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The several numbers of the series are prepared t^ teachers actively engaged in the busy work of the schoolroom, and as teachers they know the great difficulty that the' average teacher encounters in the presentation of new and crisp problems for his Arithmetic classes. The authors would most respectfully request a consideration of the followmg points in connection with their series :— I. Mechanical Work. After pupils have passed the Second Reader the usual text books provide but very scanty practice in the mechanical operations. Pupils instead of becoming swifter and morie accurate as they advance in years frequently lose the speed and accuracy which they had acquired in the lower forms. To meet this difficulty the present series proviues over 5,000 operations in mechanical woik, which the teacher will find tested for him without the labor (and loss of time) of performing the work himself. This feature alone should commend the present series to every teacher of the subject II. No Answers. In the Pupils' Edition no answers are provided ; the Teachers' Edition alone contains the answers. lit Saving in Time. The time of the teacher 3s too valuable to be taken up in the dictation of problems to a class, when for a mere trifle each pupil may be provided with a set of exercises for himselL - .h. pupil'. n.tad .L^„";.'SS:;^1"»«™««< '• fi. fenmofAriUimetic. ^^ """•'""""»« of the lodaicl •tocolyped ptoblen* '^' «-"wi«Mw,t of old, «P«,™« find. «,l,rf ,0 u„ lUIH?^"^ *• "-i^. IX. Book of Butel.M. m ._■ T^ TocobUh August, i8^. Tmt AuTHois, •et bjr the ■vvenU (h« '"ff formal cted to fix e technical » problems "School ' of old, arranged grouped hgree of •tionsof • pupil's ^•Cher's lyiense edtext. ken for I hand iching. oit. MECHANICAL WORK. (I) 625456 31221S 763617 513315 767806 123432 (5) 361 22 I 212133 622331 524123 458416 468495 697261 644605 329185 518768 ExercUe l.-ADDITION. (2) 279807 502136 796736 452432 967875 23434s (6)T 642272 347447 872638 615465 421 64 I 879848 956925 508575 467259 752342 (3) (4) 876390 507648 763769 727659 507648 307523 727659 423237 432140 876948 541546 768275 (7) -r (8) 423426 782167 7091 5 I 4813" 820737 591479 253897 611512 541111 703608 422343 122291 735625 914572 156851 234210 481318 357444 423805 452468 Without putting the figures down. (9) Adc 4's (the same number of 4's in each successive Ime as there are figures in the line they are being added ARITHMETIC rSfli^^ t 552729 + 526063 578834 + 218272 ^. lyBS.t 121268 + 73956, + 366721 J76277 + 395587 + 821,85 810468 + 404432 + 4,5075 + 169962 + 827946 + 143478 + 434747 + 382427 + 6789,3 (19) 848703 + 7225,4 + 6353,3 22i7i| + 823135 + 288.74 34227^ + 68471? + 583.86 l^^fi i 5'68'3 + 642082 820818 + 902802 + 7C2.06 . 237833 + 6J6913 + 8743M (30) ^ + 433827 + 563725 + 434958 + 367624 + 233647 + 454739 285135 472244 318217 187149 735846 + 722445 + 182174 + 714924 + 358462 '+ S13534 ^S»353 + 224456 + 82.745 + 276287 + 714924 + 762875 + 584627 + 875697 t ^47287 + 7C6978 + 728733 + 7^3457 + 873346 + 875438 _ (' (> (• of re be 7's ca ca ca ExercUe II.-SUBTRACTION. (I) 625456763 3122155,2 (2) 876390763 432137698 ** (3) 825721423 376948768 811 (8) (12 (4) 825125427 327587998 (7) 514723272 278976785 MECHANICAL WORK (5) 823012345 759158576 (8) 62721 1335 378589657 (6) 713627230 273976735 (9) 914232013 267548129 Subtract 213987854 from each of the following : (10) 373967873 ; (I I) 972725879 ; (12) 958378327 ; 13 7212851 13 ; 14) 813246201 ; htS 5?23;65i3 (16) 931467842 ; (17) 712353768 ; (li) 472651997 ; (19) Without putting the figures down, subtract lines of 3 s successively, from 62447901 224, as far as the seventh remamder. (20) Subtract in succession 4's from the above num- ber as far as the seventh remainder. (21) Subtract .5's* (22) Subtract 6's. (23) Subtract 7 s. (24) Subtract 8's. (25) Subtract 9's. (26) Find by repeated subtraction how often 73869745 can be taken from 592410478, and give the remainder. (27) Fmd by repeated subtraction how often 41689754? ''*Mx*S*'5 ["*"" 3966641 141, and ^ive the remaSicIcr. (28) h md by repeated subtraction how often 975318643 can be taken from 10187754329, and give the remainder. Exercise lll.-MULTIPLICATION. Multiply each of the following by 357 :—(i) i8otd2 • <^,) 3^3^456; (3)2705.3; (4) 36^4;% 541(^61^(6) Multiply each of the following by 468 :-<7) 122553 ; (12) 735318 ""' —-'— ' ^--/ j-^/^y/t \»*/ ^yw-j^i ana 8 ARITHMETIC each 'of Z ''mZll"^'Jrj''!. ■""■•'P«ca.ion of and 87468. ^ ; "^^' =9"S6 ; 43734 ; 65601 ; Ustf i S a fecSr r™ """'"'ive times. Us nf A rf J " **'^" consecutive times (29) Usinf 8 S a fSr ^f" '^""secutive times. U Usi^^|Sa^S;iS:ScZ1c\".t t'E eighT-il^ r ??/; 'SN'-^'-r »« consecufVe," ;; the (32) 17676 • /«\ ofirr. ^'/ ' ?' *^ '^'^tO" :— (31) I32C7 . 3950. ; (4<) /,Ul7ISd (46?^7Sf' <«> 39336; (44) number lll^JJT'msV' L% '^.1, '**, "'v *« ''<•"'>'''"? '8432 ; f572457W«S itS.8 3/^^' ^«> '6384 i (5o3 (55) 49152: aSd (56) 5^2^*^^' (53)32768; (54)368&,; Exercise IV.— DIVISION. Dittde Jach ofthl mI, ^'^^ t"**^'" ; (16) 802^4^^ (.8) :27^5<,^f .°[,'^,« fo«o.mg by 437 M_.;/,8657l% /4oa9M2 ; and (32) 83957751^"' ' ''"'' 5dy/*o34i (2I> 'i3) 132456; 794736 ; and 'J9) H3712 ; 574848 ; and plication of 34 ; 65601 ; times, times, times, times, times, times. elv by the 30 132??; >77i; (36) 39) 13112; '336; (44) following J84 ; (50I 4) 36864 ; 3769154; 3598120 ; J370832; '4; (13) 0224992. >657278 ; 4; (21) MECHANICAL WORK 9 (23) Divide 8635547648 consecutively by 4 for 8 quotients. (24) Divide 5123828125 consecutively by 5 for 8 quotients. (25) Divide 39430665216 consecutively by 6 for 8 quotients. (26) Divide 81422872867 consecutively by 7 for 8 quotients. (27) Divide 394969219072 consecutively by 8 for 8 quotients. (28) Divide 506573812728 consecutively by 9 for 8 quotients. (29) 3552714396-^726. (30) 3489514378^406. (31) 445886497875-^4875. (32) 5963879065-^9307. v(33) 2975019839-^5423. ^(34) 11516639848344-^704006. Ekercise V.— REVIEW EXAMPLES. A. (i) Multiply the difference between 4396408 and 9206000 by 346. (2^ What is the product of 67489 and 758 ? (3) Find the quotient and remainder when the product of 86947 and 496 IS divided by 387. (4) A man bought.26 cows at $32 €ach, and 1 17 sheep at $6 each. How much less than two thousand dollars did he pay out ? (5) A man earns $22 a month and spends $14 of it. How long will it take him to save as much as he earns in a year ? 4-(6) Multiply the suhi of the numbers between 38 and 52 by 769. (7) In an orchard there are r rows of trees and 18 in each row ^iive barrels of apples are got from every two irees. What is the crop ? 10 ARITHMETIC » A'gr '-">• *'^-nce. p^duc. ana <,„„««„. «, B. ««n>^ foi^"^ ?'*''5 " •'»y> ho" much will ,5 „«, ' foriV,s'"H",te°;:^e5'.W.andayofc.„fox«, Sheep cost ? payment 80 sheep. What does a (io> Divide the sum of 7i8co .,/i,^ . j "' 73359, 4637 and 59428 by 684. REVIEW EXAMPLES II quotiem of es loo steps m hour? nts a yard ; re stockings she receive rth Si,52i. each cow »d forty IS nd ending [containing ime at 35 >Tnent 146 h does he ^at is the ust I sell » 16 years r did he 15 men 5 of oxen t does a by 684. (2) If II men can sod an acre of ground in I2 days, how many days will 4 men take to do the same work ? ($) Multiply 76493 by 8973. (4) A man sold chickens that cost him 35 cents each, for 76 cents a pair, and gained $2. 7a How many pairs did he sell ? (5) What nimiber subtracted 88 times from 80005, ^^^ leave 13 as a remainder ? * f^{6) Write in figures : seventeen thousand and eight; nine hundred and one thousand six hundred and four ; eighthundred thousand and two ; XCVII.; CD.; CCCV. and XLIV. (7) Divide 121 marbles between John and Tom, giving Tom 19 more than John. (8) What will a telegram of 44 words cost, if you have to pay 25 cents fo^ the first 15 words and 2 cents for each of the remaining words ? (9) ^. boy was told to multiply 720 by 304, and gave as liis answer 24480. By how much did his answer diffef from the correct product ? (10) How niany bushels of wheat at 69 cents a bushel rhouldbe^ven for 6210 pounds of sugar ft 5 cents a pound ? '^ I Iambs, get for REDUCTION. BssreiA • VI.-OOLLAR8 AND CCNT8. 9; How many ten.r#.nf «: ^ff /^^ J9; How many ten-cent pieces in Lq \ ^ ('o) How many fiv#» I.o«l -^^ *98.9o ? S3.3o+$4.4c? ^"y «^«-cent p.eces in $,.,o+$,.2^ + 4«»»9 cents ; and 1908190 cents ' ^ ^ °°°^ ^'^^^^ J (9) Exercise VII.-TI we. f '? Write the table, in /h^o5°lrhi; -onds in 6 minutes ; in ,3 „.•„„,,, ^ (12) REDUCTION 13 ITS. 87.04 and '7? ? i-$?.2<} + ints ; (2) ^4 cents; tnts ; (9) (3) How many seconds in i day ; in i week ; in 19 •lays ; in 2)4 weeks ? (4) How many seconds in 5 hours, 7 minutes ; in 12 hours, 51 minute^, 37 seconds ?. (5) How rtiany seconds from 6 o'clock a.m., to 7 o'clock p.m. ? (6) How many minutes in a year ? How many minutes in a leap year ? (7^ How many seconds in tlie year 1897 ? (8) How many hours in the month of January? in the month of September ? (9) How many days in the spring months? in ther summer ? in the autumn ? in the winter ? j (10) How many iiays are there in four centuries ? ~^ ■; ' B. (i) How many seconds in 17 days, 5 hours, 15 min- utes and 35 seconds ? (2) How many minutes in 180 seconds? in 1980 seconds ? (3) How many hours in 10800 seconds? in 183600 seconds? » - ^4^ How many hours, etc., in 34896 seconds ? (5) Reduce 28974 minutes to days, etc. (6) How many weeks, etc., in 2308589 seconds ? (7) How many days from August 24, 1896, to January 7, 1897? (8) How many Saturdays in 1897, Friday being the first day of the year ? How many Fridays ? (9) If a clock ticks seconds, how many times did it tick in February, 1896 ; in February, 1897? (10) Reduce 8 years, 340 days, 17 hours, 57 minutes to seconds, reckoning 365 days to the year. mutes , BxerciM VIII.— DRY AND LIQUID MEASURES. ^1} Write the tables. (2) How many pints are there in three quarts ? i gal- 1 5 - 1. i . 1 u-i a ^ . AWTHMETIC cents a peck? ® ®' '7i3 bushels of potatoes at 9 fro.iVirge"'^"^^?':^^"^^^^ o' berries could L ^Hed ■ gallon ? ^ ^^''^^ containing 2 bushels, 3 pecks i gain on at 15 cents a quart; find hil ^"«4{?^t'Z.?^.S^^^, »'<« for $,6. What ii.i.xt5:?arn-r-r-i:« chete';'ct^»ut' ""^"'"^ ^ l-*'. ' gallon. „, a. f i ^ITshef ~^' °' - ""'h^H ^ pecks of g„«s seed cenjVhe'';r^':""«'°f 'S bushels of cn.b apples at . (6) Find the value of re t^^i - -ts a pound, assl'^-^f ^- 3,uans.f^^^„ ,. « ■•tttlT/effs'TiiS.it'^ P»'^ of ™">- and wia, >? REDUCTION 15 (8) How many pint bottles will be required to hold 6 gallons, 3 quarts, i pint of vinegar ? (9) A grocer bought 2 bar»^ls (31 >^ gallons each) of syrup for $1 5. He sold half of it at 18 cents a quart, and the remainder at 22 cents a quart. How much did he gain ? (10) Find the cost of 23 gallons, 3 quarts of vinegar at five cents a quart. (11) If $10 was paid for a barrel of molasses, which was retailed at 20 cents a quart, find the gain.* Bxerci8C<(^— AVOIRDUPOIS WEIGHT. much A. (i) Write the table. (2) How many lbs. in 4 cwt.? 7 cwt.? i ton ? 8 tons ? 6 cwt., 53 lbs.? 14 cwt., 90 lbs.? 14 tons, 13 cwt., 79 lbs.? in 14 stone? (3) How many ounces in 8 lbs.? 25 lbs.? 3 cwt.? 2 cwt, 15 lbs.? II cwt., 82 lbs., 14 oz.? (4) How many lbs. in i bbl. of flour? i bbl. pork or beef? in i bbl. salt? (5) How many pounds in a bushel of each of the fol- lowing: Wheat, peas, potatoes, clover se^ com, rye, barley, buckwheat, timothj^ seed, oats ? (6) How many grains in i pound avoirdupois ? in i ounce? in 8 ounces? in half a pound? in i}4 pounds? (7) How many ounces in 19 tons, 12 cwt., 73 lbs., 15 oz.? (8) Reduce 3 cwt., 1 5 lbs., 8 oz. to grains. (9) Reduce 13579 ounces to higher denominations. (10) How many bushels of wheat in 3 tons, 4 cwt., 20 lbs.? (11) Bought flour at $7 per bbl., and s.>ld it at $4 per cwt. Find the gain on 27 bbls. (12) Find the cost of 1365 lbs. of hay at $12 the ton. (13) If an ounce of sugar cost half a cent, what will 2 cwt, 15 lbs., 12 oz. cost? 16 ARITHMETIC (i) How many cwt t»ti^iJt , ^ Find the value of .^^^"^^ ^767 ounces ? (2; 2750 lbs. of wheat 'af rv^ (3) 2584 Jbs. of oats at i.^ "^t"*' ^^' ''"^hel. (4 2704 lbs. of bariey a1^6^?'%P^'-b"«heJ. (5 1896 lbs. of timothy seed ^ri ^^' ^'''^^^' (6 1896 lbs. of clover seed i«r^'*^' ^^' ^'''^^^' (7) 73 1 5 lbs. of Indian coi^ \ ^^' '"^ P^^ bushel. (8 8964 lbs. of peas at ?c^..^'' ""'' P^' bushel ,. (9) Find the worth of 1 tc?/^ ? ^' ^"^''^J- ibs.at96 3perbushelV°^^°^-^eat weighing 4,85 '95 pounds.. Findtysumofthdr^dXs?"" "^'^^^^ Exercise X.-TROY WEIGHT. jl) ^"te the table. - 3 oi^7wtT.r ^"' '" 7 dwts. ? in ,3 d^ts. ? in , ^z. ? \3) How many o^r«i m ^ ^ ■j^s; j?EJK ""■•»■.,-..«.„„ f1^?\S?'"'^'''^°8ST"' '*^'' ashing. „.., can 0') Reduce .23 lbs. ,og,i REDUCTION .IT fi2) Which IS the heavier, i lb. of feathers or i lb. of gold ? I oz. of feathers or i oz. of gold ? How much heavier, give your answer in grains ? (13) How many pounds Troy, in 15 !!>s. Avoir., and how many grains over ? (14) How many pounds Avoir, in 15 lbs. Troy, and how many grains over ? "^Exercise XI.-APOTHECARIES' WEIGHT. lib.? (1) Write the table How many grs. in 2 scr. ? in i dram. ? in i oz. ? in (3) Reduce 6 lbs., $ drs., i scr., 19 grs. to grains. (4) In ten thousand grs., how many lbs., etc. ? (5) How many grains of calomel in 1 1 oz., 2 scr. ? f6V Find the number of lbs., etc., in 791 scr. ? (7) How many morphine powders of i gr. each can be made from 2 lbs., 2 oz., 3 drs., 2 scr., 7 grs. ? (8) Which is the heavier, i lb. Troy, or i lb. Apoth. ? (9) How many pounds Apoth., in 20 lbs. Avoir., and how many grains over ? Exercise XII.— LONG MEASURE. (i) Write the table. (2) How many inches in 2 ft. ? in 7 ft. ? in S ft. ? m 14 ft. .<• (3) How many inches in i yd. ? in 5 yd. ? in J^ a yd.? n sH yd.? (4) Express in yards i rod ; 4 rods ; i mile ; iX miles. (5) How many feet are there in 3 miles ? in 5 miles ? ^16 miles ? (6) How many inches in 3 yards, 2 feet, 1 1 inches ? (7) Reduce 6 miles, 24 rods, 3 yards to yards. (8) How many inches in 25 miles, 78 rods, 4 yards, 3 fcct, 5 inches of distance ? ^-:.i 18 AKITHMBTIC .Jn) Reduce 4 miles. 4.5 yards, . fee,, 4 i„che, ,0 4 yi^t "Z^rJkSr '■" ^ ■""^'- 5 f-'-S^. 3^ rods, B. Express 1239 inches in yards fr^f o«^ • u f xSr''' r^98 yards in mUe 'and y'ardr^"'' •fc-xpress 64016 inchi»«s in «,:i /^ras. Reduce a/^f inchesNo m eTy'^l^' !''• H^^ress .He ^di^^X"^ ^^ ii:oaf„arcJ-.S.r^^^ Exerctae XIII.-SQOABE MEASURE. m a square foot. number of square inches in i?,u?ryi^t «lr ^^Sr 07"""°^ ^«--^«' square rod. ' "i" <>» . 1. of surface ? How ma^Ts, Ja^etnU^^^^^^ «-ny square fee, o.hUAc^'r.filn'X'^i^ '/ii-"" "y*'-"?^ and an- inches m each board ? "°^ "*^'' "^Juare •■i."'^ REDUCTION feet, ^I iches to 32 rods, >9 1 wide, dsand nches, feet. iches 5 feet in a in a feet an- Liare (7) How many square inches in 5 square yards 8 square feet, 73 square inches? ^ ^ ' (8) How many square yards in 4 square rods ? in 6 square rods? m 12 square rods ? ^ 59) Reduce 2 square rods to square inches. lon^'^d";;^ k:tll^:r '"^'^ •" ^ ''*^''*"*^'- ^6 feet I B. How many square yards in i acre ? C2) Express 8 acres in square rods. (3) A cellar is 36 feet long by 24 feet 6 inches wide. How many square yards in the floor ? (4) What is the difference in square feet between 10 :?«:;: ya^is?"' " '^^^ ^^"^^^' •" ^^-- -<^-" ^« hoifll?Ti*"^y ^3"**^ ^^^^ of carpet are required fora yalds? ^ ^"^ ^^ ^^^^ wide Thow many square ^6) Reduce to acres and square rods each of the fol- l^owmg: 1000 rquare rods; 1250 square rods ; i32Ssquare (7) How many acres and square yards in each of the squrTaid'sl?' ^"""^ '^' ■• '-'a/square yards, ^^ (8^ How many acres in a lot 200 rods by 80 rods ? (9) A ten-acre field is 80 rods long. Express the dis- tance around the field in yards. » f «« ui* (10) Reduce 8642898 square inches to acres, etc. ^ [i) Findthe number of acres in the following fields ; rorf. t..^ ^V^^'lJ^ T^' ^y 32 rods ; 80 rols by 36 rods ; 140 rods by 96 rods ; 100 rods by 96 rods. ^ ■i\. ^^2 .**°^«»any acres in fields whose dimensions are: ^23 chams by 10 chams ; 32 chains by 2? chains: ^o -^ f byls'chains?''^"''' ^^ "^""^ ^^ ^^ '^*'^' ' ^^ ^^"^ 'vi n: ARITHMETIC (3) How ,„anya^T«8 in fields whose length md^Mdths respectively are : 26 rods by lo chains ; 64 rods by « chains ; 240 chains by 96 rods ; 100 chains by .44 rods^ 100 rods by 144 chains? ^ ^^ • mnm^Vj^"."/^"^ ^'^"f *^ y^?"?^ ^'^ *^"« '" the walls of a poom, 21 feet long, 15 feet wide and 13 feet high ? h\A^^ m'*^"" " ^^ ^^^* '°"^\ '^.^^*^' ^'^e and 15 feet c^liiig ? "^^ '"^"^'^ ^^''*' ^'^ ^^""'^ •" ^*^^ ^*"s and AcJfl7Kl^'7^^^' ""^ I rectangular plot of ground is f^Jf \ t ^'^^•■ence between the length and breadth ^t\^i """^ T'^y '^"^'^ '"c^es are in the plot ? squl?e;^er. ^Ct fs ttU^r '" "^'^' ^°"^^'"^ '° co.i'^osTua"VaUr?'^ °' ^^^* ^^ inches wide will , ) A souare yard of paper is cut into rectangular pieces 3 inches by 2 inches. How many pieces are there ? D. (i) How many pupils would a rectangular school-room 40 feet long, 32 feet, 6 inches wide accommodate, allow- 'n&/o square feet of floor for each pupil ? » JaIJ^'^IT^^ ^""I^^J ^^*'» ^""^ t^e*'^ »n a square field, a side of which is 7260 feet ? 1 . «= ". vai^^ Ji"'l*^-'^°^*^^*°**^'"«fa ^awn 66 feet long, 16 yards, 2 feet wui •, at 6 cents per square yard. (4) Reduce 7964820 square inches to acres, etc. make 6 > '^ ^ ^^^^ ^'^®' ^°^ "^^"^ ^^""^^ °^'* '^'" rnH^il"^* ^'55 an acre, what is the value of a farm 240 rods long and 90 rods wide ? (7) At 2 cents a square foot, find the cost of fencing i mile of a railway track, both sides, with a close board fence 4 feet high. oni^.l y^¥^ •'^'" '* i. '* ''^ P^''« a roadway 2 miles long and 15 feet wide at $( ^ qu.of.« yard ? (9) Find the prit< >: p,. - ^ of land 86 miles lon^ and 4 roqs wiae, at $44. k> •::, r,? n I f s c REDUCTION BzerclM XIV.-CUBIC MCa^URC. at I (iVWritc) he rnhle of cubic or solid ini„«sure. * (2) Show by diagrams the number of cubic feet in a and the cubic ynrd ; the number of cubic feet in icord number .i ubic inches in a cubic foot. (3) Jiovf many cubic in. are there in « cubic ft. : m x cubic ft. ; m 17 cubic ft..> ^ (4).How many cubic ft ir^ 3 cubic yds.; in 7 cubic yds. ; m 23 cubic yds. ? / . / .^ (5) How many cubic in. in a cube, one edge of which IS 2 ft. ? ' o (6) What is the volume of a solid 8 ft. long, 5 ft. wid«j and 3 ft. thick ? (7) How many cubic ft. of earth must be removed ii' digging a cellar IS u. long, lo ft. wide, and 6 ft. deep? How many cubic yds. ? (8) How many cubic yds. in a cellar 27 ft. long, i ? ft wide and 7 ft. high ? / »» a (9) How many cubic ft. in a block of stone 13 ft. Ion?; II ft. wide and 17 ft. thick? ^' (10) How many cords of wood are in a pile 242 ft long, 28 ft. wide and 12 ft. high ? (i i) A sleigh upon which 4-foot wood is piled is ib ft long. How high should the wood be piled to make a cord? '^ (12) How many bricks are required to build a wall ii ft. long, T2 ft. high and 2 ft. thick, if 21 bricks with the r-ortar .o'M make a cubic foot of wall ? B. , (1 ) Find the value of a pile of tan-bark 1 28 ft, long, 40 ft. wide, and 16 ft. high, at $3.25 a cord. (2) How many cords of wood can He piled into a wood- shed 20 feet square and 16 ft. high? (3) A box 24 in. long, 16 in. wide and 18 in. deep will contain about •» bushfils. Hn«, _ ve in a bin lalft. long, 6 ft, wide and'5 ftrdeep? Wiicai 33 ARITHMETIC .6 feet thick and jjfcethi^li','' "»""•"• "' » ■*"« long! avei^in^ 8 in dSp ?' ^™' '° ''= ^'^ ' «• *We and 7Xya,5scost%' °' *««'"«f » «"" 35'X24'X9', if teni'°A^KnV6ltig'^V/t.r1r"''"""J «^ ^•^ cords, and %% ■h » ,.™U i- .? getting $4.25 a cord for u he re^elJe foi'Se Z^ j*^"' ">« «" "fit- Ho» much di^ %i\o>crtiTStS"--^^^ < I . ' c. maif cIJdThl' thl'L"! T?""'?' -•»' X t' X * • How SaUons doe? the cistern hpld? " ^ x 4 x j . H"w many ™. by 5 in., mile long, i required wide and '7 ft. long ng, 12 ft ng, i8 ft. I? 24' X 9', if "f 64 ft. rd for 14 nuch did I ft. high 5 a cord. >ng, 4 ft. ft. long, trd, and square »od, the :? nd 6 ft. How ay $18 a rec- quarts. many REDUCTION 23 .f/^^-^** T^*.^^ ^**® ^^""Sth of a rectangular bin 4 ft. wide by 5 ft. 4 ,n. deep to hold 300 bushels ? W A gallon of water weighs 10 pounds Find th*. weight of water in a rectangullr cistern 6 ft. long and ! ft. wide, the water in the cistern being i ft. 4 in deeo ^ (9 There are 31^^ gallons in a Lrre .^ How £anv barrels of water are there in a rectangular waTer ta^k 6 ft. 9 in. wide 7 ft. long and 5 ft. 4 in. deep? ^ (lo) A cubic foot of water weighs 1000 ounces How many pounds are there in a rectangular cistern 9 ft long . 4 ft. wide, the water in it being 2 ft 6 in. deep?^ ^' ^ (u J ,." a swamp in Dereham, the townshin council had a ditch dug one mile long, 3 ft deepTnd 6 ft wide at the surface, and 4 ft. wide at the bot?om^ Find the total cost at 9 cents per cubic yard. Exercise XV.-BOARO MEASURE. • A. How many feet, board measure, are th^re in : Vol I u J '^ ^'•i'*".8^' '2 in. wide and i in. thick? h\ ? UA^' i^r^• ^°"«^' '^ •"• ^»^e and I in. thick? }i{ l^K^'^5' '^ ^h ^?"«^' 9 in. wide and i in. thick? }il \l t'^''^^' '^'^^i^onS^' 'o>n- wide and i in. thick? (fl f. K "^'f'' 'V\ '°"«^' ^ '"• ^>«*e and 2 in. thick? (6) 24 boards, 12 ft long, 12 in. wide and 2 in. thick? (7) I plank, 12 ft long, 8 in. wide and i^ in. thick? S L^if ^u' 't./-i^7^' 9 in. wide and 2 in. thick? (9) 20 planks, 8K ft long, 16 in. wide and 3 in. thick ? o ,3 planks, 16 ft long, ,3 in. wide and I iS. thick ? (Vl I f ^" .'"8^' »2 ft ong, 3 in. wide and 2 in. thick? J ^{ 1 ''^"^Ir^' 'l^t l°"8^' 4 in. wide and 3 in. thick? J^ !« f an 1"&. 16 ft ong, 5 in. wide and 4 in. thick ? (14) 48 scantling, 18 ft. long, 6 in. wide and 4 in. thick ? * B. (1) How manv KoarJ faa«. «r 1 'ong, 14 ft wide and i inch thick? .. 1 a floor iS ft. H ARITHMETIC ft lln^K»d'.'Si"?'/rul^V""'"' "" "'^^ °f "■"''" - (7) Find the cost of the lumber for a nlatf««,, ^.^ «W "^ "'''" 1"^ ^ '"• 'hick at $.2 Ar'^AouSid ' . (8) How many feet long will a plank ?o in wiS- »nH .ain'IUtaSLl^'"• P"""^ '^ ■»• -"e, will con- per M.; all the boards are 14 ft. i„ lengih ' ^ °'^° BxercUe XVI.-GENERAL TABLES. ill ?°1 '?*">' ""''5 '" ' gross ; in 3 CTOSS 7 dozen ? ^c^ SS''.** E"" °' '"° *'»"« of flour at $3 percwt each" " ■""' °f "• '■"«" brooms at ,8^0™!* cos^^f's^eatsl"^'"'^'' -^""^ '* ''■"^- What is the .aii?g'?rsh'i"oV"'''°'"'"P '" 5 fl"*^. «>* con- REDUCTION 25 (8) Ifa box of pens be bought for 80 cents and the pens sold for a cent each, find the gain on 2 dozen boxes (I box contains i gross). ""xcs, cents a tenT^ ^""°"' '"" ^' P"^^^^^^*^ ^«^ ^ ^' ^S (10) In 105 12 pens how many boxes ? honlV? H^.r"'?? fu*"* ^472 eggs at 9 cents a dozen, and bought cloth with the money at 27 cents a yard. How many yards did she buy ? ^ VUJ terclse XVII.-STERLING MONEY. S fi) Write the table. ^i i in" gT^inet? ^"'' '" ^ '**"""^' ' '" '" ^^"""^^ ' '» p) pP^ess 96134 pence in pounds, etc. rl u ^ Sru'neas how many pence ? in ii.iinp'!,'^ J"?T^i,""*' '" ^ shillings; in 12 shillings; in 2 guineas ? (Taking 24 cents to a shilling). ^ ios.^?\".°r$r86^t"^"^'^^^^^ -^^9; in ^3 ?«^ p T ""^r^ ^"'"^^.^ '" ^42 ; in ^147 .? M S-^*!,"''^ -^'3 4s. 8d. to farthings, guineas d'^erence in pence between ^109 and 89 (10^ Reduce 76841 halfpence to £, etc. pieces ? ""^"^ P""""^"' ^*''' '" 3927 three penny (12^ Reduce ^13 19s. 7d. to halfpence. {13) How many shillings are there in /? ics • 2 ^"Tfri' \f^TT^^: ^ ^^^^"u^ .' ^"^ =^ six-?encei ? ' our money f^^^^^'^°^ '"""^ '^ -^^ '«*• «q"^» *<> »> (15) How many pence in ^63 9d.? I Ini Hour mii<->h ...III iU— Ti i ^ .». » •--,- »....-,xi n^jn i«u X3uiiiv or loronto charpp to discharge a debl of ^,59 in .Liverpool at $^88 ^rT?. 36 ARITHMETIC Bmrcise XVUL^ARTICLES SOLD BY THE 100. Find the value of; 7250 lath at 30 cents per hundred. 2900 pine apples at $13 per c. 2425 lbs. sugar at $3 per cwt. 8175 lbs. cheese at $16 per cwt. 275 lbs. of beef at $6 per cwt. 2160 lbs. of pork at J8 per cwt. 15 bbls. flour at $2.50 per cwt. 47800 bricks at $8 per thousand. 47200 shingles at $3.50 per M. ' 4320 feet of plai.k at $40 per M. 20750 ft. of lumber at $16 per M. 25500 shingles at $4.50 per M. B. 3500 lbs. of hay at $18 per ton. 25360 ft. of lumber at $27.50 per M. 0400 lbs. of hay at $9 per ton. 8 tons, 1000 lbs. coal at $5 per ton. 6325 bncks at $8 a thousand. thicWar$??pe? m"' " ''' *°"^' " '"• ^'^^ -d 3 in. (7) Find the cost of 17640 feet of lumber at $11.50 ner ^•Vt?l368o lbs. of coal at $5.50 per ton. ^ ^ (8> How much would it cost to shingle a roof 40 feet long, each side bemg 15 feet wide at $2.65 per M ^ (i«S shmgles cover 10 ft. square) .> ^ i^L!?!?'^^*"/ l^'^u*^'.^' V^} *^°^«^^ t^« two sides of a Jf, each side of which is 27' by 14' 6"? t«n^',^^«iJ??** i^^r!''*!*''''^ ^^^^4o lbs. of coal at $6.25 a ton, 17860 feet of lumber at $13.50 a thousand. C. ill Kinrf th#» ffict- nf istM lU- ~et . mt^ roo REDUCTION 2'- th^^^l^Jtl^ 'f ^? y^/^^ *°"8^ *"^ 220 yards wide. Find It $5? ^r M.'^ ""^^ ^°'* * '^^'^ ^*»*'^ *^"" 6 ft. higl^ (3) Find the cost of inch flooring at $17. so oer thou- sand for a floor 28 ft. by 16 ft. '^ ^ t^J^^ :^ ^M^!*" P"ic»»ased 4250 lbs. of hay at $10 per ton and sold it at 68 cents per cwt. ; find his gain ^ ^ll Al"?tl l^'^fi! ''^^''op Dine apples at $12^ per C. r^Jf , P^*^ thousand, liow much will the lumber cost for a close board fence 80 rods long and 6 ft. high ? i6'x\^^!^^?or^ """ " T* *^ '^y ^^^ ««o^ of a room ?«\ \A * ^^ u ^"l"?!®. (a square = 100 square feet) ? (8) How much would it cost to lay a floor 7 yards long by 5 yaMs wide, at Su^sH a square ? ^ ^ (9; How many bunches of shingles will be required to 7f^? «°^ ^"^ ^ J^ • • ( J' ^^^^^ 4 bunches to the square ? (ip) How much will it cost to shingle a roof, theJenffth ofthe rafters on each side being ,5 ff. and the bSng 35 ft. long ; the bunches costing $1.16 each? "'"'°'"« i'i. COMPOUND RULES. Exercise XIX.— ADDITION. $987 63 . 429.92 38.34 927.74 9.00 $ 96.24 198-78 647.92 68.34 928.87 $719.43 921.99 86.86 50.00 9-37 (4) $9836.74 968.10 91.98 7.54 .87 . <5) yds. ft. in, 23 2 7 34 I 6 52 I II 74 2 7 61 2 9 miles. 18 73 196 584 762 (6) yds. 897 936 1042 1 197 1264 miles, chams. yds. 6 40 II 7 29 19 8 37 8 7 16 5 3 74 21 miles. rods. 6197 50 8193 47 604 123 897 235 68 39 mileSi ehains. rods. 16 13 2 12 22 3 »7 15 3 26 73 2 59 68 2 (28) COMPOUND ADDITION (lo) miles, yd*. 17 8.7 918 69 8 94 832 912 1013 in. II 7 8 9 6 sq. yds. 56 48 20 39 M (n) sq. ft. 4 5 8 6 7 sq. in. 76 23 38 96 (12) sq. mis. acres. 817 89 76 934 518 72 104 216 317 94 29 rods. 138 147 25 16 118 (13) sq. miles, acres, sq. yds. 87 39 193 92 217 763 31 318 1082 986 169 2162 14 4 894 (I) ttjns. cwt. lbs. 18 7 37 17 18 45 9 12 53 8 16 61 26 18 77 (14) acres, sq. rods. 186 89 175 76 123 94 loo 123 98 119 B. (2) tons. lbs. oz. 719 187 4 816 913 II 43 486 7 219 1732 9 8 58 8 (•5) acres, sq. ch ins. 114 8 96 5 l^-K 7 64 9 257 3 (3) lbs. oz. dwt. grs. 5 9 II 18 17 29 26 7 4 6 38 II 17 13 6 21 14 3 6 8 IS. rods. 2 3 3 2 2 (4) ;£ s. 27 16 81 17 93 9 67 9 72 14 (5) d. £ 8. d. 3 9 4 5 7 W 86 72 474 79 6 8>^ 13 9>^ 15 7 9 7X 9 83i<: (6) ;£ s. d. 987 15 4H 764 17 7X .99 9 9K 87 II iiX 986 13 io>^ 30 ARITHMFTIC <7) wlu. d«yi hi*, rain. m& 8 I 9 32 27 9 2 II 36 31 '9 4 17 40 35 17 3 19 44 39 26 5 21 48 (9) 43 tons cwu qrt. lbs. oz. drs. 14 12 I 13 5 9 23 13 I '5 7 8 37 17 3 9 9 6 iS 19 2 17 S 7 8 4 68 8 2 ^16 (") CnatRToss grou. dos. nnits. IS 7 5 6 13 8 6 7 29 9 4 8 76 5 9 10 13 4 7 [I (8) y^ da3^ bn. mltu mc. 98 217 12 47 28 87 221 16 51 36 76 318 18 55 42 35 247 24 49 48 42 108 29 43 24 ( .0) bus. pks. gals. qts. pt 897 I I 2 I 26 3 I 2 3 2 3 I 41 I I 3 I 768 2 I 2 (12) thous'd. hund'd. tens • units. 6 9 1 4 7 3 5 S 4 8 6 2 6 9 7 I 7 5 4 a amiiiu r iJr the "Ter "=Mof°1 " 'Ijl ''"'"""■'^ J..3..8 ; frui't, $168 JSd ,u„dri« Volk ' 'h^"""""?; did the whole come to ? ='""™«s. W9-«i. How much L\ COMPOUND ADDITION 3< MC. 28 36 42 48 34 I o I I o (3) A farmer sold 6 loads of wheat, the first contain- ing 1 819 lbs., the second 2037 lbs., the third 2036 lbs., the fourth 1926 lbs., the fifth 1673 lbs., and the sixth 2162 lbs. How many bushels did the six loads contain ? (4) A merchant sold the following quantities of mo- lasses : on Feb. 1st, 15 gal. 3 qts. i pt. ; on Feb. 2nd., 23 gal. 2 qts. I pt., on Feb. 3rd, 31 gal. 3 qts. ; on Feb.4lh, 9 gal. I pt. How much did he sell in the four days ? (5) A grocer sends off the following quantities of butter : 47 cwt. 56 lbs. ; 83 cwt. 86 lbs. ; 26 cwt. 34 lbs: How many tons did he send off? (6) A man has owing to him the following sums : ;6i3^ips. 7d. ; £^6 5s. 8Xd.; and ^49 19s. 5>^d. How much IS owmg altogether ? (7) A jeweller receives on Mon., 16 lb™. 4 oz. gold; on Tues., 9 lbs. 5 oz. 18 grs. ; on Wed., 6 lbs. 15 dwt. 2ogrs.- on Thur., 5 oz. 10 dwt. ; on Fri., 13 lbs. 3 oz. 16 dwt. 16 grs. How much does he receive in all ? (8) Three fields have an area respectively of 17 acres 139 sq. rd.; 16 acres 76 sq. rd. 25 sq yd.; and 9 acres 12? sq. rd. 18 sq. yd. What is the total area ? (9) What is the entire length of a railway consisting of 4 different lines, measuring respectively 189 miles I76rd. 2 yd. ; 85 miles 60 rd. 4 yd. ; 100 miles 224 rd. 3 yd. • and 59 miles 174 rd. 4 yd. ? (10) Find the total quantity of wood in 4 piles con- taming respectively 20 cords 1 5 cub. ft. ; 23 cords 59 cub. ft. ; 16 cords 68 cub. ft.; and 29 cords 125 cub. ft. Exercise XX.-SUBTRACTION. $8976.43 987.49 A. $3427 63 2197.21 $1600.87 384.93 ja ARITHMETIC (4) JS s. d. 1089 12 7 423 IS 9 (5) I ■. d. 784 14 8>^ 457 16 11^ (6) ^ •. d. 563 IS (>A 138 19 7X (7) cwt qrs. lbs. 200 2 20 99 3 21 .(8) miles yards 8943 67 4817 943 (9) miles rods 1376 21 987 237 (10) tons cwt, lbs. oz. 714 13 y? II 286 17 49 13 00 lbs. ^z. dwt. grs. 576 9 19 4 89 10 16 15 (12) y«. da. hr. min. sec. 4083 200 10 30 15 2186 319 19 39 34 0) ac. sq.rd 197 57 103 96 B. (2) •C. sq. yd. 283 1239 118 3674 ' (3) cords cub. ft. 893 76 275 127 (4) miles rd. yd. ft, 768 29 5 2 5 94 138 3 2 7 in. (5) ac sq. rd. sq. yd. sq. ft. gq.in I30I 31 29 3 23 423 38 13 8 76 (6) bus. pk. gal. qt. pt. 710 2 O 2 O 186 3 I 3 , (7) tons cwt. qrs. lbs. 02. drs. 716 13 2 16 2 7 176 16 3 20 9 8 COMPOUND SUBTRACTION 33 I ^r. min. sec. lo 30 15 »9 39 34 (3) Is cub. ft. J 76 ; 127 -• y 1 (5) I started for a walk 3 hours, 37 minutes, 29 sec- onds after noon, and returned at 9 p.m. How long was I away ? (6) From 15 years, 3 days, 16 hours, 29 minutes, 6 seconds, take 9 years, i week, 3 days, 22 hours, 50 min- ates, 40 seconds. (7) A wagon loaded with hay weighs 34 cwt., 72 lbs • the wagon alone weighs 9 cwt., 96 lbs. Find weight of the hay. ** (8) A barrel hoWs 31 gals.; there was poured into it 14 gals., I pt. of vinegar at one time, and 3 gals., i qt. at another. The barrel was then filled with water. How much water was poured in ? (9) A farmer had 1000 bush, of wheat. He sold 249 bush., I peck at one time, 448 bush., 3 pecks, i gal. at ano'her, and kept the rest for flour and seed. How much did he keep ? (10) A man travels 8 miles, 216 rods by railway and 17689 yards by boat. Which way does he travel the farther, and how much ? 34 ARITHMETIC ions 4 cwt. ; 2 tons m cwi co Ih. ',"*^ respectively j lbs How much is K';h'-'s't''o"i; ?""" ' """ '^ ^'^'- M 3sq*;?i^,^:;7^:\'^;;- f"--.'>.e firs, has 75 acn=s yds^ and the^thirda; muchasth^"''!."'^ ' "?' "*• '» "*• 3 3,. rds. .,s<,. yds. Horurh'lrnS'iL'L'SaS Exercise XXI.-MULTIPLICATION. (( «( • •• Multiply $573.52 by 49. 13 cwt. 5 lbs. 6 oz. by 12. 13 bus. 3 pk. , gal. 2 qt. i pt. by 57 &'^5'^:-b7r-'-'''-^y37. /4911S. 8^d. by8. 6 days 15 hrs. 32 min. 17 sec bv ^71 23m,les,76rds.4yds.by22. ^^^^• olbs 30Z, i5dwt. i7grs.byiQ 12 miles 560 yds. by 23 ^ ^' 17 miles 83 yds 2 f^ 1 1 ir, u .: J /us. 2 It. 1 1 ,n. by 63, using 30 rods 4 yd. 2{!^Xd" "^ * ''"'^"' «^'d avejie'?„',.^,^i«^^^,^,^9 r^iles in length, and its road. =*P"'^ 35-37. J* md the cost of the •aini'ni^tihe'sVp^cL-l'Kn."' t'H- -^h ™"- .5 ^itf i-ht -r'-" 4 -^^^^^^^^^^^ peas a. COMPOUND MULTIPLICATION 35 A, 9LI . iV^^^l f'^'i''^ '^ ^"^^^ '6'^*- ba^'ey at 45 cents a bush. ; 56 bush., 45 lbs. wheat at (/, cent, a bubh., and 10 bush., 17 lbs. oats at 40 cents a bush. ^^^(8) Find the value of 7683 lbs. of cheese at $12 per bushd/'""^ ^^^ """'^ ""^^'^^ '^'- b^^l^^heat at 72 cents a (10) If I silver spoon weigh 3 oz., 8 dwt., n ers what IS the weight of 8 dozen such spoons ? ^ ^ ' (11) A man travels 24 miles, 6 furlongs, 3 rods in a day. How far could he travel in 2 weeks ? C. (1) Find the total length in rods of 48 pieces of wire each piece being 35 yds., 2 ft., 3 in. long. ' (2) A wagon wheel 15 ft., ,0 in. in circumference makes .634 revolutions in an hour. How far in miles yards, etc., does the wagon go in 5 hours ? ' in„^!l;^.K"^ "^""^H-^ "'''^' 15 yards to school each morn- ing, and the same distance home each afternoon, for 208 time?" ^ ""^ ^^' ^""^^ ^^ ""^^^ ^"""& that (4) A farmer plowed i acre, 160 sq. rods a day for 2^ days. How much did he plow ? «* ^lay lor 23 Ion r? ^^^^ '^ *^^ ^^"^^^ ""^ 3°°° '"'''''^' ^^*^h '6 ft- 8 •"• (6) The fore quarters of a lamb weighed 6 lbs. 2 07 each and the hmd quarters 8 lbs. 5 oz. each. How much did the lamb weigh .* "lum tir/7^'^,'^''^" '^ 35 ft. II in. long and 7ft gin wide What is the length around it ? " 7 u. 9 m. wide. (8) How much coal oil is contained in 29 bbls., each containing 29 gals., 3 qts., i pt..> ^ ' (9) Multiply 89 miles, 119 rods, 4 yds., i ft., 8 in. by 7. ,«./i°^r •*'''°*'-^ •^'''".^ 3 min., 15 sec. per day. How much will It gam m a fortnight ? r I I 36 ARITHMETIC i\ ExerciwXXII.-DIVISION. DIVISOR ABSTf,M*T. 27 lbs. 12 oz.^3. 39 lbs. 5 oz. 4-4. $7624.53-^9. ^'713-^4. 3ogal.3qt ipt. .^7. 68bus.2pk. igal. 2qt.-j.8. 31 days 5 hrs. 15 min. 10 sec.^12. 84 yds. 2 ft. 9 in. -^ 5. "' v^, 13 miles 945 yds. 2 ft. 6 in.-rr 00)^157 15s. 8d.-M3. yO 73219 tons 15 cwt. 89 lbs 6 07 ^v.-*^ ('3) 287 acres 469 sa. vds.*r (14) 47 thousand, 8 (15) 5 million, 3 ten 9 tens, 8 units -^ 79. B. ,„43) D.v,de a legacy of $,<«| e,ua5irrot/,79 per- sacf^ >t-io?hLts°/cSo1i? ^™'='^"^'' '-<"'- eacl'^o^tlEf ;- eTlS'srrd%'^T^ °f -«, into 108 lots, and sold them 1, «. *'f"''"' ">« '«''">'e did he get for each lot ? ' "^^ "''• «'"' "^W"* }i) 287 acres 469 sq. yds -s- ? 14) 47 thousand, 8 hundred, 7 tens, 1 units--8 ' 1^5)^5 m.lhon, 3 ten-thousands' 6 thiisa"nTshu„d,.d, COMPOUND DlVISIOJi 37 IS gllsJloftT °^^""°"' ^^'^ ^2 '^" «o^ much will (8) Seven horses eat 15 bus. 2 pk. 3 qt. of oats in a ^eek How much is that for each horse ? (9) A father who had a 200 acre farm, gave his onlv son 80 acres, 100 sq. rods, and divided the remainder t^^'j,!::^.l,^i::r Find to a square yds^r^^ o^Pa^pe-f?u^& tSe'o^f 1^; !^ i^ ''9 acres 18 sq. yds., 7 sq. ft. less than 9 times as mud^ asB's Fmd the amount of land in the three farms -y Si: f J"^!? T? ^.^ ^^'■^^' '24 sq. rods, 28 sq. yds., vds^* Ln ff"^- A^% ^T. ^i^''^'^ '37 sq.'rods, 29 sq yds., 6 sq ft, and divided the rest among his 4 sons How much did each get? , ^ Exercise XXIll.-DiVISOR CONCRETE. JO $43.50-;- $8.70. ' $20024-13 cents. $444o-^$3.7o. IS lbs. ID oz. 4-3 lbs. 202. 4days,4hrs.-^5omin. ., 9702 gal. ^31 gal. 2 qt (7) I mile-r2 ft 6 in. (8) i6yds. 4in.-r4ft 10 in. ' (9) 50 miles, 200 yds. ^2 yds., i ft 6 in. (10) 68 tons, 1594 lbs. 10 02 -r 152 lbs. 6 oz. (11) 20 lbs. 8 0Z.-rI2 0Z. (12) 26 weeks, I day -h 3 hrs., 50 min. B. acri;\39rq.td"?" " '""' '' ^^^ ""^"^ ^^^^^'"^^ '» 36 3« i ARITHMETIC «vi?o\^°'^ long will it take to plow 147 acres 10; so rods at the rate of 4 acres, 35 sq. rods a day ? ' ^ '^• W How many turns will a wheel ia ft -.;«;« • cum erence „ake in rolling a distencTofI J m'ile"? " "" ,^A" i'"" "^"y '""«■=. each containine I bnsh , null?to ^sT"'' ''^'" '*<* " '*■ '°"f ""' "casure 2 cwt 2 a«°'in£'',ir5l!''*''! "f ^^«"' ^^"^^ containing r, cu^l^flS: rn"X-?.t- ^ «• « ">• '" ci. (12) Assuming that a person's steo « 2 ft ft ?n f many steps does he take £ walkfug'Tt^fiu's^o y'Js! ?''°"' C. 9xi'^2V^5Ttt''n;S„'r^'^^ '•• ' '"'" "-y "-ks bin 8l?xTf?T,''"'K''r'«''«" *<">'d it take to fill a man^ miles will a steambSt'^^t ^ « 'd^s^Tthe s2S: (4) A cask contains 64 ffal i nt t »^f u« may a vessel holding i at ^ m \« ^,1^^"^'°'^ "J^"^ ^"^*'^^ ^c^ TK- r ""'"'"s/ V. I pt. be filled from the cask? . (5) The fore-wheel of a carriage whirh 5« ^ r . • :res, 105 sq. 3 Jn. in cir- liles ? I bush., 3 124 bushels I measure 2 >ni a hogs- ntaining 13 of 341 tons in. in cir- d 80 rods ning from urs each. > in., how ► yds. ? COMPOUND DIVISION 39 h^ i^l ^'"? *^/ number of bushels of wheat in a bin 6 ft. bTches: ^ "^"'P' '^ ' ^^^' '' "^"^^ *° ^''^"^ ^77 cuWc is th^fidd /^^^"^ ^° """^^^ ^°"^ contains 10 acres, how wide arotto'ds^loll^r'^' °'"'^^ ' ''' ^ '^' -" ^^ -^ -^ One^UJZ^}'''^^' '°? ''**^!.°*" ^'""^ f^«^« 6 wires high. Afi Jt"i How many bushels of oats are equal in weieht to 68 bushels of barley and 51 bushels of wSeat? ^ o«^^ v^J" *^® ^^'"® °^ * ^'n of wheat 6' long, 4' wide ?ufr?s) ^'P' ^' ^' '^"'' P"^ ^'^^^^^^ <' ^"bfj ftlls ny bricks :e to fill a 5? Is. How the same my times e cask ? 7 feet in the hind nference ining 15 s of car rd? MISCELLANEOUS. Exercise XXIV.-AVERAQE8. A. « oii^^^f '^ *^® "^^^" between 10 and 80 : between o and 90 ; between 76 and 182 ? ' oeiween 7 ft.? ^^^' '^ ^^^ ^""^'^^^ ""^ *^'^^ ^^"&ths of s ft.. 6 ft., -lit'J^^ltl^sVr/r^^^' '^^ "^'^'^^ °^^ ^*^^" buslf^Yhn^h ' i^^, ^T^8^« Of four loads of wheat of 40 Dush. 45 bush., so bush., 55 bush.? ^ VS) What IS thi» averacro. «<■ tu^ r»n-_ • rifle match: 72, 73,"79,"iS,Y3; g^'T ™"""""^ '""'*' "' ' 40 ^ITHMETIC dailv receipts for the week ^^ '^^' ^ '"^ ^^^ average vearf ^ TK* *""^* *8« "f A, B, cf D, E Knd F is ,. pM' ^ B. (0 2.3 cows and i6 horses together cosr t^cfj^ tu cows^ cos, J.6 each. Find .hfTve'rage'cSi''^f elc'h 33 K. ® 5«'' 2Ubr^*!r°'' Pf;"'- of ••>« following : ® 14c.? * ' ^ ^'- ® ^*^-' ^3 lbs. @ 3,c., and ,y Ihs. a Ih^"*^, AS""'.?'"" '"Ke*" 9 lbs. tea worth ,2 ccnt^ (S) A grocer mixes 15 lbs. of coffee (cb 'ynr -, ik ^ ^nSeltewtlS ^' -« --faTaif Votdl long and 36 "^s m¥e" 4nd ,he .k';?^'*'""^^"'"'-"''' "'t)'^r'"= -»"t buTo'nSXXSg"5^« ^° '"^^ the fou„h 'rlrd— '-'-t:^'"^'' "'^'^''^ => ">»• '«^^ "ha" * -^^ "'^ i"c weight 01 eaca. AVERAGES 41 s 1896 lbs. Jay, $200 ; 'day, $325 , le average ps. Wliat 1 ; 2 at $23 2. I sold id F is 31 s 28 years. 5O6. The : of each bUowing" : s J 24 lbs. allowing : id 17 lbs. 32 cents Find the 3 lbs. @ f pounds irms, the 200 rods r 20 rods pounds ,• ond, but ess than 15 @ 17c. (8) Fihd the average price per lb. of the following : lbs. @ 15c.; 16 lbs. @ 14c.; 18 lbs. @ iic, and 13 lbs. Exercise XXV.— APPLICATION OF SQUARE MEASURE, (i) Find the area in square yards of the following square fields, whose sides respectively are : 15 yds., 24 yds., 37 yds., 59 yds. :» ^ » 'f (2) Find the area in sq. yds. and sq. ft. of the follow- ing square fields, whose sides respectively are : 9 yds 2 ft.; 12 yds. I ft.; 17 yds. I ft.; 25 yds. 2 ft. (3) Find the area in sq. yds., sq. ft, sq. in. of the fol- lowing square fields, whose sides respectively are : 4 yds 2 ft. 5 in.; 7 yds. 2 ft. 8 in.; 9 yds. i ft. 9 in.; 15 yds. 2 ft. 10 in, * ^ J J (4) Find the area in sq. ft. of rectangular fields having respectively the following dimensions in feet : 24 by 20 • 27 by 18 ; 33 by 27 ; and 1 12 by 97. (5) Find the area in sq. yds. and sq. ft. of the follow- ing rectangular fields : 5 yds. 2 ft. by 7 yds.; 3 yds. i ft. by 10 yds. 2 ft.; la yds. 2 ft by 12 yds. i ft; and 26 yds. 2 ft. by 24 yds. 2 ft (6) Find the area in sq. yds., sq. ft., and sq. in., of the following rectangular fielcis : 2 yds. i ft. by 4 yds. i ft 3 in. ; 5 yds. i ft. 4 in. by 5 yds. 2 ft. ; 6 yds. 2 ft 8 in. by 3 yds. 2 ft ID in. (7) A plank is 18 in. broad, find what length most be cut off to make a square yard. (8) What part of an acre is a field 120 yards long and 25 yards wide? (9) A street is a quarter of a mile long ; find the number of square yards in the pavements 3 feet wide on both sides. 42 ARITHMETIC ing II inches by 8 inches ' ^P^n^'neasur- wi,/a JSjXX7'l^-Vk'^ 9 in. wMe meSn^'gls'ft.VfcTt 1un„"' •"""■ "t"" '" " ^oon, qui«asp\cepf27i;,?by'.8gr""«^ '*"='' P'"°" "> «■ aveiage four treeVo^ o^eaAl^r^ chjir"^ "" - widl''^ing on an path 2 yds. Find how e required iquired to Is, with a land 4235 by 12 ft. sr square J^ yards, se a rec- find the 'w much i&i wide? CARPETING Exercise XXVI. -CARPETING. 43 A. Find how many yards of carpet running lengthwise will be required for rooms of the following dimensions : (j) 18 ft. by 15 ft., carpet a yard wide. (2^ 25 ft. by 18 ft., carpet a yard wide. (3) 18 ft. by 12 ft., carpet 27 in. wide. (4) 21 ft. by 9 ft. II in., carpet 27 in. wide. Find the expense of irpeting the following four rooms, the dimensions and cost being : (5) 24 ft. by 21 ft., carpet a yard wide and 90 cents a yard. (6) 30 ft. by 15 ft., carpet a yard wide and $1.20 a yard. (7) 18 ft. 6 in., by 13 ft.^ in., carpet 27 in. wide and 75 cents a yard. , (8) 43 ft. 4 in. by 24 ft. 9 in., carpet 27 in. wide and 99 cents a yard. (9) How many yards of stair carpet will be required for a straight stair of 21 steps, 11 in. wide and 7 in. high, allowing for 2 extra yards ? (10) How many yards of carpeting 27 in. wide will be required for a room 17 ft. 4 in. by 14 ft. 5 in., if the strips run length-vise of the room, and 8 in. per strip be wasted in matching ? (11) How many yards ot carpeting, i yard wide, will be required for a room 30 ft. by 16 ft. 10 in., if the strips run lengthwise of the room, and 9 in. per strip be wasted in matching ? (12) Find the cost of carpet for a room 22 ft. 7 in. by 14 ft., if the carpet be 27 in. wide and cost $1.20 a yard, and 6 m. per strip be wasted in matching, the strips running crosswise of the room. B. (l^ How manv varHs of thicl*- r»ar»»i- ^/> :« ...:^« ...:!! cover a floor 20 ft long and 18 ft. wide ? 44 ARITHMETIC ?i^ FinTSf "^"."'"Z lengthwise of the room:' ry X«,!)^o •.? '^ *^°^^ ^° ^^^Pet a room 2?' 6" lontr mH wide and tunnfJhnl^wi^f'u^ ""T",? ''''■'« '7 in. • at 87>i cents a yird^ . """^ """* "<""'' " <=«' in. widens «".s a 'v^rr *° "'"' ^-^Sthv,'^' carpet 3> -IK--^^^^^^^^^^^^ to cheaper, and how much, to fa ' tht 4/4 ^Jh '' *' p./aprde'in'd''c;f.i^;'^,r<^,^7/4«' I* car. each case? *"™'"^ ""^^"^ ^nd matching in Exercise XXVII.^PAPERING. A. folln^'.T;i5°£ °"_,"l»'^h ;M« exercise is worked is .s -— - . . ... 3u,» ux «ie wiaiiis of doors and windows Ts PAPERING 45 5 required 5 '"• rise, long and 8o cents a if t 85 cents long and )6 cents a long, long and r $ .44 a /ise? •ed for a »g 27 in. Id it cost carpet 32 2at$i a iiore ? ie be, to arpet 27 ^ IS the iwise or ? ith car- ' 12" per :heaper, ■ much ? hing in i is as lows is deducted from the perimeter of the room, And the number of strips is obtained by finding how often the remainder contains 18 inches (The width of Canadian and American paper). The length of a single roll of paper is 24 feet. Note. — Paperhangers have a special rule : Deduct half the area of the openings (in square feet) from the area of the walls, and divide the remainder by 30. This gives the approximate number of rolls. (i) How many widths of paper will be required for a room 18 ft. by 1 5 ft., no allowance for doors and windows ? (2) How many strips will go round a room 19 ft. by^ 24 ft.? (3) How many strips are required for a room 31 ft. by 24 ft., if there are 4 windows and 2 doors each 3 ft. wide ? (4) How many rolls will be required for a room 21' 5" by 13' 4", with 2 doors and 2 windows each 3' wide? (5) How many strips are recjuired for a hall 26 ft. long and 6 ft. wide, papering the sides only, on which there are 4 doors, each 3 ft. 3 in. in width ? ^6) How many rolls will paper a ceiling 24' x 18' ? (7) How many rolls of paper are required for the walls of a room 2 1 ft. long, 1 7 ft. wide and 9 ft. high ? (8) Ho\ ' many rolls will paper the walls of a room 12 ft. by 16 ft. and 8 ft. high, allowing for i door and 2 windows each 3 ft. 4 in. in width ? B. (1) Find the cost of paper for the walls of a room 17 ft. by 13 ft. and 9 ft. high, with 3 openings, at 36 cents per double roll (each opening 2 ft. 11 in. wide). (2) Find the cost of paper 21 in. wide for the walls of a room 35 ft. by 20 ft. to the height of ^jS^ ft. at 65 cents per double roll; 1 foot on each strip is allowed for matchings, and the border costs 8 cents a yard. (3) If the paper-hanger charges $2.50, the border cost- ing 8 cents a yard and the paper 1 5 cents per roll, find the cost of papering a room 22 ft. by 14 ft. and 12 ft. high, with paper 30 in. wide, allowing 12 ft foi doors and windows. 46 ARITHMETIC r^Sf ^'1? ^^^ -"'i °/^^® wallpaper 21 in. wide, at 25 cents a roll, required for a room 20 ft. 8 in. by 15 ft. 4 in eacM it. wiSe' "^^ ^ ^' ^ '"• "'^" ^"^ ^^indowi r.ntcl^'n'^ ^^®u°'i °. *^® ^^" P^Per, 2r in. wide, at 20 cents a roll and bordering worth 10 cents a yard for a ^A? K ^^ • u,"^^' ^""^ 1 ^'"do^s each 3 ft. 10 in. wide. dJull^^ A ^ rollmake only 4 strips, and 8 strips be deducted for doors and windows, find the total co t nf papenng a hall 30 ft. long and 8 ft. wide, with paper wort^ 62 cents a roll and bordering worth 12 cents a yard ; the on the border i cent a yard. H»<^""b (7) What will it cost to paper the walls and ceiling of a room 27 ft by 33 ft. and 18 ft. high, at 35 cents ner square yard ? ' s > «>■ js t.cius per Exercise XXVIII.-PLASTERING AND PAINTING. A. «,ni^°J^~^* '^ customary in plastering or paintin? the walls of a room to deduct half the area of all ooenfnl^s etc and take for the required area the number orsquare yards nearest the remainder. ^ ^ (i) Find the cost, at 20 cents per sauare vartl «f plastering the walls and ceiling of a mom% ft Lnl' 16 ft. wide and 10 ft. high, allowin^g for 2 Tors^ each ^ ff by 3 ft., and 3 windows, each 6 fl. by 3 ft ^ (2> Find the cost of plastering the walls and ceiling' of a room 16 x 12 x 9 feet allowing for 2 doors, er.ch 7 ff by 3 ft. 6 m., and 2 windows, each 6ft bv 4 ft anH 1' skirting board i ft. high, at 15'cents per squLt yird. ^ ^ (3) How much will it cost to paint the ceiling of a box wid^^Hd ! f^f ^T Z^ P^;"*'"«^ *^« outside of a squirryard ' ^ ^' ^^ ^ ^' ^^ ^ ^'' ^^^P' ^^ '^ <^-«ts .per PLASTERING AND PAINTING 47 (5) Find the cost, at 10 cents a square yard, of paint- ing boti sides of a close board fence 4 ft. high, round a rectangular lot 132 ft. by 66 ft., allowing $3 for painting posts and scantlings. (6) How much would it cost, at 20 cents per square yard, to paint the walls of a room 20 ft. by 17 ft. andf 9 ft. high, deducting for 2 doors, each 7 ft. by 4* ft., and 3 windows, each 6 ft. by 3 ft., and also paint the ceiling at 30 cents per square yard ? (7) Find the cost of plastering the walls and ceilings of a room 24 ft. long, 18 ft. wide and 15 ft. high, the skirting board being 18 in. high, at 22 cents a square yard, three coats being put on the walls and two on the ceiling. (8) Find the cost of painting the walls and ceiling of a room 26 ft. 6 in. long, 18 ft. wide and 14 ft. high, at 34 cents per square yard, allowing for 2 doors 7 ft. 6 in. by 4 ft., 2 windows 6 ft. by 4 ft., and i smaller window 3 ft by 2 ft. (9) What will it cost to paint the walls and ceiling of a room 18 ft. long, 15 ft. wide and 12 ft. high, at 2% cents a square foot ? (10) Find the cost of painting the walls and ceiling of a room 15 ft. 6 in. long, 14 ft. wide and 10 ft. high, at 36 cents per square yard, allowing 80 square feet for doors and wmdows. (11) Find the cost, at 6 cents a sq. yd. of painting a fence 6 ft. high around a lot 22 rods square, both sides. B. (i) What will it cost to plaster a room 32 ft. long, 18 ft. wide and 13 ft. high, at 12 cents a square yard, aUowing 200 square feet for doors and windows ? (2) Find the cost of painting the walls and ceiling of a room 18' 6" long, 14' wide and 10' high, at 23 cents per square yard, allowing for 2 doors 7' x 4', and 3 w^-dows 6'X3^\ 48 ARITHMETIC Of a cistern 8 ft. bv 12 f' S 8^ hLk '^^ ^"^ ^««°»" square foot. ' ^ "' "'«^^» at 9 cents per (7) How much white learf n ;n> ;« • , , coat on a fence ,87 yards lonir Ld 6 ft ^^^"^^ ^" °"« covers 4^ square yidT? '' '• *""''■ '' " •"""d B number ong and veiling of 'ith four rd. bottom -nts per for one I pound feet by t. by i6 Fence 5 ^ts per (0 76894 68317 34567 89123 45678 91234 56789 12345 67891 23456 78912 34567 (6) 49867 71386 23456 78912 34567 89123 45678 91234 56789 J2345 67891 23456 MECHANICAL WORK. Exercise XXIX.-ADDITION. (2) 31467 28913 45678 9 '234 56789 »2345 67891 23456 78912 34567 89123 45678 (7) • 76413 31982 34567 89123 45678 91234 56789 12345 67891 23456 78912 34567 (3) 82154 67418 56789 12345 67891 23456 78912 34567 89123 45678 91234 56789 (8) 45128 81476 45678 91234 56789 12345 67891 23456 78912 34567 89123 45678 149)" (4) 98621 94628 67891 2^456 78912 34567 89123 4S'^7- 234 56789 12345 67891 (9) 12689 82649 56789 12345 67891 23456 78912 34567 89123 45678 91234 56789 (5) 73409 37645 78912 34567 89123 45678 91234 56789 12345 67891 23456 78912 (10) 90437 54673 67891 23456 78912 34567 89123 45678 91234 56789 12345 fiTRni '{ »)fi/.' 50 ARITHMETIC Exercise XXX.- SUBTRACTION. (4) 4533599 ;(sl^lUU)^ti''^' ' <3) 449o6i. , (10) 5664169 J (}; ^^^If' ^?>>*gf44i ; (9) 6068767; in succession: (n) 7i7ijci • ?..\ ., l°°^'«n times 06) 7076,73; (4^,11 U^l otll'Xll' ('5>7»7^73-. (38) 945677. ; ^.fe^'j g ^^9^3 ' ^''^ '''''^' ' in srst^n\°'^5f)1'oT.'i|« times •0376794 ; (34) 49^!,°;-(5tf.i5i|o1. ;'°5^^Ut^ Exeretae XXXI.-MULTIPLrCATION. .«8lf(T)'';3l^^°[3"°-[n? numbers by 4.7 : (,) 34576 ; (7) 3686^ i i,??^ ,' /l> '«43^ ■ (S) ^7648 ; (6) -7«f(TIf:^4°7!-3V:i;ii"f/ mte^^ by 568. (,o) (^9='^ '^^^« ' (») '^464 ; kY^e^l (~r--e (35)';'?5Vf (.6?.^^ r (^^) '^"[^(^"sntri ■■ h} '^* ■' MECHANICAL WORK Exercise XXXII.-DIVISION. 51 Divide each of the following numbers by 284: (i) 36261 12; (2) 4079376; (3) 4834816; (4) 5439168; (5) 7252224; (6) 8.58752; (7) 10878336; (8) 14504448; (9) 1 63 1 7 504. J t^t , VW Divide each of the following numbers by 9 ten con- secutive times : (10) 21527406891774 ; (i i) 28703209189032; (12)43054813783548. J -V y-j , Divide each of the following numbers by 8 ten con- secutive times : (13)1457067655168; (14)2914135310336; (15)4371202965504. Divide each of the following numbers by 7 ten con- secutive times : (16) i;35535453564 ; (17) 2303303180346; (18) 767767726782; (19) 3454954770519; (20) 1 151651- 590173. Divide each of the following numbers by 6 ten con- secutive times : (21) 5826157922304 ; (22) 8739236883456; (23) 3884105281536; (24) 971026320384; (25) 2913078- 961 I 52. N .// 7 J / Using factors, find the result of oach of the following • (26)8396741^63 ; (27)893749847^72 ;(28)8967459.^56; i,29) 9876402^84 ; (30) 45296787-J-72. . Bxerclse XXXIII.-GENERAL REVIEW PROBLEMS. (i) Divide 84 miles, 240 rods, 2 yds. by 13, and re- duce the quotient to inches. (2) A man paid$38.75 for cloth, 7 yds. costing $10.8?. How many yards did l^e buy ? o ^ (3) A boy counted the number of square inches in 4 times I acre, 49 rods, 3 yds., 7 ft., and his brother counted the niimnpr nf rmnooc ir» r^»» ^^.^^ \iri-:_i- 1 . — „„.., .^^ .„ ^^^ iwii=. Willi;!! uoy countea the greater number, and how much greater? 52 ARITHMETIC (4) John and James started to walk from Tni.rt«f« «♦ noon and walked until 20 min. af^r one ?clodc T„hn wagon going ? ^ """"''• ""^ ">»">' ">"« ^ hour is the ani^i ft "x'';!!'^ -2" °? pT«ing a room 20 ft. 6 in. lone ?!?{ Sfu ""^ • 7 miles 4 rods to iiches. ton) ^ ^^' '' '^^ ^^^"" °f "°° lbs. of hay at $8 per ills An oK?^"^i"/i^?' ^^^^ ^'■^ tl^ere '» 746859 inches? anilhi tos?s"ar2o 'rod's'S'' "^ '=™'^ '' '""""^ hour doeMhe trih, go? ^P^"" "°" """y "i'*^ »" MoXlo6.3r;^.'^nn-sJk7 *- '- -S a.m. wi./^^Jl'Jri/i^^irga-^tr '"' °'"^ ^'" s,u^\ot"'i1ot3ira^n-r!--=-^!;"«" ^3 GENERAL REVIEW PROBLEMS. oronto at :k. John ?2o yards, aart were the rate ains long ch plank wide. :tangular deep? lakes 48 ur is the in. long costing of each $8 per sd 3 in. inches.? Is wide, cents a 4 qts., econds iles an 5 a.m. What «n 23 53 (20) riow often can 2 gaL i qt. be subtracted from 36 bus. 3 pks. ? (21) A man travelled 32 miles 217 rds. 4 yds. 2 ft. on Monday, and 43 miles 276 rds. 5 yds. 2 ft. on Tuesday. How far would he have to go on Wednesday to go 100 miles altogether ? (22) A man paid for a piece of land 32 rdg. wide by giving 240 cords of wood at $4 a cord. Land being worth $40 an acre, find the length of the piece of land. (23) Find the cost of carpeting a room 30 ft. 6 in. long/ by 18 ft. 6 in. wide, with carpet 27 in. wide, at $1.17 a yard, allowing 6 in. for matching— the carpet running lengthwise. (24) Find the total r ■.■ , ,f 12 scantlings 24'x3"x4'' ; 30 planks 2 xi8"x24', and ft. of lumber at $15 per M. (25) A road is 4 rods wide and contains 32 acres, how long is It ? (26) How high must wood be piled upon a rack 12 ft. long and 4 ft. wide, so that there may be one and a half cords ? (27) Find the cost of the boards for a close fence 7}4 ft. high around a school-yard containing one acre, at $12 per M., the yard being 8 rods wide. (28) Find the cost of 3 loads of wheat containing : 54 bus. 26 lbs. ; 49 bus. 54 lbs. ; and 51 bus. 30 lbs., at 60 cents a bushel. (29) A gravel bank has a surface area of one acre, and is 3}4 ft. deep. What length of road 14 ft. wide and 9 in. deep will it gravel? (30) Divide 279 acres, 139 rods, 26 yds., 3 sq. in., by 68. . (31) Find the difference between 99 miles, 319 rods, 25 yds., 2 ft., 1 1 in., and 100 miles. (32) Find the cost at 12 cents per sq. yd. of plastering the walls and ceiling of a room 2 1 ft. long, 1 2 ft. wide and 9 ft. high. It has 4 openings, each 8 ft. by 4 ft. .(33) How many yards of carpet 30 in. wide will be re- quired to carpet a room 18 ft. long and 15 ft. wide. What will It cost at 95 cents a yard ? 54 ARITHMETIC wil/iit^gt ,vUf4pf? "' " ^'^P ' ""^ ■"-y -"«. etc.. tons and iK each ? ^*^"^^ P^'^'^"^* «°^ "^*»y (37) Subtract 16 bus. % nk i nt frr^r« «, u q... and d^ide tU. imJ^^nT^^^Jl^"^^'^ ' \ 30) Reduce 75614c inches tn 'nicrU^r. ^ ^. " . K', ^ater wpicrh Tr» iko I, »* ^°"" oz., and a erallon (4-) Exp„sf^8399Tyards in'rJJiletSd™?"' a J^th r^^vW^^^^ J12.50 per M * '• '"'^'' *'* P'*""^ 'fi in. tfiiclc, at staii^'if^''sUps'^ch'\?!i?^ "'".^'"T?' <■"' " fligh' of /'^A\ T J- P?' ®^<^" io>2 m. wide and 7 5/ in hJifh ? .on^f?8r':'iii?„^d?aird:^r'''""*°'^"'-''^^ busS.'S^ andT;5;rbs'^/'°i''|V f, *"»' '" 9^ cents a spent 60 cents Md with .^ ' ?6 cents a bushel j he ceV. a cwt" ' Vo^'r^tn^r Efh^u^;'^'" <=-' ^' 3o (50) A farm containing co acr^s •" ^r r-- J- • ' v\ \ GENERAL REVIEW PROBLEMS. 55 rnd"w?^t wiS^thr/'^^' ^'"'^ ^'^ '/^"■'■^^ *° go around it, and what will the fence cost at i >^ cents a foot ? V5i; A stick of squared timber is i8 in. by 15 in., and measuri?"^' ' '' '' ^^"^ ^' ^^^ P^'^ ^., boarS (52) A half acre lot is 10 rods long. A 5-strand wire fence IS put round it. How much wfre, at 5 cems alb will be required if 2 yards cost 3 cents.? ^ ' 2bbl. nf hf /^^ total weight in lbs. of: 3 bbls. flour ; I hulh if ^ f ' ''°.^"?- u°^ P°*^^°^« ' »2 bush, of rye 5 bush, of oats, and 9 bush, of barley. ^ f^J^^^i^?^ "^*?y ^"'"'^^ pickets placed 3 in. apart, will fence a half acre lot of 66 feet frontage ? *^ ;n.Cr.^°'^T^"y^^^'°^'"'^^^^ are required for a 12- mch baseboard around a field 40 rods by 30 rods ? h*» ri^ i **if°°";^ '^^ ^^ ^^' ^S^^"*^' ^hat must its height square ya'rds?^' ' ^''^ '^ ^^ ^""' '"">^ ^"^°""^ ^^^ (57) Find the value of a pile of wood 40 ft. long, 24 ft ^'*^; ??i^ ?• ^'8^^' at $575 a cord. ^ ^' ^ «^i^^^^'"^ t^® ^a^"e of a field 50x32 rods, at $95.50 an (59) Allowing 90 cubic feet of air for each pupil, how many pupils could be accommodated in a school-roim 27 ft. long, 18 ft. wide and 10 ft. high ? ma K^fwJ. '5,^^"*^ a square yard, find the cost of paint- Lnd2ift tlde°°''^^ ^ ^^^^^^^°^^ room 27 feet long r«,/k^^ A bag of grain weighs i cwt. 45 lbs. 3 oz., how much less than 45 tons would 18 bags of such grain weigh.? ^.-^i^K^ ^. ^"^"^T ^""^^"^ ^^*^' °^ ^3 rods I ft. 6 in. on each side, has trees planted aL around it. There is a tree in !?S''T!u°^*^^ ^'*^' ^"^ along the whole length of !«?!," V^^''^ ^'■^, 9 trees. How many trees are there, and how far apart ? ' (63) To pay his rent on 75 acres at $2.75 an acre a .!IIfrK^^u^°*'^^35olbs.ofbarleyat78 cents a sack of 100 lbs. ; how many bushels of wheat at 8« rentiRITHMETIC (64) How many times must a boy walk round a nlav ground 140 ft. long and 70 ft. wide, L order to w^kseve'n o„it^^ ^ ^**?^'" ^9'd peas in a field containing 10 acres a b1,.h JP^"i ?5.75 inlabor. He sold the peasit 85 cents !2S Y?^'^^ ^^\ "°^ "^a^y bushels per acre had he? (66) Make out thefollowingpay sheetriohrs J^day: A.. •B.. C D.. M. 9 10 .8 10 T. W. h 9 9 10 9 ID ID ID 10 10 10 8 10 10 8 6 5 4 5 $2.00$ $1.90 Si. 80 $1.60 $ Exercise XXXIV.-BUSINESS TRANSACTICNS. A. iowL" nili^^xTmptsT °' ''' ^"""'^^ '" ^^^^ '' '"^^ '^'' aJ^I ^^^ '^^- ^""erat i8c.; 103 lbs. cheese at 14c • 112 at 4Qc^?and S^'h' '^^ ^''- "^""^ ^' ^''' '^S bush. plSatoe' at 49c., and 87 bush, carrots at 58c ^6 hn.T? «ij"'^- "^^^^^^ \* ^?^-' ^7 bush, barley at 6^ • corS at 77c ^^'•' ^^ ^"'^- P"^^ ^' 57c., and^3 busli: iJuJu ^"^^- *"™'S^ ^''♦^c; 84 bush, beets at 7?c • Wh »' 'Pf'^^'P'^^^^c.; 137 bush, onions at 82c.; 20 bush tomatoes at 50c., and 85 doz. cabbages at 53c. ^ U; 137 bbls. apples at S2.M : f>A h..=K «i „ „": * BUSINESS TRANSACTIONS. 57 id a play- alk seven lo acres, 1 85 cents of labor, i had he? = I day : 3$ 3$ ICNS. the fol- jc.; 112 otatoes tt 6^c.; 3 bush. •t 75c.; 2c.; 29 c. r- _- 108 bush, peaches at $1.87 j 93 bush, cherries at $1.40, and 85 bush, pears a^ $1.95. (5) 26 lbs. rice at 4c.; 34 lbs. tapioca at 13c.; 42 lbs sago at I2c ; 25 lbs. barley at 5c.; 39 lbs. dried apples at 8c., and 22 lbs. prunes at 9c. -^(6) 25 bbls. flour at $5.50 ; 36 bags flour at $2 80 ; 18 bags bran at 85c.; 15 stone oatmeal at 37c.; 17 stone commeal at 36c., and 29 lbs. wheat meal ?,t 5c. - (7) 27 lbs. pork at 14c.; 35 lbs. beei at 12c.; 19 lbs. mutton at 1 6c.; 14 lbs. veal at 12c.; 17 lbs. lamb at 15c , and 24 lbs. ham at 13c. (8) 13 tons hard coal at $6.25 ; 17 tons soft coal at S4 50 ; 19 cords maple at $3.75 ; 24 cords oak at $3.60 ; 16 cords pins at $4.25, and 23 tons coke at $3.70. ^9) S4yd3. cotton at 12c.; 41 yds. cashmere at 57c.; 3 ? ^ -Is. flannel at 35c ; 56 yds. muslin at 17c.; 67 yds. .xmt at 1 8c., and 52 yds. lace at 99c. "^10) A man exchanges 14 lush, wheat for 24 bush of barley, when 12 bush, wheat are worth $1 1.52. Find the difference between the prices of 7 bush, wheat and 7 -, .bttsh. barley. (11) A milkman bought 40 gal. of new milk at 16 cents a gal., and 60 gal. of skimmed milk at 2 cents a quart. Having mixed together, he sold the mixture at 24 cents a gallon. Find his gain. - pencils at$,.sorgro3A°P^"\«7for2;^cents; J"oa ream, and 7»exfrdse'bSat ,T~ "^P^P" =" ■hs/S^&r^fTot-'^l.'oadtftLl^l^^^^^^ S-. 5 cents .a Ibf VhttVere^l-^s'^ri (8) A paid $i6 for 20 mt „r ■°gal. worth 60c. affaf ^H»^ fPT- ""d mixed it with a quart. Find his gffn: "^ '"''' ""= "''ole at 25 c«2 busl'l I^'^ t. ^^^ at /*|~ b'^ "^ "-- « «°c. a wheat at $,.00 a bushel ^ * '"'"'•' *"'' 47i9o lbs. of He««/> ik t . 79C. a bush.; 612 lbs. oats a 28° a bush -^i en ik^^* ^* at 42c. a bush., and 518 lbs. com at ^c a b'u's'h ''" P'"' D. bush ^ ^2/'"?'^!; ^°^^ 40^ bush, of wheat at 80c ner ^9.bs af .raCnXailS.e^m.'™'' ^^^^ ^^^^^ t^tanf^'ral.; .'ShSef VF =• ^ >^ ■""' white lead at J245 a can • ,r ft „f h':"^ ^*'='' ' ^ cans .«.n^H„gs at«.ir.^'rvL?»o:t^i^-^.f-s botfit''-^o wi''""^'" l8«>«les of wine at 70 cents a « f ^zla^^n.^-'^in'-dttVlL"^ ^°"' """"^^^^ ar.ili^7~ lbs' ^ur «t' f „"'" <■" '"e following J. 50 eaci; .~ ft ™b?lr*L^r.™aV^.'''''?„",r above account $20 was paid. '" °" *« (0) Find the total value nf rtn^., a ^ * i_ V7; A grocer sold •? oz of te-a fr»- .r !. ■""* cheaper is this thin li plr pound fi ^T "°" WAGES. 6i (lo) A grocer bought 3 bbls. vinegar, each containing jio gal. 2 qt, 4 pt., at 32c. a gal., and sold it at 9c. a quart. Find his profit. Exercise XXXV.-WAGES. (i) A man earns $2.15 a day. How much will he earn m the month of August, the first day of which is Tuesday ? (2) A man working 9 hours a day at 27 cents an hour will earn how much in 3 weeks ? (3) How much will a boy earn in a fortnight, who earns 1 5 cents an hour and works ten hours a day ? (4) A carpenter worked a certain number of days, and received $41.25 ; if he had worked 22 days more he would have received $6875. How many days did he work? (5) A man receives a yearly salary of $700, paid monthly. Haw much does he receive each month ? (6) A man earning $2.50 a day— ten hours— lost 15 hours in one week. What were his wages for that week ? (7) A man receives a yearly salary of $1196, paid weekly. How much does he receive each week? (8) At the rate of $2.61 a day of nine hours, how much should a machinist receive for 143 hours' work ? (9) If a man receives $1.95 a day, how much will he earn in the month of June, the first day being Sunday? (10) A paper-boy buys 3 papers for 2 cents, and sells them for a cent each. On Mon. he sold 64 papers, on Tues. 60, on Wed. 69, on Thur. 74, on Fri. 83, and on Sat. 112. How much did he clear during the week ? B. (i) If 20 men can do a work in 12 days, and 40 boys ran tin if m R rloirc . urKi/>K Mtlll K*. ♦!>« ' ceive f„. ,8 futeX, h^oS:; re-^A^f ?' *■= •" - ho{i, J^^'SsT- f t„^/ ^y and spends $4 a wee,, (9) A boy wSfo earn «^ =A ? «^"u 5'=- " I""-"-'- fifths of .his''s„„,trm^S t^rLtiiream r ^ '"'«- n>uc^rld\'yTef;^crrnt?^p-"-*S8.48. How shoi'i U,f Kef r?cei!f for-h*'" " ^^ "°" ""ch nuni&r^fX"-Tf lelad'l'-'e ^ "°?'"^ " «««'" would have ,e^;ed^^V*:5t 7Kis'i?,na?er "^ con^dtol.'raMil^tLrm/"'""?^-- "Pon .he month. If he receiS! ro .i» «^.^'' ''5 «"'=> «^ach his entire wages amount .of ""' """""^ *>«' '^i" or men at it takes a $36, how ges for 13 ?ether for I received '•S cents a ir day ? s, and 3 c he to re- jow much ♦ a week, lies for a i quart, ns three- j8. riow ek, how it worth wmuch y, if the certain lore he es. )on the s each iftt will WAGES, 63 (5) A man agreed to draw 129 loads of gravel for road purposes at $1.45 a load ; he paid a boy 15 cents a load for helping him with 87 loads. If it took hnn 40 days to do the work, how much did he make on an average per day ? (6) The wages of 1 7 men for a week are $ 1 59. 1 2. How much did each man earn in a day ? (7) A contractor engages 3 men and 5 bov ; ^ do a piece of work, giving a man 60 cents a day ir ore th n a boy. They are engaged nine days at th^^ work, . nd all together receive $70.20. Find their daily wi-es. (8) A boss carpenter agreed to build a woi. («!ied ior iT' ^^e employed two men for $1.25 a day v :h, and they hnished the job in 15 days. How much per day did the carpenter make ? (9) A man engaged with a farmer from the ist of May to tho 29th Nov., inclusive, at $1.25 for every day he worked. Allowing 33 days for Sundays and holidays during this time, find how much he earned. (10) Make out the following pay sheet; a dav==io hours. ' M. T. W. T. F. S. I « " ' A. . . . B.... C... D... £. .. 10 10 8 9 10 6 10 7 10 5 10 10 5 9 10 9 9 10 10 7 10 9 ID 8 10 5 4 5 5 3 $2. 50 $2.00 $1.80 $1.60 $1.50 $ $ $ $ $ $ . 64 ARITHMETIC E«ercl.e XXXVl-PROFIT AND LOSa - 4A9';c!'a7u?TiKr^,?! ««- ^ "--.and seU Wa/w^°sXVai^ '^ o' '>"«- ««■■ -c. and sold i. a. ,;c. J4.i|;peJJ„1d^Vsir,>^a'.tf8r^ "'"^ "^ ^"^ - gain? » every »ioo worth. How much does he pm^?o^e^%'rlf?~-°J*'>f .ea,^d '"^'-^ J^5 tea for? ' *'«> <>' cost. How much does he sell the aii>?an''d?rfb\''"rrtV'?A*"''5'^/°«'« -"h «c. to gain $1.94 ? ^^ ^''°"''» he have sold it for foron2yl'™rcasht'Dlns'.T/"*5*°= "e fed them the entire he?d for $27^o1ach n^-t ^* ^^' ''^«* »" how much? """^^^'-Soeach. Did'he gam or lose, and exp^n'ls\e?eVr,';' ^'nf-' *= ''~^? "' *^-75 each, his .™^df^«-So-^S^^..a PROFIT AND LOSS. 65 B. ,^^ (1) A fruit dealer bought 243 dozen of oranges at ijc. a doz.; 102 oranges were spoiled. He sold the rest at the rate of 14 for 25c. How much did he gain ? (2) A man bought a house and lot for $8375 ; he built an addition to the house at a cost of $1735. The house was d^^troyed by fire, and he received as insurance $4560 ; he then sold the lot for $2045. How much did he lose? (3) A grocer bought 49 loads of potatoes of 20 bush, each at 60c. a bush. Allowing 15 bush for waste, would he gain or lose by retailing the rest at 25c. a peck, and how much ? (4) A boy bought 210 apples at the rate of 3 for 5c., and traded them for 150 oranges, which he sold at the rate of 3 for 8 ^ents. How much did he clear ? (5) A farmer bought a horse for $125 cash ; he traded him for a yoke of oxen, and gave $13 into the bargain. One of the oxen died, and he sold the other for $72. How much did he lose ? (6) A man bought 223 head of young cattle for $27.50 a head. He paid $1 1.35 a head for fattening them, and then sold the entire lot for $6150. How much did he gain or lose ? ^^ (7) A drover bought 247 sheep ibr $5 each. It cost •^149 to get them to market, and 8 sheep died onxtfiewayT He-5old the remain4«^^«;~^.75 a head. How/inuch did -"iTe^aiM ,/^ ^\ /-^ (8)3 Jjtt cKer pays $1 1 9. 25 foT^i 39 , t tirt i£ys,,At how mudlapair must he sell them to gain $41.34? ~^" (9) A fruit dealer bought 9 bushels of cherries at $3.50 a bushel, add sold them at 20 cents a quart. Did Jift-i^ain or lose, and how much ? (10) A grocer bought 12 bbls. of pork at $14 a bbl., and retailed it at loc. a lb. Find his gain. (i i) A farmer bought a 2d-acre field of ripe wheat for $250. He paid $1.45 an acre for cutting and saving, 4 cents a bushel for threshing and cleaning, and $2 a load [46 bushels) for teaming. The wheat yielded 23 buS;^ to 66 ARITHMETIC *d Sa™er"Sl/,f "" *'-^7 a bushel. How m„:h '^ak^.^s.Sfk whTh cn^f " ^5 '^?"" "» Ae dollar a half of ft cle^ng 5c o^'eTiT'^V^J^So. He sold gain of 7c. on the I and ,hl f • ,* ""''d of it he sold at a the $. bid he glin or tie on ,h"",?',* '»= °f '^-^ on . .(13) A man buys a tenkmot s?o'::£°'^' ^"dhowmuch? which cost $2500 per invo^™'^\fi°''''„^S7c. on the $., of 7SC. on the $. How mirhV t*"* " *' an average and how much does he gaS ''^»' '^ ">* S""^^ ExeroUe XXXVII.-ANALVSIS. I A. cosfP IfS yards ofcloth cost $8.40, wha". will ,4 yards ^ J2) If ,0 yards of cbth cost $,4.50^ what will ,9 yd, ml^s c^^Tctnrs'PP'*^ '"• *« '»-'-h J'.L'L''.'?'" bought 468 turkevs a", J, .„ , .... . a man at 20 cents a dozen SselC thenff' ''^ ^"^'"^ P^P^^s How many papers did he seS? °' ^^ ^^n^^ a dozen. r^t^lnJIleVpeilZ^^ «^^o»<^' -hat is its ANALYSIS. 67 fow mu.;h > dollar a He sold sold at a f 1 2c. on Jwmuch.? n the $., average e goods, * yards J 9 yds. >r if 23 w long mount rds of much It will I, and apers ozen. s its (12) A woman sold eggs at 10 cents a dozen, gaining thereby 2 cents on each dozen. How much did 600 eggs cost? B. (i) If 40 men can do a piece of work in 60 days, how long will 15 men take to do half as muclis^ (2) Three turkeys cost $2.25, an'B three geese cost as much as two turkeys. Find the P^^ce of 5 turkeys and 4 geese. ^ (3) If6mendiga trench 34 yards long in 10 days, how long a trench can 20 men dig in 1 5 days ? (4) A father earns $6 while his son earns $2.75. When they both have earned $105, how much will belong to each ? „„**^5) If 3 horses cost $192, and 2 horses cost as much as 16 sheep, find the combined cost of 5 horses and 6 sheep. (6) If II men build a wall in 18 days, how many men will it take to build a wall three times as long in half the thetivse? (7) A man can buy a white hat which will last him 4 months for $1.76. He can buy a black hat which will last him 9 months for $5.67. How much will be, saved in 6 years by buying the cheaper kind of hat ? (8) if the yearly rent of a farm of 187!^ acres be $450, what will be the rent of a square mile for 20 montl ? (c, j A piece of work is to be done by 25 men in 16 days ; after 4 days 15 men go away. How long will it take the rest of the men to finish the work ? (10) A clock which loses 4 min. in 12 hours is 10 min. fast at midnight on Sunday. What o'clock will it indicate at 6 o'clock on Wednesday evening ? ^^11) The weekly wages of 4 men and 5 boys are 558/50. If a man earns twice as much as a boy, what are the daily wages of each ? ,>*"' «°n.ake$3o . (• A man bo^hra farS^ f^' I'll! *« §»<«'' sold for? .^S»5 on eve.. ,.«, pt^hTs et^^ -^fn^l^J'sel'llS^- h;slL'rli^e"sSir,;o^\"^:-l'- %^^ -"^ f- the owner receive ^ *'°°- ^^^ much did D. paySii2h%|;ri5"Slowe?oVr^^^^ °^ ^^75, and bv much do I pay? ^^^^"'^^^off every $ioo worth. How SHARING. 69 SO (2) If the tax on every dollar's worth of property is 2 cents, find the taxes on a house and lot valued at $4600. (3) A man's property is assessed for $7200. How much taxes does he pay, being charged 2c. on the dollar? (4) If the rate of taxation is 3c. on the $, what do the taxes on properly worth $^500 come to? (5) If the rate of taxation is 2c. on the $, what do the taxes ou property worth $2345 come to ? (6) $3645 is to be collected in a township to build a school-house. The property in the township is rated to be worth $370170. What will Frank Connery have to pay, whose property is worth $4570? (7) A money lender receives 6 cents for loaning $1 for one year. What does he receive for loaning $200 ; $350 ; $475 ; for one year ? (8) If the money lender received 5 cents for the loan of $1 for one year, what would he get for the loan of S250 for 2 years ? for the loan of $300 for 4 years ? for the loan of $425 for 3 years ? (9) If he received $5 for loaning $100 for one year, what would he receive for the loan of S630 for 2 years ? 'k74i for 3 years? $500 for six months? $224 for i}4 years ? and $360 for 2 years 8 months ? (10) A boy puts $25 in the Dominion Bank for a year. He received for the use of it at the rate of $4 for $100. How much money did he withdraw at the end of the year? Exercise XXXVIII.-SHARING. A. (1) Divide 16 apples between John and James, giving John 4 more than James. (2) Divide 60 marbles between Thomas and Henry, giving Henry 10 more than Thomas. (3) Robert has 6 pigeons more than William ; together thev have 22. How manv has ea<^ ? 70 ARITHMETIC "7, f" fiid he g» each day? ' ** '^"°"d ^ay- VS; Divide $1000 hpfw«>ir> * ^ (9) Divide Si amon^ Fri^u ', ' ^ ^^^'''^^ ^ > {. =) A man sold ? sheen %T '""2 ">« 'hird. eac^J.^r^/ht^.S^eXiLr™'"^ 37 boys, so d.a. „ (6) Divide Jgo ,6 am«n„ .1 " P""^*" « a boy. Robbie, so that ?ge fim to? lTt.^^\ ^H'- »«« and the second, but 80 cents hS;S ,tV^'* »»« *»? ./"I — _ _. Jiiifet. SHARING. 7< (7^) A mixt M re of green and black teas is made, 3 ounces of green £o tvi^ry 5 ounces of black. How much of each kind will be in 5 pounds ? (8) Divide 36 apples among 2 boys and 3 girls, so that each boy may receive 3 apples more than each girl. (9) Divide $398 among A, B and C, giving B three times -AS much as A, and C $6 more than B. /^!o> Eiiiest has $1000, Warren has as much as Ernest ks.^ $82, John has as much as Ernest an,d Warren and $"04 besides. If the whole of their money were divided equally among them, how much would Warren have more than he has no«v? (11) A man spent $240.25 in cloth at $1.55 a yard, and sold it to three men. The first man bought 35 yards more than three times the second man's purchase, but 22 yards less than the third man. Find how many yards each bought. C. (i) Divide $840 among A, B and C, giving A three times as much as B, and $70 more than C. (2) Manly, Ernest and Beulah had $1800 divided among them, Ernest got twice as much as Manly, and Beulah got twice as much as both Ernest and Manly. How much did each get ? - (3) Divide $973 between A and B, giving A $57 more than B. (4) Divid^ 27 bushels potatoes between A and B, giving A 2 bus. 3 pks. more than B. (5) Divide S500 among A, B and C, so that A will get $75 more than B, and C $50 more than A. (6) A calf, a cow and a colt were sold for $110. The colt brought $15 less than the cow, and the calf $25' less than the colt. What did they each bring ? (7) A woman sold two tubs of buttei: weighing together 60 pounds, one being 5 lbs. 8 oz. heavier than the other. How much did each tub weigh ? (8) In a basket there are nuts, oranges and apples, 135 in all. T^.ere are 35 apples and oranges, and no nranerf^a ttnA nutS Hq*" rnanv ar^ thf>r«> of *»arK ? / 72 ARITHMETIC 'he^ httt^X'/eT^^jSli? r '=""1*3. When to each ? *io98.32, how much will belong ', 1 Exercise XXXIX.-CANCELLATION A. What is the Quotient of: ,[) 42x13x6x22 divided by 4x6x7X1^? ,,, 55X2ox8T?39x,4X4ii;^ (6) 3«^138x39Xiox42X44X45x49x ,,0 3ox3ox57x78x7Jr24X99x35l?r (7)Sox5;j<54X56x5^58x6rx63x64X4 m „'*°'''*°''*5x='7X48im;?^^8^4r^ W iixi3xi4xisxi6 X35 x »x 2, x 2 'x 24 /^\ .., 39x56x40x30x70x33x48 f.o^ 7f'''*''33x72x45x6w5;rFSS856r^-^ conlZ4 ." pL?« 7;i ''^1 "*" 15 •»'« °f -^'oth, each 4 «;»hXn^ *?,^S^^^^^^^^^ -^^ ^ «• Wide and / y\ CANCELLATION. 73 (3) Nine pieces of cloth containing 30 yards each, worth $5 a yard, were exchanged for 1 5 pieces of cloth containing 45 yards each. What was the second cloth worth per yard ? (4) If a farmer exchanges 25 bushels wheat at $1.28 a bus. for cloth at 40 cents a yd., how many yds. does he get? (5) A tailor bought 24 pieces of cloth, each containmg 22 yds., worth $2.25 a yd. He made 54 suits of clothes ; how much must he get per suit, so as to make $3 profit on every suit ? (6) A brick is 9 in. long, 3 in. wide and j2 in. thick ; how many of such bricks will there be in a pile 12 ft. 6 in. long, 10 ft. 8 in. wide and 6 ft. 9 in. high ? (7) A pile of bricks is 40 x 27 x 1 5 feet, how many bricks 8x4x2 inches are there in the pile ? (8) A pile of bricks is 8' 6" high, 14' long and 15' wide (each brick is 8>i" x 4" x 2^"); What is the pile worth at $12.50 a(^ thousand ? (9) Find by cancelling the simplest value o f 6950 45x25x3. MECHANICAL WORK. Exercise XI — ADDITION. (0 47658 76584 65847 58476 84765 47658 76584 65847 58476 84765 47658 76584 (6) 56987 69875 98756 87569 75698 56987 69875 98756 87569 75698 56987 69875 (2) 76584 65847 58476 84765 47658 76584 65847 58476 84765 47658 76584 65847 (7) 69875 98756 87569 7569^^ 56987 69875 98756 87569 75698 56987 69875 98756 (J) 65847 58476 . 84765 47658 76584 65847 58476 S476S 47658 76584 65847 58476 (8) 98756 87569 75698 56987 69875 98756 87569 75698 56987 6987. 9875b 87569 (4) 58476 84765 47658 76584 65847 58476 8476s 47658 76584 65847 58476 84765 (9) 75698 56987 690/5 98756 87569 75698 56987 69875 987^6 87569 75698 (5) 84765 47658 76584 65847 5i»47^ 84765 47658 76584 65847 58476 84765 4765;? 0^ . 7569.' 56987 6987 c 9875^ 87569 75698 56987 C ?75 9 56 8. ,69 75698 56987 /-.\ ^/■s/ (5) «4765 47658 SUBTRACTION. 7$ Exercise XLI.-SUBTRACTION. Subtract 487569 ten times in succession from each of the following: (i) 5221368; (2) 5332473; (3) 5443524; (4) 5554035 ; (^) 5^59146. Subtract 57 864 ten times in succession from each of the following: (6) 5934432; (7) 6156564; (8) 6377886; (9) 6591 108; (10) 6723321. Exercise XLII.~ MULTIPLICATION. Multiply each of the following by 6 ten times in suc- cession as a factor: (1) 16209; (2) 21612; (3) 32418; (4) 48627 ; (5) 64836. Multiply eac'^ by 7 ten times in succession : (6) 12708 ; \j) 19062; (8) 25.116 (9) 38124; (10) 57186. Multiply each I S ten times in succession: (11) 1 1427 ; (12) 15-16; (13) 2- ;4; (14) 34281 ; (15) 457o8. Mulupiyeach by 9 t^^n times in succession: (16) 10608 ; (17) 15912 ; (18) 212' . (19) 31824 ; (20) 42432. Exercise XLf DIVISION. Divide each of the following numbers by 6 ten times in succession: (i) 653397497856; (2) 980096246784: (3) 1960192493568. Divide by 7 ten times in succession : (4) 1794847732146; (5) 269227 1 5982 19; (6) 3589695464292. Divide by 8 ten times in succession : (7) 817976521 5 232 ; (8) 12269647822848 ; (9) 24539295645696. Divide by 9 ten times in succession : (10) 27740856- 694356, (II) 36987808925808 ; (12) 5548 1 7133887 1 2. Divide each of the following by 29 three times ii suc- cession : (13)278424824; (14)417637236; (15) 556849648- (16)835274472. Divide each of the followmg by 347 three times m succession: (17) Q02Q9oq 19876; (18) 1354486379814 • '''9) 1805:981839752; 20)2708972759628. / , / u FACTORS AND MULTIPLES. Ex.rcl« XUV.-PR,Me AND COMPOSITE NUMBERS. . (0 Which of the fnVn^,;^^ Which are composil^: 3 c Tf "1^^''' ^'"^ P""»« ^"d 45, 5r, 57, 63 and 75 ? ^' ^' ' ^' ''' '5, 27, 35, 39, 4,, ^3^ and 50. '""" °^ ^*^« P"me numbers between 30 (4) Find the sum of thp /-««,« •. 35 and 55. """ °' ^'^^ composite numbers between . (5) Fmd the sum of hnth tu^ numbers between fo and & ^' ^"""^ *"<' '^^ composite .0 if ^ "^"'^ ""«'" ^" '"' integers less than .; and prime .ha[l'';,f„'e^^,„^"^''f 'he '""sers between 80 and .00 ,„ .(8) Write down the integers .ess than .4 and prime .«>;t"5^[tr p-.J.i'JVr"^'- -'egers between 3 aiil ? ^' "-"''^" '-^ '"- '50 are divisible by both 5 ald^'^'"^' """"^^^ '«' «•-" '75 are divisible by both 3 aii's f"^"' """^'^ '7;,^ n ^» are divisible by both PRIME FACTORS. 77 ' Exercise XLV.-PRIME FACTORS. Resolve into its prime factors each of the following numbers: (i) 30 ; (2) 36 ; (3) '08 ; (4) n2 ; (5) '28 ; (6) 210 ; (7) 324 ; (8) 504 ; (9) 555 ; ('o) 728 ; (II) 1024 ; (12) 1000; (13) loii ; (14) 1050; (15) '320; (16) 1768; (17)1848; (18)2934; (19)3456; (20)32320; (21)345345; and (22) 456456. What prime factors are common to: (23) 440 and 231 ? (24) 650, 635 and 540? (25) 55> 66, 77 and 121 ? (26) 42, 70, 156 and 210? (27) 256, 320 and 336.'' (28) 144 and 180? Find the product of all the prime divisors common to : (29) 16, 24, 40 ; (30) 108, 81, 54 ; (3O '44, 180, 216 ; (32) 64, 96, 112, 136 ; (33) 75, 125, 165 ; (34) 306, 408, (35) The product of 2 consecutive numbers is 750. Find them. (36) The product of 4 consecutive numbers is 1680. Find them. (37) The product of 3 consecutive numbers is 2730. Find them. (38) The prime factors of a number are 2, 3, 5, 7 and li. Find the number. (39) The prime factors of a number are 2, 2, 3, 3, 7, 13 and 19. Find the number. (40) The prime factors of a number are the prime numbers between 10 and 30. Find the number. Exercise XLVI. -GREATEST COMMON MEASURE. A. Find the greatest common divisor of each of the following : (i) 546 and 462 ; (2) 394 and 672 ; (3) 735 and 770 ; (4) 2 121 and 2626 ; (5) 232 and 160 ; (6) 1628 and 4543; (7) '2341 and 30401 ; (8) 15561 and i35»5 U9^ 34, 100 ftnd 120 ; (10) 32967 and 50061, 78 ARITHMETIC B. (0 279lrt\'nlT5f ft^^^^^^ of the following- *333 and $851 • U) 2Rfil^ ^"^ ^^s- and 634 rodr. ^^-^ ft. and 2788 rods%fol^e^ ^"^ 4543 gals^f (7) , ' ^;/ «M63 and 11,75' ^em?- mX^"^ "43r m nutes 'It marbles; (9) 11592 hTrse/^> ^,9 ^^^^^^ and 2 j J-.] bs and 20539 ounces ;('o 7"?J?^9 horses; (,0/987 ('2) 2769 tenths and 3195 temLl'"^' ^"^ 2057 thirds; (0 What is the leno-fK ^r ^u . exactly measure the Sth anH^^"^-' '^^^'" ^^^^ ^i" land 312 rods lone anrfn& ^"^ ^^^ ^'^th of a oier^iJ (2) Three sSltn ^ """^^ ^'^e? ^ P'^^® ^^ ft. aU 20 ?t, were cEto ?f ?"^ respectively ,2 ft ,6 equal length. Wh^r.^r.^^tXcV^''^^^^^^^^^^^^^^ o'f (3; Two cisterns hoW 11^- ,^P'ece? ga Ions. Find thTlargH h!^T'''Kf^72 and 5088 both cisterns. ^^^'^ ''^rrel capable of measuring (7) Three lots mt^a^,,^^ >°4.ft. by u8 ft! fnd "^f^KT'*' »< ft- by .44 ft out in square beds of .JJ i "'^ 9* f'- 'f these be l,L' ""^-f-^f beds tel'cht '''^"' P»-ib.e si^e^find '"he 58VW"« ^-S^rsT/n^r -" "'vide 600 and . ('o) What is the I^n^ffc r I ■■''^P«<:l>vely. «t.ck that will „^,2l '|,T\2^."'-«_ J°"««' measurin. GREATEST COMMON MEASURE. 79 following • f«ds ; (0 (5) 12341 lutes ,~ (7) nd 23023 ('o) 987 ;7 thirds ; that will piece of [2 ft., 16 ieces of d 5088 asuring rtioned ney. can be n 3588 ed for 1 from h 7 is 44 ft., 2 laid d the 4180, and inne V (11) Find the length of the longest chain that will exactly measure both 7308 in. and 8004 in. Give answer in feet. (12) Three drovers, A, B and C, bought sheep at the same rate per head. A's drove cost $102, B's $138, and C's $99. Find how many each bought. Exercise XLVII.— MULTIPLES AND COMMON MULTIPLES. Form a table of the first nine multiples of: (i) 13 ; (2) 14 ; (3) 15 ; (4) 19 ; (5) 21 ; (6) 25 ; (7) 30 ; (8) 36 ; (9)50; (10)57; (11)63; (12)75. Find three common multiples of each of: (13) 3 and 4; (14) 5 and 6, (15) 7 and 8; (16) 8 and 10; (17) 12 and 15 ; (18) 16 and 18 ; (19) 11 and 12 ; (20) 15 and 20; (21) 25 and 30 ; (22) 18 and 24. Of what two integers are the following common mul- tiples : (23) 30 ; (24) 35 ; (25) 42 ; (26) 56 ; (27) 84; (28) 96 ; (29) 121 ; (30) 132 ; (31) 187 ; (32) 119 ; (33) 169 ;. (34)289; (35)631 ; (36)221. Exercise XLViil.-LEAST COMMON MULTIPLE. A. of: Find the L. C. M. (i) 4, 8 and 12. (2) 12, 18 and 30. (3) 21, 28 and 35. (4) 2, 3, 4, 5 and 6. (5) 9, 12, 22 and 33. (6) 15, 18, 21 and 24. (7) 9, X2y 15, 18 and 20; 4, 5, 9, 12, 15 and 20. 10, 16, 24, 40 and 64. [10) 36, 45, 60, 75 and 84. [11) 25, 40, 75, 100 and 120. 80 ARITHMETIC M l\^^ 26, 39, 46 and 78. J 3; 4, 6, 8,9, 12 and 15. f 4 f, 52, 36 and 156. 05) 3, 5. 6, 8, 15, 2olnd 24. yj 5040, 7770 and 1848 3 ?8''3fA'^'^--^48. (6) 6 rods and 66 ft? (85i^f/./.^;-<^'ogaI. (»; $6o6r and $73,7 (9) I acre and 1 •»-« =« <>'> .6 days, ,8 hour^S.. minu.es. "TftH"''-^ 5-^^^^^^^^^^^ 'hat can be (9) What IS the lekst weirf.t\? -^5 cent pieces ? r^fwr'^'-°f''"'heWw?eafr,"'"' will „^e LEAST COMMON MULTIPLE, 8l D. (i) What is the smallest sum of money that can be paid all in $3 bills, in $4 bills, in $5 bills, in $6 bills, or in 4)io bills? (2) Find the least number which, divided by 6, by 8, by 15, or by 21, leaves in each case the remainder 3. (3) What is the least number which, divided by 16, by 18, or by 24, leaves in each, case the remainder 7 ? ' (4) Find the prime factors of 126 and 1^60; using these factors, find the L. C. M. of the numbers. (5) What is the least number from which 1224 and 1656 may each be taken an exact number of times ? (6) Find the L. C. M. of 7, 9, 11, 13, 15 and 21 ; divide the L. C. M. by each of the given numbers, and find the sum of the several quotients. (7) What is the smallest sum of money with which a cattle dealer can buy sheep at $4.50 each, or pigs at $7.50 each, or cows at $45 each, or horses at $135 each, and have no money over ? (8) A farmer's wife found that whether she counted her eggs by 6, or by 8, or by 9 at a time, she had an exact number of counts. How many dozen had she ? (9) What is the smallest quantity of wheat that can be carted away in either 20, 25, 30, 35 or 40 bushel carts .-• (10) When a certain number of dozens of oranges are counted by fives, or by sevens, there are three over. Find how many there are. (11) A battalion of soldiers numbering rather less than 1000 can be divided off into companies of 60, of 72, of 80, or of 90 men. Find the number in the battalion. MISCELLANEOUS. Exercise XLIX.-ON THE SIMPLE RULES. A. ^l\ Th^ ^^!,^a''-«e Of 9087064X89706^336. (S) By what number must iggg be dividsH tl,,. ,1, quotient and the remainder iS? b| the ;»^» S* quonen. and the remainder in Si vision ofTo^ bJ ,?f of t^^i ISS °/e1iS rA"t L'«^^«^ ' f .™« the result is 7 times whit numte?? ^^ "^ '" '""^^'O". fact|^,t^Vv%e1„-^Vth°i:to^S "^ "^^ ^evi ije™tars"?.t"nrda"„'it';r;4^^^^^^^ one hund'-ed thnncar.^ ^ j • =>*=^«="iy-inree millions, r^^p^S^^ M^tiply the timS\he' fjil :„Tr 1 "..6^'""^"i>. 3784875ranT seven (lo) Multiply, using factors 766485 by 63. B. 0) Multiply 83102254 by 7090. (ll FinH ?/^'°"54 by 19435. W i' ind 78 times the sum of 894967, 8a 38730. 6q3Q7 LV I ON THE SIMPLE RULES. 83 PLES. and half fourth of *■ is 343. 70 times seventy- that the as the » by 1 1 ? If one cession, by the nd and lillions, aly the • seven of the 10507 MDCCXCVIL, 467896, and divide the resuh by the .factors of 48. (4) The quotient of two numbers is 498 ; one of the numbers is eighty-nine. How much is the other less than one million ? (5) What number must be subtracted from 461634 to make it exactly divisible by 126? (6) Ho V many times must 720 be added to 514 to make 987634 ? (7) The divisor is 63875, the (quotient 46938, and the remainder the largest integer possible. Find the dividend. (8) Find the smallest number that must be added to 461633 to make it exactly divisible by 758. (9) Multiply 867349278 by 70908, and divide the pro- duct by 23636. (10) Divide 9 times the product of S9496 and eight thousand and seventy -four by LXXVIII. (i) Multiply 4786926 by 7869 and divide the projcluct by 23607. (2) Multiply 976531 by 999, short method. (3) Add 3456 to the product of 8347 and eight, and then divide the result by 1 2. (4) Find the value of (36380250^ 125) -(4024 156-!- 8903). (5) Add together 95949, 67896, 8939, 667586, 738496 and 89496. Take 59497 from the sum, multiply the difference by 98, and divide the product by 47. (6) The dividend is 74198, the quotient is 2005, and the remainder is 24 less than the divif or. What is the divisor ? (7) Divide one billion by 256. (8) The sum of the remainder and s',bt va'vjnd is 100- 190801. Find 20504 times the minuend. (9) Multiply 4567895 by 192648 h- short process. (10) Square 6384 and divide the product by 3192. 84 ARITHMETIC D. by ^jL""'"'"'' ^^^'^ ^y 7869, and divide .he product .hS' The quotient is 908 times 987, which is 227 tim.= the remainder. If the renai.H.r i. , 1 ■ ." '""^' divisor, find the dividend ™"*""'*'^ '^ 5 less than the and^iS"''"''^'^?'''^"'^" '«''»'«» *e squares of 7684 divi^ll'rh^°:;:"j '^^7, *« remainder 2,9, and the ''7^^ti£S9¥r":^^^^^^^^^^^ 1809 ? ' ^ ^ ^^ """^^^'' "*"^* ^ multiply e:, (i) Divide 1084197160c: by 1874800C (i Oft'JfJr'7l543>y 2r'6546%S (aI TK 5^i """"H" '" 7006 both divisor and quotient ? (4) The difference between 8^^72 anH tiTl ^"?"^"* ; .sll^d^oLS'^fiL*^^^^^^^^^^ "•« -""^end «maild?r% To be^»H'A^*.'"'°'r' •««. «"d the how mul/Jthe'di^id^dlnctas^edr" "''"^ *^'«' '^^ oJillt,'"""'^"' of 595 divided by 59S lives as ON THE SIMPLE RULIia. 35 5 product the result 'ove the otient of 57 times lian the of 7684 and the ifty-two visor, nultiply otient ? iuct of bsrs is 'abend id the ee, by ■ their 7 and 'es as (10) Subtract 123456789 from 987654321 and prove the result by addition. F. (i) Add together 678, 593, 457» ?^9» t^ginning at the hundreds, next the tens, and lastly the units. (2) Add together 12345, 23456, 34567, 45678, 56789, beginning at the left hand column and adding towards the right. (3) The divisor is 54321, the quotient 12345 and the divident 670605090 ; find the remainder. (4) Multiply 507308 by 4620, and verify the result by dividing the product by the factors of the multiplier. (5) Multiply 2468642 by 29 in one line. (6) What number increased by the difference between 23089 and 196 1 2 will make the sum of 20948 and 45021 ? (7) Find the remainder in subtracting 6633 as many times as possible from twenty millions. (8) If2i7 be added to a certain number it will contam 231 just 1 296 10 times. Find the number. (g) What number divided by 537 will give 129 for a quotient and leave 76 as a remainder ? (10) Find the quotient obtained by dividing the pro- duct of the seven whole numbers next in order after 30 by the product of the first seven whole numbers. G. (i) Find the product of 897643 and 999998, short pro- cess. (2) Find the. product of 11 881 321 2 and 234567891, having six Unes of figures when the solution is complete. (3) The divisor is 17 times the quotient and 34 times the rem- nder. The remainder is 358, find the dividend. ^. (4) The product of two numbers is 760669388, and one of the numbers is 26078. What is the quotient when their sum is divided by 72 ? (5) Subtract 97864 nine times in succession from one million. ^ (6) The sum of the quotient and divisor is i43/»b« 86 ARITHMETIC ^^Jh2':t' "•'"• '■' '<>"^' •» 'heir diffe^ce. Find "y 8, by how much will th^n.^Pl'^S"'^ '^^^<='^ increased - (8) If the divisor were hS"ofwh\^'!;'^'^u"''? would be 64.84. The divideni is 5?L'Ut' '^^^T'""' niamder 193. Find the divisor '^''^^ and the re- -vSh'^^he'Sr^lTenyr?*! '^ {,'''"' ""« °-- rhe^divU^teti:y:h^°3i„a^^<,3«^^^^^^ H. smaVlLrSl!!;^^ "■"■ 635r4t'o"^: f^' '^4"^ fots'l'-''^ ^""'-in? "umbers : add the re.naind^S^'; short prSetr' "* =»"'«».'»'' and;tedt^'.-;he.vi^^^^^^^^^^^^^ , ,,^^3 ■-- ffi/ri,. ^ . • ^""' ">e fourth addend fi-ifi S'.heTuin"' V''!."="'=!'"'i^ ''"d subtrahend is ..Ssf^.'^SthTremabder""'"'' ""^ ^'""^^'«"<1 i' x \\ GENERAL REVIEW. «7 (9) How many times must 347 be added to itself to make 98895 ? _(io) How many times must 127 be added to 59 times 231 to give 24170/ Exercise L.— GENERAL REVIEW. (i) A farmer gave 49 bus. of oats for 196 lbs. of cheese at 9 cents a lb. ; how much did eacl buihel of oats sell for? (2) A contractor requires two million bricks. He has 560085 already. How many loads of 437 bricks does he need to complete the full number ? (3) A farmer bought 20 steers at $33 each, and after keepmg them 4 weeks at a cost of 50 cents each per week, two of them died. At how much each must he sell the rest to gain $56 on the^ transaction.'' (4) When 4 li. 3 in. oTErass wire costs 22 cents more than 3 ft. 4 in., what is the price of wire per yard ? "^ (5) A woman sold 16 turkeys and 16 geese for $23.20, getting 25 cents more for each turkey than for a goose. How much did she get for each ? (6) A grocer mixes 12 lbs. coflfee at 28 cents and 26 lbs. at 23 cents, with 10 lbs. of chicory at 8 cents. At what price per lb. must he sell the mixture to gain $4.50 on the whole ? '"^(7) A drover bought a number of cattle for $4050. He sold 34 of them for $1926, gaining $396 on those sold. Find how many he bought, and the cost of each. (8) A woman sold two tubs of butter, weighing to- gether 75 lbs., one being sH lbs. heavier than the other. How much did each tub weigh? (9) A butcher sold 8 turkeys and 8 geese for $12, getting 30 cents apiece more for a turkey than for a goose. What did he get for each ? (10) Find the value of 57 cows, when 3 horses worth $120 each must be given in exchange for 18 cows. (11) A fanner bought 75 tons of hay at $16 a ton, and SB .-AITHMETIC SkbKe"p^tr„T„,tt!? =« *3.75 each. The re- lbs. of buttef were ^S« cents per lb. Ho* m...y diff^releinThTcosfif i";" f"^ '"" fe-™^. and the of the farm for whTch he naid Z '"" f,^^^^' The pr « an acre, and the other JST^an acre " ni'"' '"■" '^••» »4 both farms ? * ' *" ^""^ "ow many acres in lbs/4i.\:avS\tVro'."er''S " '"'V"- "-"« 3 weigh ? " ^"® °*"e'^- How much does each -^^^ Which ^ 06) On the firsrof April L 1 nf T?^^' ^^ fi^^^' for $37 50; he sold her onlht/i ^^""^ ^^"^^^ ^ ^^^^ her milk during that t;m« '^ -^^^Ptember for $20 • Bland's gain ^^.^t^tJ^'^'h^''' 'f^' month. ^^°' ""^ ^' '- < est of her keep per (17) Find the daily wa?e« nf - hours per day, and who ^ e? L 1, ''*^" ^ho works 10 a ditch 3 ft. iide and 4 ft ^deeriA?'!? ^''' '1 ^^"^^^ "^ per cubic foot. ^ ^P' " "® charges half a cent .hriijiccePirthi stiro"'v"'™^;'' "- ™' -'o second; but ^ yards lonL fu ^ P"""^^ shorter than the length of thls^cond ? "^ '^^" '^" '^''^' ^^^t was the and;^?|4 '^^rattfe'L^I^^^^^^^^^^ ^-d for $.5200, (20) A and B had II^o?? a '"4 S^^m or loss. $315. ThenAhadlwlT^mlh^a^R^^'j""^^ «P-"t each at first? '^ice as much as B. How much had J4o!^ai,^d1 JdTitcf msVerr;n3' ''r °' ^^^^ ^^ gam? y ^^"ts per pound. How much did he expenses. How long win it til^\^ .^^ ^ "^7 ^°^ (23) A farmer nafd fo. ' '!!^.^.^'"^.*« ^ave $972 ? ^ ,0. „ ^v^v ana a sheep with th^ n GENERAL REVIEW. 89 J pnce of.2 tons 8 cwt. of hay at 60 cents a cwt. The cow ' ost seven times as much as the sheep. Find the price of each. (24) At $175 a rod what will it cost to fence a field 660 ft. long and 264 ft. wide ? (25) A street one mile long and 66 ft. wide is to be built. On it there are to be 40 crossings costing $15.80 each; two bridges, one costing $6840, the other $1650; a sidewalk on each side costing $4 a rod ; and 16 lamp- posts at $3. 50 each. If the cost of grading and pavmg be $10 a sq. rod, what will the total cost of the street be .'' (26) Howmany feet of lumber are required for a 12- inch baseboard for a fence around a field of 20 acres, having a frontage of 40 rods ? (27) On every square inch of the floor of a room, 60 yds. I ft. long, and 5 y 2 ft. wide, a 25-cent piece is placed. How much money is on the floor ? (28) A clock strikes all the hours in February, March and April. How many strikes does the hitffimer give the bell in that time ? (29) From a lot 80 rods square I sold 80 square rods ; what is the value of the remamder at $80 per acre ? (30) A cellar is 18 by 20 feet, how many bricks 8 by 4 by 2 inches, laid on their sides, will cover the floor, and what is their value at $14 per thousand bricks ? (31) Find the cost of building a six-rail fence round a field 65 rods long and 40 rods wide, the rails being 1 1 ft. long and costing 8 cents each. (32) What would it cost for stone to pave a walk round the outside of a yard 40 rods long and 66 yards wide, if the walk be 5 feet wide and the pavement cost 10 cents per square foot of surface covered ? (33) A gentleman sells at $3.60 a square foot a town lot 60 ft. wide and 120 ft. in depth. Find what he should get for 3 acres at the same price. /^ A A <^^i,ora KiooL" ■sAr* fppi- to the side has a Sidewalk of two-inch plank around it. The sidewalk is 4 ft. wide. Find the value of the plank at $1 5 per thousand. IMAGE EVALUATION TEST TARGET (MT-3) ''''mJo o <^ /A 4 1.0 Im |2^ U£ Ut |M 1^ u ■ 4.0 I.I L25 iu ■ 2.2 li 1.8 1.6 — 150mm V'

02 o 7 /IPPLIED^J INA4GE . Inc ^B 1653 East Main Street ^^^- Rochester. NY 14609 USA .S^ ^ Phone: 716/482-0300 .:=r-.^= Fax: 716/288-5989 1993. Applied Image. Inc , All Rights Reserved ^V ^\ Ak ■ '* ^\ ^3. n^ '^i^>> '^ ^t^ 90 AftltHMETiC f"^,',rF^"l"''™^fe«"cer" "■"" '"<= "i"" one. . ^ . (38) Ho«r many cubtc iLh '• '«■■<;''''!': yard. *^' each at first? ^"*^" ^^ A. How much had •s ^f^^o^^^^^^ P^ed m a car which . (44) A farmer sold a ho^I ? ^'2 '4 cords? fi4-2S each, and 180S. lbs £1 ?or^i^^-^°' '^cows for the proceeds he bought sheen /f il P'^"" ^ *°n- With ^ar^s sold the sheep for c'^ai^^u^ *^^"^' ^"^ after- gam ? i' 'O"^ »S each. How much did he 8 in'^U^^^^^ box 3 ft. 4 i, long, , ft 30 hours. For how mariv df v. JIP' * '*°^« running for the stove running ? ^ "^^y' ^'" ^5 cords of wood keep -:^^^^&z^!r'^^'-^i - -i^e, is mai^cords' of w^^^^^ T""} ^^ *°"^ °f coal, how of coal in a yeaT? "'"* '^'* ^ ^»"^''y ^^at bums 26 tons dozif Lll J' ^PP'"^ ^°^t 8 cents, what will a h.^.i .r . ,_ GENERAL REVIEW. 9« (49) If 50 men do a piece of work in 12 days, working 8 hours a day, in how many days would 30 men do the same piece of work, working 10 hours a day ? (50) If 2 men or 3 women earn $1.80 a day, how much should 19 men and 27 women earn in 1 5 days ? (51) A factory tailor can make 10 shirts in 4 hours ; whether will be more profitable for him, to be paid 18 cents an hour or 8 cents a shirt ? -~ (52) Two railroad trains are 5000 miles apart, and approach each other, the one at the rate of 19 miles an hour, the other 24 miles an hour. How far will they be apart in two days ? (53) If a boy waste on the average 2 minutes ev«:ry hour, how many minutes will he waste in 4 years ? (54) If 3 horses, 4 oxen, or 5 cows can be pastured for one month for $6.60, what should be paid for pasturing 3 horses, 4 oxen and 5 cows for one month? (55) How often does the L. C. M. of 4, 21, 36, 45, 91 and 180 contain the G. C. M. of 5642 and 7462 ? (56) Divide the L. C. M. of 18, 21, 42, 45, 90, 180 and 640 by the G. C. M. of 3232 and 1952. • ^ vSTT^ftheareabfa field is 326700 square feet, and the length 540 rods, what is the width ? (58) Find the value of the rails in a straight fence 40 rods long,' each rail being 11 ft. long, and the fence 7 rails high, at $22.50 per M. (59) In eight equal loads there were 9 tons, 10 cwt. 32 lbs. How many tons, etc., were there in 5 loads ? (6b) A can do a piece of work in 6 days, B can do the same work in 8 days. If both work at it for 2 days, how long will it take A to finish the work ? (61) When hay is selling at $6 a ton, and oats at 30 cents a bushel, it costs a man $9 for hay and $6.75 for oats to feed a span of horses for one month. How much will it cost him when hay has risen to $8 a ton, and oats to 34 cents a bushel ? (62) How many feet of lumber in a plank 18 ft. long, 12 in. wide and 3 in. thick? //i^\ A ^nw^oM io jQ . There \Uj} .^x gaiiii-ii ts ij-j' j^fj: t--"ji •"• —7 ; - — -- - aiv two paths, each 6 ft, wide, running across each other c 93 ARITHMETIC X. through the centre of th« ^ /i Y V," ^°s' to diV all thAo\? * *^^"t the square -^(64) How many cS,^ vds^nf''"" ^^^«P^ *»»« Ss? tnefoundatbnofalin,,=f ^u • . °/ "masonry are thVr«? wide? Ti,« r ' . "ouse which s -ya ft / '*'e mere in ^/^, \\. V. GENERAL REVIEW. 93 > side and he square >e paths? ' there In md 1 8 ft. nd 18 in. :h would el? will pro- h. is that yard, to n. wide, unds, of els will ' long, 8 » and a ^much deep. ■ iioved for a >f the des a I day i^ould •ning oing t2S out •iil^ i 4.dollar bills and bo-cent pieces. Tnere are five times as many 5's as 4's, and twice as many 50-cent pieces as 5 s. Altogether he has $102. How many of each kind has h"* ? ' i'77> How much must be added to the product of the suni and difference of 8976 and CDIX. to make it exactly clmsible by 37^^^^ loooo lbs. hard coal. What must be the Jepth of my bin, which is 1 1 ft. long and 5 ft. wu'e, to hold^it ? A ton measures 33 cubic feet. (79) Reduce to acres, yds., etc., 11 128767 square -TSSTwhat is a bin of wheat worth, if its length be 14 ft.. Its width 7 ft., its height 5M ft, and its cost 64 cents *^(80 A house is 44 ft. long and 21 ft. wide, outside measurement. What will it cost to put two floors in it of 1 /z inch lumber, the walls being 18 in. tnick, and lumber beine wdrth $15 per thousand ft. ? ' ' (82) A square block of land is i mile 80 rods on each side Th3 road around it is 4 rods wide. Find the number of acres in the block of land, and also in the r-ad. (8^) A school-room is 40x28x14 feet, there are b windows and 2 doors each 3 x 6 ft. Find the cost of plast- ering the walls and teiling at 12 cents per sq^^"^ /J/"- ^ (84) There are 6 ft. in a fathom, how many fathoms deep could a cable la rods long reach ? „,^j„^t ^8i;> There are three prime numbers. The procUict of the first and second is 2537, of the ^^rst and third is 2881, and of the second and third is 3953- F'^^ them. (86> Divide sixty thousand and sixty- nine by 420, using all the factors of the divisor, and find true remr mder, (87) A field is 9384 ir^ches long and 73 H inches wide. Find its area in acres, ya»-ds, etc. ' (88) A cistern contains 2500 gallons If it measures ^ ft. 4 in. by 6 ft. 3 in., find its depth. (Rn\ A nlate o! couper 3 ft. wide, 3 ft- 2 in. long, and half-an-incii thick, is rolled' into a sheet 2 inches liucKana ft 7 in. wide. 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