of Ij1(?jj? C. All a,<;ricultnrist sold VJilnvf. of hemp at $7.50 per liundrc'dncight. Wliat did it coiiio to? 7. At 2.S'. l co:^ts 2| cent.s, what will be (lie cost of 140 yards ? i;;. If one bushel of apples costa ('^'2\ cents, what wdll bo the cost of 870 bushels? 11. How much wh'Mt would a field containing 17^ acrob produce, allowing each ajr.j to [n'odiice '.'MOi/ Aj>.? 15. If one yard of oxIra-superJiae ' l>th costs $9.50, wuat Vv'ili b>.» the co^t of cost.s 25. Qd. - 2.V?. ayanl, what will be tha CO 4 of l)CO • .ds? <» i if.'' \l ^ 72 tv I VXWE AND TUET. Giu)33 Wi;i(;nr iin-aiis llie \v(Mi;'lit botli of .'i;oo.(H nnd i)iickai4X', whcllier these packuges be biirrc^ls. (joxes, or .^ack . Tare is a!i fiilowancc maJc to piircliasers fur iki- weight ot the })ai'kage. TiiCT is nil aUowancc of 4 lbs. on every 104 llv^ of gouJs, for waste, or Vr i of the whole. Ci.OFF is an allowance of 2 Ib;^?. on every '^ ewf. m-ulo to tho.se who retail gooils for tiirnii)g- the .sealoK. r^urriJ'": Is what remalus after part of the a]h)ua.neo UJ taken from the i>Toss. Case I. - Whc.i -iv. aflowancr h m'file for the Tare per barrt'l , box. or sack. Wliat is Ihn not w-i;';l)t of •! libds. of siicct^.r. cneli •vvoighiiu; locwt. ',:>qyr>. 1 libs. ; tli(j turo bciiig Iqr. lOlbs. pu ■ hog^ht'iid ' Rule with Kkamti^k. — Multiply tlio weight of each Ii0[;s- hotul by 4. to liml t!it> ijji-o^'s \vci;;hL of tlu3 \vh()b\ fi-'icwl. 2qr3. ; then ctrf. cpr,. Ihs. (jr. //;,v. rrniltiply llii' lure oa each hopj:-lit"a;l, IJJ J li 1 JO ]qr. 101 bs. by tlio niimbor of iilids. 4, 4 ■] find yon fiml lli'? i:».rc lipon lliu 1 lilids. to bt! If.'wt. i(u-. 12!l)s. : plnco 55 2 1 1 U tliia under llio J hiuls., 1 1 12 55c\vt. 2 qis- . t'.nd sul>lract. Tbc rcmaindor. 51cut. Oqr. l-lbs., is the 51 IG net weight. 1. What ip the net weight of 9 chests of lea, each wcighin;;{ 5cwt. 2qrs. lOlbs. ; tare 'Slbo. per cheHt? 2. What is the net v it o'' (! chests of tea, each weighin.'; Icwt. 3qrs. 91!>s. : tare iH\Uyi. j. r clu'st? 3. What is the net weifclit of 7 hhds. of sugar, \v( 'ghir g 6cwt. 3qrs. lilb.s. gro.s? : tare 121b^ per hhd.T? I' . p 1m' I lie I ' I 7 W 1 • .. I. ,)• 1. TAr.E AM» lUKT. CaS3 II.— ^r/«.',7 the tare . au iniic'i jtcr Cwt. The gross vvoij^hl of a lo! of Miiriir is ITHcn-t. [-?qr8. ITlbs. ; tiuo IGlbs. per cwt. What is Ihc net \voi{j;lit? Rl'LK with EMAMPr.K. -Divide lb. cwt. qrs. Ib.i, the Ai'O.'- w«'i(;lit, 17;!c\vt. '.)riv>. 17 IK™;.) 173 3 17 Dm., l>y llio aliquot part of ;i (Mvt ■:•■' V .....J. .v.. 1 ... », X..,..., ,j , itiiis. 1 llbfj. is Iho ,'j of a cwt. ; dividu " i' 21 2 8 > U'Miii 21 bs. i» the i of Mlbn. (l;vido by 1 ; add tlio two quotients tu.'vlhor. and 2^(^wt. '.Uiv. UUh. ai\) ol)!.iiined ; lot thi^^ bo taken from the (t 26 11 1 3 9 IJi) 8 ;^ri)SH weight. 17;M'iivt. Ilqrrn 17 lbs.. ;id liOcwt. Oqr. (Jib;-, aro obfainod, V. iiiuh i.s tho M' t W(;i,::;lit. Tho reni.i!n(i( rs have not been ijtirndod to in this quostion. as they arc not ;i.:ci.'.s.sary in Ox'do/ 10 understand it. 1. Wliat is tbo nnt w(Mj:^lit of S hhd.s. of tol;at:eo. each 3cwt '2'|i>. gross; tare 18!b3. per cwt. ;'i. The g•^o.^s weight of GO kerrr, of butter is 202cwt. 2qra Ii^Hh. ; tare lolbs. per cwt. What is the net weight? Casi: III. — When mi aUuii'nuce is made both fur Tare a/ul Tret. V/hat is the net weight of Icwl. 2qrs. lilbc- gross; tare li I' '. [» M* cwt ; tret as allowed? ilvi.r. wii'ir Ex.\MPM<;.— Find tho tare I he last. and subiract it from tho cwt. qrff. lbs. 4 2 14 gro33 2 8 tare s called, by 2ii (2i» being tho fourth of 2())I~ (i.suttla •s: divide ih[iMre( 1. t> 17 tret 17 net ;h weighing | r.. What is the net weight of Ohhds. of tonacco, wclghln'g ."> ;. 2qrs. 12lbs. each ; tare di'Abi. pir hhd. ; tret as usual? 7, \Vh it is the net weight of (5 chests of tea. each w(Mghing r.- 1, ."(jrs. ;>lbs, ; tare 18lbs. per chedt; tret as allowed? vr, wc'ghui; | H. 2t barrels of ric 5 weigh f)7cwt. 2r)rs. KSlbs. gross; tar* {'• 121!>5. per barrel ; tret as usual. Wliat is the net woigUtt , I vt. n X'1 •ii. i u TAUE ANH TUr.T. Cask IV. — ll'/un Tit re, Tr/t,anil Cloff art i^i-ovul. What is fhf n "t '.vo;;;!it f)f '1 cwt. 2 nv. 11 Dm. i;ro.^f«, li»r« llUw. pel' ova. ; Lii't iij^ .iliiiwil ; cloll' us allowfil? i.xvv and tlic lr< I Iro-n tin* ;,'r(if..' (il>l;ii!M'«l !»/ multiplyiu.u" '!'" ^"^ I by Hkj hit fiulllo bv L'. uiid -liNid- l;v ;{. re- coiviiiii; l!)'; mioiititt pounds: — li h tine 2'i) 1 «i IV livt h;t<);i ;i iTNuitic 12 iwt 0. VriiiTl I-^ tlr' p. d W(M;rht of S blid;-', ofsiii^ar, cwch woljjh- ing (i cwt. 8 qi'rf. 1 { lb;s. ; tare J2 Ib^i. per cwl. ; tret and cb)l( tui usual ? 10. Wliat i-; Ihe net W(;.i>;ht of 8 lihdH. of tabaooo, ( li).*. per cwt. ; trel and ebtll' as uHowcd. What is file ncl weight? 12. What is \\i<) net Weight of 21 lii)d.s. Wrli^liin^i", ^rosM, il cwt. 2 qrs. IS lb.-'-. ; tare 2 qrs. 18 lbs. per idul. ; Irel a,>i ii.^ual ? 13. What is the not wei;rht of \9 chesLs of [>'i\. em. !i weigbinj,^ 2 evt. Id lbs.; tare 11 I.)-'-, per cli«ui,; Iril .ib allowed? U. Wiiit i^ \h" value of the n^t wei-ht of :; hhds, rd' \.n. bacco. each weii^lsbig 4 cwt. 2 <|rs. 12 lbs., gros.^, at JCl lOt. Cd. per cwt.. alle\'. in,!*- 7 lbs. per cwt. for tare ; tret a.s u.-ual. and clotl' 2 ibs. per hhd. ? 1'). What is M.]..' net v,'Mj:^h+ of 9 hhds. of .«n;.';ar, rach wiMg))- fug 7 nwt. 2 r^ri. !3 lbs. ; tare 12 lb.-, per cwt. ; trot and clulf ftb usual ; A n work p( (Iclivert r.ecal Sil r doz. Fl ;i doz. Til 1 pair; 1' pair.^ 75 f ■I liuc i : clolV ") not 11(1 Cl'itf O. ('l\cll c.w I . '1 loWt'il, !rrt as £7 lOv. lul clulf BILL OF PAnnaA A r»Ill is ii wi'ilttMi Mcconur of (ro()(1s' piirclinsod or \\i)vk p('i-iurin(.-(l A r>ill of I'nn.Tls is that which is (hilivci'od with the '^*)oiU at the time of i)iinjhnsc. IJOOKSKM.FIi's niiJ,. Toronto, rcbruary 21st, ISOO. f.ocul Superititondont of Schoo]":;, Jhiught of Tl(i!;KUT MoPiiAir-, !■ iloz. Third Hook of L('r'SoaH,'ut ijl.i'O per doz. - i AO" 1 h School Aril'liinotic - . - - 1 12,t ilwai))casllc'"8 Alii'thra, ;j vols. • - - -a o7^ GROCEUS BJIJ,. Hamilton-, March U't, IPCO. Mr«. AVji.liambox, BOVJ^IU of Sm1T]{ & JONKH. Ti lbr> ,''{ 7 .S7.i h 1 00 76 SIMPI.i: PROFOUTION. When we have three iinin'Dors given, this rula teaches how to find a fburlli iiunihrr, which niav have the same proportion to the third iiuiiil^er, thii^ the second has to tlio first. I'm Thus, if the thrco given nrmbcrt^f be 1. 2, 'A. it is rcqiiin^d lo lind a fourth nunibcr \\iiich will have tiie Hiinic proporlion tt> 8 that the ^ has to 1 : now. Mie 2 is douhle the 1 ; there- love, the required iiunilier must be double of the o, ihut h ('). To express ])roportiou iho numbers are put down thus, I : 2 : : S : G, and are read thus. 1 in to 2 as U is to 0. Cape I. — To find out a fourth proporlional to three given jntnibers. Find a fourth proportional to the numbers 4, 8, G. RuLK wiTJL KxAMi'rK.— I'laco them thus. 4:8 : : G ni'.d multiply "fae secoiul and thii'd numbers G !of,'etlier. and divide by llie lir.-t ; the quotient ^j 4^ i.^ 12. which bears the same proportion to G 'Ju\t 8 doe? to 4.- To 3, G, 12. find a fourlh proport'oual. To (). 8. 3, find a fourth proportional 12 . 24. .4. To 8. 0, 8, find a fourth ptopoiiional IG. To G. 12. 4. find a fourtli proDortional 8. To 10. 150. G8, find a fourth proportional. . . 1020. . 10. . (18, Find a fourth p'roportional to 1020. (JS, loO, Find a fourth pr(iporiionul to loO, 10. 1020, Find a fourth proportional to G8, 1020, 10 l.OO. Find a fourth proportional to tlie following numbers : .'ins. To 2 tons. 17 tons, and 25/ 212/. 10.?. To 10 lb.. ir>0 lb., and '>s 75.v. To 9 yds., 3G yds . and 18.v 72.9. To 5 lb., 1 lb.', and lo.v :U. To 4 yds., 18 yds., and 25 95. To 1 cwt., 215 cwt., and 50.s 10750. T }''.tds .1, enght r>. I I?. v./. •l »1 PijrrLF. rno PORTION. i 1 s rulo I may r, i\vdt )pi)i'lioP ; there- , that b \\i\ thus, CC EiVCil G. G 24. 4. 16. 8. 020. 10. (;8, 150. bera : 10.-f. 75.-. 72.9. :'>.s. 1)5. )7r)0.'!. 270/. RuLK. — 1. Talce from the question that torm which is of tVr pame nature as the an^.-wer will be, and inaice it th(3 third lerm of the proportional. 2. If from th(* nature of the qiier.tion the answer will be greater than this third term, select the greatei' of tlie two remaining terms for the second lerm of the proportional — itherwisc, take the less; and the remaining term will lu- 'ho first. 0. Rcdnco the first and srcond terms to the aamc denomi- 1; ilion if necessary. 1. Find a fourth proportional by muliiplying the second >nd third terms together and dividing by the first. Thy ^Diswer will tlu'U be in t!ie name name as the third term. ExAMPi-H. — If 6 men can perform a work in 80 days, in v.liat time ought i;> men to p'.rrurm the same work? The question has n Terence to thne, select therefore th" t'nm term from the qne;-tion for the third in the proportiena). Then consider whether J:» men will require more or less tim men. Of course the more iiifu, tht; ',',<■ to AvaI 1 5 'i of 5 feet = y =. 37^ feet. The proportio7i in the qu.'^stion is, the part f-^ above tho water is to a unity as tlie length 5 //. of the part above lt;e water is to tho entire Icn^ih. 2">. uav.s. SIMPLE rr.oroKTiojT, T9 outs ill a 'I jost $25, a dny, irt perform a le to per- r? re p;ronn(i ,vo, for Oi« size ? led uniop* ■)f men iu-'l :. of wheat, utaiiiing .Mi lain a ci^'f'* ts lengtli in = 15' ■ tbe surfiicft V of it i? ^ 1 ;> _2j above the e part above It?, A farm'^r pold V of li*s bind to A, i of it to B, and the li'.maindiT, which was 100 acres, to C. llow much laud did the farmer oxra ? 17. In a cortalu scliool, 4 of the pupils ^tndy Arithmetic, I of them study Lanj^'uixgcs, and tho remaiuiuf^ 3G are em- |t!'\ved on various other subjects. Required the number ia ihe scliool. 18. A ppr?-on failini( in bu?incP3 ov/cs $5000. and is able t> pay but $-000. ILow much can be pay per dollar to bid [or.s ID. A traveller bavino: rff^ne '>ib.-> m:>- on tii.^ journey, ii'nis lh.it [i of it r:'main?s to Ire travelled. What was tho 1 ■:)(,' Hi of his journey? •Jl'>. A gt-ntloman who ov.-ned ^ of a manj.i factory, sold 4 of i his wbave for $3000. Whai was ihe ei-iUmated value of tba iiohj establlshnieiit ••>! How ma^y miles mr.st a person w^alk in 5.] days, to lyconii^lii-h a iourn'-'V vlav f r,n; /.-> \n\U at ^uniQ rate, in 15 'I'l. A bankrupt owe.'*) ST)?. 19, TT). a-i'l Iiup propr-rty amount- in;; to $2;>00. la an equitable (ll.'^i;-ii)ution. of his property, much will a creditor r ..- <^ . i. t K., w!iu;-e elaiui U $100 2-b A borrowed of B S500. v,i;;cb he kept 3.} years. On a Fulisequcnt occasion A leii'ln H '.?;]75 ; hf»vv io!!;: o!ir;-ljt B to '■»■ CO tills latt'jr sum iu return I'or the acuoinmjdatiun be had .tVi.rded A? 2t. Ailowinj^: a man to do a certain work in 3 days, and a ) -v to do it in 5 days ; iti \vhat time onf;lit the two to,a:et.her ,u lio the v.'ork ? AvALYSis, — Tiie man could du }, and i!;e boy |, of th^j r.iik in 1 dey ; then both tou-'tie-i' could i]o '.--!-l~-^,. of the njrk in 1 day; bene il)i'y eoiikl do the fntire icork iu V <^f ^J- dav. 1 ,5 1 ,j of u day, and 2'. A can dip; a ditcli in 5 dnvs, B in (1 d;ivs. and C in S days, Jn wliat time could tbe three togetlur dig the ditch? 2''). Tf AT. Iflrv/'/. of iron 1)0 conveyed 50 miles for $30, L v.' far could OT. bcwt. Zqr. be conveyed for Ibo same Bum? U! SIMI'LE Pi;orORTION\ 27. Two ma^nns to;yot,licr build a wall in 10 (lny3. Oiw (T them could liave Imilt tlio wall liiinbolf ill 15 duvB ; ia what timo could the otl'er have done it? 28. A iTn-rchaiit bought throe piocos of clolh, each con- taining '2'n/(l. "Iqr., for S500 ; and Bo!d bQyd. of it at cost. What did the 50 yards amount to? 2!). If I of + of an acre of land ^.'A\ for $18.18|, whal would a lot containing iJi. 2R. 13P. bring at that rate ? 30. How many yards of linen which is h yd. wide will W equivalent to 30^f/. of another kind v.hich is | of u v.ird wide? 31. ITow many yards of carprting which is j of a yard wide, will bo ro(j:iired to co\cr a floor that meiusurcs 2f) f •. < l In length, and 2U feet in brcadlh? 32. A farmer has a ndd 100 poles in length, and 45.2'j poles in width. He wishes to lay off another Held to con- tain the same ({uri'iiily of ground, and be 80 pules in li.Miglh : rhat nuist be iis brea'Ith? 33. The governor of a besieged place ];as provision for 51 ^ays, at the ra'.e of lllb. of bread to eacli man ptr day, b-il (s desirous to prolong the siege to 80 days, in expect ai ion of succour ; in that cas^, v.hat must the ration (.if bread b<-? 34. A pole (I f(»et liigh throv.s a shadow of 5 feet 8 ineh1 r dav, It'll :p(,'Ctaiion k-cad hr ? 8 iiiclif f-- ; )\v of i5(.> 10 v\ manv r" Itj walk- he havt- ; in whA ; in on tils' : were !'<■ y of hr.y the >^air^ 81 COMPOUND PllOPOllTION. Wbcn in order to find a fourth proportional, sov cral clrcuiiistaiices require to be considered, it is called Compound Pruporiion, If li horses cat 5fi bnsliel.s oi" oats iti IG days 5 how raany b;ishc required for 20 h<)]y,-:i ]"or 2i days? Rb'LKwrTir ExA\fiM,K. -Write li^rses 14 flown for thi' tiiird t(!rni that {\.\\< 10 22^ lyt 20 2t bush. 5(J ; nuniber whicii i:i of liie .'-ani » ku.d with the an.-w^'r r. qi,;rod — [)() 'HLhels. Tin ii take Uvo niun- Ifirsof thesaine kind --I 1 hornes and 20 horse:-" — ■^■■'r^ Cv)i.-id"r, ar, ill Simple Proj):)ri;o;i, v.helin.'r ii'om the nam re of Ih*} qu'.'S- 'ion, the greater or less is to )-,3 put in the lirsi, or seeond tei-ni. If 're it isobvions tii.ii the gi eat- '•r must b' in the see'^nd te-. m. as liO horses will eut neu'e tliaii 1 t horses. T;tk') the otlu'-- two ri'sas a. id proceed in the sam^ manner. After all th ; terms i;ave h ' n put down, multiply the two (irst terms. It and Iti. tojreth'T ; do the same witb t!je two S(.'Cond terra?, 20 aiul 21. and proceed as iu Simple I'roportion. CoN'TKACTioN'. — Let tlie question be the same as In the la^^i "xample. 4bO 28.S0 2 100 22 n2i;sb(}a20 bus. 221 418 o After the terras have been properly ar- r;iaf?;ed. the opi.'ratlon may often be j^rratly in shortened by using the following method : ^^^ ^ ^4^^ :*tk Draw a line, and place the lirst~" t*"rms, 14 ^^ X ^^^^ f v ;uid 1(), under it. and the second and third jJi x /0 terms, 20. 24. and 50. above it ; then divide fh ti any number aljove the lino and any below hy ?ny number which will divide both without leaving a 82 co.MroL'XD rKorouTiox. I >M r?m;u)iaor. It v. ill ho vsoon tl^at in all qnof-iioiis in Compound Trf. portion tivro i» oiio term th:U is lil.i! iIk ri'ijitin.-d iui^\\(-r, ninl tiiisi must bo put in the third piaco. Tin'iitill Mit.' co;r.p()-e Jt) fduM-s of lo \)d\^c6 in a slieet, GO lined in a pa,j,e, and .'>0 lotlers ia a line? Here ti'O question refers to dajf ; releet that trnn for tho '/n7-ii place' ; th.-n compare the f!ve a ^rcaftr ilii\-i thaa eO line;-, 50 : CO i)\J letLer.t. will take more tiiue thau 10 letter;-. -10 : 50 Ilavinp' plated the qurrtion. iTMiliiply nil the srrii7hl t'Tu'i fttid the third to.i-t^thi r. and divide by ii-.e pro.luet o!' u\\ tju? first teriu'^, accordiu;;': to llio l;-'M1' ral rule ; iIk; woi'k M'ill flaud tin!?, and is eai^ilv pei'.ori.ieil i'V (.■a;ier7"x'20 X 2 4 X GO X 10 "- IJ2 day;?. NoTi:. — If any of the pair;? are uut ia Ihe -am" nanu lliey ma.;t be reJaced. The teacher is rocou";mcnd''d to make' the pupil siniply .s/a/f* several of the (Vdlowiap; questions on t!ie sletr or black-board, b";'ore troabliui; him v. it!j the operation of tlie inechiinlcai p'.iri of the work ; and all (he nn(!stions should tirbt b'J uorkcd o;tt in fuU and then Ijv Canallation. oniponnd (I Ulli\\(T, ivM'ti'i'iim M'i'vc timt ' of v.svvy o 1)0 cou- qiu'sticiu. II lu):iv3 iiics in !\ I'lS of It) a u liiK'? m for tlic Iii>,t and 5 : : KJ : U : 10 : 10 : CO : 50 )7nl \.' ■ni"i )!' till (hfl wci'k \vill (t:.iy:?. lain J tlicy mply .s/'a/P ;ick-boiir«l, nt'chiiniciil COMPOUND rROrOIlTION. S3 1. If 15 moil bnilil 37 roods of wall in 27 days, how many luodK will 74 men build in (k> days? 2. If 8 mon for 5 days' work get $10 ; bow nmcli ought 32 uu:u to get for 25 days' work ? :i. If 4 men can mov/ 20 acres of graM in 7 davf^ ; how iiiiUiy acrc« can 12 men mow in 28 days? I. If 6 tailors can make 10 puil.s of clutheR In 4 days ; liow tr-my suits can 20 make in 7 days? r>. A wall, 2vS foot in hei,nht. was built in If) dayn by C8 !);• n ; bow many mea workinr;^ at the i^amo ruLe could build d v,a!i 32 I'eet liii^h in 8 davK? i.'k If 12 herpes in 5 davs dra'.V il ions of f- tones from a ii'Miry : how mauv horses wuuld it require to draw 13;i tons i;, 18 davs? T, A g-arrison of L'OO men h.as provisions for 12 we^ks, at I'.i- rate o!" 20 0111100? per day to each ii'.an ; liow masiy men w ili tlie same provlsio'.u-; maintalij. ivv 20 week^-, uHowiug each ,■;;;;;: only 8 OLinces per day? •••v If 50 mon can do a p'^ ci of woik in 100 day??, w(»rkin£» ^ liours per day ; in '.vhat lime -.vill 120 meji do ii, working (i l.wurs pur day t ;•. What is (lie intorcHt of $!:>22, for 2^1 yearn, at U poi c •'.•'{. pir annum? !i). If $;;00 iii^dA $]?0 la IS ii^nnth;^ ; how mncli will $103 :,' wa 'n\ 12 month i? 11. !{' two men can di;^ 125 rods of dIi.oh in 75 days, in ho.NT •I sny days can 18 dig 213 rods? 12. If 400 soldier:-? cousnmo 5 b^Tels of flonr in 12 davs, ].^'^' n/any soldiers will Gonoume 15 barrels in 2 dayt;? 13. If a person can travel 120 miles in 12 days of 8 honra, ' M'h, how far will ho be able to tra\el in J5 davs of 10 l;''.ivB each? 11. If a pa^'tnre of 10 acres will ford (5 horsos for 4 months i. -^s many acres will li.cd 12 horsey for 9 mcntliB? >i. m •i Ii 84 COMPOUND nioroRTioy. 15. If GO l)iisli('ls of oats will feed 21 borscB 40 days, how long will 'JiO bushels lecd '18 horses? 16. If 82 men built a wall :JG feet lon^, 8 feet hi}?h, and 4 feet tliick, in 1 days, in what liino will 48 men build a wnll Biii leet long, G loot high, and 3 IVot wide ? 17. If the freight of 80 tierces of Kugar, each weighing ?,), hundred weight, lor l.lO miles, cost S«l. what must bo paiil for the freight of oO hogsheads of sugar, each weighing J J hundred weight, I'or 50 miles '• 18. A family consisting of G persons ur-nally drink lo.i; gallons of beer in a week ; how nineli will they drink in J'2..' weeks, if the number be increas'.d to D ? 10. If 12 tailors in 7 days can linish 14 suits of cloth'-. hew many tailors in 10 days can finish the clothos of a re,c;i ment of 41)4 men ? 20. If a garrison of 'M'SO vvn\ eat a certain quantity of bread in j.*) days, at 24 ounces per daj' to eacli num. lion many men, at the rate of 14 ounces per day, will eat twice a:> much in 45 days ? 21. A company of 100 men drank $80 wortli of wine v\ 50cts. per bottle ; how many men, at the same rati', will $'if^ worth supply, when wine is worth lir)Cts. per bottle'.' 22. W the wages of IM men for 7 A days, be $110.7C, '.\h:.t will bo the wages of 20 men for 15-j days? 23. If .1, fool nan travel 204 miles in (i^ day.^ of 12,] houri- each, in how many days of 10;j hours each will he travel 121'j miles? 24. 120 men. in '] day? of 12 hours each, can dig a treic- ', of 30 yards long. 2 leet broad, and 4 feet deep, how m:niy men would be required to dig a tre.nch 50 yards long, G I'-m j deep, and U yards broad, in 9 days of 15 hours each ? 25. If 40 men can perform a piece; of work iu 12 days. Low many men will perform another piece of work three times nt« largo, iu oue-iil th part of the time ? 26. A person having a journey of 500 miles to perform, walks 200 miles iu 8 days, walking 12 hours a day ; in how "f 7 i\ ile"p ; JHMlIld •> i • 11. V.'iHt' KH) ill .1,1 • >u. \iliat !■ i ■*///. '.:-r 2 i.;u-r;s( '^mm coil roL'N \) rrioi'OUTio n , 85 s7 lay??, how I'. \\\\\ $'^^ ' i2.\ lKm!> [ravel 12l*i if^ a ti'ou'-!. ilOW TTI'-lliy onji, (j !'•■< J acli ? I dayt=, boNv eo tiuu'S '.!*> Lo peiTornr \j ; in bo>v Ti' 'My diiy^, walkiuir 10 Iinnr.s a day, will ho couiploto tha iMiaindcr of tlio Jouriu y ? :17. If ]()0') moil, b<'si(';;('d in a town, willi prrA'islons for 28 i\\\-^, ill tin; raU; of JS outics a day I'or cai'h man, bo roin- 'oriu'd by (iOO tiicn. 'low niiiny iwici's a day inu.''L (;ac!i maa if\*; tliat llic nr'.)vi,-!on uw.y hi-' ihcai I'ur 'i'J djiy.s ? ::^. JC a. bar of iron ;'>/'/. lon,i:-. 2.U"//. wide, and li]m. (.hick, v.: i;;h -I.'; lb.-.; how liiuch will a bar ol" ihc h.uue Qictal weigh ''i;.i !;- l/t. \oi]<;. :):n. widv'. .md 2.]///. thick? ::'). Fifty thousand bricks are to bo romovod a given dis- '•c'C- in 10 i\;\yA. Twelvo hors;'s can reniovc i ■ jOO in (J days ; i''\ inw.y hors;;;; can rcniovo the rLMnaludor in I days? :'0. If " nion, w()rl*in;2: 10 hour8 a d y, . \n plant a fu Id loO ' 'vl.-* bv 210 rod- in ••dass, liuw many men. ^s-orkiiii( 12 liourH ,1 duv. car. idaa .\ litld measuring- lUli rod., by uOO ruda, io Ulay^? :*,!. If 2 IS niop, in 5.5 days of 11 hours each, di}^ a trench "! 7 dotj^rcios of hardness. 2H2i yards loiig;, '6$ wide, and 2^ •l<.'"p ; in liow many days of 9 hours lonj^^ will 21 men di^ a tr'iich of 1 d(!grccrf of hardneii.s, o37^ yard^j long, f>i| widu. ;tud ;Jr} deep ". ;i2. If 1 men eat i}\ pound:- of bread in 2 weeks, how many j.^'uads will It) men eat in 7 weeks? :'.;;. If 5 o.\en reqnlro an aero of p:raJ=a *'<>r 9 days, hov* le.any acris will 20 oxtn rociniro for ilOh day : :'!. If a man travid !()■) miles in ?> days 1 1' li) lionrs each. i.'cv far miglit ho travel in i'^ days of 1J,\ honr.s each? :;.",, If tlie eonveyanco of '20nrt. 4Q miles, co?t $ir>.87,|, \\\::\t Hiionld bo charged lor the eonveyanco of iJOcwt. 'o;ERSiiip. Kx vMi'i.K.— Div'ulo $l.")i> tunr'ng ilir-j'j per?ous, A. 1) unci (\ iu ilie pruporLioii ul' 2, ai!<.l o. ri'opoitional Terms ,* .'i ) ^ Sum of the Tltids. 10 10 .10 AniouTif. : ir.O : : l')0 : : loO ; 2 to A'p nliaro. '.] to l>"s sliare. o to U's feliiire. then l.'O -^ 10=r^ ! ■ h- M 1.- X i^ = A'd bliarc ; 15 X 3 = T/i share : and ];"> X -"' "- C'b t-iiur.'\ 1. A. B, niul (?I. ciit.r into po.rtnor;^hip wiHi a capital {() h(nv.(yn three por.=ons in sneli a manner that their .shar<'s >hiiU be a.s ihe nuinlsers i"^, 4 and J. 8, A and P. };ave a joint ptoek of $1200. of which A o\\ ns SoCOO, anil h SCOO : th<'y gain in one year $2000 : what i.s each one'n t-hare of the pi'oli's? 4. A genllenian divided $10000 between In's Fon and danghter in the prcportiou of IJ to 2. What are their re.-pec- tive tjharew? 5. A, B. C, and D, have $10000 in trade, each an eqi^al share ; at the end of a yenr tJieir prolitn amount to Sh'OOO : >', llisidiii:: !i sli:iil I of {hit \d /enns. CDUOlllit is to ii.- n unci (\ lire. .irc. K \) = \V\ capital of uiiii C put gain ua? a manner :h A o\s \\% I son nnd tiir roHpcc- an '^qral rARTITlVK PUorOllTlOX, oil PAUTNTRRSIIIP. 87 wliat I*' oacli one's Fharo, nllowlnc^ A to rocoivo $50, iirul I) $;)0, out of (ho prolitM, lor extra sorviccH ? »1. A top!.i(()i' lnNjiiradv^l SlTiO'lO to lii.s widow, (lau.t^litfr, a! on''M'i^r:iiij. C onn-sixtli. It o:i"-.,' .■■liiii, and i'] wlial i.> lul't. What ■ 'iU bo llio share of ui'h? A FiKTchaiil iMn[)lov. ,] ilirco cl -rlr;-: at tlii aau o tvin;^^ uuliy of SLiUO, $100. and .i^MtO. Atthooiil of t!t. 1) IS)!!!'" Itaidvi'npt. !i>! lias but $(J50 to b • divided | ;iin,»ag them. WliuL will be the portion of cacli .' 0. Tlireo nv;M\^lianl;H loaded a vos^:' 1 wlili llonr : A loadol r')0 barrels, li 700 barrels, and \j 1000 l)arrel.s . in a storm at s a it becatn" n(>e!'ssary to throw overboard liO barrel.s. What was eaeli one's s^iiare of the loss? 10. An insolvent dr^btor owe.s lo A ?1'2')0, to B $100, and to C .;v]00. lb' is al)K; lo pay :;pl-0 ; what bhuiild each of the three creditors receive? 11. A man b>qneath(>d liis osfato toliis four pons in the fol- iowinf^ manner, vi/.: to his fii-.'t S.3U0O, to his !^i'e()iid S b'lOO, b) Ills third S blOO. to his fwnrlh SIOOO. Bat on seitlinp^ th« estate, it was Ibaad that after payin<^ the delils and expent-''-:*, only $12000 remained to be divided: hovr nmeii sliould oaeb receive ? 12. It is required to divide i^lie number ISO into three parts ttiiich shall be to one anoiher as \, j, and '\. 13. A widovN' and her two sons rrcelvt; a leoacy of SloOO, of which th(! widow is to have half, and th' two sons each a Tjiiarier. But the d to divide $1000 ])etwoon his two Rons in th(? proportion of i to .',. pi-ovided eitlier of tlvin could ascertain the amount otlered to him. What would be their respective shares? ♦ ■ t ,: .. i IMAGE EVALUATION TEST TARGET (MT-3) // "^ 1.0 I.I - Ki III 2.2 1^ IIIIIIO 11.25 ■ 1.4 11= 1.6 - 6" m ^l 7 Hiotographic Sciences Corporation 1% WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 88 COxMPOUNl) PAIITITIYE PHOPORTION. When Pai'tnerH in business {.livklc their profits iu proportion both to the amount of capital employed, and the thm it in continued iu the business, it ia called Compound Parlilive Projporlion, or Fellow- ship with Time, lluLK. — >rnUip1y each term l)y its time, and tuko the pro' ducts for tlio pro)\oi'tlonai terms, then work as bofore. Il\AMPi.K.— A puts $200 into a business for 7 m»nlhs, and H $300 for monthg. Tiiey gain $100; what is the share of uach ? A's amount $200X7 mouths=l 400 B'a amount $;iOOX9 months=2700 Gain. Sura of the products 4100 : 100 : : 1400=A'8shar»i And as 4100 : 100 : : 2700=B'a shaiY. 1. Three persona rent a pasture for $20. A puts in 20 «heep for 4 inontlis ; B 30 sheep for 3 montlis ; and C 4'! •heep for 2 months. How much of the rent should accord- ingly bo paid by each? 2. Three men hh'O a pasture for $70.20 : A put in 7 horsoa for 3 months* ; U U horses for 6 months ; and 4 liorscs for 6 months. What part of the rent should each pay? 3. A, B, and 0, contracted to make a road for $5000. A furnished 30 laborers for 45 days, B 42 laborers for 34 days, and C 60 hilKircrs for 30 days. What are their respective Ehares of the $5000 ? 4. A commenced business witli a capital of $10000 ; four montlis afterwards B entered into partnership with him, and put in 1600 Imrreli^ of (lour. At the close of the year tlioir profits were $5100, of wliich B was entitled to $2100. What was the value of the flour per barrel ? 5. A, B, and (J, In partnership, have made $400. AVhat are their respc^otivo ^harea of profit, supposing A's capital iu the businoHH lo liave been $500 for 10 mouths, B's ;i>U00 for 1 year and 3 montha, and C's $000 for 2 years? 89 noN. arofits iu L mployed, ess, it ia Fellow- the pro- ore. itnths, and the share =A'8 shara =Jj-a 8hiu>i. pats in 20 and C 45 lid accord- in 7 horses horses for B5000. A jr 34 dtiya, respective 1000 ; four ,h him, and your their ILOO. What 00. What capital iu "s ;j>yOO lor MEDIAL PROPORTION, or ALLIGATION, Medial Proportion is proportion applied to mixing two or more in^j^rcdients of diflfereut values for a compound of a given mean value. Case I. — For Two Ingredients. Rule. — Take the quantities inversely as the difference* between their respective rates of value, and the given mean rate. Example. — In wliat proportion shall Rye at 37 cents per bushel be mixed with Oats at 25 cents per bushel, to make a compound worth 30 cents per bushel ? The difference between the Rj'^e at 37cts. and 30 =- 7 .". " Oats at 25cts. and 30 = 5 Take these numbers iywersely for the answer — thus, 5 bushela of Rye, and 7 bushels of Oats. 1. In what proportion must Corn at 40 cents a bushel, and Oats at 25 cents a bushel, be taken to form a mixture which Bhall be worth 33 cents a bushel? 2. In what proportion must one kind of Tea at 75 cents a pound, and another at 90 centb a pound, be taken for a mix- ture which shall be worth 83 cents a pound ? 3. In what proportion must one kind r.f Coffee, at cent* a pound, and another at 13 cents a pound, be taken to form a mixture which shall be worth 12.^ cents per pound? 4. In what proportion must one kind of Wine, at 90 cents a gallon, and another at 75 cents a gallon, be taken for a mixture which shall be worth 872 cents per gallon ? 5. A farmer wishps to purchase two different qualities of land at $20 and $35 per acre. In such proportion that tho average rate shall l)e $27.50 per acre. In what proportion must the two kinds be purchased? C. In what proportion should Hay, at $25 per ton, and Straw at $12 per ton, be taken to form a mixture which Rball be worth $17 a tou? II mM to MEDIAL PROl'ORTIOX, OR ALLIGATION. I i i Case II. — For Three or more Ingredients. . ^ < Rule. — The ratos of tlio several injxredlonts are set one untler another, witli the mean rate on the left. Link together each rate wliieh is less than the mean rate witli one tkat is greater. The dili'erence between cnrJi rate and the 7ncan rate h set opposite the rate or rates with which it is connected. NoTK. — As the combinations are varions, most qiieetions will he snsceptible of several answers according as the terms are linked. Example. — A grocer mixes four kinds of sugar, at 5 centa, 8 cents, 13 cents, and 14 cents, to make a mixture worth 10 cents per lb. What is the proportion of each ? < > --^*- [lOc] ^V(;. 1. 5->, 4 lbs. at octs. 3 lbs. at Sets. 2 lbs. at 13ct3. 5 lbs. at 14cts. 13^ U [lOc] jVo. 2. 5 ] 3 lbs. at Sets. 8 M 4 lbs. at Sets. 5 Urn. at 18c Is. 2 lbs. at Mcts 13 J 14 Ao. 3. [lOc] 5 8 13 J [lOo.] 14--^ 5— I— I 13lJ 14 • 4 4- 3 = 7 at 4 c 5 cents ^ cents. 3 cents. 7 at 14 cents 5... 54-2 J\o. 4. 4 -f- 3 = 7 at 5 cents. 3 at 8 cents. 6 4- 2 = 7 at 13 cents. 5 at 14 cents. The work may be proved — thus, take the answers of No. 1. 4 pounde at 5 cents = 20 cents. < 3 pounds at 8 cents =s 24 cents. '■■'■ • 2 pounds at 13 cents = 26 cents. 5 pounds at 14 cents = 70 cents. ! : ' 14 pounds of 10 cents per pound. for 140 cents is at the rate 5. MEDIAL rROFORTIOX, OR ALI.TGATION. 91 m Us, :< ire set one i)k togetlu'r one tkat ih the mean vhich it is t queetions 3 the terms , at 5 cents, worth 10 bs. at 5c ts. bs. at Sets. I)s. at 18c Is. D&. at licta 9 of No. 1. at the rate 1. What proportions of coffee, at 8 eta., 10 cts., and 14 cts, per pound, must bo mixed together, so that the compound thai I be worth 12 cents per pound? 2. In what proportion must rye at 37 cents, oats at 23 cents, inid corn at 32 cents n bushel, be taken for a compound which thull be worth 31 cents a bushel ? 3. A merchant has teas worth 40 cents, 65 cents, and 75 ct.'its a pound, from which he wishes to make a mixture worth (;0 cents a pound : what is the smallest quantity of each that he can take and express the parts by \ hole numbers? ^, A wine merchant mixed brandy 1 1 30 cents pe; gallon, and wine at $1 a gallon, with water, an I found the compound to be worth 50 cents per gallon. In whit proportion were the boverttl ingredients taken, the water being rated at ? 5. A farmer sold a number of colts at $50 each, oxen at $40, cows at $25, calves at $10, and realized an average price of $30 per head. What was the smallest number he could sell of each? 0. A merchan* wishes to mix three kinds of tea, at 90 eta., $1, and $1.50 per poutul, so that the mixture shall be worth $1.25 cents per pound. In what proportion must the diflfereut kiuds be taken*? , 7. Wimt is the smallest quantity of water that must be mixed with wino worth $2.80 and $3 per gallon, to form a mixture worth $2.()0 a gallon, wheu all the parts are express- ed by whole numbers ? 8. A farmer has one tract of land worth $15 an acre, another worth $22 an acre, and another worth $25 an acre. Ill what proportion must he sell from the several tracts, that the average price shall be $20 an acre ? 9. A produce merchant wishes to mix rye at 30 cents, oats at 26 cents, and barley at 60 cents, so as to make a mixture worth 30 cents per bushel. What quantity of each must he take? 10. A grocer wishes to mix three kinds of coffee, at 18 cts., 20 cents, and 25 cents, to form a m'xture worth 22 cents per pouLd. How much must he take cf each ? M M m MEDIAL r:^OPOi;TIO\, OR AI.T.TOATION. Cask III. — ir/yr/? the qvaiitity nf vue of thf Simp/fs ift ghm, RcLK. — Fin(] Iho prnportionivl qniinlillcs ns IkTofo, tlK.'n r.j [heanioiiMt ol' the iiit^rcd'n'iit LIhih roiiiKl is to llic gi\cMj amoiim of the sjimo ingrodit'iit, ^^o is tho amount of uiiy olbrr ingre- dient to its required quantity. ExAMPLK.— What quantity of Ftigar at 12 ctp., 10 rts.. am! e given quantity is 2* pounds, therefore as 2 : 20 : : any other proportional to it* quantity. 1. A farmer mixes 10 bushels of wheat at 70 cts. per bushel with rye at 48 cts., corn at oli cts., aiul barley at 30 cis., so thai a bushel of the composition may be bold for 38 cts. What quantity of each must he tako ? 2. What quantity of teas at 12j9., lO.v., and Gs., must b« mixed with 20 pounds, at !.«. u pound, to make the mixtur* worth 8s. a pound ? 3. How much water must bo mixed with 100 gallons of rum worth $1.50 per gallon, to reduce its value to $1.25 per gallon? 4. How many poundRof Fugarat 7 cIp. and 11 cts. a pound, must be mixed with 76 pounds, at 12 cents a pound, bo that the mixture may be worth 10 cts. a pound ? 6. A farmer mixes 20 buFhelc of rye at 65 cts , with barh-y at 51 cts., and oats at 30 cts. ; how mucii barley and oats mu'jt bo mixed with the 20 bunhcds of rye, that tho provender mjy be worth 41 cts. per bufchel? 6. With 95 gallons of rum at R.*.. T mixed other rum at Cs. 8fi. per gallon, aiul some water ; then 1 found it stood m«' in (is. 4t/. per gallon. I demand how much rum and ho^v much wjiter 1 took ? oa ',i' ihf ire, lh;;n ns I en a moil n I ilbtT ingiv- 10 dp., and ko tln! mix- untify is 2< ioiial to iw per bushel cts., so thai cts. Whal s., must hi he mixtuK gallons of le to $L2u Is. a pound, iiid, BO that wlili barh'V (1 oalsmuil ,'t'iKkr nijy er mm tA it stood m<» n and ho^v CONJOTXED PROPOTITIOX. Conjoiiiod Proportion U a kind of Comp'umtl Pro- portion in w.iicii llio ratio of one <»f llic anruce- dents to its consuquont is innl(3 to depend upon tqaiva/enccs among the terms of Proportion. Uui.K.— Si't frfn'vtlfnt t at D.i itzic. I)antzic ••• =• 112 at Ijondo.i. Then 9 X 4!» x ll»» X 112 10 X 45 X m 12!> 9- 11*3. at Dantzic 1. ir 7 buslieN of* wh<*at be worth as much as H cord.s of wofKD PROPORTION. 2. If .'J barrelw of corn be jfivpn forr 7 biixhfrlfl of whoat. arvj 4 bii.xlu'lM ;)t whoiit lui* 18 of ry»?. jiimI I j of rye for "iO of oais ; how riiiiij iiiislieb uf oaia would bo an (.'(^uivalent fur 10 barrels of com? " ^ . . 8. If A can do as much work in ^ve days a^ B can do in 8 days. hihI li as iiiiioti in 4 «lays us C can do in II daysi in iioA many days could A do the samu that U could do iv 20 dav8 '.' 4. If 10} yards of silTc cost ^loJ."). and $♦! vill pnrchaso 1 yard of bi-oiidcloth, and 4^ yards of tin* cloth hf bancriMl for 2 ) yanirt of Irisli tin n ; Im)w many yards of iho silk would b"6 uii iqiiivaknit for 4l> yardn of ihc linen? 6. Allowinjj that in a c Ttaiii factory d g'rla do as much work in a d;ty as 4 boys, and 8 boys :is much its (i men ; bo.v niaiy moa would be required to do a:i much work a-< 20 girls'.' 6 Supposing A to oarn as much monoy in 4 months as B tfarns iii (> months, and li as much in 5 numths a.s C7 in 7 months, and aH much in 10 nionihs as l> in '^ months; ill wihit iimt* could [) earn the name that A could earu iu 12 muath.s? 7. If ]'l pounds in Cana'la l>e equal to 10 ponnds at Am* rterdutn. and 100 pounds at Anist rdani be equal to 120 lbs. at r.u'iis ; hoiV many pounds al Tarib arc equal to 1J>0 pounds in CaniMla ? k 8. If 1('» horses can draw as much in one day a<» 12 mnto*, and 42 mules can draw as much as .jo oxen ; now many oxeu would b required to do the work of 144 horses? 9. If .'jO bu.^htds of wh at b<* f'xchan«^(Ml for 80} bnshtds of rye. aiid .> bushtds of rye for 4} bushtds «>f c«n*n. and btiT-hela of corn for 12 bushels H p cks of oifs. and ;{i bushels of outs be worth $1 ; what is the valu*.> of 100 bushvds of wheat? 1(>. If l^h«d9 tliclK of uats wUeat? d. and lr!h iak»' 5 yardi |uivaleufr to PERCENTAGE. Oil PROFIT AND LOSS. Perccntnsie is :in jillowuncc, at a (TitHin rate, for every liuiniriMl. P^r Ct'iii. is a (•(MitiJHMjon of the Jjutin per cenhtm, i\\u\ means by Uie /iimd/ed. The ratio of Pi'rffrjtii«rf is tin; ratio ol ihi* liih- jmt cent to 100 ; thus the rjjtio of per CMiiiiine for jk-i* cent is YoTii ^*'' -^^ whicli is the rale lor eneh iiuit of the quantity on \vhi(,*j) j)ercenlage is to l)e caUmhited. NoTK. — To rxprcss tin? ratio of p'Tccntnp' d« cifnally.-dividt the rut.<* |H'r cviil. hy 100. thus tJM' ratio lor 2ii p»r cent, is 2.5 -J- 100 = 0-5 ; t li.- rate lor 4 {mt ctwil la 4 4- lOU = ^4 ;, tbo rate lor h por ci.-nl. is .05 — h/0 = .OUo. Cask I. — To Jitul the Pncvntafse on a oivcu number. ExAMi'i.K.- (.'lofji which eor)*75. and fold it at a prtriit ol' 1-.^ p r cent. What anu)ui»t of profit did he uuik«- 'i 2. A nine! suit pnrclinprd a quantify of etoth at |fi.30 p*>r yjUMl. At what pr.ce niUNt he sell the cloth to gaiu U34 Jmt cent, f ■. , • - , . ;. , ,, 3. What would b*» thf annuat freiuium of i»?8»irance onti mannfaetory. valufd ai $*J >.UtM. at U p« r ctui ? 4. A f»nM«M' lw)nj»!d buid at $4-t,7rj p» r nerc. At what price nuj*!t h«' m'11 tln' lam! i«» niako a profit <»! 2'> p«'r enuf.! o. A inercluuit bought silk for $ir0. wlreh on aeeonnt of daniaj?*' nc»'j\«'d he sold at a lo^s of oA percent. Wbal was the entire losa f ■^J '.i f 06 PFUCKNTAGR. Cask ll.—To Jintl what ptr Cttif out A umber in ofamVtfr. Exwin K.--(hi Hit inv4stninit of $S.7'>(i. a piTsoii piiiuU $Ki7}>.hi^ ; wluit wuH tli«' gtiiii jht ciiit,.? 'I'ltiK Kiik ul^o dt^pciuJs uii SinipU' rifpoiiioii. hihI iiuiy Ik* sIuKmI liiit^ — If $8-7:>0 pitii $l;«»7.1«;|. what w.ll $loo }?aiii ? lii'iico the Rn.K. — hividf Ihi* aniit ov loss liy lh»' luiinlM r t'xpff'HPing the cuiistf III ihi.' >x\.u\ }iii^ -i- $8-7.")() X I0«»= l.lltt porcfut. 7. A pi'ixm pii (I >i tux of $*>:'. S'S] on properly valued at $352r).rM) ; nt. what fati' pt r c*'nt. was lh«* tax a>M'hM'd ? 8. Th»' prop, rty of a villa^'v amounls to $1(K)(MM). and into bi^ ta\«(l to til*- niiionnt of :r2'zoO. tor pnlilic iiupiuveuicuts. At what p< ictiiniin \\\\\>\ iIm- tax ix* laid ? 9. If silk \v« n- pmrhast'd at $l.a(> per yard, and sold at $2 per yard. v\liai would l» ihr gain per (:< ut. ? 10. A f>«rm«*r puirhaH'd Ian.7.'> pi r harn-l. and pold it ut ^7. \6'\ p K )>urrel. Ilow uiugh d.d he gaiu per cent, t Capw ]If. — To fiml 'I J\*intthtr to which Pfrcnitnfre being at/ttnf at 'i ^iveu liatf. will tniminil to o cettuin Sum. KxAMi'j.K. — A tlro\«'r >ohl w h t %A entih* for $ JKM). wh'ch f/as ai a proHi of ". '.» p'-r cent. Wlmt dd he pay lor them? This nih' IK also l)a.iiriplf Proportion : for example, FUppose the cattle eost ^\{)() it is ce ttt the gi\eu proth would he :^liM» -f 2o = !.!<). therefore SujfX'Ked S»>i^ /Vir«. Titif St-r,, i'ticf. !iuj'i>«> "0 to the tpie coPt Now if tiie Mrst term. l.(». Iw d vhled l*y the third, 100, we obtain 1.2(»: henee the foUowiujr ; liLLK.— Divide the }ii\ (Ml sum hy I /'/iM the r«/io. Thus OUO -^ 1-1- .10 ~ $75'}. Ca, y .4 PKUCKN'T.UIK. 07 Kiile uUo iliiiif. — •ncc tlie lOU ; thufl lit. valued at •I'd t I. and is to uveincuts. id suld at ». and gold eiiiuiu of and Bold !unt. ? and pold cuiit. ? r/;j? being It Sutii. 00. \\hTh or tliem? fxaniple, )i piicu at ore •le coft J, 100, we rv A prncfM' prll« siipir at I*J.', p«?.t« per 11>. and 'm undoing mokoH li protit ol' 'i*» p<'i- coitt. oti i!u' cusi. Wliai did tU6 t>kijzar cusl him pel pniiiiil .' ^ 14. An u)r»'Mt nrt'lvis a n'niitfanct' nf $rjOO to pMrH»af>e cloth, and ix to rfiaiii l< pld a h)t ol' silk?* for $1012.05, finds that his pKitit is ui \[\v rule of CO per cont. U'hal wufl the cost ol" till? s iks? 1(5. A shociaaUiT sold a lot of hootM for $ 100. which was Z'.)\ p'r c<>nt advaM(*«> on thir cosd ul' making ihein. What wa8 tilt' coirh'rh Pf*'ernta?e bring subtracttd at u ^ivtn ratf, will leave a fx'ven remainder; Ex.4MPi K.-— What amonnt of Tank Ptock can Ik- hoiijrht for $475. at 5 p.r c nt ple Pro- portion: for «'.\iini]>lH - at *> p'>r c*'Mt discount $100 liuak Stock can he pnichasid lor $100 — 5 = $'.».">. thcrelorc ^ Supposed y^lliny p'itt. 475 : : 101) io th«' truo cost. Now. if the first term h" divided hy the third we hivve 1)5 H- 100 = '.♦o ; heiKM* th«- follow insx Rui.K. — l>ivide the ^liv n snni hy 1 tninns the ratio. Thtia §475 -J- .!).> = .'-';"/C0. the 8l«K!k which can Iw bought with $47.*>. NoTK — fr will be ppr'n that the only dilference lietwpnn Ca.se y/Aaiul ('use 71". is that in the loine-r tlif rate is added to loO for lh«' lirsl tertn. and iti the latter it is siibrract«'d. 17. A milh'r }»old a lot of dafnsiufcd flour at $.''..75 por barrel, which wa*' at a loss of \ *\ p«'r cent on tie- I'xt of it. What did the flour cost pi r l>arr« 1 ? 18. Wlwn rail-roswl slock sells at a discount of'7i per cent, what amount of st<»ck can he purchas«'4l for $2775? 1J>. What Hmonnt ol stock in tin* capital oT » mi ninjr com- pany, at 3.] p.r cciil diacuuut, may be purchu:iod for $IUUO? t'-' iff M > •.0 m • "I ? SIMPLE IXTKIIKST. Inteufst is the moin^y paid for the loan of money. ; The PrincJiud is the sum of nioiiry h'lit The li'Uc is the rutio of the priueipal to the inter CJ^t for I vt'iir, th«H 7 per cent sigiiilics that $100 will j^aia $7 in 1 year. The Atnijant. is t,h« interest n X .0.3 = the later' est. Hence th ; Rru.K. — Multiply the fnt(«rf*st by the r itio *»vpr«>ssi»(l in iocini;Us, Ww tli • iiiftTost of ! y»*:u*. If th»* (|ii('stioii ooiitaini yean, nn»'iths. nnd iliiys. iMiiltip!y th(* iiit<'r"St for I yytwv by the mumiIht of y<>:irs. atiil talcu the aliqsiot partri for inonihf Atid iavs, as follows: — V tAMJM.K. — \Vh If. is th«* iMtf-n'^t of $1752.96 at C per cent, for L years. 4 inoitlhs, ajU 21) days? , Mlb'lM .U't thf* ratio 12" I0ri7r7 7<> int . for I y. I0").177nx2 y. = $21 n.:r)V2 for 2 y» SUiHTytil'^nTt. for I m. 8 7<; 18X 4 m. = :i') U")JI2 for 4 m. ~ltii 1 iilut.'fi »r I a. 292 KJ X 2:» <1. =x »<.472;i.ii870 noivcy. lO intor t $100 Rule, - oiitlhs. at lite prill- $3, wli«i4 w(» have <>sso(l in Icoiitaini y»Mir l>y iiioulUi )er cent, for 2 y> tor 4 m. tor 2D d. ^'v- SIMPI.K lyrKUEST. 9<^ 1. What W tlu; iiitonHt of %i\'i^ for I yeftr, at (i\ p'>r ooni! 2. What Ih ilie itUcriKt of $871.26, fur 1 your, at 7 per cvni? a. Whiit If) tlie iiiUrcst of $r>35.50, for 7 yearn, at 6 per cent p«'r luinuni ? * 4. WImt is the interest of $1125.883, for 4 years, at 8 ficr cvnt? 6. Wlint is the interest of $119.48, for 2 ypai'P G months, «t 7 pi-r cent ? 6. Wliut is the inten-ftt of $2.i0.C0, for 1 year nior.tua, it (J per cent ? 7. Wluil is the interest of $9JG, for 5 years ami 4 months, at 9 per cent? . :> ."iV R Wliiit is tlie intTPst of $ar)8.r>0, for 1 year 8 months aD4 i (l:iy». JU 7 per ctiit ? , > 9. What is the intere!»t of $1401.75, for 4 years 9 monthi »n p r cent ? 10. What is th»' inter.'st of $1230, for 2 years 4 niouthl %n(l 12 days, at 1^ \wy cent ? 1 1. Whut is the interest of $1500, for 9 months and 20 iays, at 5 per cent ? 12. What is the interest of $15^6.25, for 10 nioiuhs aad 18 «lavs. at 8 per cent ? i:i Whut is the interest of $(140, for 3 years 2 montlw and '.♦ rhivs. at (>.] per c»Mit ? , It. What is the iut^re«t of $'J7G.50, for 11 moiilhs and 21 days, at 10 p«'r cent? ,j ^ l'>. Whi\t is the amount of $378. -12, for 1 year 5 monthi Arid 1} ilavs. at 7 p«*r cent ? * f lil. Wiiat is th«' amount of $1250, for 7 months and %\ Uays. t«t lOA per cfiit? 17. Whnt i."* tile interest, of $0500, for 2 months and 10 days, at \)ii p-r cent ? 18. Wliat is the intere.«?t of $70.50. for 10 years and 10 months, at 5| pir c nt ? lU. VVhal will $bi50 amount to in (U) days, at 10 per ceii^t v^roperty, ue«j:otiaiiii«r ImIIs, 4^c. • BnUrnfre is an allowance to a lirokcr for procur f«g sali's, iransfers of proju'rty, kv. Ivsurfnicf is an allowance ('ailed prewmm, frivon to pci>;nn«« wlio cnjiage to make good I lie loss o( 'ilii|)s, nicrrluindisv', houses, &c., that may be lost oi tianiaged l)y storms, lire, &f. St(d' is I lie debt owing by government, or the t?opii!d of railroad, banking, or oJlier companies. KoTK.- TJ!?' following exercises are all ptn'rorni'cl by th# Uuh* ot Simple Inlen'i't. ExAMPi,K.~A eoniin'ssion m'Tcliant foh\ a lot of gon(]s fot Tliich he !«'(• ivrd $7r)40 : he cliar^cd '21 \n'V cvi\i couinihulvn What wa." tli<' iitnount ot h s roiii- miHsiitn. .'okI how much mast he jmy $<.')'10 .on ovrr? \N ♦• (itnl tin* conmiission us in sinipU' |M'ic«'nt}Vii<'. l»y nmltipl viiijr SlJSh.50 cammisnon Uy th*' <1» Mjiil which "vrM'»"'>cs iIm' t:T h\ rate. The princ |ml, «liminii-lM «l l>y ,^^ -^ ^be commiss o)i. givcss tbo uniouat — '- — — U) \ni psiid over. S • •>»> i • ^'0 arnt. pd. over. EXERCISES. 1. A cominisnion mcn'haiit rrc«'ivrs ^IMOn.TT to he Invest- *d in groceries : he i> to receiv*' 'A per cent. conint!s.'*ion on 'be anioitiit ol the purchu.^e. What uaioitnt is luiU out in ijrocesio ? 2. An auctioneer sohl h house (or ^MliTi. and the furniture for ^lo. 0. Wliaf was his coimnissioa al ^ per cent ? 3. A colhctor of taxes leceiven i} per c«'iif tor collect'np: a tnx ot $.504.25. W bui wati the amuuut uf bin ])erceulage 7 npon iXC] ijront or roper ty, ' procur 7, jrivoB loss vl ! lost 01 , or the 'd by thf good? foi mmisfion . pd. over. l)e inrest- jilssioii on liU uul in Ifiirnlture ll«'Ct,*njr a [t'uiuge ? COMMISSION, RROKERACE, IXSURANCR. 101 4. A provision in<'rcl«ant poltl on coinmlssion 7.50 Iwrn-lji of iloiir at $1)'75 per imrrel. What \vu^i Win cultltul^^iOll at 24 plT CiMlt? 5. I paid an attornov (>„ por c«nt for collecting a debt of $73-0-:io. Mow inucll did I rt'ceive:? fi. I atn old <2:«'d tosril $2<»40 in bills on ih« Provincial bank« n^nii w'liicli tiMi'e is a dir<;ouiit (d' *J j per Cent. How mucU bankable nioiny will 1 rtcoive ulttr deducting ihe brokemge^ which i.« ^ p'T cent 1 7. Wy a pay tor ii, incindiug his C(>inmi>siuM ? 8. What 1m the cost w much muue/ docH A pay foi- th<' stft l>onght 'or $«5J5k4. at an advance of 14 per cent on the par vulne oi SKlO a share? 13 Wh<'n bank stock sells at a discount of 7,^ per cent, tibat Hniount of stock, at par \alne. will §:i700 buy ? 11 raid $rjO for insurance on my dwelling, valued at $7500. What was the rate per cent? lo. What wcMild be the premium for itisuring a ship And eari;o. valuecr ccui ? * c lU Si ■ li-ll I tt & '•■' I 103 COMrOUKD IXTERESt. A Compound InUresi ia wlien the interest is added to tlie |»rinci|ml at llio end t>f' the ytniVy and on that amount the interest found for nnoflier vear, and added agjiin, and so on : that is called interest ujMm intere»i. Ixvi.K. — Find the intrrest for 1 year, and add it to tb« ci|ial. whiuh ualt tho auionnt for tho iiivst year; find the inie.rest of thi« amount, which add as hefure. for th per et?nt per annum, comjiound interest/? 1st Tritioipal Ij5l00'00 Amoinit SIOG-OO fV>r 1 vear. 2f/ Trinoipal 10« (K) Amount 112?>t) for 2 \Vara. 3^/ Trincipul 11230 Amount 1 ID- lOlG ft.ro years. 1. What 18 tho nmonnt of $125, for 4 years, at 5 ph eoni per annum, compound interest ? 2. What ia tho ci»m|»ound interest of §=500, for 4 yeriTS at jter cent per annum { 3. What will $1000 amount to in 4 years, at 7 per eenr per annum, uou»p<»und interest * 4 What m the amount of $750 for 4 years, at 6 per fienr f>er annum, coujpound interest ? 5. What ia tho compound interest of $870 90. for 3} years, at (J per cent ptu' annum ] (). What iH the C(nnp(»und interest of $500 for 2 year^^ . at 8 per cent per nimnm f 7. What i« the con>pnund interest of f 3758-50 for 3 years, ai 7 per cent per annum i 8. What \n the eomp months th^ diff Tt^ntie bt»tween the true ami the conii- nion m*4hoi is n'»t noficed ; if. beco?nes nhtv iinptrtant) hov.'»»v(»r. in ne'^otintinj^ lon;»; loan;ji^i*n Mo!l;^:io»» or other ISecuritieei, as will be «een by the following exorcises. » * ' m m 1l r! 'tf I ''I •it I '4V 1 \iA w (i II 101 DISCOUNT. NoTK. — To prove tho corr<»ctnoss of thft true w.^-tlioii above, it is t»v'iin iiKMulkaiit 12 pi>r cciic on llie niorit^v he iv^c-'ives : cal hoth. unf the whole $1000 at ihe given rate and time. • ExEKt'isKs. — Oi'^count the full-nvini* ^ocnritiea hy the tn(€ method and then hy tlie common method. VVhut ur» the net proceeds or presei.t vu/uc / 1. 2. 3. 4. 5. C. 7. A 8. 9. irv 11. A 12. A Bill of ^'2")n :it 2 nionths. at 12 per cent p. aim _ 375 3 — 20 — _ 400 — 5 ('».'> — 870 — 972 Mort;'a<'eof 120) — 5720 — 9M){) Debenture of 1' MM) — 0470 9200 4 2.V '^\ o IS 1') 24 ao 13.' — H y(»ars. at 4 per cent per unu'm 4^-5 5t - 3 - , Oi i}\ '_. •' -i — —£ • ,, 20 — 2 ~ 11 -- 2\ 7| — 3 -. ' ' Case TT. — W^ren the mnnetf to hf inve^ifed. the rtde per ceift^ and the time are ficed. lo Ji-til tie amount the Secunly i m list he drawn for. Rule. — rind the interoj^t of $>'I00 at the ^\kcj\ rate and time, add it to liK) for the innnm.t. \Uru ^ny — As 100: the money to be invested : : amount of lOO. Example. — For what «nm must a hill at 2 months ]>« dniwn. HO that when di>c< muted at IS per cent its net pruoeedd or present woitk ^hall he !^o7o ? As 100 : 375 : : 103 to !^360.25 ihe umouot of the lill. Exi fn tht ind at in;i; pa to ex( ainouu 14. 15. 10. 17. IS.fnd 19. 2). 21.1na 22. 23. Case 11 time Rui.R hy the t then — A the rate EVAM years, v vhor^ed TIu 21. .Soon 25. 27. h.'V \-'\7. 105 on tho on ihe leni to- ith tho time. l)y tho hut ur9 p. aan linn in inty do i\r\<\ 10: the llhs ))« Ita net ExFunsKS — Vunous porso'*^ nla'»ft *]»(» following; sumf In the h.intls of a hrok-r for ui"«*m ni^nt. »n th«^ nianiHj» hmvi* sums. ko«ul-«d tuj ainouui for whicU eucli stiuuniy niasi ho druvi'n \ 14. 15. Ui. 17. IS. VJ. 2). 0* iy\ In a Kill at 2 months, ut 12 per cent, $4C5 4 — 3 — rnaMurtg.'igoal *i yoiii'.H. iit - 4V InaDebenturoat2l IS 21 3.) 2j 1.V 2V '6\ 900 786 874 40(Vi 6204 0425 10800 12()10 10000 hill. Case TI!. — IVJ^en the pre^ient tr )//'/. the nmnw^t. and tht tune is Liowny to Ji-nt w'nit rate //«>• been charged, Uui.E — Siihtract th<» principal frosn tlic amount, divide by the time, iho qUdiitMil is iho mr«r«st nuide in one year, then — As the j;ivcn piinoipil : 100 : : this quotient to the rate per cent. KvAMPLR. — Secuniies to thn simMunt of $1650, for 5 yours, when Bold, produc** :^12>0; what wad the rut« diorged * $lii.i I 12i»0 ■. i T)4/ir> - Then as 1230 : 100 : : 00 = 7^ per cent ' . FIND TMK K\TK PKR t'BNT. tl .Socarities amt'g. lo$lS '.O for 4 v.^ars. sell for $1480 2:>. — OVI 5nio.itha — 000 2^, - • • 27. 670 3CJ 1^ — _ 341 Vj! lOi) * Barter is llie rxclm!i«ri»ijjr of •MiO ^^^.'^in'^I*;* >i Another, nihl diivfts nuM'tthaniH wut frnth'rH \wm tii make the t'xc!iaii;j!^« vviihout kws to citfter pmrty. Rui.K. — Finil tlu"! valun of iho i!<»m;n(»(li*y whose quantitj isgivM'n: thcii titul wlutt qnittiiitjr of Uhi olh«r iit tht proposf^d nitt; uan be bought lor thu »ainu luuxiey, and h give* the auswer. ExAMiM-K — What quantity of flax at 9 ctt». per lb. musi be given io barter for 12 lbs. of iudt^o. at $*2.iy per lb. 'l 12 ibd. iri'li-^-) at $2 I'J per ib. eo?noM to )p2() 28 : tnerefoM fts 9c/.v. : ilh. : : l5N26.2.St'/v. : 21)2 /is. the aurtwer. 1. Mow nunrh wlioat at $1.2") a bushel inui^t be giver in barter fur oU Iju-bels of rve at 70 ci'ntH a btitihel '? 2. How much rice at 28,v per cwt. may be bartered (or 3^ cwr. «»f j'ai>in8 at 5./. ptu* lb. f 3. How luuuh tea at 95 ct^nts per lb. tnust bo bartered for 78 gallons of brandy, at 1?2. 1-) per gallon ? 4. A had H| cwr. of sugar at 12 etc*, per !>».. for which B gave him 18 cwt. of flour j what waM the flour rated at per poutid '? 5. B bar^erHd 3 hhds. of brandy eontainin* 69 gak eaeh. at $1.05 p(»r gallon, to C fur 125 ydsi. of cloth ; what wad tliB cloth per yani ? D give.s K 25t) yardis of drugget, at 30 cts. per yard for 319 lbs of pepper; what duos* the pepper aland him in per pound ? 7. A had -11 ewt. of rice, at $4.20 per cwt.. for which B gave liiuj $ in money, and (he rest in t»ugar ai 12J cts. per 111 : Ijow mueh sugar did A reeoive 1 8. A farmer Inid 120 buHhel-s of wheat at $1 50 per I^Hhel. fur vvbicb H gave him 100 bushels «>f btiiley. at 6S •fM. per bu-(hel. and the balance in oatn at 40 cents pef butihcl ; what quantity of otUo did the farmer receive I w dnct the r( scconc here Again of the Evoi nunibei EXTRA Toe to find duce ih RUT.K jriven nu each, bv iv^\ir(\ a towards :i of the lli'-qnoti 9, from biaiader Im« t« ly. quantity ir ait thi r lb. musi I per lb/! ifteretort r. be giver ihel ? bartered bartered for which rated ut 69 gals, [til ; what |per yard Land him m w hich lir at 121 il 50 per lloy. at 6S Vritrt per Iceive i IXVOl.CTION — EVOLUTION. IXVOLUTIOX. m When a nnmlHT is multiplied by itf^elf, the pro duct is culled the power, and the imiiiiImt invdtiplied the root Thus 2 X "2 -=■ 4 : here 4 is the stpiare o* second powir of tbc tool 2. Ajraiii, *2 X 2 X2^=:8 : here 8 is tbe «'ul)e or third pnwrr of the root 2. Again, 2X2X'2X2=16, hero 10 is the tburtli power of the root 2. 1. Find the Pocon«l power of 8. 2. Ut-qinrtHl the third p^wcr of 13. , X liaise 32 to the fourth power. 4. Involve Ifl to tht! lil'th power. 5. luvulvo 38 to the sixlli i>ower. EVOLUTION. Evolution is the method of fnurmg the roots of numbers. EXTRACTIOX OF TTIE SECOND Otl SQUAIlE tioOT. To cxtrsH't the sqiinrc root of any j»:iv«'U nnnd)er is to find a iiunil)er, when multiplied by itself, will pro- duce the ^iven number. • * What is the ^ quare root (vf 106929 "? RuT.K WITH ExAMei.K.— rvivldte th*? given iuimlnr into p« T'Otls of two figiiros each. l)y phicinjx '^ pt)int ov»r the unit (ij;iin', Hiut ovrr ev««rv alteruat«* llfyure towards the left. I'Miid t!ie square root, liof the tirsi period 10. and phtce it in th' quotient. Snl»M'nct the ^qujin* of it, 9, from »h • first period, and to the re- buiiuder annex the lurxt )>enotb ^^t f:'■ "ivi' "? 'i 1., f'ii y \\ rl u 108 SQLAUR ROOT — CIBK ROOT. % dividend. Doiililf ili^ root nlnisidy found. H. for a divisor, Mid sli|>p(l^i!l^ ill*' iiiiir li,L!:iil'i>. !l. niii Hcd. lind imw ut'U'l) it, riz. U, 1^ coiilHJiird ill tin* er, still tiie pointing is to beo:in IVoni iln? unit's pi. in; of the integers^ and :i point to he placed over every alternate ligure both right and left. The pqnan* root of a fraction is found by oxtractinn^ the square root of the nnnicrator tor a new iinincrutor. and the root of the (b-nonilnuior for tt lunv di'noininiit«)r ; if. how«*v«'r, this caniKtt b(> done, let ttic fractiua be ri'duoed to udtcimalf %ud ihc root extractrd as bfturc*. . 1. What is the sqnaic r? 2. What is th'.' sqnan; root of <)L2r)21 ? ;, 8. What is the square root of 1231321 ? . ,, 4. What is Hie square root of 20.*>2.()!) ? 6. What is the sqiian* root of 47!)r). 25731 ? , , (r. What is tint square root of 24ti74.i2C4 ? 7. What is the square root of ■^^\ ? 8. What is the sqiiure root of ^'3^5 1 , EXTRACTION OF THE TIIIPJ), OR CUBE ROOT. To extrael the Cnhe Root of sinv oivni umnher !s to find a imnihfr whirli, when innltlplied twice bjf itself, will produce the giveu number. -i^XZ divisor, )t't«'n it, ! tinu*»« ; Multi. J4. Iiom ;ed tbua 3fls arc when be dc- g is to uiui a re both tinj? t!»e aiui the io\v«»v«>r, decimal, ; . GOT. mmboT vice b/ CUBK ROOT. Find the Cubu Root of 12812904. 109 HfLK WITH I'!X- 4M1M.K. •— Divid.' tho j,'iv(Mi iiiniih''i' into IHM'iods of lhn'<» ll^- ui'<;S, b<'^i lining; at ih(* place of units. lMuc«; thi' cuIm* r«ii»t of the llrsi iMTJnd 2. in the (|tioti«'iit. And subtraei. itriciilits 8, from th«' Hr.-t \u- riod. and hrinjrduwu the next period t pn»'l(U't. 4h>7. troin thi* divid< nd, 4812; bring down another period for a new dividend, and proceed iu ths lame munuur. * . t In order to extract t!n» culv* root of a vulgar fraction reduct it to a decimal, and then extract thi* root. Iu mixed uumbtM's reduce the fractional part to a decitnaL Find the cube ntot of the followiuif numljers : — 1. of 8:3M« t). of .'>27.34.37.') 2. — .'> [X'l 7. — 7834.S748 3. — 389017 8. .0:)31o737tf 4. - -.., , 1092727 9. 4 5. — 84004519 10. — 7" 1 ' ) 1 >S: no DUODECIMAL MULTIPLICATION Tills mle is nindi* use of hy artificers in tnctiKH - injr tlieir work. The s ; tlie iticli into 12 parts euiled 8eeoiid.s ; Ike second^! into 12 p:»rts ealli-d thirds ; and the thirds into 12 parts ealled lonrths. Three seconds are nuirked thus, 3" ; thirds, thus, 3'" ^ and fourths thus, 4"". Multiply 7 feci C^ inches by 2 fuot 5^ iucb«(k Rrf-K WITH RxAMiM.K. — I*laoe the ft. in. " fiHltiplloruml rtlif uuiUiplicun*!. li't't 7 4i {♦* IikUt fvrt. iiiclu't* aialor lnch<'s, Ac. 2 5 8 ' • Ittaltiply tlx' umltipIicunM. . t»y tht' hi}rli(*st lt»rm in tlu* inaUipli«T. 2. currvin,!? Wy 12 ; thiMj niultiply Wy the* n«'Xt Utwvr ti^rm in th«' maltiplifr. viz. 6 iuclu's. *«ikin}» cure. b<>u>*^v«'r. to put th<' pro- duct oiM' place towjinls the ri^iht liaml. Do the naino w'tli iKt next lower tonu, und so oa. Add ihe dlllcreat pioductd to futber. 1. Multiply 7 fiTt 9 inchcR, by o feet (i inches. 2. Maltiply U feet 6 iiujheP 3", by 4 feet 8 inches 6". 3., Multiply V2 feet H iuche8 7", by 8 feet i inches 9", * In«tMd nt } h<>fl 0' nrr put down, bitcttUHe Umj ara (squitatoDi tiM kMue U Uuutt with Um> J iuvU. - ■ ; i . '- 15 1 « 3 1 9 9 1 10 8 S 18 o 2" 6"' a" 4. M 6. M 6. M 7'o Jim 7. Fir feet 4 ii 8. Fill 4 inches 9. Wb (8 G feel 10. R( luet 9 ini 11. A ras tb«' I U-eadth i. 12. Ho p r Coot. 12 lett 4 To Jind i 2 iiiclie.M i( It. R-q truild, am: nUOOF.OlMAL MULTIPUIATION'. Ill N mc«K« • I in t\•<^^ into 1*J t8 called thirds ; . 'riir<;e r »§. 9 io wrik iht roducla to 6". bs 9". 4. Multiply 4(i ft;el U iuchoa 8". by 12 IV.et 7". 6. Multiply 87 ftMit !)J iiichos. by 11 teta 10| incho». 6. Multiply (187 feut 7J inches, by 24 fuut 10] inches. Tfl ^/irf the supvrficiui content mulliftltf the Ifiigth by tht brvudtli. ■' 7. Finil tTjp Gontont of a board 8 feet 4 inches long and 3 and I ^^^^ "^ i"^*' ** ^"*^»^^d. , 8. Find Him area of a table 10 fuet i) inches long, and 6 feci 4 inches broad. 9. Whut {?• Uh* price of a marl»i»» slnb. th»» l«"»n'tli nf which is a feet 4 iiichi'i«. (he breudib ,i t'ect 2 inches, sif V.v. p r toot? 10. Rcqtiired the area of a square, the side «f it »^;ing 23 I'cet 9 inchcM 1 11. A priivn-ototM' was charpH nt !\s. 2»f. p<'r foot : what ras th«' prief ijf it. ihr Irngih of it being 7 fret 2 inches, the lUeudth 3 feoi (> ineht-s? 12. How much will it co«t to p-vvp a court-yard at 7.t. 8*/. T foot. th«' leii;^th of it bei'ig lilj feet 'J inches, llio breadth i fett 4 incht'rt? To find the tolid content muh'tdv the len^ijh, bieCiulh, and thii'/ini:u together. n. "What is tlj(» solid content ot* a block of irmrldo 9 f'^ot l2 iiiChe.M lonyr. ^) leet S iwclies broad, aiid 2 fi-et A incht-if thick? «jquital«ni I It. R'{ n ^ II 112 DUOnKCIMAI. Sf'MTIIM.lCATloy. 1'. A loff of iiiiilioiriiiiy \h 72 r« «'t 7Jl ImcIm'* lonjj. 5 fi-f^k r\ InciicH oi'tMil, uiid ^ Ifci <>i inclio lliiek. Ki'i|tiircil ilb bolal euutt.'iil? 10. What woiiM Ii C(i>f liiivinjr a o<'ll»r «lnjr ]Rf«'<'t4 ifrhri) \0U]f. I'J Irrl t> iliclio lllDHtl. HIHI it li.Lt (i tlicllCb (li'f{), Ul 0(/., per bolid yard 1 17. U»'fjiiin'd llif f»oIi«l iMMUi'Ml of a \off of ImmcIi, 27 fee' 6 incht'H loii;;, 2 IVfi ;'» iia-lu's lauad. and 1 lout 2 inclici thick ? M 'b> 18. What Iff 11h' valin' of* n M — • lu - iia 'n M! fit itb bul^u It MENTAL ARII'IIMETIC iM't 4 ll'lMM? ■ t . I'i'P, mK ti(/., I -To Jind the vafur of 12 aiticlcf. the price of one being ^ioen. icli, 27 fiM» fT* ut 2 inclicii Rri.K.— Ri'ckoii ♦,'vi'ry p"nii y ill thu prici! a ftliilling. and •'••! incliK n< vHiiJc Ihe valiitt of 12 articluH ut lit. each h 127., or Is. lUlck, at '» Jinn. Jln.f. \ 12 O 67. each (.«. 24® 77. ouch 14*. I «J 12— 87. — 8.y. 24 - (;j7. — lis. Cd, 12— i:w. — I As. ;jii_ !,,/. — 27ji. 12 — 4|7. — 4«. :W. :wi 10.^7. :n«. r,7. 12 — r>kd. — 6.f. ♦>7. 12— iv. 4^7. -- i(;«. :u. 12 — 7: 7. — ' 7s. !)7. 12— I. V. 7^{7. — VXh. 1)7. 12 1.". 7. — IG.-*. 87. 21 -!.<«. 87. — 'Mil. 12— 1« 7. — Hi» <)7. 24— 2.S. 17. — f>0/t. 12— 1717. — 17jt. 1)7. 4N— I.V. 37. — ma. 12— 1!)J7. — \\h. iid. 7^-is. 87. — 121)*. \ 1.0 __ 37. — 'M)a. 720 f)7. MOO*. ■ , * ■ I.O* 77. 70.V. « (> - 77. — 4!)0.». 240— 87. — 1C(U. j)()_ {]d. — 4bO». mO— 77. — 210*. lOKO- 77. — (;:{0*. ^si) — p,/. _ :m)s. l.'OO - 87. — 80. \v. 100 — 1 17. — ojUj. i;;20— i*7. — })yo*. "Wh^n tliere am h r»'W ovor or ii mI.t tli<* «1ozMn. calculatt for a duZfii, and add ur »iibti-iict us uny Ik* ivquircd. Jus. Ans. n <^ 47. each 4*. 47. 2*. fa> 47. each 8*. 47. 11 57. — A*. 10/. 2> — Ud. — ID*. «7. 1 1 «7. — 6*. ti7. lA - 87. — f)*. 07. 10— fi7. — .'»*. . 22 — 77. — 12.». 107. D— 87. — (I.t. :i7 — 1.V :{7. — 40*. 8//. i:> — 107. — I'iH. (57. :;:> —\s 47. — 4(;*. 87. * lu tliik ciutr ttuu Uic .'Udnii- lor uiie dozvii aiivl Uk« U Wa 1^ ill 1. 1 »*i 114 UIC.VTAL ARITIIMETIC. II. — To find the price of a ffrosx. the price of one articlt bein^ given. • RrLK. — Reckon tbo p<»noe in tlie pr'of of otn* article »• •hllliiijfu. atul tlitf iimn'»"r c»'" p^Mu'»'( in these t«hilliii2.s will be Hit* price of u gross in sljilliugs. Recalls*? takirijif t}i»* pt-nc*? in th'» prico as shillings is tlie sanio as multiplyiiiy: by 12. and taking th«'St' ■^hillingH a.s p^'uco Hptm is iIh* sanit' as multiplying by \'l another time, au»l li Xl:i=li4=i gross. 1 gross (S> 4ti. 1 __ _ 2hf- 1 _- _aH each 4N.<. — :i0.t. 1 gross S]il. each 1)9*. 1 „ _ 91,/. _» 111,. 1 ._ _ll|,/. _ 14J& 1 — ~ 1::J//. — l^A III. — To find the price per ftrore. the price of (*ne articU OeiN^ given. Rri.K.— Reckon a poiitid Tor fvcry shilling in tlw price Thus* th<'r- b»'in!jr lO cwt. iu a ton, the price of I ton at 7l td. per cwt, is 7/. H)s. 20 lb». ® t.f. per lb. 4/. 20 Tw. tl//. — ;V. lO.t. 40 <;>. :w. — 1-7. M)v. 60 2.*. :u. — (;/. 15.*. 80 l.v. C//. — 1 .s/. IGO n.v. ^W. - - 2G/. o.*. ♦20^ibs.^r.^. p^Tib. mi. v()0 T)*. bd. — T)')/. 401) 7.V. :{//. — 1 4r>/. {■,{)() av. 9«/. — 292/ lOi. 800 12.». — 4 SO/. 1000 2.V. lid. — 1 12/. lOi IV. — To find the value of 100 articles, the price of one Oe.nfj^ given. Rri.E — For ovory farthirig in \hv pric** tsiko a« many ponce nnd twico as many shillings. Thns. 100 pfiicils at D^d. each »8 12s. (j 4,v. IW. pr»r doz. 4\ft, 1 Is. i'ui. — Ihd. 1 — lOv lb/. h)U. 2 4.t. M. — Hjr/. n — 7.V. {id. 22^v 12. Bpcans' takinu: fho shi]!iMAi/. 1 _ in,, _ ]\y, i — J 47*. — U^ il iti 1 1- lie MRNTAL ARITHMETIO Vll. — To find the vafue ofn nhiiife article at a certain rati fH'i' ttiute. Rule. — Reckon a Bitlliliig foi' every pound tii the price. Jinn. Jtn$. lO 41. per score 4.*. 20V. 5«. P'T score 8*. <»/. 1 1)/. — JIv. 1—7/. 7.S. ti.v. — l\{)s, \hl. 2 1 'I/. in.v. — 2/. 12a. «. N/ !>/. It. '.f. 4i one tliott* «»ix thou« idrud aud sixty-four it mi I Hour Five mil- Four mil- -Two mil- 1 aud two ndred and Fifty fnit- ne millioa ndred and ty-sevou — I lid red and iiidi'til and ou&aud six IC] Eigftty-onp tbotiRand four hundr d mid ci^flify-oiu' — Mmly lour thou- BUtid and t^ighly-Mix inilli(Mis tour Imiulrcd uud twynty-oiio thouHiUnl tlirtH' liuttdrd and sixty. 't !7.] Fourteen tliousaiid and twcnfy-thri'<» millions six hundred and lbrty-oii»* thonsiml t.wo hiMdrci] mid one — Twenty ih()4isii(id t'iixlit liiiiiilnMl and sixty inllioat) two ihonsand and on(> — Forty thousand and two niillion» two hundred and two. 18.] Nmv hundn**! and s«'Vf!n thousand and sixty millions two hundred aud six (hou'^iind r.Ao liiiii.S— i;2-7(v— 77— 1)7— 84--05— 99. s.] 100—104— 2 u-(;!H—7:)()—i)0^>—!»;n)-8;)2. 4.] 4000 ~■42'^•^-^>'^'t'l —{>'{):> -70:)0— 1> lO !_80SO— G707. 6.] 101)00 ~ LjotiO -- 1 !)U1 SI— 2d.M}:>— :^»0;j8— ^00 10—56502 — 70777. «.] 400000 — 4000 10 — (100707 — 0S0000—25G975— 700707 - 9(54259. 7.] coooooo — r)4!i:rM)o — H{)U) 102 — 7 ior>7f;5 — 10010010 — 202 to o\ — 5;{0 >;iJo;{ — 85;;:) t8ii5:j — 20a I0o508 l)9aojJO0O. '.■I 120 ANSWERS. SIMPLE ADDITION. 1. 1185 25. 105 2. 124« 2(i. 293 8. 1348 27. \408 ^!' 4. 14<>5 28. 1475 5. 2249 21). 15388 i' «• 2072 30. 4257 r [..■■ 7. 2311 31. 27731 8. 285() 82. l65K28a 9. 975 33. 78151214 10. 1035 34. 53()14G 11. 151 (> 35. 75075 12. lt>5(i 30. 311013 13. S4!I57 37. $57821 14. , 218(;7 38. 2246 15. I>s0ii8 8«. 72 IB. ]<><)13 40. 204 17. 30154 41. 251 18. ISO;) I 42. 68391 , 19. 2oi(;9 43. 2203 i 20. 14372 44. $2197 1^ 21. 4110113 4({. 102 22. 351(124 6081 23. 27S538 47. 415 24. 24boU3 48. $84 iXSWERS. in SIMPLE SUDTRACTION. I. 18^ 31. 704020138873 2. 470 32. 424^5- (5325955 3, 342 33. 4I780194.')9a9 1. 4r>(i 31. 4108" '9998308 6. 5:t(> 35. 457555 6. 37."> 3(;. 1205995 7. 4(>3 37. 3599244 8. G3I 38. 57955 ». 96 39. $8072 W» 90 40. 171 11. 10175 41. 844 12. iHiun 42. 172 13. 25972 4:^. 178 11. 70747 44. lOS 15. 3(;!M9 45. 135 It. 78373 4fi. 790 17. 40::53 47, 1380517 la. 381199 48. 11 w. 22984 49. 130 10* •J 5289 r)0. 740 21. 78359 51. 2830 22. 25292 62. 875334 23. 4f»2121935 63. *4r Wilsons, 24. 435195K59 54. U 7291 4 25. 739::L'070 .55. 5320 26. ri2<5J:3992 5«. (02 27. 722m»f)4I2 57. 1794 2d. 91310919 58. 85 29. filJ^841778!)i7 5». 131 10. 7t9bO8bU00J8 eu. »• ^'M ii m 122 ANSWERS. MIXKD QUE^^TIOXS IN ADDITION AND SUliTUACTlUN. 6. 415 {fot pfife. t>. 2lil remain. ' 7. 12M").)li rxct'i'da by 8. $_87 rtmuiiiing. 1. 8:j loft. i. 2720 n tiitiin. 8. 15 '>7 ivtiiniL'd. 4. 102 to Jjfo. SIMPLE MCLTirMCATION 1 I 17101 23. 6fi82» 1 ^^ l:U')74 24. 393308 ■•'•► 4:322<;5 2.5. 78G(;i6 4 21:580 J 2(>. 580962 : m (;<)j7(> 27. 41)1(535 1 "H- C72(08 23. 884943 f. SSOMOI 29. 1179924 |. ^ 74X71^0 30. 10815&7 I t. 60 -T)-) 7 :ji. C823(>48 !•. 'lir2.'48 32. 1338(;360 It. 574875 33. 23249952 M. 6'"8(;(;8 34. 1122U09 13. 3r)(U84 35. 23150412 , H. C128'.2 3(5. 1089(5344 ri 15. 787!44 37. , 19912230 16. bTrjUi 38. 13825056 17. 2(;2<5IJ8 31). 60518410 18. 4:j77:io 40. 22039992 19. 87A4M0 41. 67ti(57(]32 20. o«;:{!!0(i 42. 71550144 21. 1050 '52 43 (53221592 22. iyuu54 44. . V 74G4480f t Fnfe. nain. 2t'('tlR by nuiulng;. 688289 393308 78G(il6 689962 491()35 884943 1179924 10815&7 0)823048 1338(1366 23249952 U22U09 23150412 i:089()344 19912230 13825056 66518416 22039992 57t}f;7G32 71550144 (53221592 74644801 ^. ♦0. 47. #9. fih 00. 6i. 62. 63. 64. 66. b^. 67. 68. 6% CO. 9h AXSWF.R3. — SIMPLE DlVI3l02f. P2I 29050420 (12. 175320' 48844096 63. $'2'.)\^ 84393932 64. 2592 te«t. 43U143168 65. 2303 U'iU'.rs, 7775(;()496 «6. 3168 boUlt% 359831X04 67. "■■■'■■ $3240> 6307:;7ii2 68. 4480 pop. 41281053 69. 865U pt'iioo. 24291591 70. 2144 2H0474U 71. 8105& 4(;3r.0';56 72. 78,1 675630377 73. m 395491873 74. 1095 hotira C49 135896 7.5. 569 iOI 64008924 76.. 76800a 3704412714 77. $15516« 403576660 78. tllC90 uilet. SIMPLE DIVISIOS? t 6911 I 12. 714097,1— » 1 13752—4 13. 3906406— 4r s. 13281-1 14. 68595.50 4. 11517—1 15. 12667006—5 5. 9553—2 16. 478066—? 6. 3186—2 17. 5894371—5 7. 6426 8 18. ' 28236344— f 6. 4206 1 19. 18824229—2 0. 636890'i 20. 14118172— t 10. 63:V/.»55 2 21. 11291537—4 11. 13771812—3 22. 9412114—5 '1 i-i u 191 1KSWKR3. — SIMPLE DIVISIOX. 23. 8067527 56 1613 38 21. 70:>JK)8«— 1 67. 1U7-513 25. 62747 45i— 2 58. 92-728 26. 6(H72(i8 \) 59. 181—26 27. 6133880 !) 60. 113-30 28. 4706057 5 61. 2«0-43 29. s 87484011— 1 62. 1-19-387 80. 24!)8!)341— 63. 12;'»-319 31. 18742;)05— 3 64. 3.V)— .3 82. 1499360 1— 3 65. 2 M -21*5 33 12494670- a iHi, 2Ji— sa 84. 10709717— • 4 67. 174 5a 35. 9371002- 7 68. 141- 2«5 36. 8329780- 3 69. 118-555 37. 7496802— 3 70. 209 41 88. 6815274 9 71. 632-155 39. '■■■.. 6217385— 3 72. 101-816 40. 26654-14 73. 167-396 41. 41315—17 74. 216-:{55 42. 40364—12 75. 127-535 48. 24«4f>6— 2 76. 1080 t 74 44. 17862—35 77 10;i2-570 45. 8703— U 78. 9591-218 4i6. 6828—33 79. 9!Mrj-383 47. 4408—28 80. 72;U-312 48. . 10!M)2— 31 81. 700-l.')07 49. 1889—64 82. 857-1713 60. 33)9-83 83. 3186—11 61. 3450 76 81. 9.k;-20U 52. 1767-22 85. 2:>13-U09 5:^ 1726-18 86. 2587-1 2i'2 64. KJ87- 8 87. 951-308 65. 1649—31 88. I0i;l--2116 lU— 38 )7-'>l3 [)2-7i8- SI— 26 -Ii)-:J87 .'»') — «U9— 41 )82-la5 iOI-8U lG7-»J)a 21()-:{55 127-53* 81)1—74 0;V2-570 51)1-218 2:u-:jr2 00-1507 ;57-1713 ;18(;— II »5;i-20U •>i:v-U09 •,H7-12»'2 j5i-:i>)H [;l-21lG AN3WF.R3. n M. 875— 2002 95. 45— 2 90. 4l8-74tJ» 9»». 3G bonrti. 91. 2252 -4l)0l) 9r. 2rtO— 2UJ09 92. 11— 1»5474 98. 20(i»i(>. rj22()8— 31(1 91. i 4 c;u- 7 lUO. 9^5— 23 1. 2. 8. 4, 1. 2. 8. 4. 5. J. 2. 8. 4. ^. 8. 1. 2. 3. 4. 6. 8. DECl.M.\L FRACTIONS. ADDITION. 071.458 6. 80i5.()98 ({. 1138.372 7. 1374.2784 8. HUBTIU crrox. C7.517 fi. 8.015 7. 34.120/ 8. 2!>7.or2l 9. ()G9.021 10. MUI.TIPLH JATION .0729 7. M.35GI 8. 77()t>.lll2 9. .01118403 10. .6(;42 11. 8.79 12. DlVlb iiox. 2.S803^- 7. 1.7844- 8. 10.3544- 9. 1.7H074- 10. .02 1 11. 2.9U 12. 4541.03777 739(1.1403 6558.5850 1341.58517 182.7044 70.0346 810.8879 242.245787 3^7.2158 11044O.f;O2l .4!)29(;l 78.^ 3.ti4(;5 .40006 .76 19.02124- 9.1144- 3.8l<>(>94- 2 IHI4. 24KUIH4, 3.4G89 11 1' .'HI 4 IN AK3frER9. »i '■ 1. 2. S. 4. S, 6. 7. S. 1>. 10. 1. 5 2. 2 8. 2 4. 6 S. i 1>iSK I. 2. £.0720+ £.7!MM>'J5 S. 4. £.»)(HU;-f £0M5 6. cwt. .S.67U2 7. yard !.4Ui(;4- wtM-k .0U1!«)8 8. mile .a4:i7 9. guinea .U1H8 0. ounce .275 1. acre .575 2. tnilu .UUUU4 BBDUCTlOy. 1. 2. 3. 4. 6. 6. 7. 8. 0. 10. II. 12. 13. 14. 15. OAKB n. iGk. :m. i ch. 9ja. 3qro. lib. 9oz. ldr« 14()z. I5«lr. 161 bs. luoz. lldr. 8^(1. 4} k — .^ ^^» COMMON MKASUUE. « 1 ► L :Ui 7 42. 2:J4 6U1248 43. li'Zi OASB UI. CA8B IT. JO 294 3fi8 14b5 iClo 819 352 1188 SP2 3-3 5304 e«325 33018 €8376 605880 "5890F 25056 9Z82 2(>1807 55575 17 23 58 4^ 11 8^ 10 58. 60. 1. 2. 3. 4. 5. G. ANSWEKS — VULGAR FRACTIONS 1^ J?. 294 if;8 1465 i(;i5 352 1188 S92 f):^Oi 33048 e8ii76 605880 25056 J)Z82 2<)1807 55575 44. C5. 47. 18. A9. 54. B5. 56. 57. 68. 69. IjS lf:i5 11)1 i;'>io m 55 J-8 1 ThO 240 2223 14<;.'{ 1716 60. 51. 52. 53. 2717 2717 2717 8073 4752 OCil IMKiH iJir;^ !H>iiiI 315588 3255,S4 u 13 CAflB T. 03 56 48 84 84 84 3(0 5(i7 433 €18 (i48 648 15f)rO 44553G 44553(1 4455;i») 310704 4455311 37<9;)38 38H3.!«)2 58(;i!):;4 25)199^9 84354(;t; 84354iM> 84;r)4(iH 8435406 105(;i 057803 1 Si)():r.5 1 (7 70 l(;;)2l)530 1111488075 12048530733 1204o.). 07:^3 1^0KS530733 K04H,530733 1738:'S'43 >8()40 201 1 70;;91 8IM) (;6l)(;58n7l252 b5738>.>-i.i.J.^O 857o82ol30b0 {)?<70OO7O840 857381:513080 3 8o7urf2543US0 17 ADDITIOV. 23 1. 1 98 * 1 ?T 68 2, O 170 -1 AflT 4 3. 9 itn 11 4. i Ol tiA 1 1 3 1 3 5. ' 1 1 !»4«7 5 1 10 6. " «l 1 ; tf fM 5 1 7. 9. 1 174 I I 25 ,53 14 11 n 5 Hi* PT83 !«I7 5« ' 7 n 4 » i 'vlli i69 t. 1 8. 4. S. t t. I. i. ■i 1. 2. 3. 4. 6. C. 4XswKnsi — VUI.0 A n rnACTioNU I. 1. auuTiiAurioN. : > 5 0. 21j 28 7. ' 31 9!) 8. 23 1 9. 73 ai 1115 U3 ^ JK] 10. ' i!-l7 11. 16 1^ ^ ' 8^5 12. C3f\ MUI/rir'MOATlON'. 15 «. ^A U2 4 . eojj t 1U 8. 9. 17|| 10. sn :)5i 11. 115,15 12. isiSJi 1)1 vn m)s. n^ 7. t8 i H. gj 'ij 9. ^? 2,*A 10. A"r 1!. C5^ ili 12. ■ i nBULCTION, CONTINUKt. IJLSB Tl. 8. yj.painro. ll?iis^ 4. . •3s fjvrthing »ritf 6. iiVii crowtt. 25. 20. 27. 28. 2Q. ao. ANSWERS. m 1 "JL 1 5 I 3 15 1^ 5A 60JJ .* ^ cum' -ft, 193 farthing crown. 6. 7. 8. 9. 10. a. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 2G. 27. 28. ao. ,'^ week, •'j"** h(mr. aoo^-704 dram, mile. • Iff! CASK Vll. 3|" farthincr. 15|5 6 ounces. »f» dwt. T^% day. CASE VIII. I 178. li -«d. lOd. 4h. 10h.3i=^min.l0;f8ec. lis. 10^— i'd. irt. 4in. 9<)Z l.'^dwt. 13 ounooH. 3qr. lllb G(a 8,^dr. Slur. 20per. 3yd. 2a. tASS IS. r^ .C2!> .25 3. 4. 5. Q. 7. 8. 9. 10. 11. 12. 1. S. 3. 4. 5. d 7. «. 10. CASE X. i2| .875 .833^ .1GG4|- .5025 .01334. .9-1114- .72724- .0715+ .00053 + I* ill' _i I 6J TTiffI _4I I fltf _?« 10 of TtTTJf ioa 4^ 44130 15 11 904 8;t 3 I; 314848 12 JO SO'iJJ,^? 1(» 91 410410 15 4 L 2. 3. 4. 6. 8. 7. 8. 9. 10. U. 12. 13. fifty. drams. lie. ][uiirtcr8. 1)7 9 03 10 12 2 17 17 5 ^ 1 18 8 14 8 10 7 « to 12 ii. d 111 £ 8, 10 95 28. IB. U>i7 8 4 29. 17. 18 11 3 30. 18. (iO 13 10 31. 19. 2<;8 2 r>4 32. 20. lODG 2 43 33. 21. 910* 8 1 «^ 3 k 22. 6505 < 2;' 35. 23. 5:i 18 8} 3(1. 24, 47 7 2? 37. 2.». 2S21 13 2j > 131 L 2. 3. 4. 5. 6. 7. 8. 9. 10. u. 12. 13. a 15. IG. 17. £5208 9 5| 3.»z()4 7 9 81G37 2 4 ^4 '> 4 4 10 j6 45 4 7| f)01 17 tt C38t> 11 Hi 37 14 20():? I ^ 20 13 DIVISION OF MONEY. 34 8 14 4 17 9 119 15 29 9 58 4 1080 19 834 5 60ri 789 IG 392 12 14 2 5 19 7 U 72 07 19 02 5 d. 10} •~1 73-1 lOi- 82- lU- 1_} 2V-J 0~j 7—1 Iff 18. 19. 20. 21. 22. 23. 2 k 25. 2G. 27. 28. 29. 31. 32. 33. 31. 3d. 490 723 778 458 730 19 4 63 2 1 8854 1 2 3 2 2 3 rf 9 3^ 19 9} 17 101— « 4 9- 7 13 7 10 17 4 14 ^2 h It S. 4 ¥1 Hi . 8i-{ IJ— u 2 (>J— 34 G 10 9fir 3 94-3^ 1 0— 4ir 134 ANSWERS. — RRDUCnOJf. H. Xfi 10 6.]— 531 52. £ff 8 04 185 ?t. 8 15 3 —454 53. 13 la 2 k * 6 3} 101) 54. 9 4 7}— 9 d9. 17 9 n~i .v>. 4 11 lU-39 10. ' 1 5 84-{ ( 46 10 5J— (J()9 &1. 1(1 n— 12 47. 12 4 U-3 «3. 25000000 die. 4& 10 7 7^-3 «4. 2862 2220 49. 12 12 8|-V5 G5. li 10 3| -388 fio. 17 Mi 10^— 8« G6. 6 02-1916 ■5 12 7 3 —64 '■ ! '' ^ ^ REDU( :tio ^, i n«g2 farthings. i 15. £188.1 lOfl. t 6:i478 p •nee. \(i. 4U47H. (Id. r. 350150 I'iiiihings. : 17. 8737 10 Ihr<'«pence8. % 1I88G5 h, ilfpfoce. 18. 67552 (lv«>pt! iices. 6. (>9552 p M1C«. Oii21 fuurpi'nceB IJd. ^ 7 ir)2() farthings. \ 20. 319320^0 Hixpenct'8. » ' 87.')52 farthings. |21. 38 1(>6 cr. 38. A 10 ;92 p fMice. :22. 1188014 Bt»ven ehilllngt. f. £\i'VM !0s. |23. 1 24. i 3H(;72 Hvi'penceB. ia. £444 13a. 3t!. 2282 cigtitponces fd. II. * K51 g ^. 18b. !25. HO 18 half mvs. 28. ^^. ^V* ' >l4«ci •. 2b 10.1. 2«. 7327539 fHrihings, I& 1130':7 fuiirp'>HC«H. 27. 28m) lUO farthii i^«. li. •88U cruwus. 128. 206072 iiiiiepeuces. 2 7 J— 9 lU-39 5)i— 109 l^— 201 3J-495 HJ— 16 8 0-12 00000 (lie. 862—2220 3 J -38g Oi-1916 ANSWERS.— WEKJirrS AND MEASURES. 29. 30. 81. 82. 33. 34. 35. 36. 37. S8. 39. 23772'» tlir r lUrMnngs. (il'Vj livtpuact'S. 17.51 2').0ii 2W.75 24.8i 18.r)i) 21.8!).J 9.27^ 21.5:{J 13.27 40. 41. 41 43. 44. 4'). 40. 47. 4«. 4JI. 60. WEIGHTS AXI) MEASURES. 135 17.55 13.29J 17 53 U.25 21. (Ji 17.51 1350' 24.72 13.53 33. 93 13.27 i| ■': ^i . Avonu>ui*ois wKiuur. cwl. qrs. IbB. 08. at. 1 1. 29 1 19 ^ 1 2. 2 2 14 15 ^ i 3. tf 2 11 (1 npenccB. 4. 7 23 14 f iHMices. 6. 40 2 14 •puncea 1 Jd. 6. a 1 17 12 ; 1 kuncfS. 7. 2 1 21 8 <^ )8. 8. 2 4 6 ^^ m shillingt. 9. 8 2 27 9 7 peiices. 10. 9 3 4 9 |i ilpcnces Jd. 11. &11) 3 19 a r KOVS. 23. 12. 21 13 12 <» ] thiiigH. 13. 2S54 1 27 2 It ihintr^ 14. 4 1 12 3 7 eptiuces. 15. 211 3 1 4 t 135 AV^WEUS. — WEIGHTS AN'D MEA3URKS. 16. 17. 18. 19. 20. 21. 8 cvvt. :> qrs». 5 J lbs. 1 cwt ii (jrs. 20 lbs. J) oz. 6,\ dr liTjl piiiei'ls. ] cwi. I qr. i:> IliR. 2 oz. 3jJ dr. 47.T ln)gslu;iuis. lUO rem. rj2 tixis. lUowt. 3qr.s. Gibs. 22. 23. ' 21. 25. 2R. 27. 28. 29. 30. SI. 32. SX 84. 35. 3(;. 37. 38. 39. 4(). 41. TUOV WKiailT. Iba. oz. dwts. grs. 194 4 IG 389 10 6 16 11 4 6 6 5 C) 15 4 1 u 8 11 11 6 80 7 8 8 3 14 >^>,*l 104 a 26- G 16 12 mis. u 118 4 92 I 16 LOXa MRASrKB. fur. 29 2 4 m 5 3 5 5 per. 36 2 SO 8 18 6 2!) 18 33 yd«. ft. 3 4 ^ 'Ah u 2 2 2 in 0^ D 1 I r ;; 10 f <3. 64. C5. 66. 67. 6«. ;5. 76. 77. IS. 19. dr in 10 ANBWERS- —WEIGHTS AN'D MEASURES. , 1 t iM • CLOTH MKARUUe. i .1 o. llPydfl. Oqrs 2iils. 48. 443yds. Iqrs. Onli. IS. 3:;u 3 40. 20* 3 1 u ^9 4i. 9 3« f)0. 47y (Is. 1 i 45. 4 5J .51. 10 1 1 ^ 4(i. 148 1 52. 11- -*{ suits. 47. ID i tq,V\ RR OR LAND MEASURR. .- ^ fiS. KJacr 2nl. Uper. 58. Inc. Ird. 9pcf 64. 18» 2 4 5J). 20 1 1« 55. 22 1 30 CO. 1 1 2«t\ 56. 24 2 30 t;i. G5 33 j 67. 2U 21 62. 2*. '6id,— I2e7. i VRA^CKIS OK CAPACITT. t3. 195q m. fibus «h. Ip €4. 3!»7 4 U C5. 10 7 2J 66. 8 6 OJ 67. 175 1 68. 16 6 2 CO. 244qr«. 3ba»h. Opk»» 7U. 41 3 3} 71. lOIHfjals. Iqt. Ipt. 72. UifitxU. 2qt». Ipt. .'JjrU 73. 224lds. 4qrs. 5bsh. 3pkf 74. tJOligals. 2qts. Ipt TIMK. /5. 173Trs. 7wks. 5<1v5«. 76. 177dyf». IJlirs. 2Sinln. ?7. ]5yrs. 47\vks .^ilyp. 78. 2n«ly.«. I'hrs. MO,nin. 79. SCwks. i:ds. llhis. 16m. 80. 2wks. OdTs. inhrs. 81. 47lirs. 7iiiln. .SOs«»c. 82. 30ds. lOlirs. 2'.Mn. 4-'»^t, 83. 3471 2(^307 Becouda. ^ t38 ANawwta— wKir.nTS and measfres. REDUCTION. AVtMUDD'OIS WhUOIIT. 1. I. 7. 9. 10. 11. 854 ll»fl. 15. 70:52 W)9. 21. 22. 2:i. 24. CI.OTII MKASrUE. 2»!» yi!s. 2 Ills. 8 shins.— 8 7 suilri. — 8 .*. LOXO MKASrilK. fc R #' 16. 245 rO piTclu's. 17. ]m:v> vtls. in. 4 in. :;0. 18. 2(M)<;4() yards. :u. 19. 67200 tiiwfl. a2. 20. 39tX)0 times. 33. 2">. 2<5. 27. 2ft. 2!). MKASUKK Oi" CAPACITY. I!»7 pints. .'SK.-inrHls. Hqts. Ipt 3X(;3 p'cks. ]n>0 bushels. 20 hi gills. TIME. 1004 hours, .'ililys. 2(Hirs. rum. r):)\ir4>i{) niinulcs. 3at)4U limea. 1. 2. 3. 4. 5. 6. 7. 3. ' \ irceU. ;AsrnE. Im. 2 Ills. s.— 8 .—8 • CAPACITY. ints. Is. Sql9. Ipt P'cks. hiishels. gi\l3. honr!». *. 2(HirR. 57m. ISO nilnutes. iO limei. 1. Z 3. 4. 5. 6. 7. 8. 9. 10. U. 3. 4. 5. 6. 7. 1. 2. 3. 4. 5. 6. 7. 8. AN3WKR8. PUACTICK. X7 7 2 13 U 2 M ft} 1 ir> lo} $51)4. M) $14« 12* X4(iO 5 A «.KU 6H7 5 $1351). 37J $2.70 12. 13. 14. 15. 10. 17. 18. 10. 2<^. 21. 22. 139 $3 11 $547.5« 538 bushcl.H i p^rk. $i iii«n. 1?^7^ miles. 72 ucreH. lo davH. 021 'ijiys. f30. 27. 2H. 30. 31. 32. 33. 34. 35. 3r». 37. OCOO men. 50 men. $471.04 3 ! ^ days. 180 niiMi. COO ni»*n. 14j| days. 7^ (lunci's. 05.04 lbs. 32 horMes. 5 men. 135.535 days 800 lbs. 13« acres. 1205!^ mi!c8. $100 70 $77.72 1^ luunilia. 1. 2. 9. ID. ANSWERS. lil 3.80 unla. 11 IS |n'r ds\y. t'r('t 2.« iu. IIUMl. ilsiyH. siy \) hour* iiiontliH. lUUlltlid. PARTITIVE PROPORTION. 1. A $1000,B $I200,C $800 2. $100, $80, $00 3. A $1714.28, B $285.71 4. $0000, $4000 5. $4030, $3980, $3980, $4010 6. $3000, $5000, $7000 7. $5000, $2500, $3333, $2500 and $6666 8. $162.50, $270.83 9. 100, 140, 10. $161.53, $193.84 11. $3333.33, $3000, 19 4f»^3 A014 ,., 1^. ^V-^ff, Ui^TJiJ, '^^oT 13. $1500 son, $3000 wi. 14. $400, $600 $210.00, 200 $64.61, $3000, $2066.60 70,' » COMPOUND PARTITIVE PROPORTION. 00 men. 1 men. 171.04 « Jays. \i) men. M) ni*n. If duys. [ OUIHH1S. ).04 11)8. 'I horties. men. 35.535 dayi '.16 ll)s. 34 acres. 205!^ miles. mo 70 77.72 l munihe. 1. $5.75, $7.77, $6.47 2. $16.38, $35.10, $18.72 3.$ 1577.84,$! 6(J9.99,$1753.16 4. 5. $7 $60.79', $164.13' $175.07' 1. 2. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. MEDIAL FcOPORTION. CASE I. 8bush. corn, 7bush. oats. 71bs of first, Slbs ot second 3. 4. 5. 6. ^Ib of first, 3 Jibs second 12 J gals. 2Jgals. 7J acres of each. 5 tons hay, 8 tons straw CASB 11. lib at 8 cts., 1 at 10 cts., 3 at 14 cts. 8 bushels rye, 7 bushels oats, 8 bushels corn. lib of each. 6 gallons brandy, 7 gallons wine, 5 gallons water. 3 calf, 2 cows, 1 ox, 1 colt. 251bs at 90 cts, 251bs at $1, and 601bs at $1.50. 3 gallons of water. 7 acres at $15, 5 acres at $22. 5 acres at $25. 4 at 36 cts, 36 at 2ft- eta, and 4 at 60 cts. 1 ak 18 cts, 1 at 20 cts, 2 at 25 ct». US ANSWERS. CASE m. 1. lObush. at TOcts., 2^ at 48cts., 12| at 36cts., 40 at SOcta. 2. 201bs. of each. 3. 20 gallons of water. 4. 751bs. of each. 5. 20 bushels of barley, 61y®y bushels of oats. 6. 95 gallons of rum at 6s. 8d, and 30 gallons of water. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. CONJOINED PROPORTION. 1. 2. 52i bushels. lolj 6. 7. 71^ months, 150 lbs. 3. 4tV 8. 144 4. 27^ 9. $92.37 5. 10 men. 10. 200 yards. PERCE] ^TAGE. 1. $6 96 11. 50 per cent. 2. 8 40 12. , 25 3. 300 00 13. 10 cents. 4. 55 93 14. $1185 18 5. 8 80 15. 675 30 7. 1 J per cent. 16. 300 00 8. ^ 17. 4 28^ 9. 83i 18. 3000 00 10. l^ 19. 2000 00 SIMPLE INTEREST. $43 S7i 60 98 224 91 360 28 20 90 26 3i 458 88 42 24i 420 26 213 00 11. 12. ' 13. 14. 15. 16. 17. 16. 19. $181 25 11 04 132 77 26 95 416 IQ 1334 21 120 0« 40 09 8590 63 8. 1. 2. 3. 4. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 1. 3. ANSWERS. 143 COMMISSION, INSURANCE, BROKERAGE. iSOcta. iter. I. 2. 3. 4. 5. 6. 7. 158 bar. 8. ^]3o9 00 34 83 115 39 164 53 6835 28 2558 16 2412 66 5320 00 9. 10. 11. 12. 13. 14. 15. 16. $21375 Of! 2135 00 3529 4 1 66 share* .^. $4000 00 If per cent. $5168 5:1 89 55 ths. ds. ter cent. ) cents. 85 18 75 30 OO 00 4 28^ 00 00 00 00 ;181 25 11 04 182 77 26 95 416 IC 1334 21 120 OS 40 09 B590 8? 1. 2. 3. 4. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 1. 'I. 3. COMPOUND INTEREST. • $516 59 5. $198 83 131 23 6. 83 20 1310 79 7. 845 83 946 85 8. 48165 93 DISCC )UNT. $214 09 15. $1055 7S 357 14 16. 853 IS 462 26 17. 1005 10 647 88 18. 6831 87 822 53 19. 6119 40 925 71 20. 7175 92 1071 42 21. 14202 00 2938 77 22. 16562 437 4948 09 23. 26500 00 8809 41 714 28 24. 6i-4-p»r ceat.J 6186 37 25. 20 — ^^ ^ \J \f \^ w 7621 39 26. 211+ - 474 30 27. 49J+ - . J-' BARTER. 28 bushels. 6cwt. 3qrs. 9ilb8. 201.21 pounds. .05;i 6. 6. 7. 8. $223 56 23J cents. ^ 737.6 pounds.: 287^ bushel&J U4 AK8WEB8. INVOLOTION. 1. .2. ^3. I. ■> ^« 4. O. 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. 6. 7.. 8. 64 2197 1048576 4. 6. EVOLUTION. 176 789 1111 45.8 69.247-f- 6. 7. 8. CUBE ROOT. 72 38 73 103 439 6. 7. 8. 9. 10. 247G099 129146796^ 157.08 -I 12 14 37 37.6 19.86-f .376 .829-1 1.93-f- DUODECIMAL MULTIPLICATION, ft in. 42 7 44 5 106 9 565 11 1040 8 17105 2 27 9 68 1 II III nil 6 7 6 9 8 9 8 4 4 2 4 4 8 4 6 6 10. n. 12. 18. 14. £7 Os. 4i— I f. 564ft. Oi?. 9" £6 9s. 7^ f. £126 9s. 4^— i f. • 116 ft. 10 in. G" 100 ft. 4 in. 1" 6'" 16. 3419ft. 2in. 7" 2'" 10"" 6'"" 16. . £2 Is. l^d. 17. 77 ft. 6in. 5" 18. £48 19s. 9|— I THE END. 247C&99 )14679e^ I 7.08 -X 37.6 9.86-f .376 .8294 1.93+ -If. 9" f. 4-if. in. 6" [. 1" 6"' ' 10"" fi""* id. 1.5"