IMAGE EVALUATION TEST TARGET (MT-3) 1.0 1.25 tutu |2.S u,m 122 :!f us, 12.0 6" JA 11116 V vl % ^> '> > 'V' Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14S80 (716) 872-4503 m v ^v ^\ ». Q ) CIHM Microfiche Series ({Monographs) ICMH Collection de microfiches (monographies) Canadian Institute for Historical l\Aicroreproductions / Institut canadlen do microroproductions historiques Technical and Bibliographic Notat / Notes techniques et bibliographiques The to t The Institute has attempted to obtain the t>est 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. Coloured covers/ Couverture de couleur n I I Covers damaged/ D Couverture endommagte Covers restored and/or laminated/ Couverture restauree et/ou pellicula □ Cover title Le titre de missing/ couverture manque □ Coloured maps/ Cai tes giographiques en couleur □ Coloured Encre de ink (i.e. other than blue or black)/ couleur (i.e. autre que bleue ou noire) n n n Coloured plates and/or illustrations/ Planches et/ou illustrations en couleur Bound with other material/ Relie avec d'autres documents Tight binding may cause shadows or distortion along interior margin/ La reliure serree peut causer de I'ombre ou de la distorsion le long de la marge interieure Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut que certalnes pages blanches ajout^s lors d'une restauration apparaissent dans le texte, mats, lorsque cela etait possible, ces pages n'ont pas ete filmees. Additional comments:/ Coinmentaires supplementaires: This Item is filmed at the reduction ratio checked below/ Ce document est filme au tauM de reduction indique cidessous. 10X UX 18X J L'Institut a microf ilmi le meilleur exemplaire qu'il lui a M possible de se procurer. Les details de cet exemplaire qui sont peut-Atre uniquM du point de vue bibliographique, qui peuvent modifier une image reproduite, ou qui peuvent exiger une modification dans la m^thode normale d« f ilmage sont indiqoes ci-dessous. □ Coloured pages/ Pages de couleur □ Pages damaged/ Pages endommag^s □ Pages restored and/or laminated/ Pages restaurees et/ou pellicuStes Pages discoloured, stained or foxed/ Pages decolorees, tacheties ou piquees The pos oft film Ori( beg the sicr oth« first sior or it □ Pages detached/ Pages detaches 0Showthrough/ Transparence □ Quality of print varies/ Qualite inegale de I'impression □ Continuous pagination/ Pagination continue The shal TINI whli Map difff entii begi righi requ metl n Includes index(es)/ Comprend un (des) index Title on header taken from: / Le titre de Ten-tSte provient: □ Title page of issue/ Page de titre de la I □ Caption of issue/ Titre de depart de la li I I Masthead/ livraison vraison depart i il Generique (periodiques) de la livraison :6x 30X 12X 16X 20X 24 X 28X D 32 X The copy filmed here has been reproiuced thanks to the generosity of: National Library of Canada L'exemplaire film6 fut reproduit grdce d la g^ndrosit^ de: Bibliothdque nationale 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. Original copies in printed paper covers are filmed beginning with the front cover arid 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. The last recorded frame on each microfiche shall contain the symbol — ^> (meaning "CON- TINUED"), or the symbol V (meaning "END"), whichever applies. Maps, 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 images suivantes ont 6t6 reproduites avec le plus grand soin, compte tenu de la condition et de la nettetd de l'exemplaire film6, et en conformity avec les conditions du contrat de filmage. Les exemplaires originaux dont la couverture en papier est imprim6e sont filmds en commenpant par le premier plat et en terminant soit par la dernidre page qui comporte une empreinte d'impression ou d'illustration, soit par le second plat, selon le cas. Tous les autres exemplaires originaux sont filmds en commengant par la premidra page qui comporte une empreinte d'impression ou d'illustration et en terminant par la dernidre page qui comporte une telle empreinte. Un des symboles suivants apparaitra sur la dernidre image de cheque microfiche, selon le cas: le symbole — »> signifie "A SUIVRE", le symbole V signifie "FIN". Les cartes, planches, tableaux, etc., peuvent dtre film68 d des taux de reduction diffdrents. Lorsque le document est trop grand pour dtre reproduit en un seul clich6, il est film6 d partir de Tangle sup6rieur gauche, de gauche d druite, et de haut en bas, en prenant le nombre d'images ndcessaire. Les diagrammes suivants illustr<«nt la mdthode. 1 2 3 1 2 3 4 5 6 Graded Exercises -IN- ARITHMETIC -FOB THE USB OF- M & FoDiHt Mlic ScM CI», -BY- R. K. ROW, HOSEMOND SCHOOL. ■«*- Sottion, (Dttt. : JaS. I. AnDKRROW Sr C.n 17/; T%rtvvxA« a^ 1883. PREFACE. ^IV^S^Z^Z"^^'' School work h., con- supplement our f^«K I* ••«5?»"y of something to a suiuKrTf;' Srd°ai:St in" ".expensive form, i, the object of thfa work ' "" u Jof%rwm'r,h™ '1*'^ '1.' °' ^*" """"ained i.sneonr.'^'oMh'aS's';:^' "^ ^-^^^^ - "> pu^ig""* '^ *"• '^^ °"y "id both teacher, and I am, yours very truly, R. K. R. Eighty.three. by ilL iSfw ^^'"ll""! ^'«*»* hundred and MISCELLANEOUS. EXERCISE L 1. I owed a man $3.79, and gave him a $5 bill; how much change should I get back ? 2. A boy went to the store with $9, and paid $2 for tea, $1.60 for sugar, 84c. for meat, and $2.85 for a pair of boots ; how much has he left ? 3. A boy earns $11 a month, and spends $5.50 ; how much does he save each month 1 4f. Mr. S. had $316.14, and paid out $79.65 ; how much has he now ? 5. Bought a pig for $9.25 and a cow for $28, and paid $35 down ; how much is yet to pay? 6. Jones had $200, he paid out $85.70, and received $104 ; how much has he now ? 7. Out of $764.81,1 paid $398.49; how much have I left ? 8. Take $17.64 from $41.25 ; $124.92 from $317.14 ; $876.01 from $1,000. 9. Out of a 50-dallar bill, I paid $9.87, $4.26, $17.71; how much have I left ? 10. A lady had $62.50, and paid $8 for a dress, $4.26 for a hat, $13.75 for a jacket, $4 foi* boots, and $7.86 on an old account : hnw mu<^h has she left ? "^ GRADED EXERCISES IN ARITHMETIC. MUcellaneoua— Continued, EXERCISE II. m^lil'^'^^'i^^i^T^^ ^^^^'^'^ each, and G4 ho^ much T' "^^'"^ '"^^ '^' ^"^^''^ «"'»' ^^^ each \ t^^^^u ^^'^?^' ^® '^"3^» 8 cows at $33 ari^frTV^^^''"'^^''^*^^ ^^"^^^ ^5 sheep at «5.5() each ; how much has he left ? ^ $l,88l?^* ^^ ^^^' ^""^ '"^''^ P^^^ ^*" ^ ^»y ^or bought ftlTo'^ '**"^^' '' ^'''^' ^-^' ^^ be ««^i. *'• ^u*"' ^- ^^^^1323 ; he can buy pigs at $7 each or sheep at $9 each ; how many mfre pia« can he get than sheep ? ^ ^^ r... o^' ^ "^ u ^""^l ^^^ ^^'^"^ <>^ 75 acres at $45 per acre, and bought another at $30 per a^ how many acres could he get I ^ ' SSfi/s'.^w^* bought 50 acres'of land for 55^,088 ; what was the rate per acre ? n.»J' ^ Tt"" ^'^y^ ^^^^ * y^"" bouse rent : how muqh must he save a week to pay it ? ^ / " on o^' ^i*J^^ ^^ bas an equal number of 6, 10 ' W *" ^ ^f/"* P'^^®«' amounting to $5,50 : how many are there of each ? , each ox ?^^** '"""^ ^^ ^""^^ ""^ *''^" ^^^* ** l«3.6o''' OBADBD EXERCISES IN AJUTHHETIC. Miscdlaneovs — Contimied. EXERCISE III. 1. If a man earn S325 a year ; hew long will it take him to earn $3,250 ? $4,550 ? $8,775 ? 2. A drover paid $8,442 for 07 horses ; what did he pay for each ? How much did he pay for 11 horses ? 3. How many lbs. of butter at 16 cents a lb. will pay for 18 yards of linen at 24 cents a yard. 4. If 24 bush, of wheat weigh 1,440 pounds, find the weight of 1 bush.^ Of 15 bush.? Of 940 bush.? 5. If a farmer can raise 258 bush, of wheat on acres; how much has he per acre? On 14 acres ? < 0. How many bush, of app^ * at $2 per bush., must be given for 28 lambs at ^i each ? 7. If nine cows cost $495, what is the price of 1 cow ? Of 4 ? Of 17 ? How many can be bought tor $1,700 at the same rate ? 8. A father left $14,484 to be divided equally among his 6 sons ; how much did each get ? 9. Sold 7 pigs for $119; find the price of one? Of3? Of5? 10. A farmer drew 448 bushels of grain in 7 loads ; how much did he take at a load ? II* At $84 each, hrfw mflnv Vint^Ao Ann T k.^.^ for $924 ? For $2,184? For $10,164 ? 6 GBADB) EXKRCiSES IN AKITWlBTId. / ^itoellmteoiu—aontiniMd. EXERCISE IV. 12s: " ^'^ ***P **' *"*• ^^ *•»» value of of rT^ng",'*'" '*"' *3"' '''»* " the value waat 18 12 acres worth at the aain>. rate ? of r fl^e^uTd'^^.^ '^' *'■''■' ^' «•« value ought^s^r riiiir •''"'""-*''•- --•■ Jch^rt^-^^fe^^P^'-^^-^^.'^ow 7. A man rents a house for $192 a vea*"- 'inv, much ought he to pay for 5 montlw' ^ ' 8. A train travels 576 miles in 24 hours • how for can a man ride on it in Shouts? ' iKi^snT^" 6 Pata of ducks can be bought for W.20 ? How much are 100 ducks worth ? m6, K ^rrrpors."' "^"^^ -' J^?^?¥ lT.«>«'s fo' «578 J for how m.-.h in«.v i seu 001 (ton, jq g^j^ jg^j - " GRADED EXERCISES IN ARITHMETIC. Miscellaneous — Continued, EXERCISE V. 1. John had $136 ; he put $75 in the bank, and spent $22 for clothes ; how many dollars had he left ? 2. Simplify 34—14+12—100+14+16—8 + 346. 3. Sam had 112 marbles; he lost 79 and found 53 of them ; how many has he now ? 4. John goes east for 6 hours, walking four miles an hour; James goes west for 5 hours, walking 3 miles an hour; how far apart are thev then ? *^ ^ 5. Bought 136 sheep at $3 each, 25 cows at $25 each, 467pigs at $1 each ; sold 5 horses for $165 each. How much did I pay out more than I got? € At $98 each, how many horaes could I buy for $1,375,592? 7. How far can a boy, who walks 4 miles an hour, 8 hours a day, and 6 days in the week, go in 6 weeks ? 8. In how long will Willie count $1,260, counting $40 an hour, 6 hours a day ? 9. Write 999 in Roman notation. 10. Write in words 95043605. 11. A man earns ^3 a month, and spends $9 ; how much can he save in three years ? CI OIUDED BOLEBOWES IN ARITHMETIC. ■^fiwellaneous—Contimced, EXERCTSE VI. r^nnon ^*"' ^J^ ^^^ °"^' ^J^ich he divided Zfl "^^^r^^'' " classmates and himseirand 2 Mary has 42 beads, Sarah has 17 more than Mary, and Jennie has 23 less th^n l^th the others ; how many has Jennie ? 8. In a basket there are 283 DPiu»h«o a^A plums, and thei^are 149 morepKh^„'^erh es ; how many are there of each ? "^ make sS^f ^SaTln^et" "'''' '°«^"'«' 183 eL^fd^h^,r^.t^^tav''' ""^ enceon^/aLdfs™'"'' *"*'■* "■"" ""^ <''«"''- 1 ?; ??" '■''^ ^^^ mai-Wes, sold 88. found 2t bought 54 and lost 19; how many h.;, he now ? .., ..^: ^■^'*^? ^^ *^"** between James and Will so as to give James 15 cents more than Will r^JJeSS:^"""* must be added to 8,021 to GRADED EXERCISES IN ARITHMETIC. 9 lbs.? REDUCTION— AVOIRDUPOIS WEIGHT. EXERCISE VII. 1. How many ozs. in 2 lbs. ? In 4 lbs. ? 10 T ^ L ^^^ ™*"y ^^^- i° ^^ 025- ? In 128 ozs. i In 9,600 ozs. ? How many ozs. in each of the following • (3.) 5 lbs., 9 ozs. ? (7.) 3 cwt, 10 ozs. ? (4.) 17 lbs , 6 ozs. ? (8.) 1 cwt., 18 lbs., 4 ozs. f (5.; 1 qr., 3 lbs. ? (9.) 2 cwt., 3 qrs., 18 lbs. ? (0.) lcwt.lqr.7lbs?(10.) Iton? Express each of the following m lbs : (11.) 1000 ozs. (14.) 7 cwt. and 14 lbs. (12.) 47 ozs., 16 drs. (15.) 3 tons, 19 cwt. (13.) 3 qis., 9 lbs. (16.) 1 ton, 13 cwt., 19 lbs. 17. Beduce 100000 lbs. to cwts. To tons. 18. What is the cost of 13 lbs., 9 ozs. of butter at 2c per oz. ? ' 19. When wheat is worth $1.92 per cwt, find the value of 3 tons, 4 cwt. 20. At 8c a lb. find the value of a pij? which weighs 2 cwt., 64 lbs. ? ^ * 21 When coal is 35c a cwt., what ifl the cost of 3 tons 15 cwt. ? Of 9 tons, 7 cwt. ? Of 11 tons, 19 cwt. ? 22. Find the cost of 1200O lbs of flour, at $3 25 per cwt. Of four barrels of flour at 3e. alb. 10 GBADED IXEBCISES IN ABITHMEtlC. LONG MEASUAE. EXERCISE Vlir. ^/: 7^T r^yj''''^^ '"^ ^^ ^^' ^ ^^et in 24 yds. ? Yards in 16 rods ? Furlongs in 120 miles ? ^ita^V^ "^t^^^^ ^ London, a distance of 10 miles, 7 fur. ; how many yards did he walk ? 3. Reduce 288 inches to feet ; 147 feet to yds. ; 484 yds. to rods ; and 384 furlongs to leagues. 4. A tape measure haa 4356 inches marked on It , how many rods long is it ? fnr' i^'''^*^^ number of inches in two miles, 3 fur., 16 rods, 1 ft. Prove correctness of answer. 6. How many halters 6 ft. long can be made from 12 rods, 4 yds. of rope ? 7. The posts for a wire fence are 1 rod apart • ^reteh ^^ "^a^y posts wiU 21180 feet of wire' 8. How many rails. 22 feet long, wiU be re- quired for 21 miles of railway ? ^ ^ re 9. From A. to B., two towns, is 1 mile, 2 rods • from C to D., two others, is 4,284 ft. ; hoV many more yds. from A. to B. than from C. to D. ? ^ Thi^;JL^®^**-'l®*x'^!.^^°^*'^^ 36 rods wide. W« T •i^'l'^ u ^ ^"'^^ ^* ^i*^ a straight fence, 6 rails high ; how many more rails willlje them I2 ft'"*" ^^'"^^^^^ Wthan if he cuts OBADED EXERCISES IN ABITBMETIC. 11 LIQUID AND DAT MEASURE. EXERCISE IX. 1. How many pints in 8 qts. ? In 5 gals., 3 qts. ? In 12 gals., 1 qt., 1 pt. ? In 19 gals., 12 gills ? 2. W; ; is the value of 9 gals., 3 qts. of syrup, at 22c. a quart ? ^^ 3. How many gals, in 4 bbls. ? In 12 bbls. « In 26 bbls. ? In 92 quarts ? In 160 pts. ? I*ind the cost of each the following quantities of milk: 4. 2 gals., J qt. at 4c. a qt 5. 4 gals , 2 qts., at 3c. a pint. 6. 9gals., 3qts., atScaqt. 7. 21 gals., 1 pt., at 3|c. a pt. 8. 13 gals., 2 qts., at 6|c. a qt. 9. 7 gals., 3 qts., at 4Jc. a pt. 10. What is the cost of 14 barrels of vinecar at 28c. a gal.? ^ ' 11. How many qts. in 3 pks. ? In 5 pks, ? In 14 pks.? ^ 12. At 7c. a qt., find the value of 2 pks., 6 qts. of peaches. ^ 13. How many bush, in 16 pks. ? In 64 qts. ? In 160 qts. ? ^ • Express : 14. 9 bush., 3 pks., in qts. 13 bush.. 1 pk. in pks. ' '^ 15. 7 bush, in pints ;" 7 pks., 18 pts., in quarts. 16. 234 pts., in bushels; 40 qts., pts., in pks. 12 GRADED EXERCISES IN ARITHMETIC. MISCELLANEOUS. EXERCISE X. In^i4°Tln^l""'2^!^*^^^ In 5 days? in iS «Ks. i Id 3 weeks, 3 days, 19 hrs. ? 2. How many days in 3 wks. ? In 1 year 45 weeks? In 960 hrs. ? In 86400 min. ?^' 3. If the pulse beats 70 times in a minute how many times does it beat in a year? ^ ^''^^^ „ \^^^ "Jf°^ ^- ^"c^es in 4 sq. ft.? In n «q.ffc.? In 2 sq. yds.? In 1.5 sq.^ds ? ' r>. Reduce 14 acres to roods. To sq. rods 8. Reduce 9 lbs, 4 ozs, 13 dwts. to grains. Express * 9. 14320 farthings in £, s. and d. 10. 7 o^s., 6 drs., 2 scrs., in grains. 11. One million mills in dimes. 12. 12 cub. yds., 1 cub. ft., in c^. a 13. £121, 14s., 9d., in pence. Jt^ '"^- y^" ^ ^"^- ^t" "52 cub. in. in cub. 15. 6760 grs. Troy in lbs. GRADED EXERCISES IN ARITHMETIC. 13 , COMPOUND ADDITIQN. EXERCISE XL 1. A owes $279.40 to B, $15.G0 to C 38765 cents to D aod 139 dollars to E: how much does he owe aU ? V .,,V .. , ' : : Z. A farmer has three pigs; one weighs"2 cwfc. 1 qr., 16 lbs. ; another 3 cwt., 13 lbs., And the other 1 cwt., 3 qrs., 11 lbs. ; how much do thev all weigh? ^ 3. A table is 5 ft., 4 in. long, and 2 ft., 10 in. wide ; how far is it round the table ? 4. It takes 2 lbs., 4 ozs., 10 dwts. of diver for a teapot, 1 lb., 8 ozs., 10 grs,, for a cruet, and 2 lbs., 9 ozs., for a cakestand ; how much silver in them all ? 5. Lis 19 mis., 7 furs., 23 yds. east from S, and P IS 13 mis., 36 rods, 17 yds. west; how fai- are they apart ? 6. I have 210 bus., 3 pks., 3 qts.,of wheat; 49 bus., 1 pk., 1 gal. of oats ; how much grain have I ? 7. Add wks. days hrs. mins. 9. Add ac. ro. per 9 7 2 13 5 1 4 19 11 23 9 54 14 45 6 19 7 29 12, 1 3 2 23 16 37 21 lbs. ozs. drs. scr 1 9 7 1 14 6 2 9 2 12 10 5 1 -1- \r-^ 1 127 2 bo 1 Ouo; 1 1 14( GRADED EXERCISES IN ARITHHBTIC. I COMPOUND SUBTRACTION. EXERCISE XII. 'Zr'^ (3.) tons <.t ,. ,K 99 8 15 6 16 3 6 (4.) ydaftiiis. 15 1 6 1 1 10 viti (5.) mis. furs, rods yds. 13 6 35 3i 1. 5 36 6 (6.yibs.o^awts.gj. (?^^:^^:^, ^'■^ ?w ?i^- T- ^"^ 2T-^'-\!^- rr^ 291 20 16 17 45 64 3 I "^^11. Ad<«lerhad234tons,17cwt lor Sqiha of coal, and sold 86 tons, 18 cwt, 2 qr ^ 24 1^^^^ how much has he left ? ^ ' ^®' ' 1^^ Find the difference between 515 bus 1 nt and 445 bus., 1 pk., 1 ^al. ' ^ la What sum added to Je987 19s lid ^ far will make jeiOOO ? ^ '*''^'' GRADED EXERCISES IN ARITHMETIC. 15 GOmPOUND ADDmON AND SUBTBAGTION. Add EXERCISE XIII. (1.) lbs. ozs. drs. (3.) tons cwt. qrs. lbs. 17 3 8 7 1 3 .19 11 15 14 18 1 7 9 7 6 6 17 1 U (2.) cwt. qr. lbs. (4.) tons cwt. lbs. 9 1 14 26 13 29 13 3 23 118 4 64 7 2 8 9 9 9 11 17 5. Add together 2 tons, 8 cwt., 3 qrs., 17 lbs., 5 ozs. and 13 cwt., 8 lbs., 13 drs. 6. From 11 tons, 12 cwt., 15 lbs., 2 ozs., 5 drs. take 9 tons, 18 cwt., 9 lbs.. 13 drs. 7. A has 2 cwt., 19 lbs. of floor ; B has 375 lbs.; C has 1 cwt., 3 qrs., 18 lbs., 8 ozs. ; how much have they all ? 8. I buy a bbl. of sugar containing 2 cwi, 2 qrs., 8 lbs., and sell 16 eleven-pound parcels ; how many lbs. have 1 left ? 9. Mr. B. made 7 cwt, 1 qr., 10 lbs. of maple sugar, and Mr. S. 539 lbs., 10 ozs. ; how much did B. make more than S. ? 10.— From the sum of 12 ft. and 18 in. take 3 yds. 1ft. *i- — '-«■ saa-" \d i7cwti of sugar and sold 9 cwt, 66 lbs., find the value of the remainder @ 8* ct». alb. ' lU UMAJJED BXEUCtSES IN AWTHMETIC. i\ t COBPODND MIHTIPUOATION. Multiply EXERCISE XIV. iUt.Vh^]''';^y*- by 12; by 32. t fl^i^ils., 3 qts., 1 pt., 1 gill by 3; by 9 3. 64 bus. lj>k., 3 qts., 1 pt by 181 ^ j^4. 2 wks., 6 lys.. 18 hra., 'l* sfcs. by 24 ; by ^ I, „l™' 15 OJB., 13 drs. by 56 ; bv 72 /. $12946.84 by 4000 ; b/256: ^ ^^8. mk,4 fum, 21 per., 4 yds., 1 ft. 4 ins. ^^10. 36 cub. yds., 21 c. ft., 96 c. in'., b^ ik ; by '^12 IV'^'.i t"' ^ '"■'•' ^** S™. by 7 ; by 28. 108. ^^•' '"•' ^ '"'°^' *5 secs.„V »; by tt iJv*' ","'1^' 2 <■»"•.. by 6; by 7i ' .M 100 ac., 1 ro., 21 rods, 16 yds.,'3 It, by S ^^ 17. &1X men average 1 cwt. 2 qw., 22 lbs 8 ozs. each; howmuch do they all 4ighf y^' 18. Three brothers have 115 acres. 1 ro ifi rods of land each ; how much hiye theyaiu" 19. A man works 10 hrs., 39mins 24 sero « day; how miinv I,o.ir=. &- IriP ^^ i ■ ^. * year (.313 days)-^/'^^""''"''P"'^ '" '" » ■iii GBADED EXERCISES IN ARITHEETIC. 17 .rlij. COMPOUND DIVISION. EXERCISE XV. Divide 1. $3572.16 by 4; by 12. 2. 129 cwt, 1 qr., 11 lbs., 7 ozs., 8 drs., by 8. a 33 tons, 2 cwt., 2 qrs., 22 lbs., 15 ozs. by 8.; by 24t. 4. 2 furs., 10 rods, 1 yd., 1 ft , 10 ins. by 7 ; by •x2s. 5. 1 yr., 13 wks., 4 dys., 8 hrs., 34 mins. l»y 11. 6. 693 lbs., 2 ozs., 11 dwts., 16 grs. by 8. 7. 4571 acres, 1 ro., 24 rods by 12 ; by 60. 8. 1 ml, 1 fur., 14 rods, 1 ft., 2 ins. by 29. . 9. 183 cwt., 3 qrs., 21 lbs. by 9 ; by 7 ; by 63. 10. 182 lbs., 10 ozs., 1 dwt, 6 grs., by 49. 11. 6297 lbs., 11 ozs, 4 drs. (Apoth.) by 84. 12. 85Q0 bus. by 800. ^r.,.^ t 13. 3yds,, I ft., 6 ii)s.by 1 ft. 6 ins.. 14. $188.75 by $3 25 ; by $9. »ft < 15. 12 tons. 9 cwt., 15 lbs. by 1 cwt., 5 lbs. 16. 2 dys., 2 hrs,, 24 mins. by 2 hrs., 6 mins. 17. 25 lbs., 1 oz., 1 scr. by 1 lb., 6 ozs., 2 scrs., 10 grs. 18. 19 lbs. 6 ozs., 7 dwts. by 10 dwts., 18 grs. 19. 9487 bus., 2 pks., by 7 bus., 3 pks., 1 gal. 20. 2833 acres, 32 rods by 9 ac„ 3 ro., 14 rods. 18 GBADED EXERCISES IN ARITHMETIC. \\t MULTIPLIOATION t DIVISION. EXERCISE XVI. 1. A bbJ. of salt contains 2 ewfe ^ ««. k\u find the weight of 12 such bbls ^^ ^ ' ^ ^^'' ^ 2^2. Multiply 9 tons, 16 cwt., 24 lbs. by 3 ; by w4l.tStt^^a^Jtch^S^0'«> finale m^chtTlS'r &' <''''•' "^ ''^ ■■ ''- 9Kl*k^Ti^® P^''^^«^en receive 5 cwt 1 nr 9. How many times can 1 cwt 1 K IKp ^ be taken from i fy^« -«7iu ' ^ ^°^' ° o^s- left? ^"' ^^ how many ozs. will be 10, How manv noffU « •-- ,. GRADED EXERCISEfi IK ARITBHETIC. 19 MISCELLANEOUS. EXERCISE XVIL 1. Find the value of 79+384—667+9+89+ 8567—999. 2. Find the difference between 3067045 ^and 4000004. 3. From one billion take the sum of 645 and 1982. 4. John has 79 marbles, James has 14 more than John, Peter has 17 less than James, and Robert has as many as John and Peter ; how many have they all ? ,6. Multiply the sum of 676 and 786 by the product of 98 and 47. 6; If a cow cost $28, a horse $64.75 more than a cow, and a house cost 18 times as much as both ; find the value of all. 7. Write, in Roman Notation, 29, 38, 47, 83, 96, 249, 499, 608, 789 and 994. 8. Express £43, 17s., 9d., 2 fars. in farthings. t4 9. How many ozs. in 17 tons, 14 cwt., 3 qrs.? 10. Bought cows for $27 each, and sold them for $44 each ; how much do I gain on 19 cows ? 11, Mr. T. has 214 bus. of spring wheat, 68 bus. of oats, and 375 bus. of winter wheat ; how miipVi ia all \\\ul urVtr.of «r/>*.f)l of ^1 ^^ n^*. '^-t'- 9 t' 12. What is the largest number that can be taken sever %es from 1090642 ? 20 OBADED EXEBOISKS IN ARITI,MBT,<-. ^ixxiUaneoue—Oontinued. EXERCISE XVIII. 1. Write in words : 67009,780,063. ^- ^.^P™» *999 in Roman Notation, to 'Vfotlndrv: ''^""""'—be^ftom 67^7 »138 Saeh ; hoVrnTch £ .ft' """^ ^^'^ «* buy with the money? ** "* *"'" ""^ •>« thet.Srjf™a^'''''^*<'-<^'«v«nai„g withl6'rd"Tom^k^pP# ™"W^^^^ ht\T.^ ^'--"^'^- Kur u' giv^D^W sl^llf* ?f * ^ong his 3 Children, ^»o.fchfi^r^o'':^ti;'t^r,S ORADED EXERCISES TN ARITHMETK' 21 Miecellaneoua — Contintied. EXERCISE XIX. The charge of sending a telegram is 25 cents for 12 words, and 2 cents for each additional word ; how much would a despatch of 32 words cost ? 2. What is the cost of 1 bus., 3 pks., 3 qts., 1 pt. at 5 cents per quart ? 3. Four apples cost as much as 3 oranges, and 7 oranges cost 28c. ; find the cost of one dozen apples and A dozen oranges. 4. Take 3 tons from 8640 lbs., and how many cwt. will remain ? 5. Divide 83D4.75 between A and B, ffivinff A 134.25 more than B. ; r,- • T ■ C. Find all the exact divisors of 280 ; 675 ; 2700. ^ ^7. A horse and harness cost $288, and the horse cost three times^as much as the harness; find the cost of each.' ■ 8. Divide a farm of 121 acres, 2 ro., 21 rods between A and B, giving B twice as much as A. 9. Whiat number is composed of the following factors : 2, 1*, 2, 2, 3, 3, 5, 7 ? 30. Kow long will it take a boy to walk round afield 22 rods long, 18 rods wide, who walks at the rate of 16 rods per minute? -v .^ r «8 OIUPBD BXKBaSBS IN ARrrHMETK. ^i»edlaneoua—Oonfinu«cl. EXERCISE XX. ^r. Fmd thecostof 87866 lbg.ofoat«»t 42c. p,.r Sfr? '^^'■' " *»• y^''^ =°^ «">ch land 'thf^^n^ri^^H^a-^^ ^reo. ana pay & ZZ°^- "^ ''"*'*' •* 24c. a lb. will pay tor J2 lbs. of sugar at 12c. a lb. ? a tiJiZt!'" ^^'""'''"'' "* • '^^ «' ^ood. Of jAange due from a 2-doUar bill ? ^ " '^ *^® .>M thl'rS».l.^ ^--* »36 each, and deducting $24 "ei^^."' """ "« •»« gain after ::.i^ GRADED EXERCISES IN ARITHMETIC. 23 \ and . giv- will Of Miacellaneous — Continued, EXERCISE XXI. 1. Find the sum of $302.03 ; forty-six dollars and seven cents ; $200 ; one dollar and ninety cents ; eighty cents ; and fifty seven dollars. ^ 2. John bought 2 lbs., 8 ozs. of can \y at 2c. per oz. ; 2 gals., 1 qt. syrup at 16c. per qt. ; and 3 bus. 3 pks. apples at 18c. per peck ; how much did he pay for all ? 3. I paid $4020 for 12 village lots anu sold them at a loss of $70 each ; how much did I get for seven ? 4. There are 4840 sq. yds. in an acre, how many square yds in 7 faims of 129 acres each. 5. How many sq. inches in a blackboards ft. long, 3 ft. wide ? 6. How many bus. of wheat at "$1.25 j^er bus. are worth as much as 22 cords of woou at $5 per cord? 7. If 18 men do a piece of work in 9i days, how long would it take 8 men to do as l uch ? ^ 8. A man ^ets $64 a month and spends $40 A: how much will he save in 7 years? 9. Divide sixteen million, eighty-four thousand and four hundred and forty by five thousand and eight. 10. Divide the product of 769 and 806 bv 906. ^ 11. At 37j^c. a pair, how many dozen pairs of mitts can be bought for $1008 ? 24 GJUDED EXEKCms W ARITHMETIC. It ^i^llaneous— Continued. EXERCISE XXII. get for $210 f ""'''' ^""^ '^y eo«W I ^2KndthevaJueof24 1b3.ofbutter»tlic. hold ho"; XgaCl^'^ P'"' """'- -« he left? • ^ ^""^ '^' ^''^ ^^^^ "luch had be Vt\r^\'r^'oittioff -«"''<' per'sf rod.*''' "''"' °'" ^^ ''O^es ofland at 2oc at $4o''pt'i;tV '''"* °' ''"« "i- '"^ of l«nd ^''- Ho^ many times will « »>,ip _:.. ,. , go round a 4 by 4 ;„. scaotling'?"" *" *°"' GRADED EXERCISES IN ARITHMETIC. 25 Miscellaneous —Continued. EXERCISE XXIII. 1. Find the cost df 7 bus., 36 qts. of berries at 30c. per gal. ; also the gain by selling them at 15 cents a quart. 2. At 00c. per yard, find the cost of 1 ml, 2 furs., 1 rod of sidewalk. 3. Sold 3 tons, 3 qrs., 3 lbs. of beef at 7 cents per lb. ; find the price. 4. A milkman bought 36 gals, of milk at 15c. per gal. ; after 1| gal. leaked out he sold the re- mainder at 6c. a qt. ; find the gain. 5. Two men start from the same place in op- posite directions, one 3 and the other 4 miles an hour ; how far apart will they be in 4 hrs. ? 6. How many minutos in 8 hrs., 3 mins. and 240 sees. ? 7. Find the value of 4 bbls. of sugar of 2 cwt 3 qrs., 5 lbs. each, at 10c. per lb. 8. A farmer spent $289 for cows, giving $23 each for two and $27 each for the others • how many did he buy ? ' 9. What would 14 cwt., 100 lbs. of hay cost at $10 per ton ? 10. At 25c. per rod find the cost of diffginff 7 furlongs of ditch. 66 s # -I 26 GBADED EXERCISES IN ARITHMETIC. MisceUaneoiLa^Continued, EXERCISE XXIV. islerWa'^SJf "" '"""'"■^"'' *° «'^« 3. A person bought 140 horses at $125 oaeh W muctr " *'-^'= ''''''* cost the mo°t.aad 4. How many Dines in 12 times 1024067? lK^;.j^'''^"'r^il^''r^"**^'*** 15 cents per lb. will pay for 16 yards of cloth at $2 per yd 9i9l\nl^'''^^\ ^^'^ ^^l^ ^^^ ^^^««s, $240 for cows, lldt^^^^f^^^' ??i^*''^ ^""^ °^^«^ implements and had.$426.75 left ; how much money had he at for^l^ot^''^ ^^^' ^^^ ™*°^ ^^""^^ *^ ^ ^"^' fltllk f""! ?t°^ ^^^ P^^"^" «*^ ^ «"»« b»y ^ifch I-:^ u x^i"^ V"^ ™*''^ ^^-^'^^^^ ^oes can he buy with what he has left ? "^ 10. How manv fimAo **aw% aqo i — x-i /. .1.. -f •r..«v« vw« ^wA uc j^Keii irom OBADEi) EXERCISES IN ABTrHlf ETIC. 2? Miscellaneotia — Contimied, EXERCIS2 XXV. 1. If 3 bus. be taken from 60 gallons, how manv pks. will remain ? •^ 2. If a man has a salary of S1200 a year and spends $2 per day, how much will he save in five years ? 3. How many sheep at the rate of three for $21 can a man buy for $763 ? 4. A field is 20 rods square, how many times must a boy walk round it to go 5 miles ? 5 How many square feet of lumber are requiW ed to floor a room 23 ft. long, 18 ft. wide ? ^. ^' If a watch tick twice in a second, how many times will It tick in a week? ^ a^.^mti 7. What is the cost of 13736 lbs. of oats at 52 cents per bus. 8. A man steps 2J ft. each time ; how many times will he step in 1 mile ? "^ ik^" R 11* y^^ °^ ®^^*^ <^st S21.00, how many lbs of butter at 18c a lb. will it take to pay for 4 yds. { A I?* ^^?.?.*^y ^^^^^ ^^ ^-^ 6id. be stibtract- ed from ;ei684, 12s., and what will remain ? II 28 GRADED EXERCISES IN ARITHMETIC. m Miacellaneous-^Continued. EXERCISE XXVI. 1. Find the price of 12 bus., 3 pks., 3 ats of wheat at $1.28 per bushel. •> qts. ot iAJ^r'Su'^y^r^^^-^'''^^''^^^^^ are necessary to bottle a hhd, of wine ? ^v-cooaijr ^ a Reduce 382 furs., SOpers., yds., in. to 4 75 bus. of oats, at 12c. per peck, will pav for how much cfcth at $1.20 per yd. ? ^ ^ a rod*'''''^ *^® ^^^ ""^ ^^ "^'^^^ °^ ditching it 50c. 95L^buir'^''^^^^ lbs. of wheat worth at 8. A horse eats 4 qts. of oats and 5 lbs. of hay three times a day; find the cost of keeping him eight weeks : oats 40 cents a bus., hay $10 ^\^^T f^^^'P ^'® ^^'•^^ 2 pigs, 5 pijrs are worth 10 calves, and 15 calves are worth $37.50. Find the value of G sheep. vur.uv, 10. A woman bought : 22 lbs. of sugar at 11 lbs. for a dollar, 2 dozen spools at 4c. each spool, z7 yds of cotton at 9c. a yard. How much change ought she to ^et DUiS f - w firet from two fft4. GRADED EXERCISES IN ARITHMETIC. 29 MisGellaneoua— Continued. . EXERCISE XXVII. 1. How many cords of wood could be piled in a shed 50 feet long, 25 feet wide, and 10 feet high ? 2 How many acres of city land at $2 a square foot can be bought for half a million dollars ? 3. If Jan. 1st is Sunday, how much can a man earn m the hrst three moaths of a leap year, at ^l.zo a day ? ^ 4. At 35 cts. a square yard, what would it cost to plaster a wall 15 feet high and 54 feet long ? 5. If a load of wood is 8 ft. long, 3 ft. wide how high must it be to contain a cord ? 6. What will 250 miles of telegraph wire cost at 3 cts. a ft. ? 7. A boy bought eggs at the rate of 3 for 5 cts. and sold them at the rate of 4 for 7 cts He gained 9 cts. ; how many did he buy ? lo^; ^n ■ ^^^^cu'^^erence of one carriaire wheel is 1.3 tt, 9 ins. ; that of another l(i ft.. 6 ins. : how many more times wHl one turn than the other in going 30 miles ? 9. How many seconds are there in the three summer months ? 10. How many acres are there in a street 4 rods wide and 2] miles long ? 30 OBADED KXBB0I8ES IN ABITBHKnC. EXEROISl XXVIII. 1. What is the quotient of the sum of 769483 and 612375 divided by their difference ? 2. How many £, s., and d. in 176,834,984 far- thmgs? 3. What is the cost of fencing a railway for a distance of 4 miles, 2 furs, at lie per rod ? 4. A load of wheat consists o£ 25 bags, each bag contains 110 lbs. ; what is the value of it at 5p2.25 percwt. ? 5. What is the value of 4 acres, 3 ro. of land atl^s. 6d.persq.rod? 6. What is the cost of fencing a field 33 rods long, 21 rods wide, at 12Jc. per yd. 7. The product of two numbers is 188973422, the multiplier is ^?.278j what is the multipli- cand?^ •;^"- ■■ *^ 8. Two boys start from the same place to walk m opposite directions, one at the rate of 3 miles per hour, and the other 3i mUes per hour ; how long before they will be 22 J miles apart ? berries, at 2Jc. per pt. ? ORADBD EXEBCISBS IN ARITHMETIC. 31 Miecellaneous — Continued, EXERCISE XXIX. 1. Express 987654321 sq. ins. in acres, rcods, 2. Multiply the difference between £257, 178 9fd. and £400., 68, 3|d. by CMIX. 3. What number divided by 496 will give 49 for quotient and 207 for remainder ? 4. The quotient is 17 acres, 27 pers., 19 yds ; the dividend 970 acres, 39 perches ; find the di- visor. 5. If 7 yds. of cloth cost $35, how many bus. of potatoes at 35c. must be given for 5 yards of , the cloth? 6. How often can the G. C. M. of 972 and 1440 be subtracted from the L. CM. of 7. 8. 9 10 11 12,13,14,16? ' \^'/"'^^' 7. How many minutes from 10.30 a. m.. Jan 20th, 1880, to 3.15 p. m., March 6th, of the same year ? 8. Find the difference in grains between 6 oz Avoir, and 6 ozs. Troy. 9. How far from the end must I cut a stick of timber 14 ins. wide, 17 ins. deep, so as to have a cub. yard. ? ^ ^<^^ "^*»y dozoa Straw bats at 8c. each c^ be wought with the piiee of 45 chickens at 40c a pair ? ^2 GRADED EXERCISES IN ARITmiETIC. GREATEST COMMON MEASURE. EXER'CISE XXX. 1. Find the G. C. Measure of I4.4 and 216 • of 296 and 407 ; of 506 and 308. 2. What is the G. C. M. of 36, 84 and 132 ? 8. Find the G. C. M. of 527 and 1207. 4. What is the G. C. M. of 204, 1190. 1445 and 2006? 5. In a school there are 812 boys and 672 girls; nnd the largest number that can be put in a class so that boys and girls shall be separate and the same number in each class. 6. Mr. A. has $296 and Mr. S. has $4^8; if both have the same kind of bills, what is the highest denomination they could be ? 7. A man has three trees which are respect- ively 42, 56 and 70 feet in length ; what is the least number of logs of equal length into which he can cut them ? 8. A grocer has 2 bus. of cherries, 2 bus., 1 pk. of berries, and 40 qts. of currants ; find the least number of boxes of equal size necessaay to hold the fruit without mixing. 9. A triangular field has its sides 48, 60 and 75 rods, respectively ; find the smallest number of trees that can be planted at equal distances round it. ....'. ,rft, 10. Find the G. C. M. of 275, 143 and 209. GRADED EXERCISES IN ARITHMETIC. 33 LEAST COMMON MULTIPLE. EXERCISE XXXI. 1. Find the L. G. M. of 4, G, 8, 9, 12 aud IS ^^2. What is the L. C. M. of 13, 24, 16. 26, aiid ^3. Find the L. C. M. of 4, 6, 10.15, 25, 45, 75, ^ 4. Find the L. C. M. of 27, 54, 8.1 . 14, 63 and 5. What is the least number that will tfive tor a remainder, when divided by 10, l2, or 15 ? 6. What is the least number to which if 11 h^ added, it will be divisible by 28, 36, or 18 ? 7. What number Js that from which it 13 be irsTor 72 ' '''""'"'^'' ^^" '^"'*^^ contain 12! w ^' J^"i ^^? ^^2^*^ number whose quotient when It IS divided by 7 will contain 13, 24, 18 or 30 h.t ^^tV«,.**\e least number which after havini^ 10 What is the smallest sum of money that' can be made up of 4, 6 or 10 dollar bills ?^ 11. What is the least sum of money with . i^^ ^ ^\" ^"y '^^^P @ ^5' cows ^ $35 loos at $14. or horses At9^^m^ ^ ^ ^ ' '*^^ at $14, Or horses at $110 ? n "m 9^90^ "'a^' "^ /'y^^ numbers is 4. the L. LoS'' ^^,^i^^^v. i. ,3^4, find ii'Sl 34* GRADED EXERCISES IN ARITHMETIC. M ' MISOELLANEOUS. EXERCISE XXXII. 1. The sum of 113 equal nurabera ffiuitiplied by 3 gives 16611 ; find one of them. 2. How many bus. of oats at 42c. a bus ought to oe given for 225 bus. of barley @ 63c. a bus. ? 3. Find the cost of 3 fur. 36 ft. of sidewalk @ $1.40 per yd. 4. I have $1650 and wish to hay an equal num- ber of sheej) a,t $4 each, and pigs at $7 each ; how many pigs may I get ? 5. What is the value of 1 cwt. S6 ozs. of butter at 12i c. a lb,? 6. A milkman bought 36 gal. of milk at loo. a gal., and after mixing 10 gal. of water with it, sells it at 5o. a quart. Find the gain. 7. How many acres in a field 40 rols wide and 1^ times as long ? 8. Bought 320 lambs @ $2.75 each, paid $64 for pasture, and sold them all at $3.40 each ; find the gain. 9. Find the total cost of: 36 qts. of berries at 30c, a gaL 10 ac. of land at $15 a rood. 4230 lbs. of wheat at $1.15 a hvok Oraded exercises in arithmetic. 3^ Miscellaneoua^Continued. EXERCISE XXXriI. 1. Express 8 lbs., 6 ozs., 5 drs., 10 ffrs.. in grains. ^ o » « 2. Reduce 12Fr. ells, 3yds. t ) feet. G. C. M. of 57, 87, 111, and 135. ^ 4. What is the value of 3 dozen and 3 spoons If one spoon is worth 4?. 3id. ? 6. Add together A, 3f . J of 2f, 5j andf J. 6. What number added to the sum of 6j and 7} will give 16 ? "^ . 7. A farmer sold i of his farm for S1675 ; what is the remainder worth at the same rate ? 8. If 5 ac. of land produce 350 bus.ofDDtatopq how many could be raised on i of 12 ac ? ' . 9. From 1 ton take 4 cwt., 40 lbs. 10. A man bought 4000 dozen eggs at 13c a dozen, lost ^ of them and sold theTem^inder at 17c. a dozen ; find his gain. "*"iaer ac . 11. How much will be gained oi lost bv buv- ing a sq. mile of land at $40 per acre aid thJn seriing It at 25c. per sq. rod ? ^^^ 12. BftlirrKf o V%o^«^l ^e ..: . . . ''^' ^--JJ r^ti^i vi viueimr at 5I4c 'staid • GRADED EXERCI8ES IN ARITHMETIC. Miscellaneous —Continued. EXERCISE XXXIV. 1. (a) Write in one number 30G billions 47 thousand and 19. (b) Express in words: 46,000,500,075. 2. The sides of a triangular field are 300, 240 and 180 yards respectively ; find the length of the two longest tape-lines that will measure each of. the sides exactly. 3. The divisor and quotient are each 345 and the remainder 344 ; find the dividend. 4. It takes 12 hrs., at 24 mis. per hr., to go from T. to M. ; how long will it take to walk back, at 4 njls. an hour ? . 5. How many yds. in 8800 links ? C. If 5 apples cost 3c., how much will 3 bus., 3 pks. cost ? Six apples fill a pint. 7. Four sheep are worth 2 pigs, 5 pigs are worth 10 calves, 15 calves cost $45 ; find the value of 2 pigs and 4 sheep. 8. 16 bus., 48 pints of apples at 10c. a pk., and 11 bus., 6 gals, of potatoes at 15c. a pk., are worth how much ? J<^» i >t- 9. I can buy pigs at 14 dollars each, and cotrs at 25 dollars each ; how many more pigs than cows can I get for $350 dollars ? iiod .ilk 10. Reduce IJ mis. to feet. ' '^^^"^l}l if' GRADED EXERCISES IN ARITHMETIC. 37 ^iscellaneou^s-^Continued, EXERCISE XXXV. ^'Ju^\T ^^""T^^^}" "Million and seventeen take eighty thousand and eight. 2. Eight head of cattle at $23 each, and 7 horses at $89 each, were given for 3 ac. 'ofLnd ; how much wa* the land worth per acre ? h.ff *?*-^ *?.l^""^ ^^ *^o numbers is 4331, and half their difference is 3353 ; find the numC 4. It 18 men can reap a field in 76 days how long will It take 19 men ? „^|a 5 A man spent ^6300 in buying an equal number of sheep at $3.50 each, and cows at «U50 each; how many did he get ? fi it; ^L^ ^^^' ""^ ^®* ^'^ '^^''^*^ ^ ^^s- of coffee, and 6 lbs. of coffee are worth 12 lbs. of sugar how many lb3. of sugar are worth 1 cwt. ^t^r o'oLi ^^"i'l i? worth 11 times as much as a of each.'' ^^ ''' ""''^^ ^^^^ ' fi'^^ *^?!U4 hviP^^nri^^'^^'^^T^'' *^^*' ^^^^ divided a Vu ' "^'^^ ^'^^^^ ^2 for remainder? l^. What 18 the smallest sum with which T can buy sheep at $6 eax^h, cows at $27 or Ws 10. What is the value oi' lafiplo'na nt li,,** at 24Jc. per lb. ? fSfi iJ f. i ^S °^ ''"*'«'^ 11. Express 83 ac, 3 ro., 17 per., 18 y^s 7 ft., 134 in., in sq. i^heg, , . 7' ' 9& OBADED EXBR0I8ES IN ABITHlfETICl. I FRAOnONS. EXERCISE XXXVI. 1. Reduce the following improper fractions to whole or mixed numbers : V* \h V> V> *f *> V> Vif»,VW»and V^ijV. 2. Reduce the following mixed numbers to im- proper fractions : 2^, 4if, 18^. 26H, 1C4J^,203^, 1261^t, 763f , and 15i|f 3. When is a fraction said to be in its lowest terms? Reduce the following to their lowest terms : ^^, U* f f > Uh and i^^f f . 4. Simplify f of f , ^ of if, | of U of 9, ^ of ^ of tV of \} and ^ of tV of 5 J. 6. Express the following fractions in equivalent ones having a common denominator : f , |, It f , I and \i, 6. Find the greatest and least of ^f, |f and ^. 7. Eatpress t^, ^^, f f , ^y, |Jf in three hundred and sixtieths. tio d> r, .9. Addf+f + J+i. 10. Add H+H+H+!f+lt ORADED EXERdSKS IN ARITHBf ETIC. 39 EXERCISE XXXVII. 1. Add 4f + 114 + 1614- 21^ + 19f 2. Add4J + lJ + ^t^+2J+3,v 3. Addi + S+l+j + 14.^^5^^^ 4. Add$4J+$2f + 5f+S7f. 5. I gave i of an orange to Sam, J to Tom and I to Mary ; how much did I give to all ? "' 6 A hotel used 2^ lbs. of butter on Monday lu rn? ^"''^*^' ^* ^^'' °« Wednesday 2i lbs. on Thursday, and 7 lbs. the rest of the week now much was used during the week ? 7. A boy has ",v of a dollar, $1 .$j and «a .^^"^"^ money has he altogether ? k^ X man leaves J of his property to his wife i to his son and the remainder to his daughter' What part did the daughter get ? 9. How much must be added to he sum of * and I to make a whole number ? hU farm ? "«P««'vely ; how U^ i. 4e QBADED EXERCISES IN ARITHMETIC FrcusHona — Continued. EXERCISE x?:x;^iiL 1. From f take J, and from jV take J. 2. What ia the difference between J of ^ and Aofi? 3. How much must be added to 1^ to make 3i. To 4| to make 13 J? 4. A owns J of a ship, B I and C the remain- der ; how much more has C than A ? 5. Find the sum and difference of (5J of ^\) and(13ioff). :^'\- 6. What number must be added to f of (i + | — iV + *) to«iake4i? '7. Find the difference between the greatest and least of f , f , ,''2 and j ; also the difference of the other two and thje sum bf these ditlerences. ' 8. A man sold ^ of his farm to A, and f of tha remainder to B ; what part has he left ? 9. Sam gave ^ of his marbles to Tom, ^ to Will, and ^ to Fred and then had 14 left; how many had he at first. * * ^' 10. Simplify J-j + J + IJ— 2J + 5. GEADED; IXEBCISES IN ARITHMEWC. 41 Fractions — Contvnued. EXERCISE ,X;^IX. 1. Multiply J by I ; ^ by |^ ; jj by 1/^, 2. Multiply f of i of 2| by 1 J of I of n^. diler^"^*"'^^^ *^^ ^""^ ^^ ^ ^""^ ^* ^^ *^®^^ 4. Find the producVof if 4 ' ^, |j and 8 J. 6. Find the value of 24 ducks @ ?5f each. ^ 6.^ What are 3 J days' work worth @ $1J per loT' ^i«^ *^«,*«»fal cost of 4^ lbs. of raisins at 12^0. per lb, 6i lbs. rice at 5fc. per lb., lU lbs 'TL^^^^i'- \^^-' ^* y^^' «1^*^ »* 37ic. pe? yd., and 4f dozen buttons at 12c, per 40?, , ;^ who gets S2J per day ? , ,, ^ ^ y» 9. Find the cost of | of A ton of coal at Zbi per ton. -^ » 10. How much must i pay for a barrel of cidei at 12^c. per gallon. ' . . ^11 Aman w^ks 3| miles p0r;hdur. how for will he go m 2§ hours ? ''- -^ '■'•' » ■- -'• Ji- in >*' ■■'■ IS GttAt>E!D tJXEBOlS^ IN AlUTHMETIC. If m FraoHons — Gontinv£d. 1. Divide 4 by 1, 12 by }, 27 by \h 2. Divide i by 4, J by 9, if by 48. 3. Divide I by J, i by 2i. H by 4J. 4. Divide ^ of if of 2§ by yV of 2+ of IJ. 5. How many times must f be taken to make 21i? 6. A boy earns $t per day ; how long will it take bim to pay for a $12 overcoat ? 7. How much must a man save in a month that he may have $}^§ at the end uf 8} i^ios. ? 8. If lambs cost $4f each, how many can I buy with the pric« of 10 pigs @ SS^V ©ach ? Q. How many cords of wood @ $4J per cord must be given for an $^i wagon ? 10. If 1 man use fib. of meat in 1 day, how long will 7 cwt. last 14 men ? | tti^; 11. How much must be added to the product of } and tV to make it equal their quotient ? QBADED EXEBCISES IN ABITHMETIC. 43 Fractiona—OontvMied. EXERCISE XLI. Find the respective values of 1. i of $12 J f of $21 ; 4 of $112 ? 2. I of 9 cwt.; I of 40 lbs. ; ^V of 4 qrs. 3. 2| of $4.27 ; H of 1 ton, 7 cwt., 1 qr. *g^dd together f of $ 3.60+1 of 9Ic f ^i^^ of 5. Add I of a ton+| of a cwt+| of a or Answer in lbs. ^ ' 6. Find the number of feet in | of a mile+S of a fur.+f of a yard+^v of a rod. 7. How mimy quarts in f of a bus.+| of a pk.+f of agal.? ^ 8. Find the value of^ of 3 cwt., 1 qr., 11 lbs. 9. How much is ^ of f of f * of -J of 33 bus.. 2 pk.,1 gaL? , , ^ GRADED EXEROISBS IN ARITHMETIC. MISCELLANEOUS. EXERCISE XLII. 1. Two men are 450 nail^s apart ; if they ap- proach each other, one travelling 30 miles a day and the other 36 miles a day, how far apart will they be at the end of six days ? 2. Bought two horses for $4)20, paying $48 more for the one than the other ; find the price of each. , 3. If two persons start from the same place, and travel in the same direction, one 7 and the other 11 miles an hour-— an average of 9 hours per day, how far apart will they be at the end of the 17th day? ' 4. A grocer buys nuts at $1J per bus., and sells them at 10 cts. a qt. ; how much does he gain on 992pts.? 6. How many pint bottles are necessary to hold 2 hogshead of wine (63 gals, each) ? 6. How often will a mile of string go round a 3 by 4 scantling ? ' i. Find the cost of IJ miles of ditching at ■,arod. , . - '!,, .. -, . , : :> MTw/^^ .<^,, Bought B][iples at 4 for a penny, and. sold them at 3 for a penny ; how much do I gain on 18^' :^ozen ? ,, K <, \i- ^ lu. .^nkv . ,nli li'ii J>-. 9. I feed my horse three tames a day ^fqts. of r^a*■a onA A l"ha nf Viov • finfl f.lift coat of IcPfinincr himi 4 wks., when bats s^ll at 40 e^nU v^ bifflh., and hay at $20 per ton piui if«| |Sl.ii ^ 4mihf GRADED EXERCISES IN ARITHMETIC 45 Miscellaneous — Continued. EXERCISE XLill. 1. A merchant having 12 tons, 13 cwt., 2 qrs., 15 lbs., 3 oz. of flour, sells 10 tons, 10 cwt., 1 qr., 3 lbs., 2 oz., and the rest he sells in barrels, each containing 1 cwt, 2 qrs. 16 lbs, 13 oz.; how many barrels are there ? 2. How many times will a wheel 8f feet in circumference turn in going 4| miles ? , 3. Bought nuts at 8 cts. a qt., and sold them at $3.50 a bus. I sold enough to gain $5.17 ; how many did I sell? 4. Addl rod, 1 fathom, 1 pole, 1 chain, 2 perches and 3 hands. Give the answer in feet. 5. Add 10 dozen, 10 units, 10 score and 10 gross. Take the sum from 1 million, 1 thousand, 1 hundred and 1^ . , 6. If soldiers on a march take 85 paces of 33 in. each in a minute, how long will it take them to march 25^ miles ? 7. If frpm home to school and back again be I of a mile, and a boy take 20 min. in walking this distance; how far will he have walked while attending school twice a day for 220 day^ ? and h,ovf many hours will he .have spent in walking ? - ■ 8.' Jlo^ many inches tallcJr is A hottee 15J hands high than a pony 13J hands high? V' 46 QRAJ>£D EXERCISES IN ABITHMETIC. K:i Miscellaneous — Continued. EXERCISE XLIV. 1. A fai'mer owning 100 acres, sold 17 ac., 2 ro., 20 per., 12 yds. ; Low much has he left? 2. How many cords in a pile of wood 86 feet long, 6 feet high, 4 feet wide ? 3. How many gold coins, each weighing 11 dwts,, 6 grs., may be coined from 31 lbs. 2 oz., 1 dwt., 6 grs. of standard gold ? 4. A man has 42 cords of wood ; how much can he get for lour-sevenths of it, at S4 a cord ? 6. Find the sum of 2i + 4i| + 3f + 8i, 6. John had $llf and lent James $^; how much has John left ? 7. A farmer had 600 bus. of wheat ; he sold 7 loads each, containing 56 bus., 2 pks., 2 qts.; how much wheat has he left ? 8. How many bus. of oats in 2725 lbs. ? '9. Express in figures, one hundred and nine million, four thousand and eleven; and express i ija Roman Notation 476. m A man bought 1 horse for $63 1, and an- other for $86§. He sold the span for $187J ; how much profit had he? GRADED EXERCISES IN ARITHMETIO. 47 Miscellaneous — Continued. EXERCISE XLV. 1. Sam. ha8 $1.89, Bill, has $3.50 more than Sam., and Tom. has 62c. less than Sam. and Bill ; how much more has Tom. than ? . 2. Multiply the sum of 264094 and 83720 fcy their difference. 3. A grocer bought 2 bushels of berries of A at 56c. a peck, and 9 pks. of B at 8c a qt. ; how much will he gain by selling all at 10c. a quart ? 4. A walks 3i and B 4 J miles per hour, they start from the same place in opposite directions ; how far apart will they be in 18 hours ? 5. In 17 mis., 16 fur, 48 perches, how many rods? 6. Find the L. C. M. of 45 and 27 and the G. 0. M. of 217, 49 and 63. 7. Add together 2f + 7 J + 4*1 + (f of 3i). 8. B owns I of a farm worth.$6,300; find the value of J of his share. .«?(-> I ; 9. A merchant has 9 barrels of stigar, each weighing 2 cwt., 63 lbs., which he sells at 11 lbs. for a dollar ; how much is the whole woiih ? 10. Find the total value of: 2130 lbs,, of wheat ^t $1.14 per bush. , -\ xu 3 cwt, 3 qm, 3 lbs., of beef at 4|c. ^ Ib.Hf , : I 48 GRADED EXERCISES IN ARITHMETIC. h- Miacellc^mouB — Continxuid. EXERCISE XLVI. 1. At what rate per foot is S21.45 for 10 rods ? 2. Mr. B Uid out $610 in buying cows; for two he paid ^2(j each, and for the othere $31 each ; how many did he buy ? 3. Multiply 9,396,089,705 by 3,090,070. Prove. 4. How many strokes will a clock that goes regularly and constantly, strike in thisvear. (1880)? ,. -. s^ru,: 6. Find the value of seven cwt., %^ lbs., 1008 ozs. cf beef at 9^c. a lb. » V 6. What is the longest pole that will exactly measuietwo ropes 2,717 ft. and 1,441 ft., re- spectively ? 7. 660 quills at 7e. per score, 918 at 4c. per dozen, and ^.50 at 34c. i^er hundred would buy how many slate pencils at 5 for 2 cents ? , 8. A bucket contains 4 cbc. ft, 10 cbc. in of earth ; how many such buckets in a box that contains 3 cbc. yards ? ', 9. Allowing 24ic. to the sterling shilling, re- duce £29, 17s, Od sterling to dollars atid cents, i 10. Add i,§, I, and 4 J. ' • 11. If a man clears 5 mills on eadh book^he prints, ho w= many dollars will he make on one million books? i w;j S GRADED EXERCISES IN ARITHMETIC. 41) ■ BILLS. EXERCISE XLVII. Make out in correct form, bills for the follow- ing purchases and receipt the last four. 1. Mr. Smith bought of Jones & Co., 2 lbs. of tea at 75c,, 6 lbs rice at 4J c, lOJ lbs sugar at 9c. a lb. 2. B bought of A 3^ yds. flannel at 420., 19 yds. print at Uj^c, 6| lbs. currents at S^c. ' ' 3. Miss Price bought of Miss Little 19 yds. lace at 12^c., 15f yds. edging at 9c., 7^ yrl^. silk ribbon at 18^c. a yard, 9^ yds. muslin at 13c. a yard. 4. M. bought of N, 1 j lbs. of coffee at 45c , 2^ lbs. tea at 55c., 1 broom 35c., 11 lbs. sugar for SI; 5. C bought of S. 25 lis of flour at $3 per cwt., 8 J lbs of oatmeal at 3c. a lb., G lbs. 4 oz., butter at 30c. a lb , and 1 pk. apples at GOc. a bus. 6V Mr. J: bought of Mr. F. 9 lbs of nails at ^c. a lb., 2 pairs of hinges at 35c. apair, 1 chisel 75c. I saw S3 J, and 1 plane Sl.50. 7. Mr.W, bought of Mr. C. 131 lbs. fish at ijc, IJdoz. buttons at lie. each button, 3 bars of soap at 12 J each, and 2 brooms atS3 a doz.' ''^ ^ 8. Mr. M. bought of Mr. R. 4 lbs. ;biscuit at 7^0;, 5 lbs. tea at 48g., and 1 dollars' worth of sugar at 9 lbs. for a dollar. . > ^0 GRADED EXEBCISES IN ARIl'HifETIO. Miosellaneous — CorUinued* EXERCISE XLVIII. 1. How much wheat is necessary to sow a field of 9 acres, if J of an oz. be sown on every sq. yard? ^ 2. A grocer buys sugar @ $8.50 per cwt., and sells it @ lie. per lb. ; what would he gain on 2250 lbs. ? 3. A dealer buys 26500 ft. of lumber @ $11.40 per M, and retails it @ $2.50 per C. ; find his gain. 4. A grocer bought a bbl. of vinegar, contain- ing 36 gals, for $12.60; I leaked out and he sold the rest @ 13c, per qt. Find his gain. 5. How many cords of wood in a pile 84 feet, long, 5 ft. 8 in. high, and 4 ft. 6 in. wide? 6. One-half of the sum of two numbers is 2182, J their difference is 461. Find the numbers. 7. A man divided his property among his three sons ; to the eldest he gave $6,750, to the youngest ^ as much and to the second H times as much as to the youngest. Find the value of all. long ; how many acres in it ? GRADED EXEROISES IN ARITHMETIC. 51 Miecellaneous — Continued, EXERCISE XUX. 1. Find the smallest number that will leave a remainder of 30 when divided by 155, 186 or 217. 2. How far from the end must I cut a board 13 in. wide, so as to have 6 square ft ? • a A field 119 yds. wide, and 136 yds. long, is divided into square plots of the largest possible sree. How many will there be. 4. I ow^ $200 and pay $43.16. How many timep ast i pay $13.07 to cancel the debt ? 6. Boucht 40 gal. of wine at $2 per gal. How much water must be added so that $30 may be gained by retailing it at $1.30 per gal. 6. Reduce J, |, -^j and f ^ to equal fractions having 3960 for a denominator. 7. A., B. and C. start on a trip with $20 each, they agree to divide the expenses equally. When they return, A. has $8, B., $6 and C. $10. Show how the account is to be made right. 8. Find the value of 3f +1| of 2tV— 5|. 9. How many cords in a pile of wood 40 feet long, 6 feet high and 12 feet wide ? 10. What is the time when j of the time stnca •noon is equal to the time until midnight ? ^f i m 52 GRADED EXERCISES IN ARITHMETIC. I f : 11 r i Miscellaneous — Continued. EXERCISE lil' 1. Divide $1630 between two persons so that one may receive § as much as the other. - - 2. J of f of a man's property is worth $6.^20, find the value of the whole of it. 3. If 36 men can do a work in 25 days, how l»ng would it tak6 22 men? 4. What part of 2 miles is 480 rods ? 5. A man gave $72 for a watch and f as. much for a chain ; what did both cost ? 6. A boy gave away J of f of his money and had 85c. left; how much had he at first? » 7. A man earns $G50 a year, he spends \ for board, ^^ for clothing and ^ in other ways ; how much has he loft ? !Oiu,> J Y®. f of 20 is how many times J ? T «)j9. A fi^ld containing 18 ac, 26 sq, ro4s, is sold for $581^ ; find, the value of a field of 8 ac^at the same rate. di> -f^' Find, the. cost of plank for a sidewalk J mile long, 3 J yds. wide.,@ $1.25 per C.(ii?ch measure.) uiiJl. Find the cost o£ oTao ibs of hiry at 814.25 per ton. ito^aftJ &di t^j I^[n>«> m . GRADED EXERCISES IN ARITHMETIC 53 Miscellaneous — Continued. EXERCISE LI. Find total cost of : 1. 16,750 ft. of boards @ $12.50 per M. 1,750 ft. of plank at $24.00 per M. 3,500 ft of scantling at $25.00 per M. 2. How. majny steps of 2^ ft. each would a man take in walking a mile ? 3. A wheel makes 880 revolutions in passing over 2 miles, 1430 yds. ; what is its circumfer- ence ? 4. How many cords of wood in a pile 140 ft. long, 4 J ft. wide and 6| ft. high? 5. A stationer bought one great gross of slates at 9 pence for each slate ; what was the cost of the whole in pounds sterling ? 6. How much will it cost to dig a cellar 40 ft. long, 32 feet wide and 5 ft. deep, at 25c. a cubic yard? rtfjb 11111 f/oV .] ,■ 7. If 5 tons of coal are equal to 9 cords of wood and a family burns 27 cords of wood in a year, how much will they save by changing from wood to coal when wood is $4.25 a cord, and coal $6.80 a ton ? ^.- ^,vj 8. What is the cost of 4 fields containing 4f ac, 2* ac, 3S ac, and Iff ac, at $25 an acr6? 9. How many acres in a piece of land |^ mile long and J mile wide? &4 QEADED EXEBCISES IN ABITHMETIC. ■ V?'. raoiMALs. EXERCISE LU. 1. Reduce the following yulgar fractions to decimals: ' ^*,i ,.ir--. 1- lJii|j|;i;H;l|. 4- l + Hi'ff + s^ir. 5. 5|of4§of,V. 6. f 4-4J+4T'V+16TVir. ;i7. tV of f+3J of ^,— li+4 8. Express the following decimals as vnlsar fractions :---5 ; -3; "7; -26. 9. 2125; 16-76; 0125. ' "••'"• ' ' '• fntfi i-'I-'O '!■**'; S'^ ■■ ' -' 10. 19; 1-052; 372; 1245. 11. 4-376; 126-0025; 1000-0001. 'fti' '^f' 12, 896-07; 4004312; 266^, 'fj^ ^Z O&ADEi) EXERCISES IN ARItflMETlC. 55 DecirmU— Continued, EXERCISE Lin. 1. Write as decimals : one tenth ; seven-tenths ; nineteen-hundredths ; and forty-eight thou- sandths. ^ 2. Express the following decimals as vulgar fractions in their lowest terms : '72, -395 ; 008 ; •0625, 073 ; 2716 ; 18955 and -00098. 3. Multiply -316 by 10, by 1000, 1000000. 4. Divide 6025 by 10, by 100, by 10,000. ^ 5. Write as decimals ; twenty-four hundredths; nine thousands; sixteen and nine-tenths; nve millionths ; one hundred and one hundredth. 6. Express the following decimals in words : •3; -22; -106; 1001; 793; 101101; 160007; •01009 ; 23000201 ; 106500000001. 7. Add together: •5-h02-f-346-|--3-f •972-F •25. 8. Add : l'5-hl325-f-119-3-|- 76854. 9. Find the sum of 7251001 +1692+11-3921 +374+000375+15-1. 10. Find the sum of |+f +H+T'if+H4^12lTV when reduced to decimals. 11. What vulgar fraction represent:^ the sum oi X ao-t-id a-f-z U0-M5 iZu f 12. Multiply -0612 by 100 and by 10^000,000. GRADED EXERCISES IN ARITHMETIC. Decimals — Continued. EXER^OISE LIV. 1. Find the difference between 31047 and 2101 ; 16125 aad 8-397 ; 132o and 69-2£|. , 2. Find the value of (1) 37*162— 26.84, (2) 742^-376, (8) 17-5— 1306021. yi^:^'' 3. Take '08 from 3; 63721 from 165'29 : 38006402 from 45 078. 4. How much inust be added to 1-6 to make 3?; to 12-39 to make 25? thW : 5. By how much does 762125 exceed 139-5 ? le. Find the value of 7'2-|-10215— 9+105C 9003 —985-75. ^-7. Simplify -0663-^1301— 9-12— -614. 8. Find the difference between three and three- tenthp ; also between seven hundredths and seven- millionths; also between ninety-8ix+ thirteen thousandths and one hundred and nine and 5 ten thousandths. .^i^^uob o4 h^t."hm /t^dw '^^0. Simplify 1639-1-1-68,914:163'^|-16-391. 10. How much added to -000062 will make 62? GRADED EXERCISES IN ARITHMETIC. 67 ^f EXERCISE LV. Multiply together: 1. 1-69 by 1-3; by 13, by 13 and by 130. 2. 2-25 by 22-5. by 225 and -0225. 3. 1200 21 by 00002 and by 20. 4. 191047 by 183 and 9641 by 0573. 5. 39264-571 by.87-243761. a Find the price of 3375 lbs. of butter at 18-75C. a lb. 7. Find the total cost of 31-5 gals, of cjlerat 12-5c. a gal., 5 625 gals, of molasses at 62'5c. a gal, 7-75 ydp. of cloth at $1375 a yd. Divide : 8. 159-6 by 42, by 4 2. by 038. 9. 173-889 by -417 and 12376 by -00026. 10. 03611 by 7-8^ and 0006594 by '0021. > Find the value of the following correct^ to three places of decimals ; 11. 1-84-^91; 76^2-rl2-3ana l7-^'Q012.,,. 12. -07291 4-r§; 962-4-r-ll-92743. 13. There^are 2218.192 cubic inches in the Im- perial Bushiel ; how many ih a gal. ? In a ok. ? In a qt. ? In 24 bush; ? .. ' 1- ^\A^ ^'375 each, how ,mapy hemcan.be bought for $24 ? For $3 ? f'^vTrrrrf jrr':'! r^i ^ >•• 3((f Ul i-Jf m 56 GBADiED EXERCISE IK ABXT4}.U;TIC. CIROIILATINe PBCnUIiS. EXERCISE LVI 1. What kind of vulgar fractions will reeur» and what kind will terminate when reduced to decimals ? Reduce the following to recurring decimals : 2. i ; A ; t\ ; iV Ui and f ' ;(-i.r 3. H; A; JH: 7f and9,v. 4. 261H; 12*H; HVAh 5. A; A; iV; and v.. ^^^^.^fes^^t Reduce the following recurring decimaiS to vulgar fractions : 6. -4; 04; 024; 923, ^' 7. 763; -215; 0063; 1007. 8. 06027; 2071; 13024. ' 9. •03'ril32; 85 60806; -300625. I^nd the value of the following correct to six places : 10. 2-Si6+14-26-f 1008-729. ' 11 • * 1t^. 721 061 + -2834+ 1^^5-f iSl 263. '^tk 72-45+ 3rf 2002 +186000^719!^'''^ ' 13. 7-45— -3; 26 24— 7(>52 ; 44^16. '14. IIS'OI— 173 864— 72-i 4 ,«'4 GRADED EXERCISES IN ABITHMBna 50 Circulating Ik(mMile--^Oontiniied, EXERCISE LVII 1. Multiply -3 by -8; 12 by 1-2; 47 by 45. 2. 906 by 142; -36 by 77 ; 3124 by 166. < 3. 18.9 by -81; 706 by 339; 9*3 by 0001. 4. Divide 082 by 123 ; 648 by -8. 5. 73-2 by 2-4; 198 by 1-42 6. 172-8 by 14i; 389185 by 157. Find the values of 7. -25 of $1; 135 of $2; 18125 of $5. Q i o o°* J V^- ^ ^'^ °^ ^ ^^- *^oird. ; -6 of 1 qr. 9. 13-2 of 2 tons; 9876 of 7 cwt.; 1-25 of 4 9. n • tL""-^ V^""^ \ ^'^ 0^ 7 y^ ; 06 of 125 mis. 1 o L^?^ f ^ ^^*- i '9 0^ 1 lb., troy. 12. 22-5 of 1 rod ; 16375 of 3 lea, 1 ml 13. 64 of 1 cord, 72 cub. ft. ; 4 of 1 qr. 6 lbs. 14 137 of 2 days, 7 hra. ; 55 of J cwt 16' It^A^^A'^^'' '^ Z^ ^ ^> 2 '^- 20 rods. It). Jj)xii.''"''^'V ' ; (c.) {(fof ^)+li }^l4-(ixlj.)l' H-n 4J+5H 2J+IS • .,,,, ,,,,i,^ 4. pf — ot .. - 3HA 5. (a.) i-^f-f 4^ ^t*T.?i X 4 (b.) 2i X 2^14 1 i 3H 4i 6. — ■ — 'fioSli^of 41 - X '6 of — — • , ' ','/ ■ V? of I i- 103 ,-376X-376— •026x025 T .?ii 3-76— 026 _^0. ,« oi at yos.-f-^vi t .9|otife.u-^'t,W A of 7tV inches. , .^ ,U lo d£.l- '.>- f!: .••. :;.^ GRADED EXERCISES IN ARlTItMETIC. 61 IISGELLANEOUS. EXERCISE LIX. 2. Simplify |(A-f J)^(3-j) J ^(j ^ 20. - /»f f f»T 2. . Simplify- Sh—2l -i-15f. i of a^-i) >,.l^ W earns $2| in 2| days; how much will he earn in 5| days ? 1 BhL\^lV7(^n ^^t^J^^^ory^^d sells f of his snare lor $31,500. Fmd the value of the factory. ^5. A bojr \x>nght some peaches at 3 cents each • had he paid 5^ cents eacfi they would have cost $2.40 more. How many did he buy ? q. Divide 200 into 3 parts, such that the TeTeco'd '^"" ''' '^' ^°' the, tbi^rtime: price^fiTfhf .* T'^' ^'P''^ ^ ^^^^^ ^^^ price^ imd the cash price of an article marked^ left' 1iJ?^i.^^''^.5''o?^V^'" oran^^s and had 6c/ lett had he naid ajc. he would have been fir* ^9rfc..^S1i^d^lfc;nuiiS?er, ^ ;::r^f*'^^ ^^r^* of a lb cost ? 62 GRADED EXERCISES IN ARIYHMBTId Miacelkmeous — Gonti/nued. EXERCISE LX. 1. How many times can the product of 26 and 209 be taken from 2980473 ? 2. Find the value of a piece of land 3 miles long, 1 mile wide, at $23 per acre. 3. What is 4600 lbs. of wheat worth at $1.25 per bushel ? ' 4. Show how to find the L.C.M. of all the pnme numbers bet^€)en 20 and 40. 5. Find the cost of making 1 ml, 3 fur , 22 rods of ditch at $6.75 per rod. 6. Bought 3 bus. cherries at $2.25 per bus. and sold half of them at 65c. a peck and the others at 10c. a quart. Find the gain. 7. Reduce J, f , f and f to twelfths. 8. Bought 120 gals, of milk at 13Jc. per gal. ; at how much per quart must I §eil it to gain $7.80 on the whole I , 9. I gave I of an orange to A ; J to B, and ^ t9 Rifng, oO rods wide ? • ?' A '^fl ^^"^^"^^ '^^ ^ ^'^ ^n*l ^Hvided it old 7 of i^ "'".''• ^^ P^'^' ^^ ^^^^- ^^^^' ^'^d left? "'^''^ ■*'®"' ^'^*'-' ^^'''^^ .10. When- 98 mk, 7 fur., 13 per, 3 yds., 2 a. 8 in. is repeatetJ 87 times ; what is the result ? ' 11. A CTHAa 1^-t mici o.. 1 rk n i .^^ . a K_l' Iv ®T" Z"-',*^—- -" »uur, xi y mis., 11 n nas him ? ' ^^"^ ^^^^^ ^ ^" overtake (H> GRADED EXEACISES IN ARITHMIfrTIC. ANALYSIS. EXERCISE LXII. 'Ir^here are 17 tons, 12 cwt. of hay on IG loads ; find the weight of 5 such loads. 2. If it cost $2.70 to carry 18 cwt. 16 miles, find the cost of carrying 7 cwt. the same distance ? 3. If 7 men can cut 84 cords of wood in 6 days, how long will it take 1 man to cut 1 cord ? 4. If 18 boys make 459000 matches in 2 days, how many does 1 boy make in 1 day ? 5. If 170 pails of sap make 100 lbs. of sugar, how much will 1128 pails make ? 6. If } of a farm be worth S4500, find the value ot } of it. 7. If $7.49 pay for J of a ton of coal, what will 8| tons cost ? 8. If $jf will pay for J of a bag of apples, for what part will $5^ pay ? '*" '' 9. if 5 of a ship cost $9750, what will f J of it be worth ? 10. if 2f yds. 6f cloth Cost $14 21, what will 14 yds. cost. ii. i{ j 01 f. CH. Of ioo. oi vqa cosi> f oi ^ oi , what will j of i of |f of a lb. cost ? :,i GRADED EXERCISKS IN ARITHMETIC. 65 Analysis— Continued. EXERCISE LXIII. 1. If 5 tnen ^^n r^ap 19 acres in 3 days, how loner wil. it take fhem to reap 30 acres ? 2. If 3 i'. ;. of cotton weave 10 yards of stuff 1^ yards wiae, how many lbs. will weave 100 yards 1^ yards wide ? 3. If the price of a 3-lb. leaf is 10c, when wheat IS 9dc. a bus., find the price of a 4-lb. loaf when wheat is $1.25 per bus. 4. A crew of 35 men have provisions for 30 days ; how long will it last if 8 more men are taken aboard and all are put on half rations ? 5' J/i^ ";®.",^"^1<^ a wall .100 ft long, 8 ft. high and 2^ ft. thick, in 18 days of 10 hrf. each, !a JJ^any days of 9 hours would 12 men build a wall of double these dimensions ? 6. If 25 sheep eat as much hay as 19 -^oats and 33 Croats cat as much as lOcows, andSScows as much as 22 horses, how many horses will eat as much as 90 sheep ? ./ ^ cau 7. Jf 6 lbs. of tea are worth 29 lbs. of sugar 17 lbs. of sugar pay for 1 bus. of wheat, 27 bus of I'jf^^i^i't^-^^^-l.^t-- of 'coal for ll wv..,, ««u ^v cows cost ^1160, how many lbs. of tea can be purchased for $20 ? / «»• wi GO GRADED EXERCISES IN ARITHMETIC. ¥ t' mSGELLANEOUS. EXERCISE LXIV. I. Find the difference between 4 hundred and 7 times 8 thousand and 40, and 3,582,207,648^ 48. ^2. Divide 9x7x16x16x1 by 21x32x2. 3. What is the highest common factor of 144, 676, 720; also of 6006 ai^ 3318 ? 4. Simplify ^ ot ^ oi 3H of 6. 5. Reduce the following fractions to their low- est common denominator : 22^, 7i, 3^ and 4^^. 6. A boy had ^^V oi a dollar, and spent ^ of it ; how many cents has he left ? 7. A grocer sells 2000 boxes of strawberrieg at 4 for 25c., gaining $25 on all ; how much did he pay for the berries ? &. When potatoes are 45c. a bag of 1| bus., and 150 bus. grow on 1 acre, how much are the potatoes on l^ac. worth ? 9. How many squares of shingles (100 sq. ft. to a square) will cover a barn roof, one of whose equal sides is 80 ft. long and 25 ft. wide. 10. How many yards must a seed drill 9 feet w:idc I'un to sow an acre ? II. Find the value of 448 cheese, each 62^ lbs. at a York shilling per lb. tv GRADED EXERCISES IN ARITHMETIC. 67 Miscellaneous — Continued. EXERCISE LXV. 1. A piece of land is 45 rods, 22 yds., 33 ft. long, and 34 rods, 11 yds., 16^ ft. wide: how many acres in it ? "^ 2. Compare the fractions J n K K and ^ " 3 0* 7 i^ 0) ?o> flTi M 2| 3. Simplify 3H7i +li-iof 4f; H 4. Sold i of a cheese, then } of it, then A of the remainder, and had 221bs. left ; find the weight of the whole cheese. 5. From the sum of 8-,V and O^V take the dif- ference between llj§ and 14^^^. 6. ^'ind the value ot : (a) i of 1 ton, 6 cwt.', 10 lbs., 9 ozs. (6) * of 5 mis., 2 furs., 28 rods. 2 yds., 1 foot. 7. If 13^ lbs. of butter are wortli $3.00, find the value of f of a quarter. 8. What is the least number that will leave one when divided by 5, 7, 15, 21 or 30 ? 9. Two clocks are set right at 12 a. m. on Mon- day ; one gains If min. a day, and the other loses ^^ min. a day; how soon will thoro be one hour's dmeience? 10. A clerk copied } of £1 instead of ^-, ; find the amount of the error. 11. Divide $210.70 among A, B and C, Hviiiir B i as much as A,and C J as much as B. k GRADED EXERCISES IN ARITHMETIC). PRICE OP GRAIN. EXERCISE LXVI. 1. What is the price of 3300 lbs. of wheat at $1.09 per bus. ? At $1.80 per cwt. ? 2. Find the cost of 1785 lbs. of oats at 41c. per bus. At $1.28 per cwt. 3. How much will 2340 lbs. of pease cost at 65c. per bus. ? At $1.08 per cwt. ? 4. A man took 3600 lbs. of barley to market, and was oflfered 70c. per bus., or $1.45 per cwt. ; which had he better take ? 5. In the market reports I find the following quotations: Wheat per bus., $1.25 to $1.28; Barley 68c. to 72c.; Pease 65c. to 70c.; Oats 36c. to 40c.; Find the corresponding prices per cwt. 6. In another paper I find the follow* ig : Wheat, per cwt., $1.60 to $1.68; Barley, oi.U to $1.22 ; Pease, $1.05 to $1.08 ; find the corres- ponding prices per bus. 7. Find the value of 2828 lbs. of clover seed, at $6.25 per bus. 8. How much has a farmer on 2500 lbs. of timothy seed, after paying 25c. per bus. for threshing, if he sells at $1.87f per bus. ? 9. A load of potatoes weighs 3270 lbs ; find its value at 48c. per bus. GRADED EXEECISES IN ARITHMETIC. *ae. 69 PRICE OP LUMBER. EXERCISE LXVIl. per'M '"""^ ^^"^ ''^^'^'' ""^^^^ ^*- ^^^»^°iber, at $9.00 M., 340 ft. flooring at $8.50 per M., and 1600 ft cost' "^ at $7.25 per k ; fi^d the total 4. What is the value of 150 boards 12 ft.Ionir m. wide, at $11 per M ? ^t.ionjr, ^ \Eind the cost of .364 scantling 16 ft. lono- s in. by 4 in., at $8.50 per M. ^' 1 ^' ^t'^ '*' ,*^^^ "'^^^^ ^f 24 bunches of shin- gles (250 in a bunch) at $2.35 per M. ? 7. Find the cost of floorinfr a barn 24 f f „r;;i« 36 ft. long, with 24nch planfat $^25 /er M ' 8 What would be the cost of lumber for a tight board fence. 6 feet high, round^ yard 10 rods long and 6 rods wide, at $8.75 per M ? ^ 9. Walnut lumber is worth $80 per M. • what i jtCs'?hil1 '""' ' ''-' '^^^■' -'^^ ^^t wide; and 35 two°inch pknClS^rW^' 'Vg ID. Wide; all at «13.50 jJer M. *' ^ 70 GRADED EXERCISES IN ARITHMETIC. CARPETING ROOMS. EXERCISE LXVIII. 1. A strip of carpet is 18 ft. long and 2 ft. wide, how many sq. ft. in it, and how many sq. ft. in each yard ? 2. How many more sq. ft. will a piece of car- pet 24 ft. long, and 2J ft. wide, cover than one 24 feet long, and 2 ft. wide ? 3. How many sq.yds. in roll of carpet 216 ft. long and 27 in. wide ? In a roll 216 ft. long, 30 in. wide ? 4. How many sq. yds. of carpet 27 in. wide will be required for rooms whose dimensions are • (1.) 18 ft. by 12 ft. ? (4.) 26 ft. by 36*ft. ? (2.) 24 ft. by 18 It. ? (5.) 30 ft. by 24 ft. ? (3.) 27 ft. by 21 ft ? (6.) 48 ft. by 36 ft. ? 5. HovT many yards, 30 in. wide, would be re- quired for rooms of the above dimensions ? 6. Find the cost of carpeting rooms as follows; 1. 18 ft. by 24 ft., with carpet 24 in. wide, at 7.5c. a yd. 2. 24 ft. by 21 ft., with carpet 30 in. wide, at $1.25 per vd. 3. 26 tt. by 36 i't., with carpet 3 ft wide, at $1.10 a yard. 4. 16 J ft. by 18 J ft., with carpot 2 ft. wide, at 90c. a yd. 6. 30 ft. by 24 ft., with carpet J yd. wide, at 85c. a yd. 8. 27 ft., hy 21 ft, with carpet f yd. wide, at $1.00 a yd. GRADED EXERCISES IN ARITHMETIC. 71 Carpeting Rooms^-Continued. EXERCISE LXIX. 9 A ^^ ''t^""^^ ^^^^-^^ *^ carpet a room 27 ft bv carjet.'' "''^"' '* ^'-'^^ ^'^ *^^ width of thi ^ 2. Find the col ) of carpeting a strip 2 ft ^ 3 The perimeter of a room is 84 ft and th« tie fln ^' ^ 1'^^ ^^"^'^ ' ^"^ '^' cost of cover ng the^floor wuh carpet 2 feet wide, at $1.25 pe? 4. The perimeter of a room is 120 ft and the it'^^h's,fi''l^^'''\^°^i^^ ^^«* of carpe^^^^^^ It with 3U-inch carpet, at $1.35 per yd 5 How many yds. of SO-inch carpet will cover a platform containincr 14 nJankQ 7 9 i« -J , 18 ft. loner ? "^ P'*"^^ ^2 ^"- wide and 6 Find the cost of matting for 2 church aisles o4 ft. long, and 3 others 42 ft Jong, all 3 ft wide at oOc. per sq. yd. ft. » ^ o ii. wiae, nnH' Jin ?''^*'' ^l^ *^ '^^''P®* ^ ^00™ 18 ft. wide 28lt't?20Tp"^ "^^^ " ^^^*^--P^^ ^ "t 121/w1!^'T^^^\' ^^ '^"P"' each 8 in. high and $1 peryd ' """^ '^' ^^°^* ^' the stair cafpet at 9. A piece of carpet is 2 ft. 9 in. wide - hnw long must it be to cover 4^4 sq. yds ? ' 72 GRADED EXERCISES IN ARITHME'ICO. SQUARE llEi^^f^URE. EXERCISE iXX 1. Fiud the cost ci' papeiiug the walls of a room 20 ft. Jong, 16 ft. wide, 10 ft 1 ,^h, a'. 12^c. 2. iuHiii! :i/5e tbi cost of plastering the walla and CG-H^g of the above mentioned room, at 7|c. a f?.'j yd. 3. How many yards of paper 2 fc wide will cover the walls of a room 18 ft. long, 1 4? ft. 6 in. wide and 9 it. 6 in. high ? 4. Find the cost of plastering the walls and ceiling of a room 22 ft. 6 in. long, 16 ft. 6 in. wide, 11 ft. high, having four windows 6 ft. high, 3 ft.' 6 in. wide, and 3 doors 7 ft. high and 4 ft. wide, and a base board 9 in. wide, at lie. a sq. yd. How much inch lumber will be required to make boxes of the following dimensions : 5. 4 ft. long, 2 ft. wide, 1^ ft. deep, outside measure, with cover. 6. 3i ft. long, If ft. wide, IJ ft. deep, outside measure, no cover. 7. 12 ft. long. 3 ft. 4 in. wide, 10 in. deep, oujb- side measure, no cover. 8. 6i ft. long, 4J ft. wide, 3^ ft. hig outside measure, with cover. 9. A box 3 ft. long, 2^ ft. wl^i ^nd 2| ft. deen. insido ; nd the coat ni Unit • 'i «y;>v. «;«« at 6c. a sq. ft. GRADED EXEftCISfiS tUt ARITHMETIC. 78 PRICE OF WOOD. EXERCISE LXXI. 1. In a pile of wood 12 ft. long, 5 ft. high 4 ft Jer coX """"^ ""'^' ' ^'""^ '^' ^^^"^ "^t^^^ 7 I' M "J!^ ff! ""^-T °^ ^ P^^® 0^ ^ood 28 ft. long, 7 ft. high, 4 ft. wide, at $5.25 per cord. _ 3 How many loads 11 ft. long, 4 ft. wide 5 ft high, must a man draw for 50 cords ? For 72 cords? For 1000 cords ? i?or /^ son f^?'^^ ''l'^^^^ '' .^ ^*- ^^^^' 1<^ ^^' wide and ?00 cords f' """'^ '^ ^^ '""'^ ^^ ^^^^^ ^^^ a cord'whit'r^"''.^^P^^'' ^^^°^<^' ^^ ^^-ISic. a cord, whose dimensions are as follows : 5. 20 ft. long, 12 ft. wide, 7 ft. high. 6. 33 ft. long, 8 ft. wide 6 ft. high. 7. 45 ft. long, 21 ft. wide, 9 ft. high. 8- 140 ft. long. 12 ft. wide, 5 ft. high. 9. A man has 17 cords of 4-foot wood • how many coi^s of 2-foot wood will it make?^d how many of 16 inch wood ? 10. Which i.^ more nrofitaWA fo t..... . ^ ir--x 74 QBADED EXERCISES IN ARITHMETIC. 11 Ji' MISCELLANEOUS. EXERCISE LXXIL 1. A farmer sella four loads of oats, weiffhine respectively 1758. 2346, 1927 and 2593 lbs, at 42 Jc per bush. ; how many barrels of flour, at $6.50, can he buy with the money ? 2. Bought 36 yds. cotton, at 9 Jc. ; 14 yds print, at 12^0. ; 9 yds. lustre, at 26c. ; 10 lbs. tea, at 46c. ; how much butter, at 17ic. per lb., will pay for these ? 3. How often must 706 be added to 116 to make 10 thousand ? 4. Divide $250 among A, B & C so that A may have $2 more than B, and C as much as A and B together. 5. At what time between 10 and 1] o'clock are the hands of a watch opposite each otaer. 6. A storekeeper uses a yard measure one inch too short; how much does he cheat a customer who buys $9 worth of cloth ? 7. Find the value of a pile of wood 22 ft. lonff 12 feet wide and 6^ feet high, at $3.75 per cord! 8. A can run 11 yards while B runs 10 ; how much start may B have that A may win a half mile race by 2 yds. 9. If a cub. ft. of ice weighs 920 ozs., find the weight of ice on a tank 15 ft. long, 4 ft. wide, the ice being 3 in. thick. 10. Find the cost of 75 scantling, 2 in. bv 4 in and 18 ft. long, at $7.50 per M. ~ ORADED EXERCISES IN ARITHMETIC. 76 Miscellaneous — Continued, EXERCISE LXXIII. of ^27^and 27^ ^'^''^"''*' ""^ ^"^^ ^""^ ^""^ difference 2. On i of a field I sow wheat ; on i of the remainder oats; and on ^ of what then remains, pease ; and the remainder, 3 acres, I plant with corn ; how many acres in the field ? 3 How long would it take a man at the rate of 3 miles an hour to walk round a ten-acre field ijU rods long ? 4 How far may a person ride going 10 miles an hour, so that by walking back at the ^..e of ^ J miles an hour he may be gone just 5 hours? &. Ihe cost of papering a room 15 ft. long, 12 feet wide with paper 2 ft. wide, at SJc. a yard was $4.95; find height of the ^oom. ^ ' 1 .^-//^c^^nges sugar for flour, but only gives 15 ozs for a lb. ; how many lbs. of flour should ne get for a cwt. ? tt. 4 m. wide, 1 ft. deep ? ^' 8 By selling a horse for $147 a man lost I he gained 'i?'"^ ™"'^ """"^^ ^' ^^^'^ ^ot had 9 A can do a piece of work in 1 day B in it !k^^' ^u^ ^?° ^^ ^^y« 5 ^«w long wiuld it take them all working too-ether ? S ll« r^"^ *'f^ '''''*^ °^ a" silver goblet weighing 3 lbs., 4 ozs., 15 grs., at 452 7s. 8d. per oz. 76 Gf>ii.UE./ iiAl!.RCISES IN ARITHMETIC. Misixllaneous — Contimued, EXERCirfii: LXXIV. 1. What ia the cost of 17 tons, 18 cwt., 1 qr., 17 lbs. of potash, at $53.80 per ton ? 2* What will it cost to dig a cellar 40 feet long, 7 yds. 6 in. wide, and 1 yd. 1 foot d^ep, at $0.75 a cub. yd. ? 3. If it cost $84 to carpet a room 36 ft. long and 21 ft. wide, what will it cost to carpet a room 33 ft. long and 27 ft. wide ? 4 If T own 4^ of a farm and sell f of my share for $2300, what is the ralue of the whole farm ? 5. The four walls of a room are each 16 ft. long and 9 ft. high ; hew much will it cost to plaster it at 14c. a sq. yd.. ? 6. B)ugL a box of soap containing 70 lbs., at 7c. a lb ; keeping it all summer it dried away J> when 1 sold ic ao 8|c. a \h , how much did I gain or lose ? 7. What is the valne of ^^^ of -^.^ of a vessol, if a person who owns f )f ' sells ^ of J l '' his share fo. $1750 ? 8. How much carpet f yds. wide is lequired for a room 27 feet 3 inches loner and 22 feet^ 6 in, wide? GEADED EXERCISES IN ARITHMETIC. 77 Miscellaneous — Continued. EXERCISE LXXV. 1. If a train pass 10 telegraph poles — which, arp 10 rods apart — in 25 seconds, and leaves Lon- don at 11 4*5 a. ra., at what time will it reach Wingham, GO miles fiura London ? 2. A farmer sold 50 bus. 30 lbs. of wheat at $2.10 per cwt. ; but by mistake received pay for 30 bus. 50 lbs. ; how much did he lose ? 3. A man plows a furrow 9 inches wide ; how far will he have to go to plow an acre ? 4. To what depth will 33000 cords of gravel cover a road 40 miles long and 20 feet wide ? 6. A man can get his pile ot 6-foo^ wood cut into 3-foot wood for $2.40; wh^t will it cost to makcv 18-inch wood of it ? 6. If 5 bus. of wheat and 9 bus. of oats cost $9.15, and 9 bus. of wheat ..nd 5 ^us. of oats cost $12.55, find the value of 1 bus. of each. 7. In a school there are half as many boys as girls ; if 10 more boys ome there will be f as many boys as girls ; find the number of each i 8. Find the cost uf pickets for fencing a field 40 rods l^V fiO l-Ailfl f !iO TkinL-zifc. Q in » what part ot a bushel may be bought for %-^ ? 6. What is the amounc of $1296 for 6 years 9 mos, at 8^ per ceiit. ? j * 7. Find the cost of carpeting a floor 15 ft 9 w ■ Ti! 1^ !n ^*- ^ i"- ^^^^'> ^^^'^ ^^rP^t f yd wide, worth $2.50 per yd. ? r * ^ , and 147 ft. long ; how many cords does it con- tain f 9. How many turns does a hoop 2 yds 16 in m circumference, make in a quarter ot a mile ? 10. A table is covered with cents, each 1 inch m diameter, and placed in rows so that none touches more than four others ; if the tabfe be 5 teet square, find the value of the cents. • "t'«"^*^ ^"^ ^mixQ of 3s scamtimff, 4 in. bv 4 m, 16 ft. long, at $9.25 per M. ^ 88 GRADED EXERCISES IN ARITHMETIC. Miscellaneous — Continued. EXERCISE LXXXVI. 1. Divide $i444 among A, B and C, so that B raay have 3 times as much as A, and C as much as A and B tofrether. 2. In 161384 inches how many miles ? 3. Bought 147| gal. of molasses at 25c. per gal. ; used 33 gal. ; at how much per gal. must I sell the remainder to get the whole cost back ? 4. Find the simple interest on $125.50 for 2 J years at 6 per cent. 5. A man gains $1.25 on the sale of $25 worth of stamps; how much would be made on 1,000 3-cent stamps^ ? n G. Subtract — bus. + 1 of 4 J of Sh qts. from 5 8i bus. + 3^j^ qts. 7. A clock which is set right gains 15 min. a day ; how soon will it again be right ? 8. A gives $5 for hay at $9 per ton, B gives $7 for some at $12 per ton ; how much does one get more than the other ? 9. Mr. S. bought 4000 dozen eggs at 14c. a doz., lost one out of every 96, and sold the remainder at 23c. a doz. ; find his gain per cent. 10. If there are 3 qts. of potatoes on every sq. yd. of a field, containing 5 acres, how much are they worth at 35c. a bushel ? 11 H inil •^l'*rf-\ ^^/^i* long, 121 ft. wide, 1 J in. thick at $8.50 per M. F ! GRADED EXERCISES IN ARITHMETIC. 89 Miscellaneous— Continued. EXERCISE LXXXVII. of $100. 1 1 +— 2. Find the value of 1 — +_ ^ H ^i 3. What is the size of the smallest vessel that can be exactly filled by any one of the foTowiW measures : 2 pints, 3 qts., 7 qts., 2 gals., 5 gl^s f 4. Frnd the value of .Vs of 5 cwts. and ex: ^o^irtrj:.^^^^^^^^^^^ 0. A gets I of a sum of money, B 4 of tlie re- maiuder C theremainder; if A gets $750 more than B, find tlie share of ea:h m 8 days, C five times as much in 12 days- in what t.mo could they all do three times M mn'ch" 4. feimplify : 8i^+2§ ' 8|.^2f* 8. A man buys 20,000 bus. of wheat at %1 05 abn.s ; he keeps it 7 mos.. durinc. wh eh it shrinks 11 per cent. ; if money be worT^ 7 pe cent., and his expenses are S.^OO- fin^ i.;^ 1:^ or loss by selling at $1.95. " • '' "" '^^^ ^^•■" 9. Define interest, simple and compound. 90 GRADED EXERCISES IN ARITHMETIC. Miscellaneous — Continued. EXERCISE LXXXViri. 1. By selling tea at 60c. I gain -^^ of the cost. ; if I raise the price to 70c., find my gain per cent. 2. A man sells 2 horses for $130 each ; on one he loses 25 per cent., and on the othei he gains 25 per cent. ; did he gain or lose, and how much ? 3. A merchant marks his goods so that after deducting JO per cent, to grangers, he still makes 25 p"? cent. ; find the marked price of a hat which cost $2.3ri. 4 Vv'jat sum of money lent for 4 years at 8 per «;• I lost 8 per cent. ; for how much should I have sold it to gain 7i per cent. ? 6. Divide $76 between A and B„ in the pro- portion of 3 and "3. 7. A can do a v^ork in 2f days, and B in 3f days; how long will it take both to finish it after B has worked 1| days ? 8. If f of a mine be worth $64,000, find the value of -6 of | of '89 of the remainder of it. 9. In how many years will $725.25 double itself ai 6§ per cent., simple interest ? 10. A rectangular field of 8 acres is twice as long as broad ; find its dimensions. i GRADED EXERCISES iN ARITHMFflC. 91 Miscellaneous -^Continued EXERCT LXXXIX. 1. Four horses are ,rth as much as 9 cows Si^timer' a\^" -n r""^ A- ^ ='"'» C. so that tte"c" stare"'" '^ "1"^' '° ''^'^^ ^'^ """^ * and ^ m thick, are required to build a wall 60 yds. long, 13 ft. high, 1 ft. 9 in. thick « the mortar supply ^ of it ? ' hot tn!h"'f ^T^ ?°'^ ^^* °""0«^ to the lb.; as to^rP^JfJi r"-"' '''"=''• P^y'"g 5 per cent, so Trice Ttt sLT ""' °" ''■^ '"""'>' ^ ^' '^^ G. How long will it take to walk round a coJ^!td"^"„-^-rbf;fn^^ 8. The interest on $3500, at a certain ratP rk^sV^rt-^ar*'-"^--"-- cent, f Uihf c^^""^^ '°'- ^^'^^ 1 1°- 1* P- 10. A dealer buys oranges at 3 for 10c i^rxA sell, them at 4c. each; li the g^n per c^nt IMAGE EVALUATION TEST TARGET (MT-3) & // // A*^ /. %o f/. IX) y= il.25 '-lis |2S f ■** |2.2 U 11.6 Photographic Sciences Corporation 93 WIST MAIN STSilT WEBSTER, N.Y. 14580 (716)873-4503 V A N^ ^ \ WrS V- ^- % "^ n GEADSQ.BXERCISES IN ARITHMETIC. i . Miscellaneous. — Continued, EXERCISE XO. 1. What is the vahie of a pile of wood 34 feet long, 3 feet wide and 5 J feet high, at $7.88 a cord? 2. Twice the sum of two numbers is 25280 and half their difference is 804 ; find the numbers. 3. If 1 lb. of tea is worth 50 oranges, and 70 oranges are worth 84 lemons, what is the value of 50 lbs. of tea when a lemon is worth a penny ? Ans. in £ s. d. 4. A pond whose area is f of an acre is covered with ice 9 in. thick ; what is the weight of the ice on the pond, if a cubic foot of ice weigh 900 ozs. ? 5. Find the difference between the true and bank discount on $425 for 1 year at 6^ per cent. 6. A man is offered $7000 cash, or $8000, pay- ble after three years, for his farm ; which is the better offer, and by how much — money being worth 4 per cent., compound interest ? 7. A merchant gives 6 mos. credit, but deducts 5 per cent for cash ; find the cash price of an article marked $3.75. 8. Sold a house for $6381, gaining ^ of the cost; find the cost. 9. Sold two lots for $240 each ; on one I gained 15 per cent., and on the other lost 15 per cent. ; what per cent, did I gain or lose on the whole ? GRADED EXEBCISES IN ARITHMETIC. 93 AiJSWERS. g-- a4) ^1-^32 fin '"'" *""^'- («-^ «*«72 rods 4 yds. 2 ft. 10 in. • *^ '"• »>- pei. (8) 12 ^5^ low^^' o^*^ ^ ^""'^ 2 cwt. 3 qr.. 6 lbs 4ozs (•^; 201 tons 3 cwt. fT) i or 90 iK. r,' (S; 1025 parcels rol 1 7 V^ -oi^' ^^^ ^"'^• Ex YVTT TrN i;< 17 times, o8i ozs. $042 01 ^^^' (^^^729366. (8) 42134 far. (11) SG^Li.'"'''"- ^'^) 1^«1^-12. :4)487iac. (10) (9)^5040.^'^- ^''^^''-^n- (8) B 81 ac. 14 rods." T^^v YYT (9) »--CXi. /CW .fk (11) 224 doz. K^; ^4.94. (4) 4,370,520 sq. yds H GRADED EXEBCISES IN ARITHMETtd. I i J: Ex. XXII. (5) $4.40, 1120 lbs. (7) 146 hrs. 40 mm. (10) 1980 times. Ek. XXIII. (1) $19.50. (2) $1984.95. (3) $425.56. (7) $112. Ex. XXIV. (1) 1839882^. (3) Horses $18481.25. (7) $1513.25. (10)2317. Ex. XXV. (2) $2344. (7) $210.08. (10) 9566 times 82 far. Ex. XXVI. (8) $16.80. (9) $20. (10)$2.61. Ex. XXVII. (I) 97 n cords. (2) SyVA ac. (5) 5J ft: (8) 1920 times. Ex. XXVIII. (2) £184203 2s. 2d. (5.) £475. Ex. XXIX. (1) 157 ac. 1 ro. 32 per. 20 yds. 8 ft. 81 in. ((i) 70070 times. Ex. XXXIII. (1) 49276 grs., (3) 45472. (4.) £ 8. 8 s. 2i d. (10) $151.50. Ex. XXXV. (3) 7684 and 978. (10) $105.02. (11) 526,024,538 sq. in. Ex. XXXVI. (8) 3 J. (9). 2tV. (10) 43 a. Ex. XXXVII. (11) 73f (2) 9t»,\. (3) Wih' (4) $19.87^ Ex. XXXVIII. (6) m (10) 5^. Ex. XXXIX. (4) ^'gV- (7) $3.84J. (12) 2||. Ex. XLII. (6) 4525f times. (9; $7.14. Ex. XLIII. (1) 26 bbls. (4) 139 ft. (6) 9 bra. 36 miQ. Ex. XLIV. (3) 665coiD3. (5) 18|. (7) 204 bus. 2 qts. (10) $37ij«T. Ex. XLV. (1) $4.77. (6) 6026 rods. (7) 16H. (10) $57.48. Ex. XLVI. (4) 57096 times. (5) $74.86. (7) 2062 J. (8) 20 + buckets. I (3) flSADED EXERCISES IN ARITHMETIC 05 11 M.-^^i"^' '*' '2 times, (o) 4+1, „.. If,, IJ (10) 7.12 |i m " '^ '**) ^.Kx_ L,. (Y) ,33„s,7,,. (4) 3IIJJ cords. (6, Kx. LVIII. (1) ,