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Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc., peuvent §tre f llmAs A d« i tsMX de rMuction diffArents. Lorsque le document est trop grand pour Atre reproduit en un seul clichA, II est fiimA A partir de Tangle supArieur gauche, de gauche h droite, et de haut en bas, en prenant le nombre d'images nAcessaire. Les diagrammes suivants illustrent la mdthode. 32X 1 2 3 1 2 3 4 5 6 PUB] Anthorizt c THE PUBLIC SCHOOL ARITHMETIC AND MENSURATION^. Authorised for use in the Public Schools of Ontario hy the Minister of hVucation. NEW EDITION. TORONTO : CANADA PUBLISHING COMPANY, (LIMITKD). )0'0 PS '-^. I \2nteied lu-cording to Act of Parliamejit of Canada, in the year 1!M)0. by the Canada Pubmshino Company (Limited), In tlie Office of the Minister of Agric'ulture. PREFACE. The main purposes which liavo been kept in view by the authors of this Arithmetic are — (1) to aid a pupil in becoming aeeiinite and rapid in calcukition; (2) to train him in independent thinking and in applying his knowledge of nximbor to the actual business transactions of life; (3) to aid the teacher in assigning s.pplieations of the various principles which have been explained. The classification of the problems has been given with this last aiu) mainly in view. Explanations of theory and all formal rule? have been omitted, the authors believing that teachers can best supply what is necessary in these respects, as the pupils are led to a clear comprehension of the principles which should be explained by the teacher before the pupils are required to examine the problems. It may be here stated that the exercises and problems are mainly intended to be used as applications of the theory taught. While no direct explanation of theory has been given, much lias been suggested by the character of the problems and by their arrangement. The definitions have been carefully prepared and stated in such a way that it is believed the pupil will find little difficulty in understanding them. Numerous mechanical and practical exercises on the fundamental rules for seat work form an important feature of the book. In many eases the answers to the mechanical tests have been omitted to enable the teacher to judge of the progress of his pupils in accuracy and rapidity. The exercises are a well -graded and progressive series, carefully arranged to develop the reasoning powers of the pupil, and at the same time to familiarize him with the important practical applications of the science of number. The Metric System has been introduced to meet the growing demands of the time. CONTENTS. Facie I.— Dkf'Nitions, Notation, Numeratkin 7 II.— TnK Simple Kules— I. AdtUtiou 11 II. Subtntetion 22 III. Multiplication 30 IV. Division 37 V. MiscellaneouH Exercises 43 III. — Compound Numbers- - Tables, Definitions, Etc 50 IV.— Simple Applications op i.ie Previous Rules— I. Bills and Accounts GO II. Simple Measurements (53 Carpeting 64 Plactering 06 Wall Paper 67 Board Measure 68 Rectangular Solids 69 III. Sharing 72 IV. Averages 75 V. — Factors, Cancellation, Measure^, and Multiples — I. Factors 78 II. Cancellation 79 III. Measures... 80 IV. Multiples 82 VI. — Fractions — I. Definitions, Notation and Numeration 84 II. Reduction of Fractions 85 III. Addition of Fractions 90 IV. Subtraction of Fractions 92 V. Multiplication and Division of Fractions 95 VI. Complex Fractions 101 VII. -G. CM. and L. CM. of Fractions 102 VIIl. Denominate Fractious 103 IX. Applications of the Previous Kules 105 Vl C'ONTKNTS. Vil. — DKf'IMAI.S— I. DefiiiitioTis, Notation and Nuinovation 115 II. Addition of Dccinmls 117 III. Subtnu'tion of J)t'<'inialM 118 1\'. iMultipliciition of Dfciniuls 121 V. Division of Doeinials 122 VI. Reduction of IhMdniiils 124 VII, Applications of tlic I'lcvioiiH Rules 125 VIII.— Pkuckntaoe - 121) IX. — API'MCATIONS of PF,K('KNTA(iK— I. Trade Discount 134 II. Profit and Loss Hid III. Commission 1;{S IV. Insurance 140 V. Taxes 142 VI. Simple Interest 144 VII. Compound Interest 14G VIII. Bank Discount 147 IX. Stocks and Dividends 14J> X. F^quation o£ Piiyincnts ir)2 X. — Pautnership ir)4 XI.— Invom'TIon and Ev<)r,i"ri(»x — 1. Involution loG II. Square Root 1.'58 III. Cube Root ir.9 XII. — Mensuration IGl XIII. — The Metric System of Weights and Measures.... 172 XIV. — Miscellaneous P^xercises — I. Cireulatiuf? Decimals 177 II. Problems Relating to Work Done 180 III. Clock Problems 181 IV. Problems Involving Velocity 182 V. Problems Involving the Sum and Difference of Two Numbers 183 VI. Review Exercises for Third Class 185 VII. Review Exercises for Fourth Class 187 VIII. Review Exercises for Fifth Class '. 190 XV.— Answers 198 ARITHMETIC. CHAPTER I. DEFIINITIOINS. INOTATIOIN. INUMERATIOIN. A Unit is a single thing or a definite quantity; as 1 lK)f)lv, 1 foot, 1 score, 1 four-oiinee weight, i half- ounce weight. A INumber is that which is applied to a unit or to a group of units for the purpose of answering the question ' ' How many ? " or " How much ? ' ' Arithmetic is the science whi<'h treats of numbers and the art which uses them in computation. Numbers are either Concrete or Abstract. A Concrete INumber is one whi(*h names the kind of unit used; as 4 tons, 6 horses, 3 dozen eggs, 5 half- ounce weights. An Abstract INumber is one in which the kind of unit is not named, as 4, 6, 9, 17. Notation is the expression of numbers by means of symbols. Arabic Mctation is the expression of num))ers by means of figures. Roman INotation is the expression of num])ers by means of (certain letters called liomati Numerals. Numeration is the reading or writing in words of a number expressed in symbols. 8 1. 2. 3. 4. 6. 6. 7. 8. 9. 10. (> If) i<; 94 2:{ (53 4'J 2H 79 AKITIIMKTIC. EXERCISE 1. rords tlic followinR : — T) 9 7 21 12 31 (>! 71 81 9;i 30 47 H({ 68 76 :i4 43 45 78 87 91 2;') 52 20 95 59 (59 48 84 04 8 4 i:i 17 18 92 74 49 07 .'{2 54 50 19 24 02 82 90 97 46 100 EXERCISE II. Write In words the following;: — 1. 500 700 800 200 000 400 2. 830 470 (509 714 800 990 3. 007 700 070 7(50 901 109 4. 847 784 478 748 874 487 5. 205 400 507 705 570 750 6. 4705 5843 91(58 2049 4905 4231 7. 8007 8070 8700 7080 7008 9045 8. 50(58 9008 0202 1508 3746 5780 9. 21.34 1234 1243 4321 4132 8009 10. 9001 1009 9001 9100 9010 9080 EXERCISE III. • Write in words tlie following: — 1. 40870 54089 30070 91111 2. 54089 40058 39007 40100 3. 81095 59100 95101 37098 4. 819075 891492 294710 410101 5. 210010 918005 231040 217000 6. 1470931 3790842 910010 2103001 7. 3091000 4007007 190100 3019047 8. 17091807 93704905 903705 21010101 9. 40097000 30910405 9317900 70000005 10. 2309400100 91491591(591 1013210012 7060700001 EXERCISE IV. Write in figures: — 1. Fifteen; twenty-one; tliirty-four; seventy-eight; eighty - seven; nineteen; ninety-one. DEFINITIONS, •.OTATION, NUMERATION. 2. One hundred; one hundred and seven; three hundred and Hix*«'»'n; four hundred and forty; nine hundred and nine; nine hundred and nineteen; nine hundred and ninety-one. 3. One thousand; one thousand, four liundred and two; eijcht thousand and six; eijfht thousand and sixty; two thousand, four hundred and ninety-six. 4. One thousand and eleven; ten thousand, six liundred and four; twenty-nine thousand, four hundrtid and seventy; eighty thousand, nine hundred and ninety. r-t. Eight hundred and four thousand and sixteen; two hundred and ninety-one thousand, seven hundred and four. 6. One million, one hundred and one thousand and one; five million, four thousand and thirty. 7. Nine hundred and fifty-four million, eight hundred and six. 8. Seven million, seven hundred and seven thousand, seven hundred and seven. 0. One hundred and forty-six million, one hundred and forty-seven thousand and forty-seven. 10. Five hundred and thirty-six million, three hundred and forty -seven thousand, nine hundred and seventy -two. 11. Six billion, ninety-five thousand, one hundred and forty-eight; seven hundred billion and one. 12. Ninety-nine billion, thirty-seven thousand and four. 13. Eight hundred and sixty-four billion, five hundred and thirty-eight million, two hundred and seventeen thousand, nine hundred and fifty -three. 14. Forty billion, four million, four hundred thousand, four hundred and fourteen. 15. Forty-nine trillion, fifty-eight thousand, seven hundred and ninety-eight. Write in Roman numerals 1. 5 2. 15 3. 25 4. 49 5. 109 6. 240 7. 404 8. 796 0. 875 10. 973 11. 1900 EXERCISE V. erals : 6 8 16 18 26 28 45 94 104 105 249 394 444 499 789 777 857 578 9(55 999 1889 1899 9 19 24 98 219 388 589 766 894 987 1849 4 •14 44 99 329 356 594 699 984 944 1904 10 ARITHMETIC. i£XERCISE VI. Write in figures: — 1. XV, XC, XCIV, LXIX, XLIV, XCIX, LXXXIX, CX. 2. CXI, CIX, CXLIV, CCXXIX, DIV, CCXLIX, DCCIX. 3. CDIV, DCCXXX, DXL, CDXLIV, DXXIX, DCXXIV. 4. DCCCXXXIII, CDLXXXIV, CCCXXXIII, CDXXXIV. 5. DV, CDXXX, CCXCVII, CCXLIV, CCCXXIII, DLV. G. MCXI, MD, MXIV, CMXC, CMXCIX, AICCCLIV. 7. MCCXC, MDLV, MCDXLJV, MIX, MCCXXII, ^ICDXC. 8. MMCCXXII, CMXLVII, MCMVI, MCD, MCvIIX, MDLV. y. MDCCXLIV, MCDXLIX, MDCLXVI, MMIX, MCXIX. 10. MDXCIX, MCM, MCMI, MDCCCXCIX. EXERCISE VII. 1. Write in Arabic Nrnnerals the smallest number that can be expressed by two figures ; by three ; by four. 2. Write in Roman Numeruls the largest number that can be expressed by three figures. 15 . What is the effect of writing a letter of less value before one oi a larger valuef Give four examples illustrating this, 4. To the left of only what letters can I be placed in Roman Notation? "). To the left of only what letters can X be placed in Roman Notation i 6. Write the significant ngures and express each in Roman Notation. 7. What letters in Roman Notation are never repeated? 8. Write in words the following sentences: — The earth is 92890000 miles distant from the sun. The lei.gth of the equator is- 'i:{827033 yards. The cheese factories of Ontario produced 13r'->b:?91G pounds of cheese in 1897. The milk used in making *iiis cheese was 1455937148 pounds. In 1898 the 98 creameries lii '.''i'" returns to the Bureau of Industries produced 9008992 pounds of butter, valued at 1632234 dollars. 9. What numbers can be expressed by means of the letters V and X taken separately or in combination? 10, Express "n Arabic Numerals all the numbers of three figures that can be expressed by means of the letters X and G taken together or separately. CHAPTER II. THE SIMPLE RULES. I. ADDITIOIN. Addition is the process of linding a number equal to two or more numbers of the same kind. Tlie Addends are the numbers to be added together. Tlie Sum is the single number which results from the addition. The sign of addition is +, called plus, and when placed between two numbers it shows that these are to be added. 1. 2. 8. 4. EXERCISE VIII. 14 41 52 42 33 21 23 12 12 21 32 13 25 15 123 421 241 222 234 321 110 345 333 311 231 242 102 123 132 313 123 410 321 321 134;-) 2111 1012 1000 4443 2231 4001 3421 1234 2224 2423 2403 1323 2423 1201 3000 3121 4231 5231 5341 2100 5123 4112 7111 7231 4132 5234 4211 5000 3412 G210 7110 5341 3123 4123 3111 4231 0204 4351 5201 11 12 5. AUITHMETIC. 71112 52123 71241 71122 82013 41231 41024 32026 20311 41012 51640 62301 41010 42133 50601 41013 70021 52401 54332 41203 6. 2031+1234+3122-f 1010+100. 7. 1207+3040+2430+112+2000. 8. 51+3027+2000+1500+1320. 9. 21021+12+32+2700+12000+102+21. iO. 12201+21+142+23000+2100+2012. EXERCISE IX. 1. John has 10 cents; Bob has 25 cents; Harry has 14 cents. How many cents have thev together? 2. A cow cost $21, a pig $14, and a sheep $12. How much did all cost? 3. A farmer drew five loads of wheat to market. He had 41 bushels in the Ist load, 42 in the 2nd, 40 in the 3rd, 42 in the 4th, and 44 in the 5th. How many bushels were in the five loads? 4. I walked 21 miles on Monday, 22 on Tuesday, 21 on Wednesday, and 23 on Thursday. How far did I walk in the 4 days? 5. A train goes 31 miles the Ist hour, 30 the 2nd, 32 the 3rd, and 31 the 4th. How far has it gone in the 4 hours? 6. The population of four cities is as follows: the first 111203, the second 21.n23, the third 11221, and the fourth. 611222. What is the total population of these four cities? 7. A merchant bou.crht four pieces of cloth. The first was 203 yards long, the eeeoud 321, the third 223, and the fourth 222. How many yards were in the four pieces? 8. An ocean steamship sailed 312 miles on Tuesday, 324 miles on Wednesday, 320 miles on Thursday, and 411 miles or Friday? How far did it sail on these 4 days? 9. A steamship leaving Montreal for Liverpool had on board 415 cattle, 240 sheep, and 131 horseB. How many head of live stock were on board? 10. A history consists of 4 volumes. In the first there are 412 pages, in the second 410, in the third 415, and in the fourth, 431. How many pages are there in the entire history? d on board ead of live ADDITION > 13 EXERCISE X. 1. 323 233 123 312 311 2323 232 222 132 123 233 3211 333 333 213 323 322 2332 233 310 231 333 113 3123 312 232 2133 321 2323 223 3213 333 23132 2323 2. 3233 32133 3233 3032 3223 2133 21332 32332 2332 3321 3332 3321 33213 32223 3123 3333 2332 2332 23323 23322 3321 2332 21321 3212 32212 3323 23213 32133 12233 3. 31333 23213 32132 23213 21332 31232 23223 32123 22321 31220 32132 21332 32213 32233 31223 33303 32013 21321 33223 32213 20301 10332 32103 33233 13322 32132 21303 12321 23321 13321 32332 21331 33233 4. 34124 41234 24134 41234 41341 21314 31413 32134 24413 44341 24143 44143 24130 24341 34123 24132 34124 21321 24133 43214 41244 41421 34143 40143 40241 43441 32412 34134 21414 21434 30213 14234 22141 21414 34140 24143 T). 13412 41324 41321 51321 32132 51324 4G712 62132 35326 41324 46213 42676 3r)273 41653 45624 41324 24132 25014 24134 25623 52334 50604 3(5213 30629 4r)0o2 32134 41302 60621 41621 46532 3r)213 43253 10343 40132 41321 42624 0. 41324 41324 41321 32562 41324 41321 34120 16213 62162 31416 30143 41032 604(52 40123 42342 20413 62143 40162 30(521 30(523 62103 401(52 40132 32162 41032 43216 66552 41324 40110 41314 41(521 2U32 45625 51602 62162 62132 14 ARITHMETIC. 7. 5232 4013 6217 3017 1472 1213 41321 00213 41002 41321 42321 41021 32134 22343 402()2 S21(i3 41323 41021 413212 413210 413210 4()r)271 017172 312711 3121 4137 5702 3502 5213 4134 37124 34135 25312 40352 70712 34372 8. 81876 41342 21341 41832 41372 41783 413^2 48324 62437 41072 47726 47807 34027 78772 24167 32171 68783 87710 18704 40724 82416 42313 27107 37872 31241 37802 37137 57717 27178 47132 01375 41371 41683 87071 37183 41367 9. 41340 41837 41372 41672 41834 41837 21347 08773 46837 37183 67832 41678 70827 41701 46713 63784 41786 38678 48372 37450 48783 32487 67138 32168 48372 75071 67187 67137 41687 41767 41071 38710 38147 47183 48371 89168 0. 41071 13716 41371 41372 71324 41674 00872 41372 02710 48637 67168 34187 41876 67187 04701 24873 32417 62184 86716 47183 37124 21437 03418 67132 40713 80713 37072 67138 40728 48667 87241 40713 48372 63418 87832 47183 EXERCISE XI. 1. 370693 732894 507] 126 770655 764845 777777 555123 432733 007755 999999 531234 456789 567643 554488 888888 135789 579040 219872 998877 777777 973124 843757 876464 776654 666606 70383 984329 597777 897987 245678 507890 432173 66466 764896 457896 2. 348037 460375 963] [72 849652 962847 272405 841681 300725 361728 777888 530034 239724 403;: 48 412381 888999 109871 763256 721003 035403 789789 093036 437891 387356 872545 678678 704543 825432 241653 400223 897987 233038 285678 u03'J 80 294867 387047 428432 310720 5321 70 811230 480578 ADDITION. 15 37124 34135 25312 40352 70712 34372 3897(53 210045 76080(5 (53(5215 253734 251600 575453 807720 403521 687489 324061 530724 623452 487(538 290731 803256 278321 829248 171320 20(>782 461027 589203 248639 730461 576037 213744 764368 305216 436720 823284 217436 592301 364728 246374 478369 287456 93(5478 184369 678456 286397 4. 379623 891371 889977 789 8000000 7542 919198 732894 723 667755 25320 171296 555123 674 44332 57644 1478(57 456013 1674 3355778 908176 182371 579646 19006 986754 73409 929292 843751 1916 71347 3147 292929 984329 ■ 986986 981675 67039 777777 432173 97979 19198 5. 3824442 67124332 25927871 3267362 7778889 4563358 31734324 71684655 2152837 4581986 1612119 19524324 69351437 4627792 3599872 5121223 53414325 35927212 3564465 2998767 8232535 57384327 21614892 2152322 9887651 6348442 42624329 74321572 4617777 8776548 3454384 75218671 69987452 3564416 7665434 2563125 83186438 25654232 2152362 6554326 4673995 41986974 71381011 4617727 5443213 6. 6739484 87665163 94358975 95639888 99888777 5263898 57946295 2848 86872569 22586972 9688626 43937568 9184 11191993 57486976 7445853 89264339 45339 32384345 21586972 6899438 2613 987672 95339888 93456975 8123814 9155 93783891 85372569 46556972 4598603 5278 26753984 14891173 25496977 2355792 87667549 66344839 36684845 47556979 1773424 49623 94982172 71739188 21457979 7. 4008811 31412 657118 294044 95299 1854239 30088 182595 199639 8720834 705 150 5520 17228 436292 14872 1500 525 17370 400283 6498119 5363277 497454 41762 2344900 1 055308 3187 57768 482511 12137980 371498 18015 23247 1027 11089359 4040559 4(5976 990019 1088534 3633750 12526543 1278225 2150113 9414575 295984 -«^ia.. 16 3 ARITIFMETIC. 8 1288153r) 624564 2610287 6214458 131917 2171188 209840 373898 1530581 3400/17 9947r)2:{, 213954 2297433 2142822 28()0765 683069 1957 109897 417 25396S 9243811 2434454 1364034 296259 71894 3086160 3975 477438 4494680 41729 8071370 7088142 585138 31211 535955 7065878 1011492 2043283 4925889 11212616 4346234 21191 559619 137990 4286131 7834359 203572 1627164 2981652 517562 9. 6967056 3196563 1108476 185658 57636799 9487210 365756 375396 1601190 63927094 79766094 49741413 10071301 13121498 19154873 4146290 95921 970738 2130102 25981652 34449379 20819542 10196".71 14487351 7165.3431 39878418 2505034 4481ii70 15367691 62327299 995670 316508 129692 49 29987988 2981850 4970 487233 1066277 7565487^^ 8139585 177681 1364378 1619386 61321716 10. 8529883 27932143 93789391 22872769 75700757 3593652 53969235 26745984 75191997 36471241 9658934 49265558 66357839 96484343 75057906 6475424 87647389 94946172 81539885 44346505 3757873 87931693 93787391 12872568 91753002 3363662 53929135 26782644 .35791979 77647300 8829744 49298258 66359199 96284343 76044071 2293413 87651589 94945222 81339885 82872633 7958882 87973397 93787511 12672568 99872517 8175659 75982231 65781737 35891219 86297761 ( EXERCISE XII. - 1. Add togeth er 763, 4663, 37, 49763, 6178, and 671. Add together 15, 7896 , 1, 13, 106, 113, 156, 100, and 2201. 3. Add togeth er 100375, 406780, 467300; ), 4112, 2478, 79, !Uid8. 4. Add together 123405, 2354210, 79431 27, 36547, and 789. 5. Add together 275L32, . 345007, 4567801, 365, 1896, and 78G9. 6. Add togeth er 70, 189, 3684, 72, 8967, and 798. 7. Add togeth er 982, 369 , 764, 8, 89, 75, and 396. 8. Add togeth er 7, 89, 8, 7098, 38, 471 , 78, and 1899. 9. Add together 968, 777 , 78, 408, 700, 9009, and 7 . 10. Add together 7698, 4, 790, 87, 3694, 78, and 897 • i.iion '^H 3400717 28(507<)r) •jriiujes 71894 41729 r):{r)9r>5 11212616 4286131 5l7r)62 57636799 a 63927094 19ir)4873 25981652 716."i3431 62327299 29987988 7565487'^ 61321716 75700757 36471241 75057906 44346505 91753002 77647300 76044071 82872633 99872517 86297761 671. )0, and 2201. 78, 79, and 8. ■; and 789. \ )6, and 7809. i 1. i 6. 1899. li 7. 897. ■ ^ ADDITION. EXERCISE XII.I. 17 1. 7634129+ 7634-f830604-|-937+856312+37140+694713284- 85'j4695. 2. 9093+846295+37G05f54+57312858+581401+393+4301201. 3. 51316281+7413819+543628+71434-717562+8319886. 4. 79+;'*(53+900832+8632+473423+644+1000000. 5. 789632+71+879002+876+970+329449. 6. 92+853+7654+65432+543210+4321098+321976+2109+ 1098+182. 7. 6290+704+713+4631+5214+289+3102+41. 8. 483+9000+648+3750+9840+24680+5096. 9. 103421538+120952657+116843889+116491051. 10. 82+92+102+873+824683+2000201+489076. EXERCISE XIV. 1. B^ind the sum of 27, 36, 45, 52, 8V, 29, 16, and 11. 2. A farmer has five fields of grain. In the first there are 27 acres; in the second, 42 acres; in the third, 97 acres; in the fourth, 86 acres; and in the fifth, 102 acres. How many acres are there in the five fields? 3. James has 27 marbles; John has 83; Harry has 116; and Tom 46. How many have they all? 4. James rode 17 mi]es on Monday, 23 miles on Tuesday, 41 miles on Wednesday, 36 miles on Thursday, 17 miles on Friday, and 24 miles on Saturday. How far did he ride during the 6 days? 5. A farm cost $4816, a house $2345, a horse and buggy $158, and a cow $34. How much did all cost? 6. A drover had 327 sheep, 245 cows, 584 pigs, and 117 horses. How many animals had he in all? 7. In a~i orchard there are 417 apple trees, 176 peach trees, 245 plum trees, and 47 pear trees. How many trees are there in the orchard ? 8. Add 294, 421, 76, 109, and 217 together, and express the result in Roman numerals. 9. In 1897 the population of the County of Oxford was as follows i Townships, 28780; Towns, 15801; Villages, 1810. What was the total population of the county in 1897? 10. To the sum of 14, 17, 25, and 96, add the sum of 18, 12, 19, and 25. 18 ARITHMETIC. EXERCISE XV. 1. Tom had 17 mnrbles; ho houj?ht 5 mor«*, and his brother gave him IS. How many had he then f 2. A man paid $22 for a suit of clothes; *$2 for a hat; $6 for a pair of boots; and $1") for underwear. What did he pay for all? 3. John's book has 216 pages; Mary's, 492; and Harry's, 162. How many jtages are there in the three books? 4. A man travelled 247 miles on Monday, 36 miles on Tues- day, and 17 miles on Wednesday. How far did he go in the three days? 5. Find the sum of 47 cents, 93 cents, 107 cents, 483 cents, and 270 cents. 6. Add $128, $1275, $468, $17, and $12. 7. A man spent $127 one day, $47 another, and $96 another. How much did he spend altogether? 8. Edwin had 35 cents: he found 16 cents, and his brother gave him 47 cents. How much had he then? 9. A man wheeled 37 miles on Monday, 46 on Tuesday, 34 on Wednesday, 52 on Thursday, 28 on Friday, and 11 on Saturday. Ho- v far did he wheel altogether? 10. A man began business with $3795. His gain the first year was $824; the second, $491; the third, $726; the fourth, $1211; and the fifth, $809. What is he now worth? EXERCISE XVI. 1. Find the sum of all the numbers, from 749 to 760, inclusive. 2. Three men bought a farm. The first paid $2468; the second, $2032; and the third, as much as the other two. Find the cost of the farm. 3. Ella picked 378 baskets of berries, and Jane picked 58 more than Ella. How many did both pick? 4. A schoolroom is 32 feet long and 21 feet broad. How many feet is it round the room? 5. Willie gave John 37 cents and Mary 48 cents. He had as many cents left as he had given away. How many cents had he at first? 6. A farmt?r bought a pig for $19, a cow for $39, a sheep for $13, and a horse for as much as he paid for the pig and the cow. How much did he pay for all? 7. My brother gave me 32 cents; my father gava me 8 cents more than my brother, and my mother. gave me as much as both. How much money did I receive? ADDITION. 19 8. Helen spent 117 cents for books, 121 cents for ornnjjes, 44 cents for peacheH, l.'Jl cents for sugar, and had 87 cents left. How much had she nt first? 9. A farmer has lo acres of whwit, 29 acres of barley, 17 a^'res of peas, 19 acres of corn. The rest of the farm is in pasture, and there are as many acres of pasture as of grain. How many acres has he altogether? 10. A drover >)ought 27 sheep for $11.'5 from one farmer; from a second, he bought 35 sheep for $142; and from a hird, 28 sheep (or $1.32. How many sheep did he buy, and how much did they cost him? EXERCISE XVII. 1. Find the sum oi $42, $9136, $254, $29, and $530. 2. At the World's Fair a man spent $37 the first week; $46 the second; $84 the third; and $9o the fourth. His other expenses were $87. How much did he spend during the four weeks ? 3. In 1897 the population of the County of Essex was 431.54; of Kent, 44183; of Elgin, 29659; of Norfolk, 29231; of Haldi- mand, 2^263; and of Welland, 30305. What was the total population of these six counties? 4. In 1896 the debenture debt of Ontario was as follows: Of township^, $2866904; of towns, $9598063 ; of villages, $1163096; and of cities, $37471231; of counties, $1848982. What was the total ^ jbenture debt of Ontario? 5. A drover bouj^ht three flocks of sheep. The first contained 967, the second 133 more than the first, and the third 450 more than the second. How many sheep did he buy altogether? 6. Sarnia is 62 miles west of London: Ijondon is 115 miles west of Toronto, and Toronto is 333 miles west of Montreal. How far is it from Sarnia to Montreal ? 7. T lost $29 by selling a-horse for $71. horse cost me ? How much did the 8. For how much must I sell a horse which cost me $91, so as to gain $29 ? 9. John has 27 cents more than Willie, who has 84 cents. How much money have both together? 10. The first of three number" is 846, the second is 987, and the third is as much as the other two. Find the sum of the three numbers. 20 ARITHMETIC. EXERCISE XVIII. H 1 1 l! Il 1. A boat Bails from St. Catharines to Toronto, 45 miles; from Toronto to Montreal, 93.") miles; and from Montreal east- ward a distance eijiial to that from bt. Catharine*? to Montreal. Find the total distance sailed. 2. Add 675, one Taillion and nine, four thousand and six, 302, fortj -one thousand six hundred and four, 21436, ninety- seven, 84, and ninety-one thousand four hundred and seven. 3. 1 bought wheat for $4')i)i], corn for $2347.1, oats for $8796. I sold the wheat at a gain of $1404, the corn at a gain of $6525, and the oats at a gain of $204. How much did I get for allf 4. After selling 1016085 oranges, a merchant had two lots left, one containing 69756 and the other 85619. How many oranges had he at first? 5. A man sold a horse for $986, and three cows for $680 each. He lost $125 on the horse and $220 on each cow. How much did all cost him? 6. How many times does a clock strike in 12 hours? 7. I bought wheat for $7962, corn for $12649, oats for $8763. I sold the wheat for $780 more than the cost, and the corn and oats at a gain of $1685 on both. How much did I get for all? 8. A lady paid $380 for a piano, $275 more than that sum for furniture, and*$2675 for a house, and has still $8375 in the bank. What sum had she at first? 9. A fai'mer gave to each of his three sons $6580, .and to his daughter $920 more than to two sons. How much did he give away altogether? 10. A man gave his wife $10560, his two sons $7325 each, and his daughter $485 more than a sou's share. How much did he give away? EXERCISE XIX. 1. In 1S97 the population of the townships of Ontario was 1113530; of the towns, 312947; of the villages, 1.33560; and of the cities, 430940. What was the population of Ontario in that year? 2. In the B'vttle of Waterloo it is said that of the soldiers engaged 36273 were Briti«)i, 7447 were Hanoverians, 8000 were Brunswickers, and 21000 were Belgian, whilst there were about 75000 French. How many were there of the four allies, and how many combatants were there altogether? 3. A father leaves an estate to" his son, daughter and wife. To his son he leaves 5355 dollars, to the daughter 500 dollars more than to the son, and to the wife 1500 dollars more than to the daughter. What was the amount of the estate ? ADUITIUN. 21 1, 45 miles; mtreal eiint- trO Montreal. ind and six, 436, ninety- nd Heven. ,ts for $8790. ain of $6525, ;et for allf had two lots How many )W8 for $680 li cow. How lurs? its for $8763. the corn and get for all? that sum for ) in the bank. iO, .and to his did he give 325 each, and much did he ' Ontario was ]3560 ; and of ntaric in that 4. John threw a hall 34 yards up the road, and another 43 yards down the roml. How fur must he walk to bring them both ba<'k agiiin ? 5. The first of four numbers is 4768, the second is 170 more than the first, the third is 90(5 more than the second, and the fourth is as much as the other three. What is the sum of the four imnibcrsf 6. Mary bought a book for which she gave 95 cents; Maudo bought oiH' for which she gave 13 cents more than Mary; aiul Maude's book cost 23 ci'iits less than Jane's. Find the cost of .lane's book. 7. Find the number of days in a year — the days of the respective months being as follows: January 31, February 2H, March 31, April .30, May 31, June 30, July 31, August 31, September 30, ()ctol»er 31, November 30, December 31. 8. Adam lived 930 years; Seth, 912; Enos, 905; Cainan, 910; Mahaleel, 895; Jared, 962; Enoch, 365; Methusaleh, 969; Lamt^ch, 777; Noah, 950; Shem, 600; Arphaxad, 438; Salah, 433; Heber, 464; Peleg, 239; Keu, 239; Serug, 2:10; Nahor, 148; Terah, 205; A>»raham, 175; Isaac, 180; Jacob, 147; Joseph, 110; Moses, 120; Joshua, 110. What is the sum of all their ages? 9. Water-mills were invented in the year 555 after Christ; windmills 744 years after water-mills; pumps 126 years after windmills; printing 15 years after pumps; watches 37 years after printing; the spinning-wheel 53 years after watches; the steam-engine 119 years after the spinning-wheel; the fire- engine 14 years after the steam-engine; the spinning-frame 98 years after the fire-engine; and the electro-magnetic telegraph 71 years after the spinning-frame. In what year was the electro- magnetic telegraph invented? 10. A man bequeathed his estate as follows: To each of his two sons, $12450; to each of his three daughters, $6500; to his wife, $650 more than to both the sons; and the remainder, which was $1000 more than ho had left to all his family, he gave to benevolent institutions. What was the whole amount of his property? f the soldiers ns, 8000 were re were about ur allies, and ter and wife, er 500 dollars 1 more than to e? oo ARITHMETIC. II. SUBTRACTIOIN. Subtraction is tlio process of ftndiiijf ilie differenco between two iiuinbers of the same kitid. The IMInuend is the number from whieli tlie other number is taken. The Subtrahend is the number whieli is taken from the minuend. The Difference or Remainder is the num1)er found by taking the subtrahend from the minuend. The sign of Su])traetion is — , called minKs, and when written between two numbers it shows that the number after it is taken from the one before it. EXERCISE XX. ». 4. i). 59 07 29 47 9() 87 99 23 54 t() 21 32 52 73 786 938 897 984 593 898 245 412 504 421 242 452 674 849 928 547 693 989 52 417 415 231) 451 472 8947 5986 9397 8946 4918 4765 4312 3241 4152 4235 3807 1234 70846 89476 91708 .59487 49387 .39587 50314 13012 40532 23152 29245 21432 6. 35276 40547 48456 57345 73840 904782 21042 31023 22304 31021 21413 130531 45987 21257 47543 31213 48053 32423 49735 13425 54398 51281 50347 12345 98764 12321 38704 32532 74820 50412 45708 42323 01895 ()2352 78456 .32012 i(» (lifFcroiKM' •li tlic Otllt'l* •h is taken he number ninuend. mhu(s, and wa that the re it. 87 J)9 52 73 503 808 212 452 G03 989 451 472 1918 4705 5807 1234 )387 39587 )245 1840 21432 004782 1413 5347 130531 98704 2345 1895 12321 78450 2352 32012 428357 423142 SUBTRACTION. 028954 039847 523412 032123 718047 715415 li 905783 120321 4370<)8 312415 800087 304015 705347 705123 308718 123718 470084 412382 10. EXERCISE XXI. 1. A niiui had 151 i-ows. JIu sold 40 of them. How many hail \w Wat 2. Harriet and VAh'ix tofrctln'r liavo 83 littln fhickons, of which Harriet owns 43. How many btdonff to Kllenf 3. A man boiijrht n horse for $\27 and sold it for $104. How much did he losef 4. A hook has 210 pajjes. Tom has read 103 pages. How many pages has lie yet to read? 5. A merchant having bought 587 gallons of syrup, sold a pertain quantity and hud 315 gallons left. How many did he sell? 0. A man paid 275 dollars for a horse and buggy; the horso cost 125 dollars. What was the price of the })Uggy? 7. In one year a merchant sold 1578 barrels of flour and 1324 barrels cf sugar. How many more barrels of flour did lie sell than sugarf 8. A drover having 1465 sheep sold 233 of them. How many had he renniining? 9. A farmer has two farms containing together 875 acres. Tn one farm there are 442 acres. How many are there in the other? • 10. A fanner liouglit a farm for 4f3()00 and sold it for $4200. How much did he gain? EXERCISE XXII. 1. 90 40 50 00 70 80 100 35 13 27 31 40 29 75 327 930 574 928 726 850 142 484 381 182 145 160 590 700 40G 732 824 751 143 178 184 185 108 328 3450 3700 4870 5340 5938 9418 1235 2340 2527 2128 2970 5493 u '"*- ARITHMETIC. 4'J:J8 5129 6248 7206 7462 4915 L'HiC} as?-) 498:5 :{K94 59158 .'5897 427:56 24:582 53829 28596 61705 28483 80727 45384 49376 31949 57146 29418 9. 400300 295246 500000 273827 506207 49185 500200 :J9:5186 400000 285458 402508 84274 700400 800500 398327 496478 600000 700000 365879 486347 604506 703605 89251 78382 300700 12:5456 400000 267410 802507 76832 600500 287684 800000 120076 907608 30709 10. 924:590 705180 527082 816141 423453 700600 4:52412 44:5544 232154 1:55212 141514 123416 1. From 2. From 3. From 4. From 5. From 6. From 7. From 8. From 9. From 10. From 1. o 3. 4. 5. 6. 7. 8. 9. 10. EXERCISE XXIII. 924 take 379; from 970 take 182. 1000 take :!78; from 1111 take 999. 2450 take 1097 ; from 6040 take 644. 44444 take 14847 ; from 44444 take 15789. 50505 take 27895; from 55,555 take 48776. 6G6666 take 278954; from 600000 take 123007. 100600 take 99999; from 777777 take 297998. 486413 take 164184; from 418786 take 219186. 600078 take 142368; from 300007 take 108819. 672246 take 487128; from 578472 take 169386. EXERCISE XXIV. 6005- 8002- 8003- 6005- 9004- 6003- 7035- 7023- 8021- 8064- -2:547 -2636 -2746 -2748 -2615 -2846 -2648 -2896 -;3472 -2397 7825-3569 H412— 3756 9000—1234 7018—6243 8765-5999 6200—4756 8006—7184 8574—6497 74S2— :5597 8100—6718 9012- 7064- 7000- 7000- 8000- 8000- 9000- 9000- 6324- 6245- -3684 -2768 -2546 -3748 -5318 -3526 -3725 -2745 -2538 -3789 :t ■a SUBTRACTION. 25 7462 5938 49376 31949 4915 3897 57146 29418 300700 123456 600500 287684 400000 267410 800000 120076 802507 76832 907608 30709 423453 141514 700600 123416 EXERCISE XXV. 44. e 15789. e 48776. take 123007. ako 297998. take 219186. take 108819. take 169386. 9012- 7064- 7000- 7000- 8000- 8000- 9000- 9000- 6324- 6245- -3684 -2768 -2546 -3748 -5318 -3526 -3725 -2745 -2538 -3789 is r I 1. .56739— 24316 36751- -2S976 431250—153697 2. 68507—47623 90006- -29384 920503—476829 3. 47865—12341 71020- -.-)43(i7 523146—286759 4. 72006—48315 43002- -27659 647352—268574 5. 65043- -17872 71300- -450.35 502304—186475 6. 81000-25143 64434- -25679 625030—274384 7. 90000—30906 76456- -29898 720301—368596 8. 90503—47628 56307- -18497 842003—459687 9. 41009—31214 70000- -39458 715324—369857 10. 43020—36748 78536- -47658 900500—465783 EXERCISE XXVI. 1. 8467321—3478271 700' rOOO— 2009001 o 3178632—1478371 6789012—700999 3. 9004100—30012 764.89687—999999 4. 100010110—990991 7000000—636363 5. 49716368—42894938 7400002—123807 6. 3714908—2916409 5000005—900009 7. 37080605—2934716" > 10101011—303033 8. 23456789— 149307()8 27689714—9337778 9. 1000000—11 476.- 5879—707070 10. 4000000—199091 5005005—1234567 EXERCISE XXVII. 1. How much must be added to 76 to make 150? 2. Take 713968 from one million. 3. From 9410068 take 3090801. 4. What is the difference between 76104 and 108403? 5. The greater of two numbers is 705, and the difference between them is 29. Find the smaller number. 6. Find the remainder, after taking 7854 as often as possible from 57692. 7. What number taken from one million will leave 473916? 8. To what number must 8764 be added to make 11342? 9. 7900000— 467846— 7()4839. 10. From the difference between 287368 and 789560, take 360194. 2G AUITHMKTIC. EXERCISE XXVIII. 1. A man l»ad 374 nhcep and sold 28;"). How nianv had he left? 2. James has I'lT') ; Tom has $'MH. How much more has James than Tom f 3. If a man receives $3415, and si)end8 $2947, how much lias he left? 4. If I buy 47964 bushels of wheat and sell 23796 Imshels, how many bushels are left ? 5. Mr. Jones has $7698 and Mr. Williams $5919. How much more has Mr. Jones than Mr. "Williams? 6. I bought a farm for $7916 and have paid $5748. How much do I still owe for the farm? 7. A owed B $378 and paid him $329, and gave him a cow for the balance. What was the value of the cow? 8. A man started to walk 3400 miles, and has finished 1968 miles. How far has he yet to go? 9. In 1897 the population of Ontario was 1990977; in 1886 it was 1828495. How much had the population increased during *;his period? 10. In 1897 there were 940236 milk cows in Ontario; in 1888 there were 781559. How many miik cows had been added to the cattle of Ontario during this period? EXERCISE XXIX. 1. A merchant sends $4796 to his agent to buy goods, and receives $3989 worth. How much does the agent keep? 2. James bought 98 marbles and then sold 59 of them. How many had he left? 3. In an army of 24907 men, there are 10908 who are over 36 years )f age. How many are younger? 4. I sold a farm for $4713 and gained $897. What did it cost me ? 5. There are 525600 minutes in a year, and 173964 in the first four months. How many minutes are there in the rest of the year? 6. Jane has two books containing 736 pages, and one has 297. How many has the other? 7. A railway cost $63475916, and of that sum $41968959 have been paid. How much is still owing? 8. A boy starts from Montreal for Vancouver, a distance of 14680000 feet, and travels 8379164 feet. How far has he yet to go? SUBTRACTION. 27 9. In 1897 there were 312947 persons in Ontario living in towns, and 430940 living in cities. How many more persons lived in cities in Ontario than in towns? 10. In Ontario in 1883 there were 53513032 pounds of cheese niaimfactured, and in 1897 13736291G pounds. How many more pounds were manufactured in 1897 than in 1883? EXERCISE XXX. 1 . A boy paid 52 cents for a geograpliy and 25 cents for an arithmetic. How much inore did lie pay for the geograpliy tliau for the arithmetic? 2. A boat had 720 passengers and lauded 438 at a port. How many remaiued on the boat? 3. A man began bnsiues« with $15264 and lost $3271. How much had he let'tif 4. A man had $100. He paid $65 for a buggy and the rest for harness. How much did the harness cost? 5. Sir Isaac Newton died in 1727 at the age of 85. When was he l>orn? (5. Gladstone was born in 1809 and died in 1898. To what age did he live? 7. The Universitv of Camltridge was founded in 915. How old was it in 1898? ' 8. Mount Logan, the highest mountain in Canada, is 19500 feet high. How much higher is it than Mt. Blanc, the highest mountain in Europe, which is 15812 feet high? 9. At an election there were 2784 good ballots cast. The successful candidate received 1459 votes. How many votes were given to the defeated candidate? 10, In 1898 the population of Greater Loiidon was 6291000, and of Greater New York it was 2321644. How much did the population of Loudon exceed that of New York? EXERCISE XXXI. 1. ^11 a school of 489 scholars there are 267 girls. How mauy more girls tlian boys are in this school? 2. I bought a house for $2127. I paid $365 for repairs, and then sold it for $2690. How much did I gain? 3. A miller bought 1000 bushels of wheat from one farmer, and 500 bushels from another. After selling 825 bushels to one merchant and. 460 to another, how mauy had he left? 28 AUITIIMKTIC. 4. A {^eiitleraan at his death left 12000 dollars to be divided between his wife, his son and his two daughters. To each of the daughters he gave 287") dollars, to the son aOOO dollars, and to his wife the remainder. What was the wife's portion? 5. A man bought a horse for $175 and another for $216. He sold both for $42;{. How much did he gain? G. A man is worth $175968. Of this $29347 is in real estate; $14743 in bank stock; $23928 in railway bonds, and the rest is in the bank. How much is in the bank? 7. A cattle drover bouglit cattle for $19376. He paid $8949 in cash, gave a cheque on the bank for $3249, and his note fcr the balance. For liow much was the note drawn? 8. There are 1760 yards in a mile. Find by su])traetion how many miles there are in 8937 yards, and how many yards remain. 9. Two persons are 375 miles apart; they travel towards each other; at the end of one day, one has travelled 93 miles and the other 57 miles. How far apart are they still? . 10. At an election 12572 votes are taken, of which the suc- cessful candidate received 7391. By what majority was he elected? EXERCISE XXXII. 1. A man deposits in the Ontario Bank 2374 dollars. At one time he draws out 897 dollars, at another time 543 dollars, and at a third time 689 dollars. How much still remains in bank? 2. A man was 21 years old in 1896. In what year will he be 75 years old? 3. A gentleman dying left 4500 acres of land to his wife, his son and his daughter. To his wife he gave 1564 acres, to his son 1449 acres, and to his laughter the remainder. What was the daughter's portion? 4. A gentleman 83 years old has two sons; the age of the older son added to his makes 128 years, and the age of the younger son is equal to the difference between the age of the father and that of the older son. How old is each of his sons? 5. A man bought three estates; for the first he gave $5260, for the second he gave $3585, and for the thii-d he gave as much as for the first two together. He afterwards sold tliem all for $15280. Did he gain or lose, and how mucli^ 6. James has 25 marbles; John has 32. The first time they played John won 7, but the next tinn; James won 13. How many marbles has each now? SUBTRACTION. 29 7. On a farm of 112 acres there are 14 acres in wheat, 15 acres in barley, 12 acres in oats, 17 acres in peas, 9 acres in hoed crop, and the rest in pasture and bush. Ilow many acres are in [»aHtur(» and bush? H. How many days are there from June 28th to September oth, inc'hisive? 9. James and Henry have together 45 marbles; Henry and John have togetiier 63 marbles; John and William have together HI marbles; William has 45 marbles. How many marbles has James? 10. In 1897 the population of Ontario was 1990977; in 1896 it was 1972286; in 1895 it was 1957390, and in 1894 it was 1936219. By how much did the population increase during 1894, 1895 and 1896 respectively? EXERCISE XXXIII. 1. From th(i difference between 17496 and 5378 take the sum of 4125 and 1247. 2. Simplify 2187+374—1763+9436—1479+8161—3948. 3. The sum of three numbers is 2897. One of these is 794, another is 497. Find the other. 4. What must be added to 1000000—6093 to give 3746918— 94786? 5. The sum of six numbers is 40917. Five of them are 4876, 9127, 4763, 8294, and 7328. What is the sixth number? (). What nuTuber added to the sum of 7089, 987, 3469, 58732, 29 and 4:536, will make one million? 7. What numl>er must be taken from the difference ]>etwe» n 3789 and 7968 to leave 1645? 8. What number added to 1271 will give the sum of 40370, .3684 and 30916? 9. From the sum of all the odd numbers l»etween 436 and 448 take the difference between 39476 and 38979. 10. The subtrahend is the sum of 784, 965, and 1894. The niinuend is the difference between 7689 and 19785. Find the remain ier. 11. The sum of four numbers is 45364. The first number is 5215, the second is 457 more than the first, and the third is 128 It'ss tlian the first and second together. Find the fourth UUnilKM'. 12. The remainder is 7894 after 9462 has been subtracted 7 times from a certain number. Find the uumJ»er. 80 ARITHMETIC. III. MULTIPLICATION. l\1ultiplication is the process of finding the sum of a number called the multiplieand, repeated as many times as inhere are units in another number called the multiplier. * The Mlultiplicand is the number to be multiplied. The IMultiplier is the number by which the multi- plicand is to be multiplied. It shows how often the multiplicand is to be repeated as an addend. The Product is the result of the multiplication. The multiplier and the multiplicand are called the Factors of the product. THE MULTIPUCATIOIN TABLE. Twice Three Four Five Six Seven times times times times times 1 is 2 1 is 3 1 is 4 1 is 5 1 is 6 1 is 7 2 . . 4 2 . . 6 2 . . 8 2 . . 10 . . 12 2 . . 14 3 . . 6 3 . . 9 3 . .12 3 . . 15 3 . . 18 3 . . 21 4 . . 8 4 . . 12 4 . . 16 4 . . 20 4 . . 24 4 . . 28 5 . . 10 5 . . 15 5 . .20 5 . . 25 5 . . 30 5 . . 35 6 . . 12 6 . .18 6 . .24 6 . . 30 6 . . 36 6 . . 42 7 . . 14 7 . .21 7 . . 28 7 . . 35 7 . . 42 7 . . 49 8 . . 16 8 . .24 8 . . 32 8 . . 40 8 . . 48 8 . . 56 9 . . 18 9 . . 27 9 . . 36 9 . . 45 9 . . 54 9 . . 63 10 . . 20 10 . .30 10 . .40 10 . . 50 10 . . 60 10 . . 70 11.. 22 11 . . 33 11 . . 44 11 . . .55 11 . . 66 11 .. 77 12 . . 24 12 . . 36 12 . .48 12 . . 60 12 . . 72 12 . . 84 Eight NMne Ten El«>ven Twelve times tiiiies times 1 is 10 times times 1 is 8 1 is 9 1 is 11 1 is 12 2 . . \G 2 . . 18 2 . . 20 i) »)>) 2 . . 24 3 . . 24 3 . . 27 3 . . 30 3 . . 33 3 . . 36 4 . . 32 4 . . 36 4 . . 40 4 . . 44 4 . . 48 5 . . 40 5 . . 45 5 . . 50 5 . . 55 5 . . 60 6 . . 48 6 . . 54 6 . , 60 6 . . 66 6 . . 72 7 . . 56 7 . . 63 7 . . 70 7 . . 77 7 . . 84 8 . . 64 8 . . 72 8 . . 80 8 . . 88 8 . . 96 9 . . 72 9 . . 81 9 . . 90 U . . 99 9 . . 108 10 . . 80 10 . . 90 10 . . 100 10 . . 110 10 . . 120 11 . . 88 U . . 99 11 . , no 11 . . 121 11 . . 132 12 . . 96 12 . . 108 12 . . 120 12 . . 132 12 . . 144 MULTIPLICATION. 81 the sum of 3(1 as many V called the multiplied. I the multi- »w often the id. plication . 3 called the Seven times 6 1 is 7 12 2 . 14 18 3 . 21 24 4 . 28 30 5 . . 35 36 6 . . 42 42 7 . . 49 48 8 . . 56 54 9 . . 63 60 10 . . 70 66 11 . . 77 72 12 . . 84 Twelve ♦ imes 1 is 12 o 24 3 . . 36 4 . . 48 5 . . 60 6 . . 72 7 . . 84 8 . . 96 9 . . 108 10 . . 120 11 . . 132 12 . . 144 1. 3040204 o 11. 5789645 EXERCISE XXXIV. 4302432 423042 340243 5 5 8950()94 5478946 4897649 5 3204302 o 974234 4963241 2 879716 2 9847456 7084567 2 3. 768064 2 578467 708096 2 598746 2 967865 4. 863428 2 768497 2 700608 2 367496 o 784967 2 5. a456454 3454645 4543456 6534356 3545464 3 3 3 3 3 6. 8768475 9647364 8769456 9484965 7899486 3 3 3 3 3 7. 3404134 4 634243 4 4137404 4 978649 4 1678343 4 6783437 4 8. 54:{7489 4 6789013 4 345987 4 4139764 4 9. 230456 5 5432061 5 3475264 5 2536472 5 1234567 5 10. 4597045 9682469 7893086 7080904 7684963 8647649 12. 3741064 34071064 3718643 41890701 4196804 6 6 (i 6 6 82 ARITHMETIC. EXERCISE XXXV. 1. 4375780 6 0892405 5080700 3(589427 () 784(5952 2. 7890905 () 4709(547 8490790 0894579 887799(5 a. 7450948 7 7045093 7 8450784 7 9009078 7 7084905 7 4. 245078 7 37425(54 7 5420034 7 4253042 7 700(5457 7 5. 4087900 4087054 3090874 4897054 9870543 7 7 7 7 7 6. 3042054 32400(55 4004503 2345035 4352073 8 8 8 8 8 7. 4794086 8887(55(5 9234507 7890543 0700809 8 8 8 8 8 8. 7684907 2503128 1536211 3306525 5010323 8 8 8 8 8 9. 1234505 5043204 2073465 4234507 5704507 9 9 9 9 9 10. 3004789 0478975 8090403 5408795 7864087 9 9 9 9 9 11. 1760689 5311695 3155093 1534091 5135491 9 9 9 9 9 12. 7689745 7000068 9506078 5078943 7684796 10 10 10 10 10 MULTIPLICATION. 33 EXERCISE XXXVI. 1. Multiply n7Sr)417H:{ hy 2, hy li, ».y 4, by f), by G, by 7. 2. Multiply 47H(JO():{U4 by 2, by :{, by 4, l>y '>, by (J, by 7. ;{. Multiply :{7S()41H:t4 by 2, by ;{, liy 4, l)y fi, by <5, by 7. 4. Multiply 4()H:{71«:{4 l»y 2, l>y ;}, by 4, l»y f), by (i, by 7. '.. Multij.ly HyiSO(»:;47 by 4, by 5, by 0, liy 7, by 8, by !). «>. Multiply ()()7S9019r) by 4, by f), by G, by 7, by 8, by 1). 7. Multiply H(i7H:{4071) by 5, by (5, by 7, by 8, l»y 9, by 10. H. Multiply G78:{418»5<) by .^), by 0, by 7, by 8, by !), by 10. J). Multiply 478:{780()r) by 5, by G, by 7, by 8, l»y 9, by 10. 10. Multij.ly 418:J4784G by 5, by G, by 7, by 8, by 9, by 10. EXERCISE XXXVII. What are the factors of 15? of "^1 ? of 28? of 42? of Uf)? 1. Multiply 4879 by the factors of 15, of 28, of 18, of 'A'k 2. Multij.ly 6785 by the factors of 14, of 18, of 25, of 42. :{. Multiply 708G by the factors of .•{2, of 3'J, of 42, of 49. 4. Multiply 9584 by the factors of 21, of 45, of 49, of 54. 5. Multiply 2539 by the factors of 24, of 25, of 3G, of 63. 6. Multiply 6407 by the factors of 32, of 45, of 54, of 72. 7. Multiply 7685 by the factors of 48, of 50, of 60, of 70. 8. Multiply 9685 by the factors of 70, of 80, of 90, of 100. 9. Multiply 7689 by the factors of 45, of 54, of 63, of 81. 10. Multiply 4875 by the factors of 30, of 40, of 50, of GO. EXERCISE XXXVIII. 1. Multiply 78546 by 21, by 31, by 41, by 51, by 71. 2. Multiply 68095 by 61, by 71, by 81, by 91, by 19. 3. Multiply 789G7 by 13, by 17, by 19, by 29, by 37. 4. Multiply 64758 by 78, by 87, by 95, by G4, by 59. 5. Multiply 47896 by 234, by 345, by 456, by 579. G. Multiply 97640 by 567, by 892, by 347, by 638. 7. Multiply 90070 by 325, by 257, by 689, by 976. 8. Multiply 76847 by 306, by 405, by 708, by 704. 9. Multiply 98764 by 4008, by 7006, by 5009, by 9040. 10. Multiply 87009 by 5090, by 7080, by 7096, by 9007. :h ARITHMETIC. EXERCISE XXXIX. 1. A train riiiiH L'~) iiiili-s iiii hour. How t':ir tlocs it run in 4H lionrH? 2. Mr. Brown luis I'WIG liorsen. Wluit uro lln-y worlii at ;{. How many ouncj-s are there in :{7U(»8 pounds, it' tln-re are IG ounces in one jtoundf 4. The earth in its annual journey around tiic sun moves altout (iKOOO miles an hour. J low far does it mov«f in a day, or 24 hours f [). Find the cost of 7H1)(5 ytirds of cotton at H cents a yard. G. In a ^rove there are 9 rows of trees and 7H trees in each row. How many trees are there in the f^rovef 7. How fai' can a iiorso travel in 'M'ui Incurs at tlic rate of 8 miles' an hour? 8. How many hills of corn are there in a litld containing 42(» rows, and 224 hills in a T-owi' 9. What will G5 miles of plunk -road cost at 2007 dollars per mile? 10. How many lemons are there in 24:5 boxes, each box containing 309 lemons? EXERCISE XL. 1. A merchant V)ought 1275 barrels of sugar of ,300 pounds each at 4 cents a pound. Find tlie cost of the sugar. 2. A merchant bought 27 bales of cloth, each bale eontaluing '}.1 pieces, and each piece containing iiG yards. How many yards were there in all? 3. How many nails will it take to shoe 74 horses, if there are 8 nails in each shoe? 4. How far will a train go in 87 days at 30 miles per hour? (1 day=24 hours). 5. How many inches are there in 475G yards, there being 3 feet in a yard and 12 inches in a foot? G. A man buys 4795 pounds of tea at 5 cents an ounce/ What did he pay for it? (10 ounces=l pound). 7. Find the cost of 78 bales of cotton, each bale containing 412 yards at 15 cents per yard. 8. Find the value of 68 farms of 120 acres, eacli at $25 per acre. 9. There are 60 minutes in an hour and 24 hours in a day. How many minutes are there in 3G5 days? 10. The Montreal Star hasa daily circulation of 146819 copies. How many papers will be sent out in G weeks of G days each? MI'I.TIPMCATIOK. 35 in it vm\ in y \vt)l'tll ut it' tlu'n< are SHU mONM'H ill ii day, or iits a yiu<l. vi-vH in •■acli lit' I'iitc of H I coiitainiiif^ 7 dollars per s, each box ' 300 pounds ar. e eoiitaraing How many I'si's, if there es Iter hour? Iliere being ts an ounce.* e containing •h at $2;') per urs in a day. 46819 copies. G days each? EXERCISE XLI. 1. Multiply tho suni of all the odd nuinin'is Itetwoen 'M niid 40 by the sum of all the evei numhers between ;{7 and 47. 2. A drover }>ought 475KJ eiittle at $4') each, and 4iM;{7r) sheep nt $5 each. How much more did the sheep cost than the cattle;' ;{. A farmer sold 'J."» cords of wood at $'A pi-rconl aii<l received in jtaynieiit four $'J0 bills. What change must lu* give liack/ 4. Kind the aujoimt of the following bill: — 14 pounds ri(M' nt, 4 cents a pound. 8 yards cotton nt 7 <'ents a yard. 19 spools thread at 4 cents a spool. 73 pounds sugar nt 5 cents n pound. r». A drovei- liough. 124 cows at $.")7 each, and 71) horses nt $90 ea<'h. How much more did the horses cost than the cows? (!. The drover sold the cows in last (piestion at a gain of $13 each, and the horses at a loss of $20 each. Did he gain or lose, and how much? 7. A merchant liought 473G turkeys in London at 75 cents each, aTui sent them to Montreal at a cost of 5 cents each. Here he sold them for $4730. How much did he gain on the transaction? 8. A merchant luid 793 yards of cloth. He sold 120 yards to one nuin and 304 yards to another. What is the remainder worth at 8 cents a yard? 9. Two persons start from the same point, and travel in oj)))osite di ections. One travels 29 miles a day, and the other 32 miles a day. How far apart will they be in 17 days? 10. A drover bought 127 head of cattle at $34 a head, niul 97 head at $47 a head, and sold the whole lot at $40 a head. What was his entire profit or loss? EXERCISE XLII. 1. The two factors of a certain nundjer are 428 and 403. What is the number? 2. The three factors of a certain number are 187, 29, and 43. What is the number? 3. Find the continued product of 11, 13, 17, 19, and 23. 4. One of the three equal factors of a number is 407. Find the numl»er. 5. The multiplicand is 40009 and the multiplier is the number whose ructors a " .">, 7, and 11. Find the product. 86 ARITIIMKTir. <5. Tho multiplicand is th« UiflTi'n'uco iM'twcM-n one million iumI ono thou8)in(l and one. Th«> nniltiplier in tliu Huui of 407, 70'J, and U(>:i. Find l\u> product. 7. TliH difference between two numl>ers i^^tlle product <)f 4',)7 and .'iOf). The Hirniller of the two nuinbei-H Ih lUOlOO. Multiply tho lar^^er number l>y .')0()0. H. The ditTerence between two numbers iH.^)0()7. The >.'r(«ater number is thu product of 70(1.') and UOOM. Find vh:: smaller number. y. How much must be taken from the product of .^>07 and 7i{r> to ^et tho product (tf r>()7 and iVAiif 10. From the Hum of •)r>XH7 antl 7«>XJ>S, take the ditTerence between 78X87 and 97X8.'). EXERCISE XLIII. 1. Multiply the sum of I'JOG and 7ri7{) by their difference. 12. How nnieh is the product of 579 and 758 greater than the product of 577 and 758* ;{. Multiply together all the uumbers that end in IJ, 5, 7, or 9, between 12 and 20. 4. Multiply the greatest number that can be expressed by four figures by the greatest one expressed by three figures. 5. From the product of 9009 and 7007, take the product of 7090 and 7909. 6. If Mr. Brown owns 3 houses, the first worth $2783, the second 3 times, and the thiil 7 times as much as the first, what are the 3 houses together worth? 7. A drover bought a drove of 33 oxen, paying as many dollars for each ox as there were oxen in the drove. He paid $514.85, and gave his note for the balance. For how much does he give his note? 8. The area of Ireland is 32535 square miles, and 5096490 acres are cultivated. How nuiny acres are uncultivated, there being 640 acres in a square mile? 9. A field of oats has 19 rows of stooks ; each row has 37 stooks in it, and there are 12 sheaves in a stook. How many stooks are in the field? How many sheaves? 10. The sum of 4 numbers is 20000; three of them are 4785, 5769, and 2807. Multiply the sum of the greatest and least by the sum of the other t"'c. DIVISION. 37 II g as many e. He paid w much does and 5096490 ivated, there 1 row has 37 How many em are 4785, and least by IV. DIVISION. Division is t]i<» pnxM'ss ]»y which, \vh«'ii th«' itroduct mid out' fnrfor an- ^iv«'ii, thf ofin r farfor is t'ouiid. The Dividend, tiic j^ivm pnMlm't, is Mic iimiilHT to Im' divided. Tiie Divisor, the pivcMi fjictor, is th«' nutidMM- hy which the <livideiid is to l)e divi(h*d. The Quotient, the faetor to be found, is tlie result of Ihe division. The Remainder is wlmt is over wlien tlie dividend does not contain the divisor an e.xaet number of times. Thus, The Dividend is ecjual to the proihict of the Pirisor and Qnotii nl, increased l»y the RemnimUr. Tlie sij.ii of Division, written — , shows that the number )re('edinj^ it is to be divided by the nund)er foHovviii}^ it. EXERCISE XLIV. NoTK. — It is recommended that this exercise ]»e worked by the Long Division plan. 1. «> 3. 4. 5. (i. 7. H. 9. 'J4— 2 4(58—2 9(53—3 484-4 r)85-7-5 (518— (5 749—7 9(58-8 819—9 10. 4r)(i8— 8 3. 2)428042 2. 2)157996 3. 3)3960(59 4. 4)534768 5. 5)1847(50 40-2 472-2 699—3 568—4 (535—5 3(5(5—6 847—7 H40— 8 918—9 7389—9 96—2 836—2 (587—3 730—4 205—5 480-6 574-7 928—8 729-9 5243—7 EXERCISE XLV. 2)208462 2)242680 2)135794 3)156945 4)784724 5)501035 2)351792 3)40:?716 4)813492 5)741800 2)424820 2)537958 3)804957 4)674508 5)357185 84—2 946^2 87(5^3 624-^4 745^5 9(50-0 945-7 728—8 360-^9 2709^9 2)462860 2)315970 3)745683 4)562732 5)9276.50 38 AniTIIMRTlO. «;. (i)»;s47r»(! 7. 7)7\4HV2 H. H) 728128 !». y)'Ji47:M 1(1. 8)810L'48 (!)()rj:}4'j 7)!Mr)707 8)!(14(i4() !tj8:t4r)(n u)Do;{(ir)4 ())H417r)2 7)r)847(i(i 8)8iM:j»;o !»)47r):!()2 i>) 748r):5«j EXERCISE XLVI. ())9;n47(; 7):{214()l 8)7412;i2 !»)<)8478;{ 7)i2:{4r)U (5)700002 7)(i;no4:{ 8)i48r.:5(; ;i)r>48:}7!> 7)y:j47(5o 1. Divide 2. Divido :{. Divido 4. Divide il. Divide (5. Divido 7. Divide 8. Divide <J. Divide 10. Divido 4178():J4 ()7();{40() 40(i78()7 G78:5S()7 41(5708() 4078(iO:{ 3070(542 3070412 4012(578 3070804 by 2, by ',], by 4, l)y f), by 2, by 3, by 4, by .^), ]>y 2, by 3, by 4, by .'), by 2, by 3, by 4, by f), by 3, by 4, by 5, by (5, by 3, ])y 4, by 5, by G, l>y '5, l»y 4, by 5, by G, }»y 4, by f), by G, by 7, by 4, i»y 5, by G, by 7, by 4, by 5, by 6, by 7, i»y <», I'y 7, by 8. I'y <i, I'y 7, by 8. i»y <i, by 7, by 8. I'y 0, by 7, by 8. I'y 7, '•yH, hy !). i'y7, i»y8, v>y 9. i>y7, by 8, by 9. I'ys, by 5), by 10. i'y«, by 9, by 10. by 8, by 9, by 10. *^i EXERCISE XLVII. 1. At $;i ]H'r ynrd, iiow niaiiy y.ards of silk onn be Iton^lit I'oi' $48? For $84? 'For $132? For $2(M? 2. Divide $968 eciuully iiniong 8 persons. 3. If I buy 12 horses for $900, liow much will one horse cost? 4. If flour costs $8 a barrel, how many barrels can be bought for $2(532 f 5. A grocer packed 994 pounds of butter in 7 tubs of equal size. How many pounds did he put into each tub? 6. Seven bales of cotton weighed 3(508 pounds. What was the average weight per luile? 7. If 5 carloads of iron weigh 7532;) i)ounds, what would be the avera,ji' weight of one carload? 8. In 1 i-oek there are 8 quarts. How many pecks are there in 4250 quarts? 9. A ship worth $38125 was owned in ecjual shares by 5 men. Find the share of each. 10. At six dollars a ton, how many tons of coal can be bought for $2274 ? DIVISION. 30 EXEKCISE XLVIII. 1. A Hliip sailed across the Atlantic Oceaii, a distance of 'JHHO miles ill days. J low far did it sail each day? L*. In one mile there are r)280 feet. How many yards are there in a mile, there bein<^ '.I feet in one yardf ;{. The wages of 8 men for one week were 104 dollars. How much did each earn per week? 4. How long will a bicycle rider who goes at the rate of U miles pel' houi- take in going 117 miles? .'). Find the price of a dozen oranges at two for five cents. (5. A drover bought 11 head of cattle for 352 dollars. What was the price per head? 7. An excursion train consisted of five passenger cars and carried -8") persons. What was tlie average number of pas- sengers in a car? 8. If a locomotive runs 289(5 miles in 8 days, what is the average run per day? 9. The sun is 9;{000000 miles from tlm earth. Light travels tills distance in about 8 minutes. What is the velocity of light? 10. Four farthings make a penny. How many pence are there in 22008 farthings? i •e bought for EXERCISE XLIX. 1. Divide 022,14 by 51, by 01, by 71, by 81, by 91. 2. Divide 17253 by 31, by 41, by 71, by 81, by 91. :j. Divide 127551 by 41, by 51, by 01, by 81, by 101. 4. Divide 105243 Vjy 01, by 71, by 81, by 91, by 301. 5. Divide 594130 by 401, by 801, by 901, by 500, by 704. 0. Divide 471582 by 301, by 501, by 201, by 007, by 809. 7. Divide 095847 by 611, by 721, by 821, by 541, by 441. 8. Divide 437650 by 531, by 651, by 751, by 654, by 885. 9. Divide 904375 by 825, by 925, by 795, by 333, by 555. 10. Divide 704578 by 972, by 492, by 954, by 870, by 385. EXERCISE L. 1. Divide 987C54 by 912, by 922, by 934, by 975, by 942. 2. Divide 785469 by 845, by 876, by 889, by 892, by 875. 3. Divide 870549 by 777, by 78^^ by 795, by 799, by 789. 4. Divide 987054 by 078, by 089, by 695, by 699, by 697. 40 ARITHMETIC. r». Dividf 7Sr)9()7 by 508, by nST, by ')[)(]. by HSO, by .lOS. (). Divide 7»)()(W() by 485, l)y 490, })y 491, by 478, by 497. 7. Divide 87()497 by :507, by :{78, by :W9, by :J99, by ;590. H. Divide 700000 by 285, by 290, by 278, by 294, by 289. 9. Divide 1000000 by 49, by iW, by 29, by 17, by 19, by :i7. 10. Divide 12:54507 by i:{, by 17, by 18, by 19, by 29, by :{9. EXERCISE LI. 1. Divide 17:J255 by the factors of 15; of 18; of 21; of 25. l> Divide 87045C by tiie factors of 24; of 30; of 30; of 42. 3. Divide 954708 by the factors of 45; of .54 ; of 50; of 03. 4. Divide 743045 by the factors of 25; of 32; of 30; of 40. 5. Divide 875976 by the factors of 32; of 35; of 42; of 54. C. Divide 900007 by the factors of 30; of 42 ; of 72; of 81. 7. Divide 397486 by the factors of 30 ; of 40; of 50; of 60. 8. Divide 780978 by the factors of 00 ; of 70; of 80; of 90. 9. Divide 987641 by the factors of 100; of 200; of 300 ; of 400 10. Divide 987685 by the factors of 500 ; of 600 ; of 700 of 800 EXERCISE Lll. 1. Divide 470880 by 6 times 12. 2. Divide 337103025 by 861. 3. How often is 77 contained in 37704821? 4. Divide 7364063 by 7 times 7. 5. Divide 888888 by the continued product of 3, 7, 8, and 11. 6. By what number must 129546 be divided that the quotient may be'27f 7. Divide the continued product of 12, 5, 183, 18 and 70 by ttie continued product of 3, 14, 9, 5, 20, and 6. 8. The product of two numbers is 2177280; one of them is the continued product of all the even numbers between 5 and 13. Find the other number. 9. What number besides 7087 will exactly divide 68070635? 10. When a certain number is divided by 478, the remainder is 205 and the quotient the same as the divisor. Find the dividend. EXERCISE Llll. 1. The distance from Montreal to Vancouver is 2948 miles. How long will it take a man to walk the distance at 22 miles per day? .f busl DIVISION. 41 ^ i>y r.98. s, I'y 497. 9, by :{9(). 4, by 2S9. y 19, by -M. y 29, by :59. f 21; of 2r). f :ui; of 42. E r)() ; of g:{. f :u> ; of 40. )f 4l>; of M. )f 72; of 81. )f 50; of GO. )f 80; of 90. of 300 ; of 400 ^t 700 ; of 800 , 7, 8, and 11. M ,t the quotient •1 18 and 70 l)y 1 ne of them in etween 5 and g ie cmiomr^ ? :'** the remainder or. Find the :S is 2948 miles. ?e at 22 miles •1 2. If $.^40^)l is equally divided among 17 men, what sum will each receive? ;{. A miie contains G.'WfiO inclies. How many steps of 24 inches each will a boy take in walking a mile? 4. How many pounds of 16 ounces each are there in 473G48 ounces? 5. A man paid $ir)i;i4 for cf«ttle at $23 each. How many head did he i)uy? 0. Tn 42 acres there are 6720 square rods. How many square rods are there in one acre ? 7. If a steamship sails 1144.5 miles in 35 days, what is the average speed per day f 8. The area of a country is 8315 square miles, and the population is 2286625. How many people are there to each Sipiiire mile? 9. If 2800 sacks of coffee weigh 470400 jjounds, what is the average weight i)er sack? 10. If 1 man can finish a work in 261 days, how long would 29 men recjuire to do the work? EXERCISE LIV. 1. There are 320 rods in a mile. How many miles are there in 572K0 rods? 2. There are 3() inches in a yard. How many yards are tiiere in 34S9624 Inches? 3. How many miles are tliere in 33440 yards, there being 1760 yards in one mile? 4. There are 48 j)otinds in a bushel of barley. How many bushels are there in a load of barley of .3072 pounds? 5. A farmer l»rought 30(50 ])Ounds of jmtatoes to market. How many Itushels had he, there being (50 pounds in each bushel of potatoes? 6. In a bin of oats there are 8330 i>ounds. How many l)usliels ar«^ there in the bin, there being 34 pounds in eneh bushel of oats? 7. ^'liere are 160 acres of land in a nuarter Rection. How many quarter sections are there in a township containing 23040 acres? 8. A cubic yard contains 27 cubic feet. How many cubic yards are there in a heap of earth containing 2025 cubic feet ? 9. There are 196 pounds in a barrel of flour. How many barrels are there in 40572 poutids of flour? 10. A pile of wood contains 90112 cubic feet. How many cords p,re there In It, there being 128 cubic feet in one cord of woodf 42 AHITHMKTIC EXERCISE LV. 1. How many times can 7H })o taken fiom tlio <'ontinued product of i:{X 7X1012* 2. Find the sum of all the numbers between 90 and ISO that are exactly divisible by llj. ;i. Divide the sum of 4077, ;59(), and 8745)1, })y the diff<'rence between (i;{84 and 7492. 4. Find the value of :{()984X 2739(5^761. 5. What is the true remainder when 69472') is divided by the factors of 10;')? (). Hew often can you take the sum of the even numbers between 241 and 253 from forty thousand and fourteen. 7. If 213X84X190X264 be divided })y 30X56X36, what will the quotient be? 8. When 82965;j is divided by 1022, the remainder is 811. What is the quotient? 9. Divide 41579 by the factors of 42, and find the true remainder. 10. The quotient of one number by another is 74; tlie divisor is 321, and the remainder is 95. Whatjs the dividend? EXERCISE LVI. 1. The divisor is 77; the quotient is 97; there is no remainder. Find the dividend. 2. The dividend is 632; the quotient is 27; the remainder is 11. What is the divisor? 3. The 'divisor and quotient are equal to each other, each bein<^ 794 and the remainder is the largest possible. Find the dividend. 4. The divisor is 801 ; the quotient is 403, and the remainder the largest ]»ossible. Find the dividend. 5. The divisor is the difference between 204 and 2^58; the quotient is their sum, and the remainder is the largest ]>ossible. Find the dividend. 6. Find the least numl»er which must be added to 17634 to make it exactly divisilde by 236. 7. What number besides 364 will exactly divide 89180? 8. Of wiiat number is ;}45 Itotli divisor and (puttient? 9. When 169 is added to the dividend it is exactly divisible by 7H5, the (piotient being 978. Find the dividend. 10. Find the smallest number which, subti'ucted from 78654, will make it exactly divisible by 458. th( MIS(!KLI-.\NKOlS KXKK(MSES. 43 livided by tlio the reniiiiiHler 'a\ to 17634 to V. IV1ISCELLAINE0US EXERCISES. EXERCISE LVII. 1. Tlie i)laypfround is 93 steps lonp and 47 wide. How many Hteps >\ill a boy take in iio'xu^ around it tliree times? 2. From 479'JO take 3H1219, and to the result add 4901 > 3. Simj.lifv 4K7 + 19(5+ 14732 — 1984 — 4756 + 1734— 1S96 + 4111412—1739648. 4. Find thevahieof 761+276—849+98—121—317+963+438. 5. Multiply 68754 by 6 and by 8, and add the products. 6. Multiply 59846 l>y 1))8 and by 105, and subtract the products. 7. In a mile there are 1760 yards. How many inches are there in 4 miles? (12 inches=l foot; 3 feet=l yard). 8. Multiply 500302 by 40102. 9. Divide 275264 by 736, and multiply 45697^ by 78, and sul>traet one result from the other. 10. Find the amount of the following bill: 473 yards cotton at 7c. a yard. 916 pounds tea at 40c. a pound. 19 pounds raisins at lie. a pound. EXERCISE LVIII. 1. Multiply seventeen thotisand nine hundred .ind forty- three l»y 5079^ 2. A ])erson earned $85 a month and spent $2 a day. How nnich did he save in 1896? 3. A numl)er divided by 243 gives 4713 for quotient and 89 for remainder. Find the number. 4. How manv times is the i)roduct of 75 and 109 contained in the sum of 2063014, 17005000, 469, 30214707, and 3885? 5. Find a number which multiplied by 369 will give the same iiroduct as 615X18;{57. 6. Wliiit number multiplied bv 86 will give the same i»roduct as 163X430. 7. Find the quotient when the i»roduct of 86947 :ind 248 is divided by 217. 8. A man Itought 52 liors»'s at .t75 each, and 214 jiigs at $\\ each. How mucli more tiiiin +()000 did all cost.' 9. The divisor is 473(5, the (|U(»tient 299, and the remainder the largest number ]>ossible. Whiit is t!ie dividend? 10. A grocer bought 16 cheese each weighing 70 jtounds for 10080 cents, and «old it at 11 cents a pound, How much did he gain? 44 ARITHMETIC. EXERCISE LIX. 1. A carpoiiter ♦■iiftaf^es 4 men nc $2 each por day. flow much will they earn in 7 weeks? 2. JV farmer owes his grocer 2640 cents; he gives in jtayment 147 pounds of butter. What is the butter valued at per lb, ;{. "A drover sold 495 sheep and 27;') laml)s for .fIJiJOO; he received $y apiece for the lamba. How much did he get for each sheep f 4. A man bought ducks at 47 cents each and sold them at 100 cents a pair. What did he pay for the ducks which he sold for 2800 cents? f). A man bought 5 pounds nails at 4c. a pound; ') gallons of oil at 1(5 cents per gallon; a stove for $l~) and an ixe for .$2. How much change will he get out of a $20 bill? (). A man bouglit a horse for $7') and :hen exchanged it for [) slieep and $G2. If a sheep is worth $7 Hnd his gain? 7. If I give $78;}0 for 90 head of cattle and sell them at $H)') ejich. How much is the gain? 8. A farmer sold 97 cattle at $65 each, and with the money l)ought sheep at $i;j each. How many did he buy? 9. What numl>er divided by 3008 gives 3875 for <iuotient and 1397 for remainder? 10. A man earns $75 a month and spends $50 a month, how long will it take liim to pay for 60 acres at $40 an acre? EXERCISE LX. 1. A certain number was divided by the factors of 35; the qtiotient was 72, the first remainder 2 and the last remainder (i. What is the number? 2. I bought 28 barrels of sugar, each weighii\g 310 pounds net, at 1200c. a barrel and sold it at 6c. ajtound. Find the gain? 3. Two i»ieces of cloth of e(|ual length cost 5()00c. and 7600('. respectively; the first piece cost 70 cents a yard, find the price per yard of the second piece? 4. What is the least number that nmst bo added to 10000000 to make the sum exactly divisible by 653? 5. A number was divided by the factors of 77, the quotient was 137, the first remainder 9, the second 6. What is the dividend ? 6. A farmer exchanged 162 Inishels of wheat at 160c. per bushel for 27 barrels of flour. What was the value of fiour ;^er barrel ? '. A grocer bought 126 pounds of tea at 68c. a ])ound. Ho kept 18 pounds and sold the rest at 80 cents a pound How much move money did he receive than Ue paid out? MISCELLANEOUS EXERCISES. 46 8. A frciith'HiMn s]>«'iit durinp: tlu' yonr IHIK} ^\{) n day mid laid away ^KK) a nioiitli. Wliat was his inconicf J). Find a nimilM'r s'lcli that it' it U' added L':5 tiiius to :;7<)(ll ill.- siiiii will Ik- 4(Hi(K». Id. The itrodtu't of two imniltcrH is l'J7«);{74 and lialf of one of tlu'U) is ;J1L"J. What is the other? i month, how EXERCISE LXI. 1. If 2 oranfict'*^ ^'^^^ ^' cents, find the oost of 9 oranges. L*. If 9 pounds of riee cost 36 cents, what will 4 pounds of rice cost? ;{. If John walk 27 miles in 9 hours, at the same rate how far will he walk in seven hours* 4. If 12 yards of cloth cost $.'30, find the cost of 17 yards of the same kind of cloth. ;'). If 17 tons of coal cost $102, find the cost of 25 tons. 0. If $40 laiy 20 yards of cloth, how many yards can be bought for $00? 7. If ir)0 yards of cloth are required to make 15 dresses, how many dresses can be made from 210 yards? 8. If 17 men can husk 1088 bushels of corn a day, how many bushels can 27 men husk in the same time? 9. If a train goes 21G miles in 8 hours, how long will it take to go 297 miles at the same rate? 10. If 2800 sacks of coffee weigh 470400 pounds, what will be the weight of U^oO sacks? d to 10000000 EXERCISE LXII. 1. If 7 men can do a piece of work in 9 days, in how many days can 3 men do the same work ? 2. Ten men can finish a piece of work in 57 days; how long will it take 6 men to do it? 3. If 12 men can build a wall in 30 days, how long will it take 18 men to do it? 4. If a garrison of 150 men have provisions for 45 days, how long will they last 250 men? 5. How long will it require 20 horses to do the work of 24 horses for 15 days? (]. If 25 men can do a piece of work in 9 days, how many men will be required to do it in 15 days? 7. If a drain is dug by 36 men in 100 days, how many men would be required to dig it in 80 days? 46 AKITHMKTIC. S. A i»i»*«'«' of work was to h:ivo Iku-ti ]>«'i'forin(Ml ])y (!0 men in 4") days, but a iiuiuh*'!' worn MiHcliar^^fil and so tin* work lasted 50 days. How many were discliarj;ed? 9. A fyarrison of 1200 men had provisions to last 4 months, but in a battle a number were killed and the i)rovisions lasted the remainder 5 months. How many were killed If 10. If 25 men can do a pieee of work in li6 days, how many men will be required to do '.i timen as much work in 12 days? EXERCISE LXIII. 1 . Divide 36 marbles between two boys so that one may have 4 more than the other. 2. Two boys together liave 50 marl»les and one has ten more than the other. How many has eachf '.i. Two loads of wheat toj^ether contain 85 V)ushols and one has 7 bushels more than the other. How many busliels are there in eaeh load? 4. Two pieces of cloth tojsjether contain 100 yards; one of the pieces is 16 yards longer tlum the other. How long is each? 5. There are 94 examples in two exei'cises. There are 6 more in one than in the other. How many are there in each exercise? 6. The sum of the ages of two boys is 27 years, and one is 3 years older than the other. How old is each? 7. In a game of cricket two boys together made 47 runs. One made 9 more than the other. How many did each make ? 8. At an election 240 persons voted. There were two candidates and the successful one beat his opponent by 18 votes. How many votes did each receive? 9. In two journeys a bicycle rider rode 157 miles. He rode 23 miles farther the second journey than the first. How far did he go on each journey? 10. Two skaters race for an hour round a circular course. The sum of the number of circuits made is 387. The winner beats his opponent by exactly 3 rounds. How often did each go round the course? EXERCISE LXIV. 1. A number when divided by 5 gives 3 for remainder, and when the quotient is divided by 7 the new quotient is 241 and the remainder is 4. Find the number. 2. The remainder after division is 97; the quotient is 342, and the divisor is 91+97+342. Find the dividend. MISCELLANEOUS EXERCISES. 47 ne may have las tt'n more :}. A drover houglit I'J7 (-attic at .$.")(» each, and 93 more at $45 each. He lost 1 of tlu* first lot and 'J of the second, and sold all the r»«Ht at $(5;') euch. Find his f?ain. 4. A train starts from Toronto for C^ucIk'c, HIG miles away, at 2li miles per hour. At the same time another starts from (Quebec for Toronto at 21 miles per hour. How far from Toronto will they meet? 5. A man earns $1180 per year. He spends $348 during the year. How much does he save per week if 52 weeks make a year? G. A newsboy buys 120 papers at 2 cents each and sells them all at 2 for 8 cents. How much dees he gain? 7. A wagon loaded with coal weighs 2612 pounds. The wagon alone weighs 1112 pounds. If the load is woi-th 450 cents, what will be the cost of a ton of 2000 pounds? 8. In a stack of hay there are 23G88 pounds. A buys it at !j<15 per load of 2632 pounds. How much is the stack worth? 9. Multiply the greatest of the following numbers by the least, and divide the product by the other number: 324, 510, 108. 10. A merchant was in business 17 years. He gained $2240 a year during the first G years and $3036 a year afterwards. What was his whole gain? otient is 342, EXERCISE LXV. 1. From the sum of 47916, 842, 4983 and 1714, take 47168; multiply tho remainder by 184, and divide the result by 46. 2. If 75 bushels of wheat cost 6375e., for how much must 1 sell 63 bushels to gain 252c. on what is sold? 3. A grocer gave 153 barrels of flour at 900e. a barrel for 81 barrels of sugar of 170 pounds each. What did sugar cost per pound ? 4. The product of three numbers is 7650, and the product of two of them is 450. What is the other number? 5. A man gave 50 geese and 35 turkeys for 55 bushels of wheat at 100c. a bushel. If turkeys are worth 90e. each, what are geese worth? G. If 65 bushels of wheat cost 8450c., what should 195 bushels cost, when the price has fallen 20c. a bushel? 7. A grocer pays 20864c. for syrup at 128c. per gallon. Some leaks out, and the rest is sold for 25920c. at 180c. per gallon. How many gallons leaked out? 8. A drover bought 68 cattle at $47 each. He sold half of them at $54 each and the rest at $45 each. How much did he gain? liBulB 48 ARITHMETIC. 9. A nncrcliiuit l»<>ii^,'lit 4S yards clotli iit 02 cvuU a yanl nnd 81 yiinis iit 7">c. a yanl. Ho s«>M tlio first lot at Sic a yaid and tlif latt«'r at HiU-. a yard. Fiiul his total j^aiii. Id. If 1!> liorst'H aii*l 'JS cows are worth .tl.M'_':», and 1 I horses are worth pj'.i'>, lind tin? value of lil cows. EXERCISE LXVI. 1. How many fj-eent pieces are there in IToc-fllOc-j-lOle. +2()r)e.? 2. How many luilf-dollar pieces are there in 1710c. +2940c. +1 5250.+ 1775c.? 3. How much greater is IS times $1054 tlian 9 times $3307? 4. A person Itonj^ht a inimber of cows at ^'<iS each and as many liorses at $90 each. He paid $2814 for all. How many of each did ho btiy? 5. If 120 feet of lumber cost 240c., what will 900 feet cost? 0. If 17 tons of hay cost $204, liow many stacks of liay, each containing 9 tons, can be bought for $1 1H8? 7. A merchant bought 07 i>ieees of cloth of 94 yards each at 240c. a yard. He sold it all at 288c. a yard. How much did ho gain? 8. A farmer bought land at $49 per acre and an equal quantity at $78 per acre. He paid altogether $31750. How many acres did he buy? 9. If 17 yards of silk cost 5100c.. how many bushels of potatoes at 55 cents a bushel must be given for 11 yards of silk? 10. If 5 hats cost as much as 9 pairs of gloves, and one pair of gloves cost 125c., how many hats can be bought for 3825c.? EXERCISE LXVil. 1. A man bought wheat at 47 cents a bushel and sold it at 50 cents a bushel. He gained 327045c. How many bushels did he buy? 2. A merchant bought 13 bales of cloth of 27 pieces each, and each piece contained 34 yards. What is it worth at 17 cents a yard? 3. A moulder has 17385 pounds of metal. Find the least number of pounds he must buy in order to mould cannon balls weighing 08 pounds each and use all the metal. 4. A jeweller sold 15 clocks and 22 watches. For the clocks he got $12 each, and for a watch 7 times as much as for a clock. How much did he get for all? 5. A man bought 103 barrels flour at $9 a barrel; 15 barrels were spoiled, and the rest sold at $11 a barrel. Did he gain or lose, and how much? MISf'KLLANKors KXKKC'ISKR. 49 I II liorm'rt fi. Tf 4 Ituslicls (if wlifiit of (!0 ])nini(ls ciM-li will iiiiiko 1 hnncl (if ll(»tir, how iniiiiy itoiiiids of wheat will he nMiuiri'd for 1(50 barrels of flour? 7. I borrowed from A OaSfic. ; from B, 40:510.; from (\ 101 HHe., and from J), DOHc. 1 paid E u debt of 197580. How much had I leftf 8. I ])ou{;ht :J24 i)onv.,ls of tea for LU.'JOOc. If I sold it at an ndvaneo of 15 eeiils a pound, what was my whole gain and my Belling ]»ri(*e j>er ]»oun(ll' 9. How mueh tea at 46 cents a pound must be given in cxelmnge for 18 gallons of maple synip at 92 eents a gallon? 10. What number multiplied by 79 will give the same product as 1279 multiplied by 55.'{? EXERCISE LXVIII. 1. In a division question the divisor is 8 times nnd tho quotient is 7 times the remainder. What is the dividend, tke renuiinder being 1()8? 2. It two steamers leave Quebec for Liverpool at the same tinie, one going 18 miles and the other 14 miles an hour, how fur will the first be ahead of the second in 37 hours? ;{. By selling 31 horses for $3100 I lose $155. For what should I sell 16 horses to gain $597? 4. If 59 articles cost 4307c., for how much must 23 of them be sold to gain 183c. on those sold? 5. A drover bought 84 horses for $11424. He sold them at $108 each. Find his gain. 0. Two equal sums were divided, the one among 9 men, the other among a number of boys. Each man received 300c. and each boy 18e. How many boys were there? 7. The salary of the President of the Fiiited States is $.50000 a year. What sura may he expend each year, and yet save $75584 in 4 years, his term of office? 8. A man bought a farm for $3012. He sold half of it at $50 an acre for $2408. How many acres did he buy and what dM he give per acre? 9. Two men had an equal interest in a herd of cattle. One took 72 at $35 apiece and the other took the rest at $42 apiece. How many cattle were there in the herd? 10. A man travels due north for 7 days at the rate of 37 miles a day. He then returns on his path at the rate of 29 miles a d;iy. How far is he from the starting-point at the end of 12 days' travel? CHAPTER III. COMPOUND INtlVIBERS. I. TABLES, DEFIINITIOINS, AIND REDUCTION. A Simple quantity is one expressed in terms of a single unit, as 4 yards, 5 miles, 16 onnees. A Compound quantity is one expressed in terms of more tlian one unit, as 4 yards 2 feet. Reduction is the proifess of (Oianjjing the unit or denomination of a simpki or eompound quantity without changing tlie value of the quantity. Reduction Descending is the i>roeess of ehang- ing a quantity from units of a higher denomination to those of a lower denomination. Reduction Ascending is the process of changing a quantity from units of a lower denomination to those of a higher denomination. Canadian Money. 100 pentH (ct.) = l dollar, or $1. Ten Mills make one cent. The mill is not coined. EXERCISE LXIX. Reduce the following to cents: — 1. 7 dollars 25 cents; 4 dollars Scents; 5 dollars and 5 cents. 2. 30 dollars 4 cents; 100 dollars 90 cents; 3000 dollars. 3. $7.0(5; $10.45; $80.07; $100.90; $27.05; $404.04. 4. $100.01; $1000; $101.81; $1000.01; $70007.70. 5. $371.75; $575.49; $6184.72; $378.84; $907.09. Reduce the following to dollars or to dollars and cents: — 6. 700 cents. 7. 1001 cents. 8. 27010 cents. 9. 97000 cents. 10. 470S41 cents. 3084 cents. 57648 cents. 47006 cents. 2000007 cents. 1010101 cents. 50 44968 cents. 10000 cents. 7400007 cents. 4710071 cents. 20600609 cents. TAHI.KS, DKKINITIONH, ANI> RKDUCTION. 61 StcrMnfl, or English (Money. 4 farthingH (fiir.) = l penny, or Id. 12 pence =1 shilling, or 1h. 20 shillingH =1 pound, or £1, 21 Hhillings =1 guinea. A farthing is written Jd. ; two fartliings, M. EXERCISE LXX. Hodiire to farthings: — 1. Hd.; 124d.; 375d.; 451d. ; 784d.; 1960d.; 7000d. Kedn('(« to pence: — 2. OS.; 71s.; lOOs. ; 241s.; 3C9s. ; 2978.; 9000s. Hcduce to shillings: — ;{. C7; i:i7; €90; £419; £48 178.; £100 12s. Keduce to farthings: — 4. 58. Gd.; 88. 4d. ; lOs. fid.; 12s. 3 far.; 19s. 9d. ; £10. T). CO 10s. ; £4 18s. ; £7 8d. ; £5 l.'Js. lOd. ; £50 lOs. 5id. licduoe to pence: — <). 30 far. ; 720 far. ; 425 fur. ; 900 far. ; 1000 far. ; 2700 far. Reduce to shillings: — 7. 80d.; 168d.; 37r«d. ; 1805d. j 17G89d.; SOOOd. Reduce to pounds: — 8. 80s. 764s. 1879s. 4.567s. 9. 768d. 3689d. 7416d. 87651 d. 10. 3084 far. 7689 far. 45672 far. 78947 far. Avoirdupois Weight. 16 ounces (oz.) =1 pound, or 1 lb. 100 pounds =1 cental, or hundredweight, or 1 ewt. 20 hundredweight=l ton, or 1 t. 7000 grains (gr. ) =1 pound avoirdupois. 437A grains =1 oz. avoirdupois. 14 lb. =1 stone. Avoirdupois weight is used for weighing all articles, except the ]»reeious metals, jewels, and medicines when dispensed. In Great Britain 2240 lb. make a ton, called the long ton. sSassfaK: iiBMi 52 ARITHMETIC. Troy Weight. 24 fcrains (gr.) =^1 pennyweight, or 1 dwt. 20 penny\veight8= 1 ounce, or 1 oz. Troy. 12 ounces =1 pound, or 1 lb. Troy. 480 grains =1 oz. Troy. 57G0 grninfj =1 pound Troy. Troy weight is used for weighing the precious metals, gold, silver, and platinum. Apothecaries* Weight. 20 grains (gr.) = l scruple, or 1 ^ _ 3 scruples =1 drair, or 1 3 8 drams =1 ouncu, orl ^^ 12 ounces =1 T>ound, or 1 Bb. Apothecaries' weight is used in compounding medical prescriptions. Long, or Linear Measure. 12 inches (in.) = l foot, or 1 ft. 3 feet =1 yard, or 1 yd. 5 J yards =1 rod, or 1 rd. 320 rods =1 mile, or 1 mi. mi. =320 rd.=1760 yd. --=5280 ft,^80 cfiains. A huTid, used in measuring horses, --4 in. A knot, used in navigation, =6086 ft. A fathom, used in measuring depth at sea, =6 ft. Gunter's Chain, used in measuring land, = 100 links. 1 chain=4 rd.=22 yd. =66 ft. =792 in. Square, or Surface Measure. 144 square inches (sq. in.) = l square foot, or 1 sq. ft. 9 square feet =1 square yard, or 1 sq. yd. 30i square yards =1 square rod, or 1 sq. rd. 160 square rods =1 acre, or 1 A. 640 acres =1 square mile, or 1 sq. mi. 10000 square links (sq. 1.) =] square chain, or 1 sq. "h. 10 square chai'.is =1 acre. ^4840 sq. yd. 160 acres =1 quarter-section. TABLES, DEFINITIONS, AND REDUCTIONS. 53 Cubic, or Volume Measure. 1728 cubic inches (on. in.) = l cubic foot, or 1 eu. ft, 27 cubic feet =1 cubic yard, or 1 cu. yd. 128 cubic feet =1 cord, or 1 cd. Firewood and rough stone are measured by the cord. A cord is equal to a pile 8 ft. long, 4 ft. wide, and 4 ft. high. Dry Measure. 2 pints (pt.) = l quart, or 1 qt. 4 quarts =1 gallon, or 1 gal. 2 gallons =1 peck, or 1 pk. 4 pecks =1 bushel, or 1 bu. In Great Britain gr.iin is sold by the quarter (8 bushels). Certain articles are sold not by bulk, but by weight. The following table gives the weight of a bushel of a number of these: — Dried Apples, 22 lb. Oats, 34 lb. Barley, 48 lb. Buckwheat, 48 lb. Timothy See'l, 48 lb. Flax Seed, 50 lb. Indian Corn, 56 lb. Kye, 56 lb. Fine Salt, 56 lb. Beans, 60 lb. Peas, 60 lb. Clover Seed, 60 lb. Wheat, 60 lb. Potatoes, 60 lb. Turnips, 60 lb. Onions, 60 lb. Liquid Measure. 2 pints {pt.) = l quart, or 1 qt. 4 quarts =1 gallon, or 1 gal. The Imperial gallon contains 277*274 cu. in. A cubic foot of water weighs 1000 oz. or 62i lb. and contains Gi gal. Thus a gallon of water weighs 10 lb. Time Measure. 60 seconds (sec.) = l minute, or 1 min. 60 minutes =1 hour, or 1 hr. 24 hours =1 day, or 1 da. 7 days =1 week, or 1 wk. ,'565 days =1 common year, or 1 yr. I)(i() days :=1 leap yt;M'. Tliirty days have Septehil>er. A]>ril, »luiie and November. 'V\u' other months, cxM-cpt Fcltruary, liavc ;J1 days each. Felti'uai'y has 28 days, except in leaj* year, wheii it has 2iK Sj«e 54 ARITHMETIC. The leap years are those whose numbers can be divided exactly by 4, except in the ease of the even hundreds. These must be exactly divisible by 400. Thus 1892, 1896 and 1600 were leap years; 1894, 1897 and 1900 were not leap years. Each day is considered to commence at midnight. Circular, or Angular Measure. 60 seconds (") = 1 minute, or 1'. 60 minutes =1 degree, or V. 360 degrees =1 circumference, or 1 C. A degree of the circumference of the earth at the Equator contains 60 geographical miles, or 69' 16 statute miles. Miscellaneous Units. 12 units =1 dozen, or 1 doz. 12 dozen — I gross, or 1 gro. 12 gross =:1 great gross. 196 lb. 20 units. =1 score, or 1 sc. 200 lb. 24 sheets=l quire, or 1 qr. 20 quires=l ream, or 1 rm. = 1 barrel of Hour. = 1 barrel of pork. 29 lb. 7 t. 1200 ll>. nso oz. :J671S4 oz. 128 lb. 7 t. b') oz. 7162 oz. 789641 oz. 29 ft. :} in. 145 It. (i in. EXERCISE LXXI. Reduce to ounces Avoirdupois: — 1. 2 lb. 5 lb. 2. 2 t. 3 t. 50 11». Reduce to pounds Avoirdupois :- 3. 36 oz. 480 oz. Reduce to tons: — 4. 4216 lb. 82161 lb. Reduce to inches: — 5. 7 ft. 9 ft. 8 ill. Reduce to yards: — 6. 27 ft. 464 in. Reduce to square inches: — 7. 8 sq. ft. 17 sq. ft. 100 sq. in. Reduce to square yards: — 8. 78 sq. ft. 876 sq. ft. 3()89 sq. in. Reduce to cultic inches: — 9. 3 (Ml. ft. 5 cu. ft. 9 fii. ft. 121 (Ml. ft. 100 (mi. in. Reduce to cords: — 10. 1768 cu. ft. 5768 cu. ft. 9764 cmi. ft. 96."341 cu. ft. 37'6i") in. f) sq. yd. 17854 in. ^q. ft. 17(5415 s<|. in. TABLES, DEFINITIONS, AND REDUCTIONS. 55 96 qt. 1 pt. 568 pt. EXERCISE LXXII. Reduce to pints j — 1. 4qt. 7 qt. Reduce to gallons: — 2. 27 qt. 761 qt. Reduce to bushels: — 3. 4768 lb. wheat. Reduce to pints: — 4. 3 gal. 5 gal. 1 qt. Reduce to gallons : — T). 17 pt. 245 pt. Reduce to seconds: — 6. 7 mill. 5 sec. 17 hr. 15 min. Reduce to days: — 7. 120 hr. 71856 min. Rediu-e to seconds: — 8. 24' 768' 17" Reduce to degrees: — 9. 700' 471 qt. 1 pt. 9765 pt. 57896 lb. oats. 76891 lb. rye. 7 gal. 3 qt. 9 gal. 1 qt. 1 pt. 7689 pt. 2010 pt. 5 da. 1 hr. 7 min. 33333 min. 796841 sec. 34° 15' 19" 956' 7689" S«'lect the leap years out of the following: — 10. 1760 1815 1800 1837 EXERCISE LXXIII. 1856 171° 51" 76451" 1890 Add the following: — 1. £ s. d. 24 12 6 25 13 9 17 18 10 15 7 8 o c\v*. lb. oz. 17 xG 14 18 21 10 18 16 7 i-1 9 4. 3. vd. ft. in. 15 I 7 23 2 9 35 6 2 11 £ s. d. 25 16 8 17 13 9 14 17 11 16 10 7 t. cwt. lb. 40 16 16 16 18 94 47 15 87 21 9 75 yd. ft. in. 3 o 10 4 ') 5 5 6 4 2 7 £ s. d. 123 14 6 137 18 10 246 19 11 301 8 9 t. cwt. lb. oz 7 17 15 15 18 14 47 12 19 8 76 10 9 20 87 14 y*i- ft. in. 17 2 11 14 1 9 12 1 7 13 6 I 56 ARITHMETIC. 4. bu. i»k. qt. 5 1 3 6 I 1 2 3 2 5. gal. qt. \)t. 13 2 1 2 3 15 _ 7 1 _1 Subtract the followint?; G. £ s. d. 7 9 6 4 5 9 V>ii. ])k. qt. i»t. 6 3 5 1 8 16 1 9 2 5 7 3 4 1 da. hr. mill. see. 15 18 50 49 1 13 59 59 4 23 4 10 11 1 4 f?Hl, qt. pt 36 ') 1 42 1 1 25 3 28 3 1 10. t. ewt. lb. 27 14 56 16 18 94 1)U. l.k. qt 56 1 27 3 1 da. hr. mill. sec 5 16 21 18 2 22 12 37 o / ,'/ 48 51 17 17 57 28 £ s. d. 50 1 30 10 10 yd. ft. in. 14 1 4 10 2 11 bn. ]>k. qt 27 1 1 18 1 3 wk. da. hr. min. sec . 1 2 13 40 30 2 6 10 8 3 5 22 55 45 2 3 4 1 15 ewt. lb. oz 20 45 7" 16 22 13 yd. ft. ill. 54 6 19 gal. qt. pt, 4 10 3 2 1 wk.da. hr. rain. sec. 3 4 23 45 30 1 6 16 30 45 25 36 15 18 45 36 c. yd. eft. c.iii. p. yd. eft. c. in. 48 16 1000 100 760 16 2^ __! 245 4824 1 000 EXERCISE LXXIV. Multiply the following: 1. £ s. d. £ H. d. ewt. lb. oz 13 5 10 5 75 15 8 6 15 18 9 9 3. t. ewt. IV). oz. 7 14 16 7 8 bu. pk. qt. i)t. 4 2 3 1 4. gal. qt. ]>t. 15 2 1 12 yd. ft. ill 17 1 11 12 bu. pk. qt. l»t 7 3 7 1 12 dit. 11'. mill. 17 17 17 9 yd. ft. in. 87 9 11 gal qt. pt. 4 3 1 7 da. lir. mill. sec , 5 19 41 52 8 TABLES, DEFINITIONS, AXD REDUCTIONS. 57 qt. pt. 2 1 1 \ 3 3 1 min.sec. 40 30 8 3 5a 45 1 15 t. lb. oz 45 7 ; 22 13 I. ft. in. i 3 1 9 il. qt . pt. 4 1 3 2 1 . D ' ft :5 36 15 S 45 30 •.ft. 0. in 760 24 1000 lb. o/,. 18 9 9 . ft. ill. Ml 9 n ll. qt. pt. 3 1 7 . mill Hce 1 41 52 8 5. 17' 41' 57" t 84" L>7' 28" 5 f. yd. eft. 7 24 e.in, 245 11 J Divitl t- tlu' followiiif^: — 0. £ s. d. 4)81 17 8 & 8. d. 7)36 7 5 cwt. lb. 6)47 15 oz. 4 r t. cwt. lb. oz. 8)20 5 16 8 yd. ft. in. 6)75 2 6 yd. ft. 1;)83 2 in. 3 8. bu.pk. qt. pt. 7)34 2 5 1 bu.pk. gal. qt. 9)73 1 1 1 gal. qt. 5)78 pt. 1 y. gal. qt. pt. 7)30 2 1 hr. min.st'. 9)1479 57 36 diX. hr. mill 3)563 17 47 . sec. 51 10. 4)77° 2' 48" 7)876° 5' 48" e.yd. eft. 9)178 14 c.in. 81 EXERCISE LXXV. Divide the following: — 1. £30 6s. 8d. by £2 6s. 8d. ; £8 18s. by 5s. 6fd. 2. 3 t. 16 cwt. by 19 lb. ; 1 t. 16 cwt. 83 lb. 12 oz. by 105 lb. 4 oz. 3. 44 yd, 2 ft. 9 in. by 33 in. ; 7 yd. by 6 in. 4. 78 A. 71 sq. rd. by 1 xV. 3 sq. rd. ; 100 sq. yd. by 1 sq. ft. 36 sq. in. 5. 327 eu. ft. 1094 eu. in. by 1 cu. ft. 14 cu. in. ; 74 cords by 148 eu. ft. 6. 87 bu. by 1 qt. 1 pt. ; 29 bu. 1 pk. 1 qt. 1 pt. by 5 pt. 7. 33 gal. 3 qt. by 1 qt. 1 pt. ; 30 gal. 2 qt. 1 pt. by 7 pt. 8. 12 hr. 48 min. by 16 sec. ; 8 da. 3 hr. by 1 hr. 15, miu. 9. 2° 42' 30" by 2' 5"; 7,C. by 1° 30'. 10. 35 rm. by 15 sheets; 75 rm. 15 qr. by 5 qr. EXERCISE LXXVI. 1. Wliat is the height of a horse that stands 14 hands high? 2. How many pints of molasses are there in a hogshead containing 63 gallons? 3. Find the number of hours in January. 4. How many parcels, each weighing 15 lb. 4 oz., can be made from 1 ton, and what weight will be remaining? m m % 58 ARITHMETIC. f). If nil onnoo of i>iiro pnld is worth C3 17s. lO^d., find thr value of 11 l»ar of pur** f^ohl wj-ifjclilii};; 2 ll». G o/,. (}. What IS the value of K2 marks, when a mark is worth 138. 4i\.1 7. A rect.aiffular box is 4 ft. 4 in. long, 1 ft. 10 in. wide and 17 in. deep, outside measurement. Find the lengtli of a string that will go round it — (1) lengthwise, (2) crosswise. 8. The angles of a triangle contains 180^. One angle is 42° 36' 45", another is 29° 42' 37". Find the third angle. 9. If the posts in a telegraph line are 45 yards apart, how many are there in 9 miles? 10. If the wool from a sheep each year weighs 7 lb. 8 oz., find the value of the wool from a flock of 300 sheep at $19.()0 per cwt. EXERCISE LXXVII. 1. A merchant bought tobacco at $55 a cwt., and sold* it at 4 cents an ounce. How much did he gain on 3 cwt.? 2. How many telegraph poles are there in 1(5 mi. 80 rd. of line, the poles being 4 rd. apart? 3. Find the cost of a pile of wood containing 3328 c. ft. at $4 per cord. 4. A farm is 50 chains long and 20 chains wide. How many yards long are the boundary fences? 5. Find the value of 17 sq. miles 85 ae. of land at $15 per acre. 6. Find the number of minutes from 17 minutes to ten in the forenoon till 25 minutes past three in the afternoon. 7. A grocer bought a cheese weighing 45 lb. 6 oz. He sold 2 lb. 4 oz. to one woman, 1 lb. 8 oz. to a second, and 3 lb. 12 oz. to a third. How much of the cheese remains unsold? 8. A cubic foot of water weighs 62 lb. 8 oz. How many tons of water are there in a tank containing 480 c. ft.? 9. A gallon of water weighs 10 lb. How many gallons art* there in the tank in question 8? 10. Find the cost of grading a railroad 57 miles long at $5.50 per yard. EXERCISE LXXVIII. 1. How many tons of provisions are required to feed 480 men for 60 days, if each man receives 3 lb. 2 oz. each day? 2. How many silver spoons, each weighing 2 oz. 8 dwt., can be made from a bar of silver weighing 12 lbs. ? 3. How often can 2 ft. 3 in. be subtracted from 81 yards? TABLES, DEFINITIONS, AND REDUCTIONS. 5U 4. If Mar> takes 'J miii. 20 see. to reiul a l)af,'o ol" a book, how many such pa^^es ean sh« read in I{r> minutes? T). If a bicycle rider jroes 2 miles 'Ait rods every (i min., how far will lie go in '2 hours? (). A merchant bouf?ht 7H0 yards of doth at J)s. lid. a yard, iind retailed it at 12s. Id. a yard. Find his total gain. 7. If it costs 12s. Gd. more to build a fence ^5 yards long thiin one IJO yards long, find the cost of building 75 yards of such fence. 8. A man bought 3G72 lb. of oats at 27 cents a bushel and 3136 lb. of rye at 4G cents a bushel. How much had he to pay? 9. Seventy-five bushels of wheat at 68 cents a bushel will buy how numy yards of cloth at 85 cents per yard? 10. A merchant bought 71) reams of foolscap, for which he paid $237. How nnich did he pay for a quire? EXERCISE LXXIX. 1. A merchant sold to one man 19 gal. 3 qt. 1 pt. of molasses; to another he sold 27 gal. 2 qt. 1 pt., and had 48 gal. 1 i)t. left. How much had he at first? 2. Out of a cask having 27 gal. 1 pt. of vinegar, 14 gal. 2 qt. were sold. How much remained in the cask? 3. A farmer sold six loads of wheat which grew on one field, as follows:— The first weighed 47 bu. 36 lb., the second 48 bu. 15 \h., the third 47 bu. 35 lb., the fourth 47 bu. 55 lb., the fifth 48 bu. 19 lb., and the sixth 38 bu. 56 lb. How much wheat grew on this field? 4. There are 12 acres in the field referred to in the last example. Find the yield per acre. 5. A clock which gains 45 seconds every 8 hours is set right at noon on Monday. When it is 8 o'clock in the evening of Wednesday what time will the clock show? 6. Find the weight of two dozen sterling silver spoons, each one weighing 2 oz. 4 dwt. 7. If 2 lb. of gold are coined into 89 guineas, find the value of i)ure gold per ounce. 8. 7000 grains make a pound Avoirdupois, and 5760 grains a i)ound Troy. How many pounds Avoirdupois are of the same weight as 350 lb. Troy? 9. Find the cost of feeding 120 horses for 20 weeks when hay is $8 a ton and oats 30 cents a bushel, if a horse eats 20 lb. of hay and 10 quarts of oats a day? 10. A wagon with 128 packages weighs 2 t. 60 lb. If the wagon weighs 1 t. 140 lb., find the average weight of a package. CHAPTER IV, SIMPLE APPLICATIONS OF THE PREVIOUS RtLES. I. BILLS AND ACCOUNTS. A Debtor, in business transactions, is a pureliasor, or a person wlio receives money, goods, or servi(^es , from another. A Creditor is a seller, or a person who parts with money, goods, or servi(*es to another. A Bill is a detailed statement of goods sold or of services rendered, and of payments, if any, made. It should show the place and time of each transaction, the buyer and seller, the quantity, price and cost of each article, and any payments received. Mrs. F. S. Brown. Form of a receipted Bill. Toronto, Jan. 12, 1900. Bought of Hii.r. & Weir. »ee. 26 ( < 27 28 u ( ( 12 yd. Calico, @ 16 ct. . . . 2 Silk Scarfs, @ $1.35 . . . . 30 yd. Linen Crash, @ 21 ct. . 4 pair Kid Gloves, @ $1.50 . . Ik doz. spools Cotton, 60 ct. 1 piece Ticking, 42 yd., @ 37 ct. Received Payment, 1 92 70 6 30 6 00 90 15 54 $33 Henry F. Wat^^rbury, for KtLL & Weir. 60 36 BILLS AND ACCOUNTS. 61 i RULES. Li'chaser, servi(^es arts with old or of aacle. It usaction , and cost 12, 1900. 1 92 70 6 30 6 00 90 15 54 $:j3 36 EXERCISE LXXX. Make out Bills for the following, supplying names of places and dates where necessary: — 1. Mrs. James Brown bought of John Marsh: — pair shoes (li) .$3.25, 8 yd. silk @ $2.40, 3 pair gloves @ $1.25 and 9 collars (a) 25 ct. 2. Mrs. John Green sold Charles Jenkins: — 75 bu. apples (ff>j S5 ct., 5 tons hay @ $10.85, 50 bu. potatoes @ 60 ct. and 50 cabbages @ 10 ct. 3. John Smith sold Peter Brown: — 25 horses @ $115, 143 cows @ $27, 24 oxen @, $45 and 175 sheep @ $5.50. 4. J.ames Sparrow bought of Messrs. Jones & Son: — 52 lb. butter @ 18 ct., 16 yd. silk @ $1.45, 23 pair boots @ $2.40, 19 lamps @i $2.35 and 28 lb. sugar @ 6 ct. 5. Mrs. R. Philp bought of the R. Simpson Company: — 6 l»ureaus @ $8.75, 3 easy chairs @ $15.25, 12 dining chairs @ $4.(50, 15 mattresses @ $4.50, 2 tables @ $18.75 and 4 mirrors @ $9.75. 6. Samuel Purdy sold Mrs. T. Jones: — 125 lb. sugar @ 8 ct., 17 bbl. flour @ $7.75, 48 lb. lard at 11 ct., and 48 lb. meat 13 ct. 7. Mrs. T. Rorer bought of Messrs. Jones & Co.: — 4 yd. cloth @ $1.25, 12 pair stockings @ 38 ct., 6 pair kid gloves @ $1.15 and 27 yd. ribbon Qt} 5 ct. 8. Simon Brown sold Mrs. T. Smith:— 21 lb. butter @ 22 ct., 12 lb. cheese © 16 ct., 114 doz. eggs @ 15 ct., 23 qt. milk @ 6 ct., 27 bu. potatoes at 45 ct. and 32 bu. carrots @ 40 ct. 9. Mrs. Blake bought of the T. Eaton Company: — 2 lb. candy @ 15 ct., 5 books @ 25 ct., 3 slates @ 12 ct., 2 quires l>aj)cr @ 10 et., 1 box pens @ 35 ct., and 1 box slate pencils @> 10 ct. 10. The R. Simpson Co. sold Mrs. P. Scott: — 25 lb. sugar @ 7 ct., 32 lb. tea at 45 ct., 84 11). coifee @ 35 ct., 62 lb. raisins (<i/ 9 ct., 39 lb. currants @ 8 et. and 47 lb. biscuits @ 10 ct. EXERCISE LXXXI. Make out bills for the following, supplying names of places and dates where necessary: — 1. .Tames Smith bought of Edward Jones: — 75 cords hard- wood @ $4.50, 10 tons coal @ $6.50 and 15 cords pine @ $2.50. He ]»aid cash $150. 2. Peter Douglas sold James Rogers: — 10 lb. sugar @ 5 ct., (5 lb. tea @ 35 ct., 8 lb. colTee @ 25 ct., 5 lb. rice at 7 ct., and 9 lb. cheese @ 16 ct. He took in exchange 4 bags potatoes at 90 cts. and the balance in cash. Make out a receipted bill. IR. ■1 m ARITHMETIC. 3. William Taylor bought from John McMurtry:— 10 lb. sugar @ 8 ct., 6 lb. tea @ 45 ct., 1 set dishes @ $10. .50, 1.') lb soap @ another. 15 ct. He paid $5 iu cash at one time and $1 at Make out tin* bill. 4. Thexton Bros, bought from RoV>ert Smith:— 25 tons hay ® $7.r)0, 66 bu. rye Qi^, 40 ct., 104 bu. barley (n), iV.i ct. and 9H bu. wheat @ 72 ct. They give iu exchange 5 bids, flour Oi} $7.25, and 75 lb. oatmeal @ 3 ct. and the balance in cash. Make out a receipted bill. 5. Smith & Weir bought from Thomas Scott:— 1140 lb. wheat @ 84 ct. per bu., 1802 lb. oats @ 45 ct. per bu., 540 bu. peas© ^0 ct. and 1200 !b. barley @ 48 ct. per bu. On Oct. 17, 1899, he received $100 in cash and the balance on Oct. 28. Make out a receipted bill. 6. Mrs. Brady bought from Smith & Jones:— 7 doz. eggs @/ 18 ct., 19 lb. soap @ 11 ct., 10 lb. butter at 22 ct., 13 lb. cheese @ 17 ct. and 20 lb. rice @ 4 ct. She gave in exchange 5 geese weighing 54 lb. @ 6 ct. and the balance in cash. Make out a receipted bill. 7. Mrs. R. Porter bought from Jones & Co., Belleville: — 27 yd. flannel Qi} 80 ct., 32 yd. calico @ 9 ct., 6 pair gloves at 90 ct. and 16 yd. muslin (a) 12 ct. She paid $10 cash. Make out her bill. 8. John Smith bought of Hill & Groves, London: — 16 yd. silk (a>, $1.15, 72 yd. ticking @ 14 ct., 42 yd. shirting @ 15 ct., 12 yd. flannel @ 40 ct. and 24 yd. print @» 13 ct. He paid cash. Make out a receipted bill. 9. Thomas Taylor bought of Lewis & Sons, May 5: — 5 doz. coat hooks @ 35 ct., 7 door knobs @ 20 ct., 25 lb. nails @ 4 ct., June 1st, 5 door locks © 75 ct., 12 doz. screws at 7 ct., 3 sets fire-irons @ $3.15. Thomas Taylor sold Lewis & Sons, June 10, 1 pair boots @ $3.50, 1 pair rubbers @ 75 ct. The balance was paid June 20. Make out a receipted bill. 10. Henry Philps sold to Aaron Brown: — 75 yd. Bri.ssels carpet @i 96 ct., 1 piece cotton, 31 yd., @/ 11 ct., 1 box hooks and eyes @ $1.75, 1 piano cover @ $5.50, 1 table cover @ $3.25. Brown worked 10 days @ $1.40 per day for Philps and paid the balance in cash. Make out a receipted bill. 11. June 14, 1899, Samuel Farwell bought the following items of H. J. Thompson & Co. : 9 lb. of paint at 12 ct. a pound; 10 rolls of paper at 20 ct. a roll; 28 rolls at 8 ct. a roll; 44 rolls at 10 ct. a roll; 4 rolls at 25 ct. a roll; 34 yards of border at 6 ct. a yard; .58 yards at 2 ct. a yard; 60 yards at 1 ct. a yard. July 7, 1899, Mr. Farwell returned 3 rolls of paper at 8 ct. a roll, 5 rolls at 10 ct. a roll, and 5 yards of border at 6 ct. a yard. Make out Mr. Farwell's ivccount. SIMPLE MEASUREMENTS. G3 II. SIMPLE IV1EASUREIVIEINTS. A Rectangle is a flat surface bounded by four straight lines and having its four angles equal to one nnother. A Square is a rectangle contained by equal sides. A Rectangular Solid is a space enclosed by six rectangular surfaces. EXERCISE LXXXII. Draw the followinj^ rectangles and find their perimeter: — 1. 2 in. by ii in., 4 in. by 3 in., 5 in. by 6 in., 4 in. by 4 in. 2. Tlu3 ceiling of a rectangular room is 16 ft. by 12 ft. Find its perimeter. 3. A rectangular lot is 50 yd. long and 40 yd. wide. Find the cost of fencing it at 25 ct. per yard. 4. How many boards 12 ft. long are there in a fence round a rectangular lot 60 yd. long and 40 yd. wide, the fence being 5 boards high. 5. The posts in a fence round a rectangular lot 60 ft. by 144 ft. are 6 ft. apart. Find the cost of digging the post holes at 5 ct. each. 6. How much will it cost to fence a farm 200 rods long and 80 rods wide at $1.25 per rod? 7. How much will it cost to fence both sides of a road for 1 mile with wire which weighs 1 lb. per rod and costs 8 ct. per lb., the fence being 5 wires high? 8. A square cattle ranch is 2 miles long, how many yards of fencing will enclose it? D. How much will it cost to enclose a mile square with wire- fencing at $4.50 per chain? 10. A rectangular room is three times as long as it is wide. Its perimeter is 320 feet. Find its length and width. EXERCISE LXXXIII. 1. Find the area of each of the following rectangles: — 34 ft. by 36 ft. 32 ft. by 38 ft. 72 yd. by 78 yd. 2. Find the number of acres in each of the following rectangular fields: — 36 rd. by 40 rd. 25 rd. by 64 rd. 75 rd. by 32 rd. 70 rd. by 96 rd. 48 rd. by 50 rd. 38 rd. by 80 rd. 3. How many square feet are there in a board 18 ft. long and 12 in. wide? 64 ARITHMETIC. 4. How many sciimre yards are thfro in :i rt'ctaii>?ular floor 33 ft. by l»l ft.f 5. A Bqiiare garden is 48 yd. long. How many Kqiiaro yards doeH it contain f 6. A close board fence 6 ft. liigh and 100 yd. long is to bo painted. How numy square yards are tliere in the fence? 7. How numy square inches are there iu the surface of a brick 8 in. long, 4 in, wide, and 2 in. deep? 8. How many square foet are there in the walls of a rectan- gular room I'J ft. high, 28 ft. long and 1(5 ft. wide? 9. A rectangular i)]ot 00 ft. by 130 ft. has a path roiind the outside 5 ft. wide. Find the number of square feet iu the path. 10. How many square feet are there in a board 18 ft. long and 13 in. wide at one end, 19 in. wide at the other. EXERCISE LXXXIV. 1. A rectangular floor contains 48(5 s(i. ft. It is 27 ft. long; find its width. 2. A rectangular surface contains (i48 sf|. yd. If it is 108 ft. long, find its width. 3. A rectangular field containing 1(5 acres is G4 rods long. IIow wide is it? 4. A rectangular field containing 18 acres is 80 rods long. Find the cost of fencing it at $1.25 per rod. 5. A rectangular lot contains 1(500 sq. yd. Its length being 240 ft., find the cost of fencing it at 25 ct. per foot. 6. How many boards 12 ft. long would be required to enclose a rectangular lot containing 9600 sq. yd. with a straight fence 5 boards high, the lot being 240 ft. wide, 7. The walls of a room contain 96 sq. yd. The room is 12 ft. high. Find its perimeter. 8. A bought a farm containing 220 acres. If it is 176 rods wide, what will it cost to fence it iu at $1.25 per rod? 9. To paint a close board fence 6 ft. high at 15 ct. per sq. yd. costs $36. Find the length of the fence. 10. At $25 an acre a farm costs $2000. This farm is 200 rd. long. • Find the cost of fencing it at $1.25 per rod. CARPETIINCi. In computing how nnicli carpet is needed for a room there are two modes of procedure — (1) the mathema- Heal, where the quantity equal to the floor space is SIMPLE MEA8URKMKNTS. C5 found, and (2) tlio p)'((r(iral or (wbifnu'i/, whcro the iimiilMT of strips of cjirix't r('«|i.ir('d is first found, imd, an allowance beinj^ made for nuitchint? tln^ pattern as well as turning? iind<'r ait the side when necessary, the ([uantity reciuired is then computed. EXERCISE LXXXV. 1. Find what length of ciupt't 30 iti. wide is required for a H'ctanK'iln''' room 24 ft. by 15 ft. 12. A r«'('tan{,'ular floor ^(5 ft. by 25 ft. is to bo covered with oilcloth GO in. wide. How many yards will be rc(niiredf ;{. How many yards of carpet 27 )u. wide will cover a rectangular room 18 ft. by 12 ft. 4. A rectangular room is 27 ft. by 17 ft. 6 in. How many yanls of cari)et 27 in. wide will cover it? 5. There is a square room 42 ft. long to be covered with carpet 1 yard wide. How many yards are required? G. Find the cost of carpeting a rectangular room 24 ft. by 18 It. with carpet 27 in. wide at 90 ct. per yard. 7. A rectangular room 15 ft. by 12 ft. is covered with carpet :») in. wide which costs 65 ct. per yard. Find the cost. 8. Find the cost of carpeting a rectangular room 36 ft. by 20 ft. with carpet a yard wide at $1.25 per yard. 9. Find the cost of carpeting a rectangular room 12 f1 . by ^S ft. with carpet 27 in. wide at 75 ct. a yard. 10. Find the cost of carpeting a stairway of 24 steps, each step being 11 in. wide and rising 7 in., with carpet at $1.05 per yard. EXERCISE LXXXVI. 1. How many strips of carpet 36 in. wide are required to cover a rectangular room 27 ft. by 18 ft. — (1) if the strips run lengthwise, (2) if they run crosswise? 2. How many strips of carpet 27 in. wide are needed to cover a rectangular room 18 ft. wide, if the strips run lengthwise? 3. How many strips of carpeting 30 in. wide are needed for a square room 40 ft. long? 4. How many strips of oilcloth GO in. wide are required to cover a room 40 ft. wide, the strips running lengthwise of the room? "). A rectangular room, 22 ft, 6 in. wide, is covered with carpet 27 in. wide. How many strips are there? * •.I 'cm 66 ARITHMETIC. 6. How many yards of carpet 30 in, wide will be required for a rectangular rooru 27 ft. V)y 20 ft., the strips running lengthwise of the room ? 7. How many yards of carpet 36 in. wide are needed for a rectangular room 24 ft, by 18 ft., the strips running lengthwise of the room? 8. Find the cost of carpeting a rectangular room 24 ft. l>y 21 ft., witli carpet a yard wide at $1.05 per yard, the strips running lengthwise of the room. 9. Find the cost of carpeting a rectangular room 27 ft. by 20 ft., with carpet 27 in. wide at $1.10 per yard, the strips running crosswise of the room. 10. Find the cost of carpeting a rectangular room 30 ft. l>y 22 ft., with carpet 30 in. wide at $1.25 per yard, the strips running crosswise of the room. PLASTERING. Ill reckoning tlie area to be plastered in a room, there are two methods of procednre— (1) the mafhema- tiraJ, wliere the exact number of square yards is found l)y finding the total area within the boundary line of the work, and from thi leducting the area of all the openings; and (2) the irbitrarij or practical method. In this case the total i.i'ea within the boundary lines of the work is found. From this area, half the are?i of the doors and windows is subtracted. The nearest whc^ d number of square yards in the remainder is the area for which the plasterer is to be paid. EXERCISE LXXXVil. 1. How many square yards of plastering are there in the . ceiling of a rectangular room 30 ft. by 24 ft. ? 2. How many squar(^ yards of plastering are there in tlie walls of a rectangular spf-ce 38 ft. long, 25 ft. wide and 12 ft. high ? 3. How many square yards of plastering are there in the walls and ceiling of a rectangular rocm 30 ft. by 24 ft. and 12 ft. high? 4. Find the cost of plastering the ceiling of a rectanguhw room 24 ft. by 18 ft. at 19 ct. per square yard. 5. Find the cost of plastering a surface equal to the walls and ceiling ot a rectangular room 27 ft. by 18 ft. and 12 ft. high at 23 ct. per square yard. ^^- SIMPLE MEASUREMENTS. 67 6. A rectjuij?ul!ir room 27 ft. by 18 ft. and 10 ft. high has 3 doors, each 7 ft. by 4 ft.; '.i windows, eaeli (5 ft. by 3 ft., and 1 window G ft. by 4 ft. Find the area to \m plastered on the walls only — (1) mathematically, (12) practically. 7. Find the cost of pljiHterin<j: the walls only of a rectangular room 30 ft. by 'J4 ft. and 112 ft. high, there being 3 doors, each 8 ft. by 5 ft.; 3 windows, each 7 ft. by 4 ft., and 1 window () ft. by f) ft., at 20 ct. ])er sq. yd. — (1) mathematically, (2) pi-aetically. 8. At 25 ct. per sq. y^.., And the cost of plastering tlie walla of a rectangular room 25 ft. by 20 ft. and 10 ft. high, there being 2 doors 7 ft. by 5 ft., 3 windows (5 ft. V)y 3 ft., and 1 window 5 ft. by 4 ft. — (1) mathematically, (2) practically. 9. At 25 ct. per sq. yd., find the cost of plastering the walls and ceiling of a rectangular room 24 ft. by 21 ft. and 12 ft. liigh, there being 3 doors 8 ft. by 4 ft. and 3 windows 7 ft. by 4 ft. — (1) mathematically, (2) practically. 10. At 27 ct. per sq. yd., find the cost of plastering the ceiling and walls of a hall 3G ft. by 27 ft. and 14 ft. high, there being 2 doors 9 ft. by 8 ft. and 9 windows 7 ft. by 4 ft. — (1) mathematically, (2) practically. M WALL PAPER. Ill Canada and in the United States, wall paper is usually made into rolls 8 yd. long: <>i' donl)le rolls IG yd. long and 18 in. wide. In Great Britain the usual width is 21 iu. EXERCISE LXXXVin. 1. How many yards of pape. '''' in. wide will paper the ceiling of the room in example 1, last exercise? 2. How many yards of paper 21 in. wide are required to pai)er the walls of the room in example 2, last exercise? 3. How many yards of paper 18 in. wide will paper the walls iiiid ceiling of the room in example 3, last exercise? 4. How many yards of paper 18 in. wide will pap^u- the ceiling of the room in example 4, last exercise? 5. How many yards of paper 18 in. wide will paper the walls and ceiling of the room in example 5, last exercise? 6. How many yards of paper 36 in. wide will paper the walls of the room iu example 6, last exercise? 7. The room in example 7, last exercise, is papered with piiper 18 iu. wide. How much is "required for the walls and ceiling? <'A B\ !?;• .1 asm 68 ARITHMETIC. 8. The walls of the room in example 8, last exercise, are papered with paper 21 in. wide. How nmch is needed? 9. Find the cost of covering the plaster of the room in example 9, last exercise, with paper 18 in. wide at 15 ct. ]>er roll of 8 yards. 10. Find the cost of papering the walls and ceiling of the hall in examjjle U), last exercise, with paper 18 in. wide at 25 ct. per roll of 8 ^ards. BOARD MEASURE. Boards one inch or less in thickness are sokl by tlie square foot. Thus, a board 18 ft. long, 1 ft. wide and 1 in. or less thick contains 18 ft., board measure. Boards more than an inch thicik are sold by the number of feet, board measure, to which they are equivalent. Thus, a plank 18 ft. long, 1 ft. wide and 3 in. thick contains 54 ft., board measure. EXERCISE LXXXIX. 1. Find the number of board feet in the following :- (a) A board 12 ft. long, 9 in. wide and 1 in. thick. (b) A board 18 ft. long, 16 in. wide and 1 in. thick. (c) A board 16 ft. long, 18 in. wide and 1 in. thick. {(i) A board 16 ft. long, 9 in. wide and 2 in. thick, (e) A board 16 ft. long, 10 in. wide and 3 in. thick. (/) A board 18 ft. long, 16 in. wide and i in. thick. (g) A board 16 ft. long, 9 in. wide and i in. thick. 2. How many feet of lumber are there in a close board fence 5 ft. high, 660 ft. long, the boards being 1 in. thick? 3. How many feet of lumber are there in 100 pieces 14 ft. long, 6 in. wide and 6 in. thick? 4. How much lumber is required to put a 12 in. board around a rectangular field 220 yd. by 150 yd.? 5. How many ft. of lumber are there in a sidewalk 160 yd. long, 8 ft. wide, the ])lanks being 2 in. thick? 6. How many feet, board measure, are there in 8 planks, 4 in. thick, 18 ft. long and 16 in. wide? 7. How much lumber is there in 220 yards of fencing, con- sisting of 5 six-inch boards? SIMPLE MEASUREMENTS. 69 'W 8. A pile of lumber consists of 250 boards, each 16 ft. long, 10 in. wide and 3 in. thick. How many board feet are there f 9. Find the cost of 500 planks, 10 ft. lont?, 12 in. wide and 3 in. thick, at $20 per thousand, board measure. ■ 10. What is the value of a pile of inch lumber consisting of 2000 boards 15 ft. long and 12 in. wide at $18 per thousand? RECTANGULAR SOLIDS. EXERCISE XC. 1. How many e. ft. of air are there in a rectangular room 18 ft. by 16 ft. and 10 ft. high? 2. How many c. ft. of timber are there in a rectangular stick 35 ft. long, 3 ft. wide and 2 ft. deep? 3. How many cubic yards of stone are there in a rectangular pile 15 ft. long, 12 ft. wide and 9 ft. high? 4. How many cubic yards of earth are taken from a cellar 30 ft. long, 21 ft. wide and 9 ft. -eep? 5. White pine weighs 24 lb. per cubic foot. What is the weight of a rectangular stick of such timber 28 ft. long, 3 ft. wide and 2 ft. thick? 6. What will the digging of a cellar 18 ft. long, 15 ft. wide and 9 ft. deep cost at 45 et. per cubic yard? 7. A gravel pit 60 ft. wide and 360 ft. long is excavated to the uniform depth of 17 ft. How many cubic yards of gravel are removed? 8. How many cubic yards of stone and mortar are in the fourrdation of a barn 60 ft. long and 36 ft. wide, the wall being 2 ft. thick and 8 ft. high? 9. How many cubic feet of masonry are there in the founda- tion of a house 40 ft. long and 30 ft. wide, the vtaii being 9 ft. high and 2 ft. thick? 10. Find the cost of 24 rectangular blocks of stone, each 9 ft. by 6 ft. by 5 ft., at $5.75 per cubic yard. EXERCISE XCI. 1. How many cords of wood are there in a pile 24 ft. long, 16 ft. wide, 10 ft. high? 2. Find the number of cords of wood in a pile 48 ft. loirg, 14 ft. high and 12 ft. wide. 3. Find the number of cords in a pile of wood 120 ft. long, 4 ft. wide and 8 ft. high. 4. How much should be paid for a pile of 4-foot wood, 128 ft. long and 7 ft. high, at $3 per cord? •'-m till ■n>s ■"Tlfgl 70 ARITHMETIC. .". Find the value of l(i pileis of w^oil, each 24 ft. long, 4 tv. wide, 8 ft. high, at $2.25 per cord. G. Find the cost of a pile of wood 112 ft. long, 5 ft. wide and 8 ft. high, at $2.15 per cord. 7. There are GO cords of wood in u pile 8 ft. wide and 12 ft. high. How long is the pile? 8. There are ;{5 cords of wood in a pile 14 ft. high and 64 ft. long. How wide is the pile ? 9. Tiie cost of a pile of wood at $3 per cord is $;{60. It is 240 ft. long and 8 ft. wide. How high is tiie pile? 10. At $2.25 per cord a pile of wood is worth $2;{G.25. It is 5 ft. wide and 12 ft. high. How long is the pile? EXERCISE yxil. 1. There are 70 e. yd. of earth taken from a cellar 18 ft. long and 15 ft. wide. How deep is the cellar? 2. A rectangular room 30 ft. by 25 ft. contains 8250 c. ft. of air. How high is the room? 3. In a pile of wood there are 6 cords. The i)ile is 4 ft. wide and 8 ft. high. How long is it? 4. A stick of square timber contains 180 c. ft. It is 30 ft. long and 2 ft. wide. How thick is it? 5. A brick wall 2 ft. thick and 40 ft. high contains 89G0 c. ft. How long is the wall? 6. A l)rick contains 64 c. in. How many bricks are there in a rectangular pile 12 ft. long, 8 ft. wide .and 7 ft. high' 7. There are 3072 c. ft. of masonry in a stone wall 8 ft. high and 2 ft. tliiek. How long is the wall? 8. If the wall in example 7 is the stone foundation of a barn 60 ft. long, how wide is the barn? 9. A rectangular box 48 in. long and 30 in. deep, inside measurement, contains 25 e. ft. How wide is the box? 10. A rectangular cutting 360 yd. long and 25 ft. wide has 17000 c. yd. of earth taken out of it. What is the average depth of the cutting? EXERCISE XCIII. 1. Two-foot wood is piled 6 feet high. How long must the pile be to contain 3 cords? 2. How much will it cost to have a tin roof put on a stable, each slope of which measures 25 ft. by 14 ft. at $5.75 per 100 sq. ft.? n SIMPLE MEASUREMENTS. 71 3. From a lot 40 rods square IGO sq. rods wtM-e sold. Wlint is the value of the remainder at $120 per acre? 4. A cubic foot of black spruce weif^hs 2K lb. Find the wcifjfht of 10 planks of this wood, each 16 ft. long, 1 ft. wide and o in. thick. f). A ton of hard coal occui)ies 4L* c. ft. How many tons of hard coal will a bin 1(5 ft. long, 12 ft. wide and 7 ft. deep holdt 0. How many tons of water will a tank 1<) ft. long, 12 ft. wide and 8 ft. deep hold? (1 c. ft, weighs 1000 oz.) 7* A street (»()0 ft. long and 24 ft. wide lias to be filled in to the depth of li ft. How many cubic yards of earth wil' be required? 8. Find the cost of laying a tile drain a mile long at 15 ct. per foot. 9. What will it cost to enclose a mile square with wire fencing at $4.50 per chain? 10. What will it cost to shingle a barn, the roof of which is 80 ft. long and the slope on each side 30 ft. at $1.50 por 100 sq. ft.? EXERCISE XCIV. 1. How much will it cost to ])aint a close board fence G ft. high around a rectangular lot 36 yd. by 32 yd. at 12 ct. per sq. yd.? 2. What length of road 66 ft. wide will contain one acre? 3. How many rectangular sods each 20 in. by 9 in. will be required to sod a rectangular lawn 60 ft. by 75 ft.? 4. What must be the depth of a wagon box 10 ft. long and 4 ft. wide that the contents may be 120 c. ft.? 5. A rectangular box is 6 ft. 8 in. long, 4 ft. 6 in. wide and 3 ft. deep, inside measurement. Find the cubic content of the box. 6. A bicycle wheel is 10 ft. 1 in. around the tire, and turns 17280 times in a journey from A to B. How far is A from B? 7. What length of board 16 in. wide will contain 20 sq. ft.? 8. What length of board 15 in. wide will contain 11 sq. ft. ;{G sq. in.? 9. How many square yards of oilcloth will be required to cover a rectangular room 20 iiu, 3 in. long and 16 ft. wide? 10. A rectangular box 11 ft. 3 in. long and 5 ft. 4 in. wide contains 300 cu. ft. How deep is the box? Ill m 72 ARITHMETIC. III. SHARIING. EXERCISE XCV. 1. Divulo !f40 bt'twoiMi two )»oys so that one may have $6 more thau tlie otlier. 2. James and Thomas have 41) yd. of cloth, and James has 11 yd. more tlian Thomas. How many has each? ',i. Divide 84 marbles between James and Robert, giving Robert 12 more than James. 4. Divide $99 between two boys, giving one $1.50 more than the other. '). Divide $50000 between A and B, giving B $4000 hiSs than A. 0. A hovso and bnggy are wortli $375, and the liorse is worth $55 more than the bnggy. Find the value of each. 7. A man earned $790 in two years. In the first year he earned $54 more thau the 2nd, find the amount earned each year. 8. Two trains start at the same time from Montreal and Harnia, a distance of 508 miles. When they meet one has gone M miles less than the other. How far has each gone? 9. 750 votes were polled for two candidates. The elected one had a majority of 34. How many votes had each? 10. A house and lot together cost $5750. The house cost $3250 more than the lot. Find the cost of each. EXERCISE XCVI. 1. A yacht and its fittings cost $0400. The yacht cost $3840 more thau the fittings. Find the cost of each. 2. A farmer raised 4375 bu. of wheat in two years. In the second year he had 247 bu. more thau iu the first. How many bu. had he in each year? 3. A merchant bought $4908 worth of hardware and groceries. The groceries cost $484 less thau the hardware. Find the cost ot the hardware. 4. The perimeter of a rectangular field is 1200 yd. and the length is 119 yd. greater thau the width. Find the length and width of the field. 5. Three times the sum of two numbers is 1830, and one is 18 more than the other. Find the numbers. 0. Four times the sum of two inimbers is 3984, and one is 72 less than the other. Find the numbers. SHARING. 78 <! t 7. Two men topfether chopped 52 cords of wood. One chopped 3 cords 50 c. ft. more chan the other. How much did each cho])? H. Two adjacent fields together contain 20 acres. The larger contains 90 sq. rods more than the other. Find the area of each lieUl. 9. Two men are ten miles apart. They walk straight towards each other, and when they meet one has gone 90 rods less than the other. How far has he walked? 10. Two loads of hay together weigh 3 t. 8 cwt., and one weighs 12 cwt. more than the other. Find the weight of each. EXERCISE XCVII. 1. Divide 120 marbles between two boys giving one three times as many as the other. 2. Two books together contain 762 pages, and one has twice as nniny pages as the other. How many p'tges are in each? [i. Two pieces of cloth together contain 115 yards, and one piece is 4 times as long as the other. How long is each? 4. Two houses are together worth $12250. One is worth 4 times as much as the other. Find the value of each. 5. Two men have together $243. One has $18 more than twice as much as the other. How much has each? (). Two lots are together worth $607. One is worth $27 more than thrice tiie other. Find the value of each. 7. Two farms are together worth $139.50. One is worth $150 more than three times the other. Find the value of each. 8. Find the length and breadth of a field whose perimeter is 240 rods and the length three times the breadth. 9. A and B together own 120 acres, A having 24 acres more than B. A sells his part at $84 an acre and B sells his for the same amount of money. What does B get per acre? 10. At an election 4977 votes were polled. The successful t-aTulidate received 17 votes more than three times as many as liis oi>ponent. How many votes did each receive? EXERCISE XCVIil. 1. Divide $84 between two men, giving the first $3 as often as the second gets $4. 2. A mixture of 210 bu. of oats and peas is made up as follows: — For every 2 bu. oats there are 5 bu. i)eas. How many bushels are there of each? 3. A roll of bills contains $153. It is made up of an equal number of $5 bills and $4 bills. How many are there of each ? ^'!ii 74 ARITRMETIC. 4. Divide $19500 between two men so that when the first f^ets $2 the second may get $3. 5. Two books together contain 605 pages. B^or every five pages in the first bool< there are six pages in the second. How many pages are there in each book? 6. Divide $120 among three men so that when the first gets $1 the second may get $2 and the third $'l. 7. Divide 150 marbles among t' ~ boys so that when t'le 1st gets 2 marbles the 2nd may get . :.d I . 3rd 5. 8. A sum of money, $2.40 is made n of Ir-- ct. pieces, t( n ct. pieces and twenty-five ct. pieces and the ^.-XAie number 3f each. How many are there of each? 9. Divide $1120 among A, B, and C, so that A may have 3 times as much as B, and C may have as much as A and B together. 10. Three houses are together worth $16410. The first is worth twice as much as the other two together and the second is worth $570 more than the third. Find the value of each. EXERCISE XCIX. 1. A man sold three sheep for $31. For the second he received $2 more than for the first, and for the tliird $3 more than for the second. How much did he receive for each? 2. Three men weigh 456 lb. The 1st weighs 18 lb. more than the 2nd and the 2nd 18 lb. more than the 3rd. Find the weight of each. 3. Three pieces of cloth contain 444 yd. The 1st has 25 yd. more than the 2nd but 19 yd. less than the 3rd. Find the length of each piece. 4. Three loads of hay weigh 6400 lb. The 1st weighs 200 lb. more than the 2nd and the 2nd 400 lb. more than the 3rd. Find the weight of the 1st. 5. Three pigs weigh 402 lb. The 1st weighs 27 lb. nfbre than the 2nd but 48 lb. less than the 3rd. How much does each weigh? 6. In three days A rode 125 miles upon his bicycle. The 1st day he went as far as on the other two days all but 5 mi. The 2nd day he rode 15 mi. less than the 3rd day. How far did he go each day? 7. The perimeter of a triangular field is 249 rd. The 1st side is 36 rods longer than the 2nd but 42 rd. shorter than the 3rd. How long is each side? 8. In three books there are 108G pages. The 3rd has 74 more than the 2nd and 196 more than the 1st. How many pages are there in each book? AVERAGES. 75 9. In three years a man saved $1593. In each year he saved $81 more than in the preceding one. How much did he save each year? 10. Three bins contain 573 bu. of wheat. The Ist has 110 bn. more than the 3rd and 53 bu. less than the •2nd. How many bushels are there in each bin? 11. The cost of 5 bu. of oats and 8 bu. of wheat is $(>.80 and the cost of a bu. of wheat is 33 ct. more than a bu. of oats. Find the cost of a bu. of oats. 12. A box contained 286 marbles, red, blue, and white. There were 192 red and white, and 199 blue and white. How many of each kind were in the box ? IV. AVERAGES. The Aggregate of a nuni])ei' of qnantitios of tlio .same kind is their entire number, or sum. The Average of a number of quantities of the same kind is the quotient arising from dividing their sum by the number of addends; thus, the average of 4,^8 and 9 is (4+8+9)-3, or 7. EXERCISE C. Find the aggregate of the following: — 1. 47, 275, 368, 495, 784 and 6. 2. 571, 0, 100, 367, 2461, 78, 96 and 10. 3. 6746, 89745, 3689, 4875 and 78964. Find the average of the following : — 4. 5 and 9; 7 and 13; 4, 8 and 15. 5. 9, 12, 16 and 19; 0, 7, 12, 15 and 21. 6. 26, 37, 49 and 60; 27, 0, 0, 16, 25 and 28. 7. A man trolling caught three fish; the 1st weighed 16 lb., the 2nd 11 lb., and the 3rd 15 lb. Find their average weight. 8. A's age is 45, B's 30, C's .35, D's 60, E's 70 years. What is the average of their ages? 9. A man sold goods in six days to the following amounts: $80, $75, $92, $64, $210, $193. What did his sales average per day? 10. Seven houses are worth, respectively, $10000, $12000, $8500, $7525, $4260, $4180, and $3200. What is their average value I ittl 76 ARITHMETIC. EXERCISE CI. 1. Tho avpi'njjo woipht of 9 boys is 73 \h. 't oz. Find tlieir nfXfiff'di^tt* weipfht. 2. The nvornge speed of a triiiii for 1*2 hours is 21 mi. 120 rd. Find the distajiee travelled during that time. 3. A farmer sells loads of wheat havinj? an averapje of 45 bu. 30 lb. per load. Find the value of tho loads at 75 ct. per liushel. 4. A woman sells 12 turkeys of an averjipe weipfht of 13 lb, 8 oz. What did she receive for the lot, turkeys being worth H ct. per lb. 5. A farmer brought to market a load of 15 hogs of an average weight of 2 ewt. 35 lb. What was the aggregate weight of the hogs? 0. The aggregate weight of turkeys is 113 1)». I oz. What is the average weight of a ttirkey? 7. A train goes 333 mi. in 10 lir. What is the average speed per hour? 8. In one of the classes in a school the aggicgate attendance for the week was 225. What was the average attendance each of the five days ? 9. A earns $3900 in a year. What does he earn each week, there being 52 wks. in a year. 10. The aggregate weight of 24 tubs of Itutter is 591 lb. Find the average weight of a tub. EXERCISE Cll. 1 . Bouglit 1 cow for $36, and 2 others for $30i a piece. What was their average cost ? 2. A grocer mixes 9 lb. of sugar at 5 ct. a jmund with IS lb. at 8 ct. a pound. What is a i)Ound of the mixture worth? 3. A jeweler mixes 20 oz. of gold 18 carats fine with 12 oz. 10 carats fine. How fine is the mixture? 4. A grocer sold 7 lb. of tea at 55 ct. per lb. and 21 lb. at 35 ct. per lb. What was the average price? 5. A grocer mixed 20 lb. of sugar of a certaiji kind with 40 lb. worth 9 ct. per lb. The whole was worth 8 ct. per lb. What was the price of the first kind of sugar? 6. I bought 500 bu. of wheat, part at 70 ct. per bu. and the rest at 75 ct. per bu. The average price was 72 et. per bu. How many bu. of each kind did I buy? AVER AUKS. 77 7. The ftvcrnj^c iM'i^lit of 4 boys is 5 ft. 1 in. Wluit \h t\w iK'i^'lit of u fifth boy, tlie uv«'i'ag«' hei^'lit of the five being 4 ft. 11 hut K. The aggregate weight of ') men is 800 lb. Tlie aggregate weiglit of tliree of them in ,'iJli lb. Find the average weight of the otlier two. 9. A ])erson mixes 1 lit. of his best eoiTee with ') lbs. at Is. 4d. a lb., and produei s a mixture wortli Is. 4id. a lb. What is the priee of liis best eoffee/ 10. If 1") lb. of sugar are bought at 4d., jind 24 lb. at 6^d., iind if the two quantities ar«' tlien mixed and sold at 7d., how much will be gained/ EXERCISE cm. 1. The weights of some hogs are as follows: 250, 320, 27'), H22, 415, 2i:{, 244, 214 and 195 pounds. What is the average of tiieir weights atid their aggregate weight? 2. In 1898 the value of hay and clover grown in the counties bordering on Lake fh-ie was as follows: — Essex $5;J019.'{, Kent $()9;{773, Elgin $(539646, Norfolk $404300, Haldimand $597953, and Welland $559775. VV^hat was the average value of this croj) per county? 3. If a doz. eggs weigh 1 lb. 8 oz., what is their average weight? 4. A merchant mixes 4 lb. of coffee worth 32 et. a pound 3 lb. worth 35 ct. and 2 lb. worth 41 ct. What is the mixture worth a pound? 5. Of candidates for office, 7 were 20 yrs. old, 12 were 22, 12 were 23, and 1, 24. What was the average age of the candidates? 6. A drover bought 30 cows at $22 a head, 40 at $25 a head, 30 at $28 a head. What was the average price per head? 7. A merchant mixed 24 lb. of sugar at 5 cents a pound, 30 11). at 6 ct. and 26 lb. at 10 ct. What is the average price of the mixture? 8. A merchant bought 2000 lb. of wool at 47 ct. ])ev pound, 3000 lb. at 43 et., 5000 lb. at 49 et. and 8000 lb. at 45 ct. Wliat was the average cost i)er lb. ? 9. In a factory a certain number of men receive $13 each per week, 4 times as many receive $9 each per week, and 10 times as many receive $5 each per week. What is the average weekly wage per man? 10. A goldsmith combined 8 oz. of gold 21 carats fine, 12 oz. 22 carats fine, 18 oz. 20 carats fine, with 28 oz. of alloy; required the fineness of the composition. '"ik-S CHAPTER V. FACTORS, CAINCELLATIOIN, MEASURES. AND MULTIPLES. I. FACTORS. Whole Numbers, or Int('<?t'rs,are oitlior Odd or Erf h. An Odd INumber is a nimihcr not cxactlv ilivisihlo by 2, as 7, J), &(\ An Even Number is a nnnibcr oxactlv divisible bv 2, as H, 10, &i',. A Factor of a iiuinbcr is a number wliieh will divide the given iminber exactly, as 2, 3, 4 or 6 is a factor of 12. A Prime Number is one which has no integral factors, ex(^ept itself and ouf, as 13. A Composite Number is one which has other integral factors than itself and one, as 12. The Prime Factors of a composite number are the prime numbers which, multiplied together, prodm^e that number; thus, 2, 3 and 5 are the prime factors of 30. EXERCISE CIV. Find the prime factors of the following: — 1. 12 56 84 2. 196 231 252 .3. 876 948 1052 4. 1095 1113 1127 5. 1202 1214 1218 Find the prime numbers in the following: — (i. 781 797 821 7. 1157 1187 2067 8. 2543 2521 2007 9. 2273 23:!9 2417 10. 3397 3197 3013 78 30. 384. 1059. 1156. 1555. 1437. 2117. 2013. 2967. 3119. OANCKLLATION. 79 EXERCISE CV. rind tho prime fuetors common to the following: — 140 and .'JH."). 4129 and 1001. H8S and 948. 1. 4. (). 7. r)() and 70 10.~> and 'J:M .')y.') and ir»47 4K4 and 470 (548 and r)40. 7120 and 748 9()0 and 912."). Write the numbers less than 100 of wiiich 3 i8 a factor. Write the numbers between 700 and 800 of which 1 1 is a factor. 8. Find the larpjest factor otlier than the number itself of each of the following? numbers:— (JO, I'Jf), 825, r)79, and 88(5. 9. Find three prime numbers that will divide each of the following:— 30, 105, 385, 1001, 3553. 10. Resolve the followinp; into as many pairs of factors as possible:— 60, 150, 100, 240, 3(i0. II. CANCELLATION. Cancellation is tlin process of rejecting erinftl fjKitors from both Dividend and Divisor, and thereby greatly shortening the operation of Division. EXERCISE CVI. 1. Divide 15X16X18X20 by 5X8X3X4. 2. Divide 7X24X30X35 by 14X36X70. 3. Divide 60X66X80X90 by 15X20X88X180. 4. Divide 75X85 X 120 XI 14 by 57X102X125. 5. Divide 48X54X60X72 by 36X54X18X80. 6. Divide the continued product of 7, 8, 9, 12, 18 and 24 by the continued product of 3, 4, 6, 6, and 6. 7. Divide the continued product of 16, 18, 20, 24, 25 and 27 by the continued product of 4, 9, 30, and 36. 8. A lot is planted with potatoe. There are 75 rows; each row has 120 hills, and each hill has on an average 16 potatoes. How many bushels are there, if it takes 20 potatoes to fill a gallon? 9. Five pieces of cloth, each containing 60 yd., worth $1.50 per yard, are exchanged for 6 pieces, worth $1 per yard. How many yards are there in each piece of the latter? 10. A bicycle rider goes at the rate of 10 miles per hour for 12 hours a day during 16 days. How many days must another ride at the rate of 8 miles per hour for 6 hours per day to go as far? 80 ARITHMETIC. III. MEASURES. A IVIeasure of n number is one of the factors of that number. A Common IVIeasure of two or more numbei-s is a factor common to the {^iven numbers. The Greatest Common IVIeasure (G.C.M.) of two or more numbers is the largest factor common to the given numbers. Numbers tliat have no common factor otlier than one are said to be prime to one an otlier. EXERCISE evil. Find the G.C.M. of: 1. i 12 and 56 48 and 128 65 and 91. 2. 2 10 and 455 230 and 506 210 and 294. 3. 288 and 360 352 and_384 336 and 884. 4. 27, 36, 108 32, 48, 128 56, 63, 315. 5. 75, 225, 500 210, 462, 546 546, 462, 882. 0. 216, 360, 405 168, 132, 352 146, 365, 219. 7. 36o, 511, 803 192, 576, 1760 671, 781, 1441. 8. G39, 873, 747 808, 568, 1112 455, 403, 481. 9. 352, 992, 672 550, 770, 1210 154, 210, 420. 0. luOl, 1365, 1820 715, 1001, 1287 1615, 969, 2261. EXERCISE CVIII. 1. What is the length of the longest pole that will Pleasure 84 ft., 56 ft., and 70 ft.? 2. What is the length of the longest stick that will measure 15 ft. 7 in. and 18 ft. 5 -i.? 3. What is the largest number that will divide 202 and 266 so as to leave 7 and 11 as remainders respectively? 4. What is the greatest equal length into which throe trees can be cut, the first being 84 ft. long, the second 105 ft., and the third 119 ft.? 5. What is the greatest width of carpet that will fit three rooms — the first being 18 ft. wide, the second 22 ft. 6 in. wide, and the third 29 ft. 3 in.? 6. A rectangular field 611 ft. by 364 ft. is fenced with rails of equal length, and this the greatest possible. The fenc-^ being straight, what is the length of a rail? MEASURES. 81 7. A farmer has 441 bn. of oats, 567 bu. of wheat, and 315 bu. of rye. He wishes to make exact loads of the same number of bushels of each kind of grain, and have as few loads as possible. How many bushels will there be in a load? 8. Three debts of .$200, $1250 and $300 were paid with bills of the same denomination. How might the debt have ])een paid? How was it paid if the bills were the largest possible? 9. B has $620, C $1116, and D $1488, with which they agree to purchase horses at the highest price per head that will allow each man to invest all his money? What will be the cost of each horse? iO. How many rails will Inclose a rectangular field 14599 feet long by 10361 feet wide, provided the fence is straight, and 7 rails higl>, and the rails of equal '' ngth, and the longest that can be used? EXERCISE ex. Find the G.C.M. of the following: — 1. 1008 and 1026 1225 and 2247 2761 and 3263. 2. 1391 and 2247 1866 and 3421 1957 and 2987. 3. 4004 and 5772 4427 and 7219 7813 and 9015. 4. 2542 and 5487 4735 and 6629 3029 and 3961 . 5. 2951 and 3477 4559 and 7003 4055 and 7299. 6. 8128 and 8472 5544 and 8008 7956 and 9724. 7. 15444 and 13068 69615 and 92872 23673 ami 60203. S. 45H62 and 29026 43155 and 81564 53712 and 659(51 . 9. 15249 and 27807 30429 and 88641 18577 and 20006. 10. 13230, 44100, and 118125 720100, 913330, and 211109. EXERCISE ex. 1. Find the G.C.M. of 1365 and 1785, and from this find all tlu' common measures of these two numbers. 2. Find the G.C.M. of 37 d. 13 hr. and 55 d. 5 hr. 3. Find the G.C.M. of 7 mi. 259 yd. and 11 mi. 407 yd. 4. Find the G.C.M. of 6 bu, 1 pk. 1 gal. and 10 bu. 3 pk. 1 gal. 5. What is the largest number that will divide 2000 leaving a remainder of 11, and 2708 leaving a remainder of 17? 6. Find the greatest laimber that will divide 13956 and 14565, and leave a remainder of 7 in each case. 7. Find the greatest number tliat will divide 2293, 4245 and ."):U8, and leave i-emainders 18, 20 and 23 respectively. S. Whiit is the largest number of men amongst whom 209 .'ip])]es and 3(51 oranges can be distributed, so that every man gets as many apples and as many oranges as any other man? Ei 1-1* 82 ARITHMETIC. 9. Two masses of silver, weifjhing 1169 oz. an;l 139.'? oz., respectively, are eacii to be made, without loss, into medals of the same weij^ht. What is the weight of the largest possible medal? 10. A farmer has 1134 sheep and 1260 lambs. He forms them into separate flocks, with the same number of animals in each flock. The flocks being the largest possible, how many animals are in each? IV. MULTIPLES. A IVIultiple of a imml)or is the product ()l)t}iined by multiplying tlie given number by any whole number. Thus, if 7 is multiplied sueeessively by 1, 2, 3, 4, .">, &(^, the products 7, 14, 21, 28, 35, &c,., are multiples of 7. From this, it follows that every multiple of a number is exactly divisible by that number. A Common IVIultiple of two or more numbers is a iium))er which is one or more times each of the given numbers. Thus, 24 is a common multiple of 2, 3, 4, 6, 8, &c. The Least Common Multiple (L.C.M.) of two or more numbers is the least number that is one or more times each of the given numbers. EXERCISE CXI. Find the L.C.M. of the following:— 1. 4, 6, 8 6, 8, 10 2. 5, 15, 25 25, 30, 40 3. 5, 7, 9 12, i:^, 17 4. 12, IS, 24, 30 18, 30, 30, 42 f). 32, 48, ()4, 72 30, 40, 50, CO 6. 14, 18, 20, 21 51, 187, 1.53, 105 t . 10."), 198, 242 312, 429, 572, 715 8. 510, ,^)95, G80 432, 840, 693, (iOO 9. 19;')-), 2001, 3451 2041 , 8470, 3423 10. 1554, 1058, 18058 4410, 7350, 7875 8, 10, 12. 36, 48, 60. 13, 15, 19. 24, 36, 42, 56. 60, 66, 72, 77. 203, 429, 494, 570. 287, 451, 455, 715. 253, 345, 414, 495. 2743, 400l», 4199. 2001, 4278, 4495. MULTIPLES. 88 9;i oz., jdals of possible ns them in eac'li animals 3, 4, r>, lultiples >le of a ibers is a :lie given 6, 8, &(^ of two ov } or more 10, 12. 48, GO. 15, 19. i, 4'2, 56. ), 72, 77. ), 494, 570. 1,455, 715. >, 414 495, 4()0it, 4199. 4278, 4495 EXERCISE CXII. 1. Find the L.C.M. of the first six even nuni])ers. 2. Find the smallest number of apples that can be arranged in gi'OU])s of 8, or 9, or 15, or 20 each. .'J. Find the L.C.M. of the prime numbers between 4 and 18. 4. Find the L.C.M. of all the odd numV)ers between 8 and 16. 5. What is the least number from which 16 and 24 may each be taken an integral number of times? (). Find the least number that can l)e divided by 7, 20, 28 and ;J5 respectively and leave 3 as remainder in each case. 7. What number is the same mi Itiple of 7 that 1962 is of 9? 8. Divide the L.C.M. of 23949 and 26610 by their G.C.M. 9. What is the shortest piece of wire that can be cut into exact lengths of either 6 ft., 8 ft. or 10 ft.? 10. Wliat is the capacity of the smallest cistern the full contents of which will exactly fill a four-gallon, a ten-gallon or a fifteen -gallon measure a certain number of times; EXERCISE CXIII. 1 . What is the smallest delit that can ]>e ]>aid with an exact number of 2-dollar, or 4-dollar, or 10-dolIar i>ills? 2. What is the gresitest weight of which 1 t. 19 cwt. 4H 11). iind 4 t. 14 cwt. 47 lb. are multiples? '.). What is the greatest weight of which 2 t. 4 cwt. 18 lb. and 5 t. 4 cwt. 34 lb. are multiples? 4. How often does the L.C.M. of 5, 12, .36, 42 and 84 contain the G.C.M. of 7266 and 8022? 5. A rides at the rate of 6 miles per hour, B at the rate of 1(1 miles per hour, and (' walks at the rate of 3 miles per hour. Find the shortest distance each may go in an integral number of hours. . 6. What is the least number which divided by 8, 9, 10 and 12 respectively gives in each case a remainder of 5? 7. What numbers less than 200 leave 2 .as remainder when divided by 3, or 4, or 5, or 6. 8. What is the smallest quantity of wheat that can be taken lo market in either 20, 25, 30, or 40 bushel loads? 9. The prodiu't of four consecutive numbers is 43680. What lire the numbers;' 111. One pound Avoirdupois weight contains 7000 gr. and one pniind 'i'roy weight 57(50 gr. Find the least weight whicli can be expressed integrally in l)oth Troy and Avoirdupois pounds. ■ •,^1 CHARIER VL FRACTIONS. I. DEFIINITIOINS, INOTATIOIN AIND INUMERATIOIN. A Fraction is a number whieh expresses one or more equal parts of a wJiole, or unit. A Common or Vulgar Fraction is expressed by two num))ers, one above and the other below a short horizontal line; thus *, ro, iiud /a are Common, or Vulgar frjietions. The Denominator is the nuniber below the line, and shows into how many equal parts the whole, or unit is divided. The Numerator is the number above the line, and shows the number of equal parts in the fraction. The numerator and denominator are calle'i the Terms of the fraction. A traction indicates also the quotient arising;, irom dividingr the numerator l)v the denominator. Thus 4 f means i. Four of the parts when a unit is divided into five equal parts, ii. The quotient when four is divided by live, iii. One-fifth of tour units. tXERCISE CXIV. Express in fif;«i!'ps: — I. Two-thirds; 'J, Five ei^-.iths; ;{. Six-sevenths- 'ihree- fourths ; Four- fifths. Five-nintlis; P''ive-twelfths. Six-tlnrteeuth:- ; Six-seventeenths. 4. Seven-twenty 3i'!its; Sevt-n-twelfths; Seven-thirtyseconds. 84 ii\ Ml oi «> b<i 1 rioiN. s one or •essecl by w a short union, or the line, wlioU', or line, and tion. ;alle<l tlie Isin^^ ii"f>»^ ,r. Thus Ivided into )V tive. lis. llt'ths. Iiteeuths. lirty seconds. REDUCTION. Write in words: — 5. f 1 4 A. 6. i\ H il H. 7. H H ^1 il. Explain tlie meaning of the following fnietionB: — 8. f in. f ft. B a. $t\ . 9. I hr. H 1 3 21 1^\. 10, 1 cord. H cwt. Ub. h t. 85 II. REDUCTION. A Proper Fraction is one of which the nunier- iitor is less than the denominator, as j;, L An Improper Fraction is one of whili the numerator is equal to or greater than the denomin- ator, as r, V . A mixed Number is a number which consists of the sum of a whole number and a fraction, as 21. A fraction is in its lowest terms when the numer- ator and denominator are prime to each other. Similar Fractions are those that have a common denominator, as f , f , i and V". When the terms of a fraction are both mutti- plied by the same number or are both divided by the same number, the value of the fraction is not altered. A Simple Fraction is one in w^hich the terms are ])oth whole numliers and which expresses one or more of the equal parts of unity, as f, |. A Compound Fraction is one which expresses one or more of the equal ])arts of a fraction, as I of 3, a or T. A Complex Fractio^i is one in which one or i 4 2] 'Mm l>otli terms 'are fractir-Tis, a.- ■>, Oj, Si;, •-Ar^-. ^-> 86 ARITHMETIC. EXERCISE CXV. Redupe to improper fractions: — 1. 2i 4J 21 43. 2. ek 7i 81 41. 3. 51 6* 8 A 9.^. 4. 18 i 192 2U 25L 5. 43 i\ 101 1 1411 262V5. 6. 163 t*j 275 ^ 4611^ 403^1. 7. 20711 H.lO^r 908 y 78U]. 8. 310A 5694 3 678,V:t 6982V0. 9. 1001, V OCrin 8080f,l 7000 i,V, 10. 7018A 705?!!? 368 l-n 37^1 01. EXERCISE CXVI. 1. .John has two apples. To how many boys can he give half an apple? 2. Among how many jrirls must -5 melons be divided 'lat each may receive i of a melon r ;>. How many fifths are there in ii api>les? 4. How many persons will 5^ cords of wood supply, if each one receivjs i cord? 5. A gave $i to each one of a number of boys. He gave away $151 . How many boys were there? 6. Express both '1 and 7 as fractions with denominator 15. 7. (^liunge 48 to ninths and 57 to tenths. 8. What fractions with denominator 24 are equivalent to 3, 5, 8, and 12, respectively? 9. A walked a mile each quaricr hour. He walked for 3i hours. Hi w far did he go? 10. To make badges i yd. 'oug for n :;lass, 5^ yd. of ribbon are needed. How many pupils arc tiiere in the class? EXERCISE CXV5K Reduce to whole numbers or to mixed numbers: — 1. f 1 5 8 3. S 5 4. Hi ¥/ ¥ ¥. V .{ 5 T2- H u. w 8 «H ^5 REDUCTION. 87 i), G. mm i. H. !). 10. H31 I 35 H (Ml 1 1 ff 4 » t » 24 76 84 2:1 8 :< 6 4 1 925 21 f mi. 54 I 1 2:1 6 01 700 1 830 1 fill ' 764 3 1 gal. cords. 9 7 8 1 5 I 5 2 3 1. 52.7 6 89 7 1 9 3 f 6 8 1 « 7 ^V da. 36 9 TT yd. 1 (I n I) 7 3 . 17 18 1 I 3 3 • 76 84 9 223 1 8 5 6 7 8^3 • 253 S 6 94 TT 11). oz. EXERCISE CXVIII. 1. How much money has John who has $'/? 'J. If a basket of peaclies holds i bu., how many ])ushels are tliere In ;{69 baskets? 15. A walked from X to Y at the rate of a mile each i hr. He walked h^ hr. How far is it from X to Y? 4. A druggist has 97 psiekages of medicine, eaeh weighing h lb. How many pounds does the medicine weigh? 5. How many bushels of wheat are there in 964 bags, eaeh oontaining i bu.? 6. Which is the he.ivier — 786 packages, each holding i lb., or 6'J9 packages, each holding i lb. ? 7. Express ^ in., fs lb., H:- oz., eaeh as a whole inimber. 8. A bottle holds i gal. of wine. How many gallons are there in 5 doz. such bottles? 9. The perimeter of a rectangular room is -^ ft. It is' four feet longer than wide. Find the length and width of the room. . 10. A farmer sold a load of oats consisting of 79 bu. at $i per bushel. How much did he get for the load? EXERCISE CXIX. 1. Reduce i, i and | , each to twelfths. h r and i, twenty-fourths. 3. f, t and 1, eighteenths. 4. 3 f and A, twentieths. 5. !, f and A, thirtieths. G. f and 1, twenty-fourths. 7. i fV and IL thirtieths. s. f, 1 and i forty- seconds. 5). 5 8, i\ and i\, forty-eighths. 0. 5 rV and H, sixtieths. iii 88 ARITHMETIC. EXERCISE CXX. 1. llediKH' '> 3. 4. 5. 6. 7. 8. 9. 10. 1. ^1. 3. 4. 5. G. 7. i. 9. 10. 1 2 30 4 4 26 .id 2 6 4(1 1 4 4ft 66 93 68 1 T55 20 3 5 n u 25 *0 4 4 80 1 5 3 5 51 T 9 1 3?f and and and and and find and and and and is, 4 9, \l 38 20 97r, 1 4 3 34 1 , 316 6 24, each to fourths. ' tifths. sevenths, ninths, eleventlis. eighteenths, twentieths, twenty-fourths, rhirty-tirsts. fifty-seconds. EXERCISE CXXI. Supply numerators in |=t? 1 ( 4 = 33 l=TTr I 2 16=4 84 14 4 = T? Supply denominators in |=*® " " "535 II = it " "11154 12 = it a "81 12 = " " 4^8 2 3 6- 5 9- 6 13- 15- 25- T 5 _ 1 - 7 _ 11- H-- 6 TT= 8 ^4 = 3 8 '8 =7T -m '-T -T . 28 .12 1 -.7 2. .1 6 ■a. ; t 1 1 1 - 1T = 5"5 1 4 an-- 5 5 TS2 = 1 I 1 s — y 6 3 it = 9 2Tt = 9 TS = -1^ 44 feXERCiSE CXXII. Reduce to equivalent fractions in lowest terms: 1. 1 2. H 3. 80 TTJ 4. AV 5. 3 2 T57 6. 4» 2 7. 2 6 40 2])To- 8. 1242 2 3 2 ;t 9. 56 8 TT f T 10. 3 1 -10 9^3 9 T2" 27 4? 9 T5S 1 5 9 5TT 19 2 3 1 2 7 5 5 3 3TF 3 6 2 IT 9 3 2 112 T T TT 4 2 2 7 7 2 8971 42 ¥8 72 25 2 09 21 5 36 5 "5TT 1428 T530 26 5 1 326 5 "9¥T0Tr 2 6 194 8 1 3 2 14 4 12 20 4 — 7 28. 3 6 63. 1 5 2J5- 22 1 2ff0. 3 1 6 T4 6 • 1 144 170 • 226 8 3444. 47 7 6T9^D. 6 53 9 T¥7-g^3- 3 6 73 IS. lis. ^nths. ^ths. -fourths. firsts. iconds. ^— n 1 t _44 1 S = 19 6 3 n ^^ « H 1 2fi = 9 3 Id— • 14 4 12 2 4=^" 1 28. 36 6 3'- 1 5 » 221 3 1 6 T4 fi- ll 44 22 6 8 3 4 4 4 • 4 '•0-5 6 53 9 T 2¥¥3 • 3 6 13^ HKDUCTION. 89 EXERCISE CXXIII • Keduee to equivalent f ruet IOI18 having leant common denominator: 1. 1 and i H and 5 1 6 A and |]. 2. '\ and 2\ 5 and 2\ A and n. 3. 2 and 3 i and 1 6 i and J . 4. 3 and I 7 and 5 9 A and "6. 5. I and 9 ": and A i and A. 6. i\ and TT A and iPi A and 2^. 7. 6 Jtnd h i\ and i\ f\ and 2^. 8. A and t\ 9 and n A and li. 9. iV and 11 1 1 and 2 3 2t U and 42. 10. U and A 2 8 and 'h 24 and 12. EXERCISE CXXIV. Keduee to equivalent fractions with least common denominator; 1. t, 2. I 3. A., 4. 6 '1» 5. A, 6. i\, 7. A, 8. 8 T5, 9. 1, 10. 9, 5 12 4 25 6 1 T2, 1 1 T8, A, ii, 11 5 1 H» A, and t\ and ^V and U n and 11 and u and -A and tV and A and M and 1 3 14 1 1 T8 1 1 ^4 1 1 36 EXERCISE CXXV. 3 I» 2 Tf, 3 19) 2 5» 3 4, 1 1 1 &, 1 7 24? 1 7 2 , 5 I 1 , 1 H 2 6? 3 14 6 TJ 5 7 8 5 T, 1 7 2 0, 1 3 2f, 5 'IT, 5 t, 23 4 5' and and and 4 46' 2 8 2T tV 1 1 14 1 3 24 1 1 2f 2S I 8 and and and and and and and 1 II • 1 1 4 2- 1 9 24- 1 5 28- -A. 1 3 71- Which is tlie greatest and which the least of the following fractions? 1. 2. 3. . 4. f, I and f 4 , i and |. 17 6 .,,,/] 5 21, T ana 6 f, -A and I. 4, Ti and U 1, A and 1 . A, At, 2'8 and 1 1 3 6 At, U, U and 11 90 AIUTHMKTIC. Armn^«' the followinp: fnictioiiH in onlcc (tf lunpfnitiuU' : — \L ki, U and A A A 11 1 1 7. 1 1 1 B 1 3)) t 3 3« » 1 t\ Jiiid 1 it, JO HlUl HO 24, 4 I's, 1^8, 2 6 and U .•ind U. I'^s, L^. and U. H. Find a fniftion with 00 for (Icnominutor intcnnt'diatc in valiH' Ix'twcon I and J;. y. Find a fraction with H4 for dcnoniiniitor ^'rcater than f; and k'HK than ". 10. Find a fraction witli 72 for denominator as much U-sh tlian g as it is j^rcatcr tlian i'^^. EXERCISE CXXVI. Kcduce the following eonijtound fractions to 1. 2 3. 4. 5. G. 7. 8. 9. 10. of G 1 1 I of ^ ^ Of H i of 1 I of 1 2 J 2 IT 4 1 2 O fi of I of 4^ of 3G of^ ofl I of i I of A 8 If lof iij I of A 4 of ^^ I<'f4^ i of r)G I of I of f of I of 9 2 5 implc! ones: of g. of {i. of if. of h of il. of 4L of 72. of I of 1 t 5 I 1 6 7 8 6 t 5 .5 ,'5 I 1 of 1 1 . of n. 21 of G5 of 13 of 10^ 81 of m of lOi (,f 7 J Find the sum of III. ADDmOIN OF FRACTIOINS. EXERCISE CXXVII. 1. ^ • 3. 4. f). 6. 7. 8. 9. 10. A, IT, IT tV, fV, iV 1 IT, A, t\ 4 5, 3 4, /.r i A, 41 I 1 6, 4 t, tV, If if, H, II H, 15 4 4 , H f, 5, 9 1 T, S IT, 2_ ? 6, 2 T, .3 T, 4 ¥) ^\, M, f, 2 3^, 1 7, 5 «, 5 6, 1 1 T4, 1 9 3 4, 3 5, 3 "f 8 IT 8 ^S H 5 t\ 1 3 ?8 9, 4 4 TST, 3 !^, 3 4, 5 6, -X- h I 2 T3, 5 3 , 4 T, O M 5, T'fT, tI, 0, 8, t\. 9 f¥. If. 9 ■3^8. t\. 20 . 4 ■2T. 9 TI- ADDITION OP FnAOTIONS. 91 HI EXERCISE CXXVIII. !U1 11 udi'i. nd \l- tMliiitc ill T than il MH'h less es: — 1 5 a. [9 Of H L' " 2 S o f 71 i, 5 f\, A A, A 1, If ■f, 9 ^8 2 5» iV If, H M, A i, A f, A 1. Add i to i < to li i to^ 2, iv'M li to i \ t.) iV I to ,', 8. Add ;; to A S to A 8 i... H 8 to 1 J 4. Add g t«» 2^ 1 to 1 4 to l^ T). Add 1 to A if to A Vf to A G. Add A to A A to A A to iV 7. Add /, to .'^T A to A A to i\ S. Add I to ,\ i to-rV } to ,^6 9. Add 1 to •? 4 tog i to A 10. Add U t<) {3 n to 11 Htoll EXERCISE CXXIX. Sini)) lify:- 1. l +,^ + 1 + 1. 2. 3 +^ + J + 5 + A. 3. 2 1 2 + 2^« + 5 + A. 4. 1 1 4 8 +9 + ^ + r, + 1 +u. T). t + A + A + 1 18 + 21 +20. G. t2l +31 + 71 + .)! + C1. 7. 7i\ + 3 A + 4.^ + G,^ 1 +8A +GA. 8. 2:1 +3] + 4i + .-)^ + 21. 9. 11 + ^ + 2A + 7i + c. 10. 3i +9^ + 7A + >■> + 42V. EXERCISE CXXX. 1. John spent i of his money on Monday, i of it on Tuesday and w of it on Wednesday. What part did he spend altogether? 2. A fanner has three fields; the first contains 10| acres, the second 91 acres, and tlie third 9tij acres. How many acres had he in all? 3. How many pounds of butter are there in four tubs weigh- ing respectively 274 lb., 24| lb., 30* lb., and 29A lb. 4. How man^' tons of coal are there in four loads weighing respectively li t.. If t., Ira t. and larr t. 5. What fraction is that which exceeds S^ by i? i:h IMAGE EVALUATION TEST TARGET (MT-3) 1.0 !f"- 1^ 1.25 S *^ III 2.2 I.I 1.*^ 1^ 1.8 1.4 nil 1.6 ■y ^ *? />^ ^'^ %. # 7 Photographic Sdences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 <V iV <^ ^^ ■\ C\ \ o^ '% 92 ARITHMETIC. 6. A weighs 172| lb. ; B weighs 5^ lb. more. How much does B weigh? 7. What number is that from which if 4 J be taken the remainder will be aff? 8. One man rode 17ts mi. Another rode 4A mi. farther. How far did the second one ride? 9. A- grocer has ii barrels of molasses. The first contains JJ3i gallons, the second 45i gallons, and the third 35| gallons. How many gallons are there in the 3 barrels? 10. On Monday A rode 35f mi., on Tuesday 40^ mi., on Wednesday 361 mi. and on Thursday 20 r* mi. ride in the four days? How far did he IV. SUBTRACTION OF FRACTIONS. Subtract : t^tK« ;idt CAAAI. 1. i from f f from 1 1 from V. 2. 4 from f A from ii f from |. 3. TIT from f A from 1 f from |. 4. T*i from f f from f 1 i from H- 5. 1 fromi: 1 fromH f from M. 6. 4 from 1 1 from^^ A from A. 7. A from If A from i 1 from U. 8. U from U A from H fl from if. 9. U from H 11 from H A from Ih 10. J from 2 f! from 3 4 froni 5. Simplify 1. ._ EXERCISE CXXXII. g — i ¥ —I 1 -i 2. f -1 A— A l-f. 3. l-l A-A H-ii. 4. j\-j\ H-i§ u-n. 0. •sPt— /^ il-A fi-A. Find the difference between; — 6. A and A A and A 1 andA- 7. -1 and il A and A li andM. 8. TT and ii ^h and A A and If. 9. U and V2\ IS andl? ' 11 andAV 10. tV and tItt 41 and U A\aiid|I. SUBTRACTION OF FRACTIONS. 93 ni 1^ mi., on far did he I is white, f red, and the rest green. How What EXERCISE CXXXIII. 1. Henry had I of a dollar and spent I of a dollar, much had he left? 2. Of a pole part of it is green? 3. How much must be added to hi to produce '§? 4. How much does the sum of i and i exceed the sum of i and i? 5. Subtract the difference between /g and tj from the dilTer- ence between ^V and /?. 6. The sum of two fractions is fj and one of them is H- Find the other. 7. Find the sum of the greatest and least of the fractions \hi hri, 1, I, and subtract this sum from the sum of the other two fractions. 8. A traveller went VV of his journey on foot, A by railroad, and the remainder on horseback. What part of the journey did he go on horseback? 9. Find the difference between the sum of i and ^ and the Slim of -^5 and ^pg. 10. The sum of three fractions is MS- Two of them are is and ■i;j. Find the third. Simplify: 1. 2_ 3. 4. ^ ;). 6. 7. 8. 9. 10. EXERCISE CXXXIV. II 9 6 — Jj~^ — iff T^ S^% -3A 6tV -2il 7/4 -41 19 -4f £?1 S 04¥ 32U-5lf Ml -161 41/2-171 r:l 2 8A -5i*i 71 2 <T5 - -2 A. 5i -41 71 - -7tV. 7A -2/ir StIt- -2 A. 8t\ -3A 7A - -2 A. 4A -11 m - -5f|. 36 -12i*i 24 - -3M. 4H -4il 21A- -lOA 27A-6|i mi- -7iL 561 -1711 48! - -161. IGA-^h 26^, -^Vs EXERCISE CXXXV. 1. From a barrel of vinegar containing 31i gallons 14| gallons were drawn. How much was left? 2. From a piece of cloth containing 35i yards a merchant cut 21 J yards. How much was left? 94 ARITHMETIC. 3. A man staited on a journey of 45 J miles, and travelled 28S miles. How far had he still to travel? 4. The sum of two numbers is 56i, and one of the numbers is 251. What is the other number? 5. If I have $437i, and pay out $341iV, how much have I left? 6. From a farm containing 1648^ acres, 4J^ acres were sold. How many acres remained in the farm? 7. John's monthly salary is $1661 and his average expendi- ture is $971 i. How much does he save each month? 8. What must be taken from 35i to leave 22|? 9. The sum of two numbers is 26^^. One of them is 10^. Find the other number. 10. From a barge load of coal consisting of 540i tons 375^ tons have been taken. How many tons are still on board the barge? EXERCISE CXXXVI. Simplify: — 1. 31 +4i -6f • 81 -71 +U. 9 mm • 51 -21 -1 8 -f +3! -li 3. lA -/^ -.v 11 +5i -fl. 4. 5^ +4t\ -4i 15 -3f -21. 5. f? +41 -! m +m -1/t. G. 7\ -2f +5 -7M 5oA-4f -n -s^\. 7. 2G -51 -61 -2h 30 -U -fi -h 8. 4^ -3^ +5-/T-2f 151 -101 +71 -5tV. 9. 31 +41 -7-^j-hdl 141 -lOA-41 +II/1 10. 3A -11 -U +7A 8A -211 +41 -8A. EXERCISE CXXXVII. 1. From 144 lb. of sugar there were taken at one time 171^ lb. and at another 28r^ lb. What quu,ntity remains? 2. A cask of wine contained 42i gal.; of this 13f gal. Y^ere drawn off, and 12 J gal. leaked out. How much remained in the cask? 3. A grocer bought 89i lb. of tea; of this he sold 13i lb. to one customer, 9i lb. to a second, and 12f lb. to a third. How many pounds had he left? 4. What number must you add to the sum of 126| and 2401, to make 5601? MULTIPLICATION AND DIVISION OP FRACTIONS. 95 travelled umbers is ch have I were sold. 5 expeudi- sm is lOU. tons 375U I board the h If -li n :K 4 S - 3 "8 ■ -3A. :i -5tV. one time lins? ]s 13t gal. remained lold 13i lb. Ito a third. and 2401, 5. A man had to walk 97f mi. He walked 30j mi. the first day, 33i mi. the second day, and finished the journey the third day. How far did he walk the third day? 6. A drover bought 4 cows for $168i, and after paying $341*0 for pasturage, he sold them for $203i. Did he gain or lose, and how much? 7. James had $12?, and Jane as much, lacking $l\i. How much money had they together? 8. Bought a quantity of coal for $140f , and of lumber for $456L Sold the coal for $175i, and the lumber for $516i^. How much was my whole gain? 9. A merchant had 3 pieces of cloth, containing, respec- tively, 19f yd., 36i yd. and 33f yd. After selling several yards from each piece, he found he had left altogether 711 yd. How many yards had he sold? 10. A merchant sold a customer 22i yd. of silk, 3i yd. of paper muslin, li yd. of silesia, 5t yd. of cambric, and 5i yd. of ruffling. How many yards were sold? V. MtLTIPLICATIOIN AND DIVISION OF FRACTIONS. EXERCISE CXXXVIII. Multiply " — 1. h by 3 f by 4 i by 6. 2. t\ by 5 t by 7 4 by 6. 3. $A by 9 $41 by 6 $A by 8. 4. A by 36 A by 26 1 by 24. 5. i\ by 32 rV by 12 f by 16. 6. f by 24 hi by 10 A by 12. 7. TT by 22 4 by 21 1 by 36. 8. 1 by 27 A by 35 i by 27. 9. A by 21 A by 25 U by 15. 10. U\ by 20 4f by 14 31 by 24. EXERCISE CXXXIX. Divide :- - 1. f by 2 if by 4 H by 3. 2. M by 8 if by 7 tVt by 12. 3. 61 by 3 201! by 4 28U by 7. 4. 3411 by 17 27if by 9 54M by 6. 5. 6f by 9 4f by 10 15^ by 23. I m ml P 06 ARITHMETIC. Divide: • G. 2f by 5 61 by 6 10^ by 5. ^ 7. h hy 3 3 by 5 I by 4. 8. ^ by 9 1^ by 6 A by 5. 9. n by 7 11 by 9 5]^ by 9. 10. 711 by 8 1 84f by 12 EXERCISE CXL. 36 A by 7. Multiply: — 1. 6 byi 12 byl 20 b> 1. 2. 1 by! I hyl 4 byi 3. 1 by! 1 byf 1 by 1. 4. f by 4 t\ by a 1 by I 5. i byil f byf f by V. 6. f byV- V byl 1 by V. 7. 1 by^ M byH i by U. 8. if by 1 n by if HI by A. 9. Mby4 !4 byT%^ 11 by If. 10. H by 11 nt by n EXERCISE CXLI. V- byV. Simplify: — 1. 4^ x4^ 51 x5| n x7i. 2. 51 xf)^ 6f x6f 8f x8! 3. 61 x6f 71 x7| 12|xl2t 4. ^ xf xl 1 xl xlf f x^ xH. 5. 1| x2|x3| 3i x? x5l 3i x4l XtV. 6. 21 xMxl 5i Xt\x3^ 81 xA .x5i 7. U xlhx^h 2f X 41x15 3 x7i x-U. 8. 21 x3ix4f 3i xl xl? lAxljVxf. 9. $31 xtjV $3ix/2 925 mi. x|. 10. $37ixir) 140oz.x2|i 21 lir.xlL EXERCISE CXLII. 1. Find the cost of 9i yards of cloth at $4i a yard. 2. When flour costs $6| a barrel, how much will 26f barrels cost? MULTIPLICATION AND DIVISION OP FRACTIONS. 97 by 5. by 4. by 3. by 9. rby 7. by I. by I. by I. byi by by by II 5 8 5 i 111 by S^ by by V- x7i. x8! x^ xH. x4l xiV. xrr X'")^- x7i xii PtxIjVx^- If) mi. X 5. hr.xla- lard, ill 261 barrels 3; Find the cost of 51 dozen eggs at 121 ctH. a dozen. 4. John walks at the rate of H'i miles an hour, ilow far will he go in 2i hourHf ;'). A piece of clotii contains KJi ydw. Find the cost of i of the piece at $',H per yard. 6. If it takes If bu. of wheat to how an acre, how many bimhels will it take to how 7s acrenlf 7. If a man earnn $\Vih per week, how much will he earn in a year of 52 weeks ? 8. If one horse eats ? bu. of oats in a day, how many bushels will 14 horses eat in G days? 9. A man owning X of 156| acres of land, sold i of I of his share. How many acres did he sell if 10. At $95 per ton, wiiat will be the cost of i of § of a ton of hayf EXERCISE CXL!II. 1. A boy spent j of his money and had 96 ct. left. How much had he at first? 2. If I buy ? of an estate for $18000, what should I give for the whole of the estate? ',i. After going 121 miles I have still f o of my journey to go. Find the total length of the journey. 4. Seven -ninths of a post is in the mud and water. There are 8i ft. in the air. How long is the post? 5. A traveller 'finds that 175 miles is A of the distance he has to go. How far is his journey? 6. A man at his death left his wife $12500, which was | of c of his estate. What was the value of the estate? 7. If f of a certain number is 42ro, what will } of l|f of it be? 8. In a battle a general lost n of his army. He still had ;{4500 soldiers left. How many soldiers liad he at first? 9. John has read -^ of a certain V>ook. He still has 112 ]»ages to read. How many pages are there in the book? 10. A person dying left i of his estate to his wife, rs of it to his daughter and the remainder to his son. His son received $16400. What was his estate worth? Simplify: — EXERCISE CXLIV. 1. 3. 4. fx(l|+2H 8x(3-f) (4H2|)x2| (4^-21) x2A 7x(6-2^). (3J-2f)xl. (3i+2i)xU. y» ARITHMETIC. Simplify: — , .'). (i + l) of ,«, (32^6-5'',) of lA. G. (^ + i-i)xl2 (2^3^-4^x12. 7. (^-Ul)x24 12x(2R4j-3i). 8. i\ of U of Axa2 1x1 of 4 of A. 9. (4^-2.1+51) of 4J (^>f3-iof |)x2A. 10. (1 of n+2i of l-?)of A (31-1 of U) of lA. EXERCISE CXLV. 1. If a train of eai*s runH 22i mi. an hour, how far will it run in Si hrs.? 2. A merchant bou^'ht 500 cords of wood at $2| per cord. He sold 75i cords at $4i per cord and the rest at $5. Find his gain. 3. A merchant purchased 150 yards of cloth for $675, and sold I of it at a profit of $f per yard, and the remainder at a loss of $^ per yard. How much did he gain? 4. There are 50i bu. of wheat in a bin. How n^uch remains after sowing a field of 7^ acres at 2^ bu. per acre? 5. A bought 319 acres of land at $200 per acre; he then sold 250^ acres at $250 per acre, and the remainder at $266J per acre. How much did he gain? 6. From the sum of 3^ and 2i take their difference and multiply the remainder by 2f . 7. What number added to 14|f+?+^+4TSV+lH wiU malte GOT 8. Three men own a hou.p worth $6250; one owns VV. the second ^ of it. What is the value of the share of the third? 9. A grocer bought 100 barrels of flour at $6| per barrel ; he sold 49 barrels at $7i per barrel, and tixe rest at $7i per barrel. How much did he gain? 10. A drover bought 64 sheep at $71 apiece; he then sold 30 of them at $6^ apiece, and the remainder at $8| apiece. Did he gain or lose, and how much? ivide : 1. 10 by 4 20by| 3. 5 byf 4. 12 by tV 5. 16 by 3^ EXERCISE CXLVI. 6 by I 25 by i\ 8 by I 25 by i 25 by 4| 12byi 36 by A. 9 byT*t, 27 by I. •) j. 3C by -^ ;t 4 MULTIPLICATION AND DIVISION OP FRACTIONS. 99 Divide:- - 6. 42 by 6J 45 by ')l 7. 20 by 31 25 by 61 8. 3 by^ 1 byl 9. ! byl I by 1*5 10. 31 by liV 21 l)y 41 EXERCISE CXLVII. Simplify : — 1. 71 - -4! /. - -M 2. i\ - 4 -6 u - -II 3. U - -fl iSS - -U 4. 11 - -41 8i - -12^ 5. iiA- -12^ s\ - -2^ 6. 33^ - -lOH VA - -n 7. 6i - -2i n - -n 8. 121 - -31 4T«r - -51 9. 71 - -41 51 - -7^ 10. 18 - -2i 12fT- -81 74 by 61. 42 l)y 5L I byt. JTbyli. 52 by 55. J - — Afif HI 21 • 9J TTT- --301. 5^ 181- 8! 171 501 3. 4- lif •Itl 31. ";8 -2J. i>S3 -3 6. 8*6 . EXERCISE CXLViei. 1. At $* per yard, how many yards of cloth can be bought for f.*}U? 2. A man rode 37i miles in 4i hours. How far did he ride in one hour? 3. A farmer sold 25f acres of land for $072. What was the pi'ice per acre? 4. A vessel sails 464 miles in 26j hours. Find its rate per hour. 5. A miller has 27i bushels of meal which he wishes to put into bags, each bag to contain 2f bushels. How many bags will be required? 6. If 3i pounds of beef cost 431 cents, what is the price of a pound? 7. If a man travels at the rate of 271 miles an hour, how long will it take him to travel 784i miles? 8. By what numb'^r must \Q\\ be ruultipliad to produce 1481? 9. A fivmer sowed 478i bushels of grain on his farm. If he sowed 2^ bushels per acre, how many acres did he sow? M Si S; ; ■I 100 AUITHMETIC. 10. A Mnuitoba faritipr thranlu'd 10127 IuihIu'Is of wheat. This WHH ail av<'raKe yield of 127A ))UHlielH jun- aore. How many acres liiul he in wheat? 11. If the cost of carryinpf 'jr)?')^ biisliels of wlieat from Winnipeg to Montreal is $31)4.9] , find the rate charged per bushel. 12. If a man can do a piece of work in 18 days l>y working 14!j hourH per day, in how many days can he do the same work, if he works 8i hours each day f l.'l. When 3')! bushels of potatoes cost $28.60, how much should be paid for 4i bushels? 14. Find a number which divided by 3i, the quotient increased by li, and the sum multiplied by 7i, the product is 54. Simplify: — EXERCISE CXLIX. 1. (r)|+3U-iJ (8|-31)-U. 2. (8i-3i)^U 4j-(3^-2l). 3. 7\^{-,^,-2\) 20- (51-41). 4. (3-n-(3+i) (4i-2!)-(4|4-2!). 5. (5H4^)-^(.J^-41) (2U-18t\)-(2U+18A). 6. (|_i+l)-.(H^-l) 3?-.-5f of jV. 7. 201 x3i of Ty*„+21 (2Uli)-(3ix5n. 8. (8lx3Ax2!)-^3l (2R3j)xl2^4i. 9. 1 of? of 2-4^ of 3i (4i_3i)x8i^l()0. 10. 7i^(4l--3l-5i) 72-i-44-f-04-|-«>3 . EXERCISE CL. {Simplify: — 1. hxl-\xl i of Kl of I 2. ixKl-l KKi-i 3. 51 of 8|xll 4. 5^ of 81-21- of 3^ 5. HI of l-l of I 6. 8|-16f+^ of I 7. f of fUlof IB 8. 3|-|xl| 9. (12|-8f) of lA 10. T^?-lix2A 51x8.1^21x3^. 7l-6A-6A-7i. f of U of 91-1 of 3|-i of If. 12!-8t of lA. 12!-8fxlf*T. A-ll of 2A. 3f GOMPLKX FRACTIONS. 101 of wheat. How many VI. COMPLEX FRACTIOINS. EXERCISE CLI. Simplify 1 "^^ • 1. 1" 3 4 6 * 2, 8 i 8 "4 9 3. 2\ r)i 4i 3i 4. 5. 41-3.^ 7^-5] 41+3^ 7i+oi 6. 3l+4i 31-12 G^+1,V 93 5 -4 — J» 7. 1^ of 11 7h-2} 11 of i\ ^ of 3^ 8. 2i of 2h 21 of U li of 3| 5^ of 31 9. n 16 li of A of 3| t\ of 2A of H 10. (2-U)x2i 4h of 5l-f2| i of Ih 4^ of r)i-iof EXERCISE CLII. Simplify: — 1. (321+71 )-f of t\. (5i+3f)-(94-5U. (i^V+Uf fx|)-(/ir-iof|+n. rV--(/oof H)xiS-.UxU. I of 9?^+3g-r8To — Tlor. 6. 3j-2^x4i-4TV+3TV. 2. 3. 4. 5. '•I 102 ARITHMETIC. 7. U-|-2§x32+U-Ux38. G]-5i Gi-r-fji 3 9. ( i+' 1 G' +''!)-iixJ5i. 3 4ft/ «i2 10. 2|-.^ of lii + ii 6 + 3 <>t H— bX 86 EXERCIltE CLIII. 1. What must be added to |-f ^+7J to make 10? 2. Subtract the sura of 4j{- and IJi from the difference between 151 and .'i§. 3. Multiply :H+5f Vjy 4,^ of U and divide the product by 8-1^. 4. Bv how ranch does the sum of i+i+i+a+u exceed the sum of l+i+A+if^? '). The sum of J of 1X2 and f of |X4i of ^ in equal ^.o how nnmy times their difference? 54x G. The smaller of two numbers is ^ — - . ; and their difference f of 4* is . . Find the larger number. 7. What number divided by 4|— i of Siif+i^ will make the quotient 2f ? 8. The product is 124; the multiplier is 8f. Find the multiplicand. 9. Find the sum, the difference, and the product, of ^j and H; also find their quotient, making the greater fraction the dividend. 10. What number multiplied by | of |X3f, will produce ff? VII. G.C.IVI. AND LX.M. OF FRACTIOINS. EXERCISE CLIV. 1. Find the G.C.M. and the L.C.M. of A, M and U- 2. What is the G.C.M. and the L.C.M. of i, ^ and H? 3. Find the G.C.M. and the L.C.M. of 4, 2f and 2f. 4. What is the length of the longest measure that can be exactly contained in each of the two distances, 18f feet and 57i feet? G.C.M. AND L.O.M. OF FRACTIONS. 103 r difference f>. Wlmt aio tlio longest Hectlons of wire fence, of equal length, with which I citn enclose a triimgulnr plot whoHO sides are respectively 'J'Jjf t'«'«'t, 'M\k f<"et, and !){) fe«'t? I low many sections are recpiireil to enclose the n»'l(lf (J. How nuiny times do«'s the L.C.M. of Hi, 48 and 5i contain the (l.C.M. of these nunihersf 7. What is the smallest sum of money with wiiich I could purchase a numl)er of sheep at I'Ji each, a number of calves at $4i each, or a numher of yearlings at .$98 each? How many of each could I purchase with this money f H. A farmer has H'M buHluds of corn, ()7i bushels of rye, 70| busliels of wheat. He wishes to put this grain, withoiit mixing, into the smallest numlxM' of bags, each of which shall contain the same quantl^iy. Required the quantity each bag will contain and the number of bags. 9. A merchant has three kinds of wine, of the first 1.34} gal- lons, of the second 128it gallons, of the third lloi gallons; he wishes to ship the same in full casks of equal size; what is the least number of casks he can use without mixing the different kinds of wine? 10. A, B, atid C start at the same place and travel round an island, A making the circuit in J of a day. B in ^ of a day, and C in ^ of a day; in how many days will they meet at the start- ing place, and how many times will each have gone round the island? VIII. DEINOMilNATE FRACTIONS. A Denominate Frj'ction is one in which the primary unit of the fraction is a denominate number, as I oz., f mi., 3 gal. EXERCISE CLV. Reduce each of the following to lower denominations: — 1. £| ^\s. Is. 2. $1 n $f. 3. It. I'lr cwt • I lb. 4. f mi. Ird. f yd. 5. f A. TT sq. rd. V'ff sq. yd. 6. 1 cd. A cu. yd. ^\ cu. ft. 7. Ibu. Ipk. fgal. 8. 8 gal. 1 qt. 1 gal. 9. i\ wk. A da. i% hr. 10. r tc. 6 ° I ; I. ' ' HI ^r^K^/^jzsL^raf— 104 ARITHMETIC. EXERCISE CLVI. Reduce the following: — 1. 7 mi. 5 id. 1 yd. to incheH; 2 mi. 2 ft. to inches. 2. 7456 ft. to miles, etc.; 2745 yd. to miles, etc. 3. 3f mi. to inches; 7| rd. to inches. 4. 5 A. 7 sq. rd. to scj. inches; 98 sq. vd. 14 h({. yd. to sq. inches. 5. 57896 sq. ft. to acres, etc. ; 100000 sq. ft. to acres, etc. 6. 2| A. to sq. inchei.; 3ri sq. rd. to sq. inches. 7. 4i t. to pounds, 2§ cwt. to ounces. 8. Ti mi. to rd., yd., etc.; i^ A. to sq. rd., sq. yd., etc. 9. 47212 sq. yd. to acres, etc.; 6912000 sq. in. to acres, etc. 10. 1 t. of water to gallons; 7000 gal. of water to tons, etc. Find 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. EXERCISE CLVII. the value of T^i of $140.76; f of $50,40. I of £3 7s. 6d. ; t of £1 8s. 4d. I of 5 t. 8 cwt. 6 lb. ; I of 2 t. 15 cwt. 9 lb. I of 7 mi. 35 rd. 1 ft. ^ of 3 mi. 45 rd. 3 yd. ; f of 4 A. 50 sq. rd. 3 sq. yd. ; | of 2 A. 100 sq I of 3 cd. 120 cu. ft. ; t of 12 cd. 72 cu. ft. f of 3 bu. 3 pk. 1 gal. ; | of 2 bu. 2 pk.' 5 qt. I of 7 gal. 2 qt. ; ": of 15 gal. 3 qt rd. f of 1 da. 8 hr. 40 min. J of 15" 45' 18"; f of 17° 24' 36". 1^- of 8 hr. 33 min. 20 sec. EXERCISE CLVIII. If 1 ft. is the unit, what immber expresses 8 ft.?, 12 ft.?, 21 ft.? If 2 is the unit, what number expresses 8?, 12?, 21? What part of 8 is 2? Of 12 is 2? Of 21 is 2? What fraction of 8 is 2? Of 12 is 2? Of 21 is 2? 1. Reduce I lb. to the fraction of a cwt. 2. What fraction of a pound is |d.? 3. What part of a bushel is §^ gal.? 4. Reduce f yd. to the fraction of a rod. 5. Reduce i in. to the fraction of a rod. 6. What part of a pint is ufo bu.? 7. Reduce atho cwt. to the fraction of an ounce. 8. What fraction of $9f is $7i? 9. What part of 2 mi. 130 rd. is 1 mi. 30 rd.? 10. What part of a foot is ir/sBi) mi.? APPLICATIONS OF THE xiEVlOUS RULES. 105 H(l. yd. to sq. in. 20 sec. EXERCISE CLIX. 1. Whftt part of a pound Tro> wt. is 10 oz. 13 dwt. 8 gr. ? 2. What part of £8 is U s.? 3. What fraction of a mile 74 rd. 5 yd.? 4. What part of 3i yards square is 3i sq. yd.? 5. What part of 5 weeks is 7 da. 23 h. 20 min.? 6. What fraction of a cubic yard is 7 cu. ft. 8G4 cu. in.? 7. What part is 26 gal. 2 qt. 1 pt. of 3H gal. ? 8. Reduce 35 rd. 3 yd. 2 in. to ihe fraction of a mile. 9. What part of a pound Avoirdupois wt. is 1 lb. Troy wt.? 10. Reduce 86 sq. rd. 4 yd. 5 ft. 127^3- in. to the fraction of an acre. EXERCISE CLX. V. 91 sq. rd. 7 sq. yd. 5 sq. ft. 29 aq. in. to sq. are equal to 432 lb. 1. Reduce 5 inches. 2. How many pounds Troy weight Avoirdupois weight? 3. If a pint of milk costs 2i ct., how many quarts can be bought for $8.45? 4. If a sheet of paper is 13i in. long and 8J iu. wide, how many such sheets will be required to cover an acre? 5. The circumference of a buggy wheel is 7 ft. 4 in. long. How often does it turn in 6 miles? 6. How many paces 2 ft. 8 in. long are there in 3 miles? 7. What is the cost of 12 bbl. of vinegar averaging 41 gal. 3 qt. 1 pt. at 12i ct. per quart? 8. Find the value of a pile of tanbark 100 ft. long, 39s wide and 181 ft. high at $3.20 per cord. 9. A merchant paid $35 for 8 bbl. of chestnuts averaging 2 111). 3 pk. 2 qt. per bbl. He sold them at 5^ ct. per pint. Find !iis gain. 10. Find the value of a pile of wood 225 ft. long, 5i ft. high and Q'k ft. wide at $4| per cord. IX. APPLICATIONS OF THE PREVIOUS RULES. EXERCISE CIXI. 1. If a cubic foot of broken stone weighs 168 lb., find the weight of 5 ed. 63i cu. ft. of such stone. 2. A pile of wood is 168 ft. long, 6 ft. high and 4 ft. wide. How many corde are there in it? 3. What will a pile of stone 240 ft. long, 8 ft. high and 4 ft. wide cost at $2.50 per cord? II \'^ 106 ARITHMETIC. 4. What are 3 bu. of strawberries worth at 2 et. per pint? 5. A gardener sells 495 crates of berries, each containing a bushel, at 2 ct. a pint. How much did he receive for them? 6. In 1896 how many days were there from Jan. 10th to Oct. Drd, inclusive? 7. How many minutes were there in Jan., Feb. and March, 1899? 8. How many more minutes were there in Feb., 1896, than in Feb., 1897? 9. What is the value of a barrel of syrup containing 29 gal. li qt. 1 pt. at 9 ct. a pint? 10. How many poles each 7i ft. long, placed in a straight line, will reach 2 mi. 280 rd.? EXERCISE CLXII. 1. Divide 13 cwt. 63 lb. equally among 29 persons. 2. A pint of water weighs 1 lb. 4 oz. How many pints are there m 22 t. 11 cwt. 40 lbs. of water? 3. If 178 cwt. 61 lb. are divided into 53 equal parts, how many ounces are there in each part? 4. How many tons, cwt., etc., are there in one million ounces? 5. How many parcels each weighing 2 lb. 12 oz. can be made from 2 t. 9 cwt. 50 lb. of sugar? 6. Find the cost of 4 t. 19 cwt. 99 lb. of sugar at 5 ct. a ])ound. 7. How many ounces of iron are required to make 32 iron bars, each weighing 2 lb. 7 oz.? 8. I bought 3 cwt. 19 lb. of tea for $127.60, what did I pay per lb. for it? 9. Out of a box containing 3 cwt. 78 lb. of sugar, how many 2 lb. parcels can be made? 10. A railway truck weighs 5 t. 3 cwt. On it are placed 97 iron bars each weighing 3 cwt. 76 lb. Find the total weight in pounds of the truck and bars? EXERCISE CLXIII. 1. How many grains in 11 silver medals each weighing 4 oz. 5 dwt. 6 gr.? 2. If 7 silver medals each weighing 10 dwt. 13 gr. are melted and the silver divided equally among 11 persons, how many grains would each have? 3. In 2468 grains of gold dust, how many ounces are there? 4. In a silver box weighing 10 oz. 16 dwt., how many grains are there? APPLICATIONS OF THE PREVIOUS RULES. 107 er pint? ataining a ■ them? 3th to Oct. nd March, 1896, than ling 29 gal. . a straight 18. [ly pints are [ parts, how one million lean be made at 5 et. a ake 32 iron at did T pay r, how many placed 97 tal weight in re 'ighing 4 oz. \ are melted how many Is are there? Imany grains 5. How many grains of gold will be required for 12 orna- ments each weighing 1 oz. 18 dwt. 12 gr.? 6. Reduce 58376 grains to lbs., oz., etc., Troy. 7. How many forks averaging 2 oz. 9 dwts. each can be made from 5 lb. 1 oz. 5 dwt. of silver. 8. How many lbs. of silver in 270 spoons, each of which weighs 1 oz. 13 dwt. 8 grs.l 9. Express 4040789 grains in lbs. oz. dwt., etc. 10. A pound Troy contains 5760 grains and a pound Avoirdupois 7000 grains. Find how many pounds Troy there are in 94 lb. 8 oz. Avoirdupois. EXERCISE CLXIV. 1. How many inches are there in a mile? 2. A lake is 112 fathoms in depth; what is its depth in inches? 3. A wheel is 13 ft. 9 in. round. In turning 768 times, how many miles does it pass over? 4. Find the cost of 20 miles of telephone wire at 35 cents a lb. supposing a lb. stretches 80 ft.? 5. Find the cost of 4 miles of barbed wire if 4 feet cost 8c. 6. What will it cost to survey 25 miles of road at 25 cents for every 66 feet? 7. The distance from London to Harrisburg is 61 miles 224 rods. How long will it take to walk that distance at 32 rods per minute? 8. How many inches are there in 5 times 4 mi. 319 rd. 5 yd. 1 ft. 6 in.? 9. How many more inches are there in 3 times 7 mi. 1759 yd. 2 ft. 2 in. than in 4 times 3 mi. 319 rods 5 yd. 6 in.? 10. A boy going to school walks 126720 inches every day. How far will he walk in a school year of 220 days? Answer in miles, etc. EXERCISE CLXV. 1. At 40 cents a gallon what would be the cost of 5 bbl. syrup, each containing 36 gal.? 2. A man bought a hhd. (63 gals.) of molasses for $18.90 and sold it at lOe. a pint. How much did he gain? 3. 1 bought a bushel of chestnuts for $4.80. What will be the cost of 13 qts.? 4. A gardener has 13 bu. 2 pk. 1 gal. 2 qt. of strawberries. How many quart baskets will be needed to hold them? 5. If 376 gal. 3 qt. 1 pt. of milk be divided among 9 charities, how many piuts will each receive? I ■i i; ' f if 108 AHITHMKTIC. 6. A man bought 14 bags of beans, each containing 2 Vm. 2 pk, for $21, and sold them in boxes of 1 bu. 3 pk. eacli, so as to neither gain nor lose. Find the price per box. 7. How many loads of apples of 27 bu. 3 pk. each can be bought for $53.28 at 48e. per bushel? 8. What is the value of 324 bags of beans, raeh containing 2 bu. and 1 pk. at 70c. a bushel? 9. A milkman started with 10 gal. of milk. He sold i pt. to each of 52 people and a pint to each of 50 others ; how much has he left? Ans. in quarts. 10. Reduce 143 bu. 3 gal. 3 qt. 1 pt. of wheat to pints, and find the value at H cents a pint. EXERCISE CLXVI. 1. A farmer travels .!00 miles in 8 days, liow many days will it take him to go 4224000 ft.? 2. A man walked 13G miles in 45 hrs. 20 min., how many feet did he go per minute ? 3. How many times is 195 yd. 1 ft. 8 in. contained in 1 mile? 4. A train goes 30 miles an hour, how many feet does it go l>er second? 5. A rate of 22 yd. in 5 seconds is equal to what rate per hour? 6. A tank has 12000 gal. of water in it. How long will it take to empty it, if 5 pints are emptied in a minute? 7. How many days of 10 hrs. each would it take to count 30,000,000 sovereigns at the rate of 100 per minute? 8. Find the cost of 3975 lb. bran at $1.44 per cwt. 9. A farmer paid a laborer $1.75 a day for the month of August, what should he get if the month began on Wednesday? 10. Find the cost of 40 lb. of ice, delivered three times a week from April 1st to October Gtli inclusive, at COc. per hundred pounds. EXERCISE CLXVII. 1. Find the difference in the cost of 17 bu. of wheat when sold at Ic. per lb. or le. per pint. 2. A pile of 4 foot wood is 64 ft. to contain 10 cords? 3. How many steps each 2 ft. take in walking 3| miles? 4. A farm of 111 acres is divided into fields of 7a. ()4 s<|. r'l. How many fields are there? 5. How far can I walk in 10 hv. 45 min. at the rate of a mile in 15 minutes? 6. How many more hours are there in January than in February, 1896? long. How high should it l)e () in. ill length will a man APPLICATIONS OP THE PREVIOUS RULES. 109 taiuing - how many 7. How. many paces each 2 ft. 8 in. are there in 2J miles? 8. Rednce 3 weeks 19 hrs. 2") min. 15 sec. to seconds, and lii'S weeks 6 days 19 hrs. 5 min. 45 see. to seconds, and divide the larger quantity by the smaller. 9. The circumference of a wheel is 16 ft. (J in. lon^. How often will it turn between London and Hamilton, 76 miles If 10. A coach wheel 10 ft. 9 in. round, turns 12 times in 10 seconds, at what rate per hour is the coach going? EXERCISE CLXVIII. 1. Find the weight of a dozen and a half silver spoons each weighing 4 oz. 4 dwt. 22 gr. 2. Add together .£:J7 17s. 4id.. £19 12s. lOid, £18.1 19s. .3d. and £52 Os. Hid. and take £93 lv;s. 5d. from the sum. 3. Multiply 3 cwt. 3 lb. 3 oz. by 69 and subtract the result from 11 tons. 4. A bicyclist travelled 50 miles in 3 hrs. 3 min. 20 sec. What was his rate in feet per second? 5. A train travels 95 miles 1100 yd. in 2 hr. and 50 min. How far does it go in 1 minute? 6. If I walk 350 yd. in 2 min. 40 sec. how long will it take me to walk 560 yd.? What distance can 1 walk in 7 min. 28 sec. at the same rate? 7. How many yards per minute faster is the rate, 42 miles an hour, than the rate 20 yards per second? 8. How many bags of sugar each holding 235 lb. are there in 6 t. 6 cwt. 90 lb? 9. A grocer buys 13 hhd. of sugar weighing 6 t. 8 cwt. 57 ib. How much did each weigh? 10. How many trees will be required to plant 27 a. 91 sq. rd. 22 sq. yd. 2 sq. ft. 36 sq. in., allowing 105 sq. yd. for each tree ? EXERCISE CLXIX. 1. How many more inches are there in 3 yd. 1 ft. 6 in. tlian in 3 ft. 6 in. 2. Three men can cut 8 ae. 36 sq. rods in a day, how long will it take them to cut 57 ac. 92 sq. rods. 3. How many days from March 13th, 1898, to July 3l8t, 1899, both inclusive? 4. How many miles will a boy walk to plough 6 acres turning 9 inches of a furrow? 5. A man bought 3 bu. 3 peeks of nuts at 75e. a peck and sold them at 10 cents a quart. How much did he make? r <f3 no ARITHMETIC. 6. A farmer in tlie North- West had 4H(> acres of wliejit, and the averaj^e yiehl was 27 bus. 'A pks. G qts. 1 pt! i>er a'.'re. What will the whole be worth at GO et. i)er bushel ? 7. The price of broadcloth at lOs. 8d. per yd, is jCUG 128. How many yards are there of it ? 8. A boy bought a bushel of nuts for $1 and sold them at 5 ct. a quart. How much did he gain f 9. If sound travels at 1144 feet per second, how long would it take to travel to the moon, a distance of 240500 miles? 10. If a wheel turns 780 times in going over 1 mi. 1G85 yd. What is the length of its circumference? EXERCISE CLXX. 1. What 's the difference in weight between .3 dozen silver table spoons weighing 5 lb. 9 o/.. 8 dwt. and as many silver tea spoons weighing 1 lb. 9 oz. IG dwt. 18 gr. 2. How many times is 391 yd. 4 in. cc-ntainbd in 2 mi,? 3. If a man walk i mile in 5 minutes, how many hours will it take him to walk 36 miles at the same rate? 4. Find the number of days between Sept. 23rd and Jan. 11th, one of these days included. 5. A man walks 1 mi. 47 rd. in 20 minutes how long will it take him to walk 123 mi. 276 rd. 6. How many boards each 11 ft. 6 in. long and 10 in. wide will be required for the flooring of a room 23 ft. long and 17 ft. 6 in, wide? 7. How many turns will a wheel 3 yd. 2 ft, 3 in. round make in passing over 198 miles? 8. How many silver spoons weighing 1 oz. 18 dwt, 12 gr. can be made from 23 oz. 2 dwt, of silver? 9. What is the rate per hour of a horse that travels 18 mi. 1620 yd. in 3 hr. 4o min.? 10. Find the cost of 260 lb. of tea at 3s. 3fd. per lb. If 20 lb. of it be spoiled, how much is gained by selling the remainder at 48. lid. per pound? EXERCISE CLXXI. 1. How much oats will it take to seed 87 acres, using 2 bu. 1 pk. 5 qt. to the acre? 2. A miller ground 7845 bu. of wheat. How many barrels of flour did he obtain, provided each bushel yielded 39 lb. 3^ oz.? 3. A and B togeth<-r bought a web of silk; A piid for ,\ of it and B for the remainder. The difference between their shares in 5i yd. What is the share of each? APPLICATIONS OF THK PRKVIOUS Kfl.KS. Ill 4. If A travels 24 mi. 198 id. 4 yd. in (5 )ir. 30 min., how far will he go in 9 hr. 45 min.? 5. A field 80 rods long contains 1;') acres, while another field of the same width contains 9 acres: wliat is the length of the latter field? 0. A lady bought 15 yd. of velvet i yd. wide. How much silk I yd. wide must she buy to line itf 7. Mrs. Brown wishes to carpet a room 18 ft. long by 15 ft. G in. wide, with Brussels carpet I of a yard wide, at $1.25 a yard. How much will it cost her? 8. If 4^ lb. of pepper cost $2.15, what will .30 lb. cost? 9. If 30iV tons of iron cost $1728, what will 7ii tons cost? 10. If drk tons of copperas cost $333J, what quantity of copperas should be received for $500. EXERCISE CLXXII. 1. If A of a barrel of flour costs $2.25, what will a whole barrel cost? 2. If T^ lb. of a drug costs $2.52, what is the value of ^ of a lb. ? 3. If 41 tons of coal cost $28, what will 15 tons cost? 4. When $8 are paid for If yards of broadcloth, how much must be given for 8| yards? 5. Sold 7i^ busLjls of apples for $7.28. What should I receive for 19t5 bu.? 6. How many yards of muslin, at 62i ct. per yard, must be given in exchange for 34 bu. of sweet potatoes, at 50c. per bushel? 7 How many pounds of btitter at 18f ct. per pound, should be exchanged for 40i yd. of calico at 12i ct. per yard? 8. If a man works Si hr. a day, he can finish a piece of work in 12J days. How many hours per day must he work to com- plete it in lOl days? 9. If ^ of a yard of ribbon cost $|, what will 5| yd. cost? 10. Paid $7888tt, for 83A acres of land. What sum did I pay for each acre, and what would be the cost of 7 acres? EXERCISE CLXXIII. 1. How many parcels each weighing 41 lb. 8 oz. can be made up out of goods weighing 1 ton, and what weight will be remaining? 2. How many pounds of sugar at 6i cents a pound will pay for 12 dozen eggs at 16S^ cents a dozen? 3. If a man can drive lOf miles in H hours, how far can he drive in 5f hours? tA 112 AlilTHMKTlf. 4. How many yards of cambric | yd. wide will it take to line 14 yards of (;l(;tli li yd. widt*? 5. After selling? 'H of his sheep to n, drover, and Jt of the remainder to hia neififhbor, a farmer has 100 left. How many were there in the Hock at first if (5. A road to the top of a hill has a rise of A of a foot in 10 feet. How many feet is the total elevation of the hill, if the length of the roud is 2 miles? 7. From 120 A. of land 32lf A. are soM to one man and J of the remainder to another. How many acres are unsold? H. A grocer buys 'M lb. of tea at 48 ct. a pound, and '}0 lb. at 64 ct. a pound, and having mixed them sells 40 lb. of the mixture at oG ct. per pound. At what price per lb. must he sell the remainder that he may neither gain nor lose? 9. A gentleman gave i of his estate to his wife, I of the remainder to his oldest son, and f of what then remained to his daughter, who received $750; required the whole estate. 10. A man has 4 lots containing 4| A., 6fB A., 9i A. and lli^ A. respectively. He wishes to divide each lot into the largest sized building lots possible, each lot to contain the same area. How much land will each building lot contain? EXERCISE CLXXIV. 1. A wine merchant bought a pipe of wine (126 gal.) and bottled it into an equal number of quart, pint, and half-pint bottles. How many bottles of each size had he? 2. At $6.40 a cord, what is the value of two piles of wood, each 4 ft. wide and li yd. high, but the one 2i rd. in length, and the other 15i yd.? 3. From two fields 482 bushels of corn are gathered. The first field yields i as much as the second. How many bushels does each field yield? 4. What must be paid for a pile of wood 25 ft. long, 3^ ft. high, and 6f ft. wide at $4|^ per cord? 5. If lOi lb. of milk make a lb. of cheese, find the value at 9 ct. per lb. of the cheese made from 350 tons of milk. 6. A cistern 7i ft. long and 5i ft. wide contains 3321 eu. ft. What is its depth? How many gallons of water will it hold? 7. At 12 cents per cubic foot, what will be the cost of a block of stone 9 ft. long, 5i ft. wide, and 4 ft. thick? 8. A father divided a piece of land among his three sons thus: he gave 12i acres to the first, I of the whole to the second and to the third as much as to the other two together. How many acres were in the piece of land? APPLICATIONS OF THE PREVIOUS RULES. 113 9. A man bequeathed $37000 to his family. He gave i to his wife, i to his son, and divided the rest equally among 5 daughters. How much did each daughter receive f 10. A young man lost i of his money in betting on races, jt of the remainder In stock jobbing, | of what was left by invest- ing in foreign bonds, and has now $1750 left. Find the amount of his property at first. sq. was rd. were divided wide, EXERCISE CLXXV. 1. From a tract of land containing 365 A. 90 sold 110 A. 110 sq. rd., and the remainder equally among 5 persons. Find the share of each 2. In digging a cellar 24 ft. long and 10 ft. wide, 1860 cu. ft. of earth were removed; how deep is it? 3. If a pile of bark 24 ft. 6 in. long, and 4 ft. 6 in, contains 9ooi cu. ft., how high is it? 4. A gentleman sent a silver tray and pitcher, weighing 3 lbs. 9 oz., to a jeweller, and ordered them to be made into tea spoons, each weighing 1 oz. 5 dwt. How many spoons should he reefeive? 5. A man having a piece of land containing 3844 A., divided it between his two sons, (r'.ving to the elder 22 A. 60 sq. rd. more than to the younger. How many acres did he give to each? 6. A and B own a farm; A owns -^ of it and B the re- mainder. The difference between their shares is 15 A. 68i sq. rd. How much is B's share? 7. The forward wheels of a wagon are 10 ft. 4 in. in circum- ference, and the hind wheels 15i ft. How many more times will the forward wheels revolve than the hind wheels in running from Boston to New York, the distance being 248 miles? 8. What will be the cost of plastering the walls and ceiling of a room 36 ft. long, 26i ft. wide, and 15 ft. high, at 21 cents a sq. yd., making no dedtictions? 9. A man has a piece of it.nd 201 1 rods long and 41 J rods wide, which he wishes to lay out into square lots of the greatest possible size. How many lots will there be? 10. A gentleman gave J of his property to his son James; i of it to his son William ; ^ of the remainder to his daughter Mary; and the balance to his wife, Mary received $2243.26 less than James. What was the amount divided, and how much did each receive? m EXERCISE CLXXVI. 1. A can dig a fi^ild in 5 days. B can dig it in 4. If both work together, what part of the field will they dig in one day? ;« 114 ARITH;ilI::TIO. 2. A can do a piece of work in six days which B can do in 8 days. Tliey work together at it I'or 2 days. How much of the work remains to l>€< done? '.i. A can mow a piece of grass in 4 days, and B can do it in 2 days ; liow long will it take both working together to do it * 4. A and B together can do a piece of work in 18 days, l>nt with the assistance of C they do it in 12 days. In what time can C do it by himself? 5. A and B together can do a job in 7 days, b«it it would take A alone 12 days to do it. How long would it take B alone to do it? 6. A and B together can do a piece of work in 20 days. A can do it alone in UG days. After A lias worked 3 days alone, how long would it take B to ftnish it alone? 7. Three men can do a piece of work in 4 days; the first can do it in 15 days, and the second can do it in 12 days. How long will it take the third to do it? 8. A can do a piece of work in 3 days, B can do it in 4 days, and C can do it in 5 days. How long will it take them to do it together? 9. A can mow a field in 10 days, B in 8 days, and C in 5 days. When working together, how many days will they need? 10. A can build a wall in 8 days, B in C days, and C in 5 days. A and B worked together for 1 day, when they were joined by C. How many days will they need to complete the remainder of the work? 11. A and B working together can mow a field in 10 days; A and C can do the same work in 9 days ; and B and C in 12 days. In what time can C do the work alone? 12. If 4 men or 20 boys can do a piece of work in 12 hours, in what time can 3 men and 30 boys do the same work? 13. If 5 men, 8 women, or 12 boys can do a piece of work in 20 hours, in what time can 1 man, 2 women and 3 boys do this work? 14. Three men are employed to dig an acre of land. A can dig 40 sq. rd. in 6 days, B can dig 60 sq. rd. in 8 days; and C can dig the whole in 16 days. If all begin to work together, in what time will they dig the acre of land? 15. A can dig a garden in ')l days; B can dig the same garden in 4f days. If they begin to dig together in what time can they dig the entire garden? 16. A can do a piece of work in 6j days; B can do the same work in 7i days and C can do it in 8^ days. A works alone at the job for 2 days when B begins and the two work together for a day. Then C joins them and they all continue until the work is done. How long does A work? an do in 8 ueh of the an do it in to do it? S days, i»ut I what tiiue lit it would ike B alone 20 days. A days alone, the first can , How long it in 4 days, hem to do it , and C in 5 1 they need? and C in o \n they were loniplete the ^1 10 days ; A in 12 days. Jin 12 hours, lork? le of work in jboys do this land. A can lays; and C I together, in Isame garden Ime can they lo the same [rks alone at [together for \e until the CHAPTER VII. DECIMALS. I. DEFIINITIOINS, INOTATIOIN AND INUIVIERATIOIN. When the numltcr 10000 is divided by 10, tiiequotient is 1000. When 1000 is divided hy 10, the quotient is 100. ' When 100 is divided by 10, the quotient is 10. When 10 is divided by 10, the quotient is 1. When 1 is divided by 10, the quotient is ra and ir ritten .1. Wiien .1 is divided by 10, the quotient is Too am is written .01, etc. Such nnin])ers as .1, .01, .001, .34, 5.7, etc., are called decimals, or deeiiiial fractions. Decimals, or Decimal Fractions are fractions in which the unit is divided into 10, 100, 1000, etc., equal parts. A decimal is expressed by writing the numerator of the fraction with a point so placed as to indic^ate the order or place of the decimal. This i)oint which separates integers from decimals is called the Decimal Point. When there is a i>art of the nunil^'r to the left of the i)oint, this is Cc'Ucd the integral part, and that to tiie riglit, the Decimal part, of the given numl)er. The following table shows the relation of the various orders ov plaees to the right iind left of the unit's place to each other, tliiis the order tens is lirst to the left of units, the order tenths is iirst to the right of units; the order hundreds is secoml to the left of units, the order hundredths is second to the right of units, et". 115 no aimtiimktk;. Notation ank Nr.MKitATioN 'I'ami.k. i o r. C lu O TS fQ K a o <■* a H 4 a o H a W XI a '/J a o H 01 7: a a o ja H a a W ]() 9 K 7 () T) 4 ;{ a ^ 22 - .2 ^ a •- ^j a I ra "3 a • a a a •/. a 1 ,2 1— ii ■/I a a H 1 a a a • p-4 1 a 0; a ^ 0) • ^ a> H W H H W ?^ H I a o iNTKCiKKS. . 1» ;; 4 ;') <) 7 H I) 10 i Decimals. EXERCISE CLXXVII. Koiul or writ*' in words: — 1. .9 .45 .75 .08. 2. .17.') .087 .006 .209. 3. 'J.OG 7.001 10.07 9.207. 4. .:5875 .0562 .0083 .0006. 15. l.()31 1.315 48.007 87.0006. G. 201.201 78.567 100.001 709.224. 7. 612.612 13.0108 700.625 5.6006. H. 10000.001 1000.0001 100000.01 1000000.1. 9. 200.2006 2002.006 20020.06 20.02006 10. 78965. 4.*{2 789.65432 7896.5432 789654.32. EXERCISE CLXXVIII. Write in fi^ires: — 1. Three limidretl siiid twenty-five, and seven tentlis. 2. Four hundred and sixty-five, and fourteen hundredtlis. 3. Ninety-three, and seven liundredths. 4. Two hundred and tiiirteen thousandths. 5. One tliousand, and six ten-thousandths. Thirty-sev^n, and seventy-two thousandths. Seven Inindred and eighteen ten-thousandths. Two liundred and forty thousand, and four hundred and six thousandths. 9. Fifty-six million, and fifty-six jnillionths. 10. Seventy million, and seven millionths. 6. ( . 8. AnniTION OF DKCIMAL8. 117 J a • o X ^4 *-• • r-* tt-4 ■/! _o 1^ 1 / xa '»— ; -fl -S *j • ^4 01 ■»-> •-< o ?^ o 1 PI • •^ S 7 H J) 10 VLH. .08. .209. 9. '207. .000(5. 87.000(). 709.224. r).()00(). 1)00000.1. 20.02006. 1789654.32. Miths. lundredtlis. tidred and six Add togt'tlier: — 1. 359.6 35.964 520. 43.7 .876 1.01 II. ADDITIOIN. EXERCISE CLXXIX. 7.04 3«).475 90.007 0.689 367. 7.82 200. 1.01. 36.010 19.00!). 7.7 178.6. 84.09 6.83. 785.3677 20.761. 6.005 .84. 2. 18.79, 147.072, 856.709, 185.8761, 397.05784. 3. 4. 3.584, 387. <), 5.894003, .00397, 8.889. 6. 7. 8. 8939, 8.939, 89.39, .89.39, .00089.39, 893.9. 56.6794, 5.76, ..579, 342.1, 34.21, 7000, 9.7646. 47.21, .946, 154.172, .000457, 17.46, 173, .05409. 4.71, 3.967, 17.10845, .04075, ().154, 99.876. 27.16, 47.148, 9, 9.2387, .()047(), .0853, 78. 9. $47.19, $27.15, $364.10, $.75, $4,085, $65,075. .10. $7,009, $7, $871, $.065, $1,005, $21,075, $6,675. EXERCISE CLXXX. Sini)dify: — 1. 64 + .78 + 479.543 + 66.8 + 3^5.4876. 2. 34.084 + .088 -f 96.7854 + 78 + 42.89. 3. 9.3 + .04 + 8.0067 -f 778.7 + 47.0.393. 4. .365.84 4- 19.07 + 17.8 + 78 + 584.3671. 5. 729. + 2.3788 -|- 35.68 + 7806.7 + .379. 6. 19.7864 + 3987 + .9 + 577.17 -f 93.8 + .48. 7. 9.7 4- 64.36 + .587 + 97 + .00487 + 54.7. 8. 76.54 + 3896.0484 -|- 77.3456 + 68 + 78.99. 9. 87.4785 + 78 -f .84 + 37.84672 + 18.75. 10. 3698 + 786.4 + 7 + 4.9 + 36.847 -j- .099. EXERCISE CLXXXI. 1. A man lias in one field 27.9 aeres; in another, 45.755 acres; in a tliird, 135.125; and in a fourth, 73.625. How many acres has he in all? 2. Add together two hundred and nine thousand, and forty-six millionths; ninety-eight tliousand two hundred and seven, and fifteen ten-thousandths; fifteen, and eight hundredths; and forty -nine ten -thousandths. 3. What is the sum of the following numbers: twenty-five, and seven millionths; one hundred and forty-five, and six hundred and forty-three thousandths; one hundred and seventy- five, and eighty-nine hundredths; seventeen, and three hundred and forty-eight hundred-thousandths? :m 118 ARITHMETIC. 4. A merchant bought at one time 23.75 yards of cloth; at another time, 57.375 yards; and at another, 34.6875 yards. How. many yards did he buy in all ? 5. A farmer sold 2.87-5 tons of fodder; 8.3125 tons of oats; 5.4.55 tons of hay, and 7.625 tons of clover. How much did he sell in all? 6. Add the following numbers: fifty-nine, and fifty-nine thou'andths; twenty-five thousand, and twenty-five ten -thou- sandths; five, and five milliouths; two hundred and five, and five hundredths. 7. What is the sum of 304 thousandths, 5103 hundred - millionths, 61032 millionths, 413 hundred-thousandths, and 603 ten -thousandths? 8. Jones bought 4 loads of hay, weighing 1.475 tons, 2.085 tons, 1.516 tons, and 1.424 tons, respectively. How many tons are there in all? 9. What is the sum of forty-nine, and one hundred and five ten -thousandths; eighty-nine, and one hundred and seven thousandths; one hundred and twenty-seven millionths; and forty-eight ten-thousandths? J 10. What is the sum of three, and eightet.'n ten -thousandths; one thousand and five, and twenty-three thousand and forty- three millionths; eighty-seven, and one hundred and seven thousandths ; forty -nine ten -thousandths ; forty -seven thousand, and three hundred arid nine hundred-thousandths? III. SUBTRACTION OF OECIIVIALS. EXERCISE CLXXXII. 1. From Take From Take From Take 7.84 3.67 39.3 * 1.6789 7.6 2.847 81.01 27.08 5. 1.678 3.842 1.9678 36.006 21.783 76.89* 7.397. 2. 6.1 1 .99999 41.7 21.9767. 3. .0067 .0009 7. 1.345. 4. From 8, take 2.7689; from (5.5, take 2.378. 5. From .8, take .347; from ()!), take 7.9684. (). From 25, take 12.789; from 17, take .0007. 7. From 100, take .0001; from 10, take .01. 8. From 87.1, take 5.6789; from 1, take .87654. 9. From 74.8, take 37.456; from 5.08, take 1.675. 10. From 385, take .0076; from 1001, take 7.0006. SUBTRACTION OF DECIMALS. 119 Simplify: — 1. 7— :5.45() »>_ 2.5—1.7859 :j. 8.275—5.185 4. 70.5— .0375 5. 9.008— 4. 75G3 G. 10— .0005 7. .75— .075 8. 600— 6.r)() 9. 4— 3.87G5 10. 100—3.145 17—6.435. 5.1 — .7^45. 3— .214. 17—9.0067. 1— .0001. 25—3.675. 785— .785. 1— .175. 3.65—1.19. 7.89646—6.9. EXERCISE CLXXXIII. 15—2.34 .36— .0897 2.0132—1.25 6.4—3.876 2— .745 100—99.875 735—7.85 5— .275 ■ 28—2.8795 5 — .5555 EXERCISE CLXXXiV. 1. From seventy -three, take seveiity-three tliousandths. 2. From twenty-three hundredths, take three hundred and seven ten -thousandths. 3. From three hundred and sixty-five, take forty-seven ten- tliousandths. 4. From seven thousand, and seventeen millionths, take .0004125. 5. From one million, take one millionth. 6. From eighteen thousandths, take five hundred and nine- teen millionths. 7. From three million, and one millionth, su, tract one tenth. 8. From one thousandth, subti'act one millionth. 9. From fifty-three, and ninety thousandths, take ten, and three hundred -thousaTuiths. 10. From seven thousand and seven, subtract seventy-seven, and four thousand and seven hundred-thousandths. Simplify: — EXERCISE CLXXXV. 1. 25.000315 — .00045 + .2801 — 16 + 21.001. 2. 8.14 -f 38.124 — .9175 — 16.28 + 46. 3. 16.945 — 2.994387 — .06735 — .0007 -f .953 + 0.8. 4. 7.654327 — .3793080 -f 9.06990 — .00999 + .345. 5. 78 — l(i.45 — 32.08 — 11.709 -f 24.305 -\- 7.09. 6. 100 -f 1.005 — 41 — 36.008 — 21.07 -f 1.225. 7. 84 — 7.(59 -f 9.0S9 — 3.425 — .S25 — .006. 8. 1.6 -f 7.92 -f 6.859 — 3.9999 — 2.5554 — .0(;4. 9. 75 - 25.8 -f 36.08 — 25.755 -f 42.375 — 21.875. 10. .008 -j- 10.01 — 3.5876 — 2.8497 -f 7.854 — 2.345. li 120 ARITMHETIC. EXERCISE CLXXXVI. 1. A farmer owning 957 acres of land sold at one time 225.7 acres; at another, 175.45 acres; and at another, 327.375 acres^ How many acres did he still have? 2. A merchant, having $1000, invested it as follows, viz. : $145.75 in calico; $275.56 in shoes; $95.25 in hats; $156,375 in broadcloths, and the remainder in groceries. How much did he invest in groceries? 3. A is to ti-avel 597 miles in 3 days. The first day he travels 196.4 miles, and the second day 201.25 miles. How many miles must he travel the third day? 4. A man received the following sums: $27.40, $68.75, $810.47, $381>.59, and $2.20. He paid out the following sums: $78.67, $129.72, $119.46, and $3.88. How much had he left? 5. A man owning 875 acres of land divided it among his four sons as follows: to tlie first he gave 213.65 acres; to the second, 192.375 acres; to tlie third, 206.625 acres; and to the fourth, the remainder. Wliat was the fourth son's share? 6. In 1897 tlie rainfall in Ontario for six months was as follows:— April, 2.52 in.; May, 3.38 in.; June, 2.83 in.; July, 5.36 in. ; August, 2.62 in. ; and September, .83 in. How much did the rainfall during the second three months exceed that during the first three? 7. A gardener sold his cabbages for $212,875 and his turnips for $118.33. The cost of raising the cabbages was $119.75, and the cost of raising the turnips was $99,875. What was his profit on the two crops? 8. A speculator, having 57436 acres of land, sold at different times 536.74 acres, 1756.19 acres, 3678.47 acres, 9572.15 acres, 7536.59 acres, and 4785.94 acres. How much land had he remaining? 9. From a hogshead of sugar containing 397.25 lb., a grocer sold parcels as follows: 110.25 lb., 64.5 lb., 14.25 lb., 29.375 lb., 39.23 lb., and 16.33 lb. How much was left? 10. A flagstaff is made up of two parts, the upper part being 27.84 ft. long, and the lower part 57.86 ft. long. If the lo-er part is set 11.97 ft. in the ground, how many feet of the whole staff are above tlie ground? 11. Four men dug a ditch. The first dug .123 of it; the second .234 of it; and the third .343 of it. How much of it did the fourth man d' jf? 12. On Monday the mercury of a barometer was 30.356 in. high. It fell .017 in. and .15,3 in. during the next two days. During the next four it rose .008 in., .027 in., .231 in., and .018 in. On the seventh day it fell .132 in. Find its height at the end of the seventli day. MULTIPLICATION OF DECIMALS. 121 IV. MULTIPLICATIOIN OF DEC1IV1ALS. Multi 1. o .3. 4. 5. G. 7. H. J). 10. EXERCISE ply:— 4.8 by 4.2 3.5 by 3.5 4.5 by 3.58 240.5 by .25 32.7 by 2.35 G1.76 by .071 .0009 by .0009 .0068 by .0062 7.006 by 4.05 CLXXXVII. 5.4 by 5.G 12.7 by 12.3 .37 by 4.3 .45 by .21 .009 by .07 .6101 by .061 .084 by .086 .0125 by .0125 75.6 by 75.04 7.007 by 7.007 1.0001 by .001 7.1 by 7.9. 10.8 by 10.2. 5.25 by 3.75. .27 by .0009. 12.5 by 12.5. .1234 by 1234. .073 by .077. .075 by .075. 245 by .245. 34.56 by .008. Simplify: — EXERCISE CLXXXVIII. 1. 72.5 X .006 2. 37.654 X 13.45 3. (2.45 + 3.08) X .0024 4. 3.075 X 80 X .15 5. .008 X .019 X 25000. G. .0525 X 10000 7. (101 -f 10.1) X 101 8. 1.0005 X (3.4 + 5.66) 9. .0003 X .003 X .03 10. .012 X .0012 X 12000 8.45 X .008. 7. 0805 X 5.0006. (7 - 1.234) X 5.65. 895 X .475 X .004. 123 X 12.3 X 1.23. .0927 X 1000. (7 — .564) X 8.5. 7.245 X (75 — 36.45), 1000 X .0006 X 8. 64 X .125 X .004. EXERCISE CLXXXIX. 1. Multiply 123.456 by 10; by 100; by 1000. 2. What is the product of one thousand and twenty-five, multiplied by three hundred and twenty-seven ten-thousandths? 3. Multiply one hundred and fifty-three thousandths by one hundred and twenty-nine millionths. 4. Multiply five thousandths by seventy-three hundredths. 5. Multiply three hundred and fifty-six thousandths by one hundred and forty- five ten-thousandths. 6. Multiply 4.5 by 10; by 100; by 1000; by 10000. 7. Multiply eiprht hundred and forty-two thousandths by five hundred thousand. 8. Multiply'one hundred and seven thousnnd, and fifteen ten- thousandths by one hundred and seven ten-thousandths. M 1>)0 AKITHMETIC. 9. Multiply twenty- five ten-thousamlths by two hundred and seventy- five, and fourteen hundredths. 10. Multiply thirty-four millionths l»y twenty-six ten-mil-' lionths. EXERCISE CXC. 1. If a nnm can walk 27.25 miles in a day, how far can he walk in 7.;') days at the same rate? 2. A cubic foot of water weighs 02.5 pounds. Whsit will be the weight of 7.25 cubic feet? :J. What is the profit on one million yards of cotton cloth at $0,007 per yard? 4. How many solid feet are there in a pile of wood 7.3 feet long, 5.7 feet wide, and G.5 feet high? 5. A roller 4.15 feet in circumference makes 208.4 revolu- tions in passing from one end of a field to another. Find the length of tha field. G. A is .875 times as old as C, and C is 1.08 times as old us B. B is 25. How old is A? 7. If one cubic inch of pure water weighs 252.458 grains Avoirdupois, how many grains will 1728 cubic inches, or one cubic foot, weigh? 8. A and B start from the same place at the same time, and travel in opposite directions, A travelling at the rate of 22b miles per day, and B at the rate of 24.04 miles per day. How far apart will tliey be at the end of 12.45 days? 9. From a cistern containing 27G5 gallons, 56.25 barrels, of 31.5 gal. each, are drawn off. How many gallons remain? 10. A man made a journey as follows: He travelled 7.75 hours by rail at the rate of 22.75 miles an hour, 9.875 hours by stage at the rate of G.75 miles an hour, and 11.75 hours on foot at the rate of 4.G2 miles an hour. What was the length of the jourf^iy? V. DIVISION OF DECIMALS. EXERCISE CXCI. ivid e: — 1. .8 by 2 8 by .2 2.5 by .05. 2. 12 bv .06 124 by .31 .09 by .003. 3. .08 by 5 .9 by .12 1 by .125. 4. .51 by .015 .005 by .020 .375 by .025. 5. .008 by .04 .12 by .0000 .004 by 2.5. G. 155 by .0025 .00025 by 25 25 by .30025. 7. 272.G3G by 6.37 281.8585 by 3.85 9.6188 by 3.40. 8. 40.1975 by 54.35 .014274 by .001 345.15 by .075. 9. 3.0 by .00000 75 by 10000 4.30 by 10000. 10. 216.32 by .00512 5058 by .00i23 4.110 by .0075. DIVISION OF DECIMALS. 123 iidred and ten-mil- fav can J»6 tiat will be on cloth fit wood 7.IJ iA revolu- Find the iraes as old 1.458 grains has, or one le time, and rate of 22| day. How 1 barrels, of eraain? ivelled 7.75 75 hours by Durs on foot ngth of the Simplify: — 1. 01.04 EXERCISE CXCII. by .05. by .003. by .125. by .025. by 2.5. by .)0625. by 3.46. by .075. by 10000. by .0075. 3. 4. 5. G. 7. 8. 9. 10. (JO. 25 H- 3.125. .0045 -:- 225. 5.007 — 375. 154.28 ^ .0004. (28 + 11.75) -^ 1.25. 1.2 X .7 ^ 12.5. 100 X 4.0125 -r .004. (7.89 — 3.0111) ^ .015. 12"— (.832 — .757). 11.25 X 11.25 ^ 937.5. 4.30 9005 — .049 327.6 -r 0.25 10 — .0004 (0.05 + 3.75 — .0048) -> .4 .06 X .08 -H 3.2 8 ^ .025 X .01 12 -^ (.015025 + .040875) (.06 + .006 — .00000) ^ .06 3.225 — .75 X .01 EXERCISE CXCIII. 1. Divide one hundred and forty-seven, and eight hundred and twenty-eight thousandths by nine, and seven tenths. 2. What number must be multiplied by .0017 to give 595? 3. By what must .7847 be divided to give 1.9 for quotient? 4. Divide seventy-five thousand eight hundred and one by two thousand two hundred and ninety-seven ten-thousandths. 5. What is the quotient when 10.9536 is divided by 1000 times .4564? 6. Divide three hundred and twenty-three tiiousand seven hundred and sixty-five by five millionths. 7. Divide 123.45 by 10; by 10( ; by 1000; by 10000. 8. What is the sum of the quotients of 24 by 9.6, of 42.75 by 11.4, and of 17.85 by 4.2? 9. The product of three numbers is 2.94294. Two of these are .21 and .11. Find the third number. 10. Divide seven, and five tenths by one hundred; by one thousand; by ten thousand. EXERCISE CXCIV. 1. If 25 men build 154.125 rods of fence in a day, how niueh does each man build? 2. There are 16.5 feet in one rod, and 5280 feet in a mile. How many rods are there in a mile? 3. How many bushels of clover seed at $6.25 a bushel will Itay for 25 barrels flour at $10.5 per barrel? 4. A man has 324 bushels of apples which he wishes to init into barrels containing 2.25 bushels each. How many ) ."Is will be required? 5. Tlere are 31.5 gallons in a barrel. How many barrels can be tilled from 2756.25 gallons? ■i 124 ARITHMETIC. 6. A speculator bonglit 78.2') acres of land for $9781.25, and sold it so as to gain $3.50 an acre. How much did he get per acre? 7. A man bought a farm containing 64.5 acres for $177.'1.75. How much did he pay per acre? 8. Twenty -five hundredths of a farm cost $3000. Find the cost of .9 of it. 9. If 20.5 acres of land produce 322.875 bushels of wheat, what is the yield per acre? 10. If a train goes at the rate of 24.75 miles per hour, how long will it be in going 128,7 miles? VI. REDUCTION OF DECIMALS. EXERCISE CXCV. Reduce the following decimals to vulgar fractions in lowest terms: — their 1. .35 .48 .25 .125. 2. .625 .75 .375 .64. 3. .016 .225 .875 .035. 4. .275 .575 .0375 .005. 5. .068 .024 .175 .0175. 6. .99 .021 .123 .003. 7. 2.75 4.76 7.45 5.. 36. 8. 3.25 9.75 12.725 5.064. 9. 6.0125 16.075 7.875 11.625. 10. 5.3125 2.1875 7.9375 9.6875. EXERCISE CXCVI. Reduce the following vulgar fractions to decimals: — 1. i o 5 8 8. t\ 4. h 5. A C. 1 8 TJ5 7. 4^\ 8. i%z 9. T5 10. 1 31 625 3 11 40 q89 o 1 1 H SI 40 1 1 1 nil «J4 711 441 15 25 3 tV. 1 3 Iff. 1 8 33 4 (J- 2 1 1 73 9 '40- 8/5. 311 625- APPLICATIONS OF PREVIOUS HULKS. 126 EXERCISE CXCVII. Expiess each of the foUowiiif? as oonipound iiuinlior.s: — 1. £.79002.') 2. .83125 cwt. 3. .787") mi. 4. .907") A. n. .9370 on. yd G. .875 bu. 7. .875 gal. 8. .495 da. 9. .975° 10. .0125 fathom. £.705025 .08745 t. .2525 mi. .881 25 A. 7.875 ed. 2.375 bu. 5.175 ^'al. 7.875 wk. 2.8475" 17.875 rra. EXERCISE CXCVIIi. £1.809375. 3.8975 t. 21.30875 mi. 13.4375 A. 0.75 cu. yd. 5.475 bu. 7.75 gal. 9.95 wk. 17.3875°. 7.75 gro. FiX])ro'ss oMoh of the following as a dofimal of its highest deuominatiou: — 1. £1 10s. Od. 2. 9 t. 17 cwt. 8 lb. 3. 7 mi. 35 rd. 2 yd. 2 ft. 3 in. 4. 9 A. 48 sq. rd. 5. 7 cd. 112 cu. *t. 0. 7 bu. 3 pk. 2 qt. 7. 27 gal. 3 qt. 1 pt. 8. 3da. 13hr. 24min.3Gsec. 9. 3'^ 52' 39" 10. 5 nn. 17 qr. 18 sheets. £7 13s. 7.1d. 5 t. 14 cwt. 7i lb. Gmi.28rd.2yd. 1 ft. 11.04 in. 7A.45sq.rd.8sq.yd.4.23sq.ft. 7 en. yd. 18 cu. ft. 972 cu. in. 5 bu. 3 pk. 4 qt. 1 pt. 14 gal. 1 qt. 1 pt. 2 wk. 5 da. 9 lir. 4G niin. 48 sec. 17° 7' 25.5". 24 grs. 9 do 55. VII. APPLICATIONS OF PREVIOUS RULES. EXERCISE CXCIX. 1. What will l>e the cost of filling in a street GOO ft. long Mild (55 ft. wide, averaging 4i ft. below grade, at $.52 a cubic yard? 2. Goliath of Gath was 6i cubits high. What was his luiglit in feet, the cubit being 1 ft. 7. 108 in.? 3. What will be the cost of the wood that fills a shed 20 ft. long, 10 ft. wide, and 8 ft. high, at $4.75 a cord? 4. Which will contain more — a box 5.5 inches long, 4 iiichcs \\idc, and 4.25 inches deep, or one 0.5 inches long, 4.5 inches \\i<t(', and 3.5 inches deep? 5. How much gold may be obtained from a ton of quart/; 'uck, if it yieWs .0010 of its weight in gold? 126 ARITHMETIC. G. At ()7i «'ents per eu. yd., what will be the cost of iligging a cellar 15.5 ft. long, 12 ft. wide, aud 5 ft. 4 in, deep? 7. How many yards of carpeting 1 yard wide will b« required to cover a tloor 33.5 ft. long aud I22i ft. wide? 8 What is the cost of slating a roof 52 ft. lU in. long, each side being 20 ft. wide^ at $15.25 per square, a scpiare being 100 sq. ft.? 9 If 1 cu ft. of water weighs 1000 oz., what will be the weight of the' water iu a cistern 8.5 ft. long, U ft. 3 in. wide, and 3 ft. 9 in. deep? 10 At $13.60 per square, what will be the cost of tinning both" sides of a roof 36 ft. 6 in. in length, and each side 18 ft. 9 in. in width, a square being 100 sq. ft.? EXERCISE CC. 1. If 11.8 A. of land cost $236, what will 20.7 A, cost at the same rate? 2. Find the cost of 8725 ft. of boards at $12.50 per thousand? 3. A drover bought sheep at $3.37i a head, and sold them at $3.87i a head, and gained $37.50 by the transactions. How many sheep did he buy? 4. What is the cost of 24 ewt. 87 lb. of sugar at $6.50 per hundredweight? 5. The contents of a chest of tea weighing 87.5 pounds are made up into an equal number of 1 pound, i pound, and i pound packages. How many packages are there of each kind? 6. What would 7| bales of cotton cost, each bale weighing 537.5 pounds, at $0.11 J a pound? 7. Boys in playing hare and hound run 3.875 miles. The hares drop a piece of paper every 5.5 feet on the average. How many pieces do they drop? 8. A merchant sold 4 pieces of matting, each containing 35.5 yards, at $0,375 per yard. How much money did he receive ? 9. Divide $47.10 among 6 men and 11 youths, giving a youth 0.525 of a man's share. What is each man's share? 10, The great pyvitmid of Clieops measures 763.4 feet on eacli side of its base, which is square. How many acres does it cover? EXERCISE CCI. 1. Bought land at $62.50 an acre, and sold it again at $75 an acre, thereby making $846,875. How nuiny acres vvei'( bought ? 2. If .875 of a man's age is 35 years, what will .7 of his age l.>e? APPLICATIONS OF PREVIOUS RULES. 127 i ve(iuued long, each tare being nil be the 1 in. wide, of tinning side 18 ft. A. cost at $12.50 per d sold them tioiis. How at $6.50 i»ev pounds are [ound, and i f each kind? |ale weighing miles. The the average. Ih oontaininp; }oney did he iving a youth foet on each lucres docs it afi;ain at $7.> ly acres wert LiU .7 of his ;{. If .75 of a ton of steel rails is worth $7i!, wluit is the value of 275.875 tons? 4. Divide 1(5. .'1-4 into two parts, so that one i)art may be 1.50 larfrer than the other. 5. A ujan spent .875 of his money and has $1.29 left. How much had he at first? G. Bought G7.75 acres of land at $62.50 an acre, and hoUI the lot for $5081.25. Was there a gain or loss? How much was gained or lost on the whole, and how much an acre? 7. Divide $133.26 between A and B so that A may have $18.48 cents more than B. 8. What number is that which, being diminished by 2.75, the remainder, multiplied by 4.6, and the product, increased by 6.75, gives 70? 9. How many cu. ft. of water will pass under a bridge every 12 min. if the stream is 125.125 ft. wide and 4.8 ft. deep, and flows at the rate of 2.5 mi. per hour? 10. Two men who are 17.82 miles apart start at the same time to walk towurds each other, one at the rate of 3.27 mi. per hr. and the other at the rate of 3.48 mi. per hr. How i will each walk before they meet? EXERCISE ecu. 1. What is the price of 20 joists, 10 ft. long, 6 in. wide, and 2 in. thick, at $25 per M. ? 2. What is the cost of 576 fence boards 16 ft. long and 9 in. wide, at $14 per M. ? 3. During a week the barometer stood as follows: — On 3 days at 29.46 in., on 2 days at 30.05 in., on the other two days at 29.48 in. and 30.85 in. What was the average for the week? 4. In walking 3.6 mi. a girl took 7040 steps. What was the average length of her step? 5. Find the average of 2.6, 2.37, 3.025, 2.973, and 0.516. 6. Find the G.C.M. and L.C.M. of 2.25, 3.375 and 2.8125. 7. How many boxes 4.5 ft. by 3.25 ft. by 2.875 ft., outside measurement, can be stored in a room 52 ft. by 36 ft. by 345 ft. ? 8. If a block of English oak 3i ft. long, 2 ft. l)road, and 1.75 ft. thick, weighs 710.5 lb., find the weight of a cu. ft. of English oak. 9. What will be the cost of painting the walls of a room, at $.30 per sq. yd. the length being 19 ft. lOi in., the breadth 16 ft. 1* in., and the height 10.25 ft.? 10. A merchant fails in business and his assets pay $.425 on the dollar. How much does a creditor receive to whom he owes $453,60? . -i I Tr 128 AKITHMKTIC. EXERCISE CCIII. 1. Fiml llin sum of tlic su?n, <lilT«n'<'ii(M<, mid lu'odiid of seven, iiiul t\vouty-tiv«5 Imiulredths iiiul tlirco, uud eif^hty-foiii' ImiidiMMlths. 'J, Find tho sum of the sum, dilferunco, jn'oduct, and two quotients of l.G and 4. I{. -.5 tiincH the sum of two nnmhers is 35.25 and one is 2.8 more than the other. Find the numbers. 4. Two ni<Mi toj^etlier eliopped 50.75 cords of wood and one cliopped 1.45 cords more than the other. How much did each ciiop? 5. Two men are 120.25 miles apart. They walk straij^ht towards each other and when they meet one has gone 7.75 mi. less than the other. How far has eaeli gone? G. If a merehant deposits !)!;i75. 50 in a bank at onetime, ami $487.75 at another, how much will remain after he has with- drawn $17().;{7 and $340.83? 7. Bought 1 ])arrel of flour at $8.50; 3 })ushels of corn at $.505 a busliel; 24.5 jmunds of sugar at 8.ic. a pound; 3 gallons of molasses at 37ie. a gallon; 2 pounds of tea at 624c. a ])ound; pounds of cotfee at 35e. a pound ; 15 pouiuls of rice at 8c. a pound; and 4 pounds of butter at 22c a pound. What was the cost of the whole? 8. A guinea is 21 shillings. Reduce 7i guineas to the decinuil of £10. 9. A stick of square timbor is 17.5 in. wide by 13.5 in. thick. What length must be cut off to contain 7 cu. ft.? 10. What must be the length of a plot of ground, its breadth being 70.23 yd., to contain 232.848 sq. rd.? 11. Divide $302.50 among A, B, and C so that A may receive 1.5 times us much hh the otiier two together, and B, 1.75 times as much as C. Find the share of each. 12. In sinking a shaft it is found that .375 of it passes through earth, .075 of it tlirough shale, and the remainder through solid rock. The shule is 90 ft. deep. How much of the shaft is in the solid rock? 13. A stick of square timber 32.5 ft. long, 2.5 ft. wide, and 1.125 ft. thick, weighs 4387.5 pouiuls. Another stick of the same kind of timl)er is 21.75 ft. long, 1.875 ft. wide, and 1.25 ft. thick. How much does <he second stick wiMgh? 14. A piece of work can l)e done by A in 17.5 days; by B in 22.5 days; and l»y (' in 15.75 days. If A works alone at it for 5.5 days and is then joined by B and C, how long mus^ the three work together to finish the remainder? M CHAPTER VIII. PERCEINTAGE. The expression Per Cent. (L.itiii per ceiitiiin) nnnuia for, or hij tlic Inindnd. A Rate Per Cent, denotes u eerluin mmiber of liuiidredths, as G per cent, denotes 1 0,7 or .00; 4 per eent. denotes liyOr .0075. Tlie symbol " „ is used for the phrase per cent. EXERCISE CCIV. Express the following as hundredths: — 1. -)% 7% 10% 1.-)% '2. 7i% (U% 12i% 20% Express the following deeimuls in percentage: — ;{. .05 .07 .1 .17 4. .055 .0725 .105 .125 27%. 50 % . .1725. Express the following — (1) iis decimals, and (2) as common fractions in their lowest terms: — O. '070 5% 8% lGf% # 10% 37J% 12.i% 75% G. 1U% Express as hundredths and also in percentage 20%, 87^%. I t\ S. 3 i i 4 8 . Express the following as fractions in their lowest terms: — 9. 4% 40% 80% 15% :{0%. 10. •m% Gi% Si% 5§% G2i%. r29 PI KJO ARITHMETIC. Kiihl IIh' following: I. :\'/ro\'^HM li. 4'/f> (tf lOOiicros. i't^^fi <»r 'J.')!) words U)% of ")()() Itoys 20% ofsUl";')!) I7r of 200 men. 2)i% of $2(500 n.'.T^'of 270yil. U)''r of $7.M ;{. 4. T). (>. 7. s. !). 10. EXERCISE CCV. r)%of!»!ioo H%of 2r)0 A. C)'/t' of "mO vvonlH 100'? (if 79 io7'> of !)<:{r>o 2r)%or7r>0 mi. •i'^ of 400 yd. 12.i% of 400 11. X]k'/r of 7r)0 slu'cp. 2')7f of lOiiO mt-y. S7i% of lG()4yil. 7% of !fir»oo. U>7 of 75 A. (i'V of !)00 COWH. 10% of I'tOyiirds. 7.')% of 00 JM-IIH. r^% of .1(200. H,^%of<)GOnu'U. ('))}% of 4r)0co\vs. ;57i % of r)7GI»ooks. 22^ % of .1!720U. EXERCISE CCVI. Find thf rjitc ix'r cent, equal to t'lich of the following: — 1 . $5 IMT !i«2r) 2. 1 hr. per 10 lir. Wliat per eeut Jh: — 3. 8 of IG? 4. 3 ft. of GO ft.? i). 240 lb. of 1 ton? G. 24 da. of 480 da. ? $8 i)er !i!80 5 lb. per 1 cwt. $1;') per $G0. $G0 per .$480. 20nii.of 4.')0mi.? 880 ft. of :i mi.? $<)G of $1920? 5 qt. of 10 gal.1 $.") of $40? 7 mi. of 100 mi.? 84 men of 1200 men? 50 men of 80 men? Find the difference between the following: — 7. 'M7o of $100 and f of $100; G0% of 200 A. and J of 20f) A. 8. t of 80 lb. and 50 % of 80 lb. ; I of 80 gal. and 80 % of 80 gal. Find the sum of the following: — 9. $40 and 5% of .$40 $100 and 7% of $100. 10. $G0 and 50% of $G0 50 mi. and 10% of 50 mi. EXERCISE CCVII. 1. A f.irmer having 1200 sheep lo.st 37% of them. How many did he lose? 2. A lawyer collected $2575 for a merchant, charging 4% for liis services; what was his charge? 3. A ship loaded with 1875 bales of cotton was overtaken by a storm, and the sailors threw overboard 12 per cent, of the cotton; how many bales were lost? 4. In a warehouse 1920 boxes of tobacco were stored; the warehouse haviiig taken fire, 15% of the tobacco was burned. How many boxes were burned? PKRPF.NTAOK. VM f). A iniin'M inoniuc is (I'lSOO ii y«'ur, (if wliit'li \iv piiys 1)1% for lioiiso rent. Whiit. r«'iit iloos Ik* pay f (5. A iiiiiii owns 'J I'lirms. Tli«' first contuiiis .'H!0 A. iiii*l tli«' ikiiiiImt (tl" iicrcs in tin- second is l.'td'f of tlif ininilx-r of iicrcs in tin* lirst. Find the nnniltcr in tlic st'cond farm. 7. If copjHT ort' yields {]% of pure metal, how many jto.in.'s of copper will lie obtained from I t. of ore* S. A l>on^'ht ;{*J() acres of land, and sold (ilii"/ of it. JJow many acres did he sell? !». In an orchard of 900 trees, '.V.\h% are peach trees. How niiiny peach trees are there in th.* orchard? 10. A nnm havin<; 11250 bu. of wheat, sold 'Sf/r of it. How mnch did he sell 1 EXERCISE CCVIII. I. A man has an income of .$4000; he spends {>'>% of it. How much does he save? '2. A lionse post .fOTOO and 20% of the money is ])aid at nnee. How much still remains unpaid? 'A. \ man has a farm of 200 acres. He sells 40% of it in viliaj^e lots. How much has he left? 4. A man bouf?ht a farm for $;{000. How much must he sell it for to fi;ain 12i% on his outlay? r>. A speculator invested !i!3r),400 in stocks and lost 168^% of his investment. How much had he left? (). A shepherd luid 5,800 sheep b>it lost 15% of them in a snow siorin. How many had he left? 7. In a seliool 420 pupils are enrolled, 45% of v/hom are tioys. How many girls are enrolled? 5. The population of a certain city is 18775. What will it be ill one year from this time if it jrains 8% ? i>. If 5% is deducted from a bill of $755, how much will pay the bill? 10. A farmer having a flock of 1200 sheep lost 27% of them, Wliiir per cent, of them, and how many sheep, had he left? EXERCISE CCIX. 1. A cask contained 42 gallons of vinegar, and 14 gallons leaked out. What per cent, was left? 2. In an orchard of 4000 trees, 80 died. What per cent, if'tnained? ;{. In a school of 50 j)upils, 10 are absent. What per cent. are ]»resent? 4. A merchant bouglit shoes at $2 a pair, and sold them at f'> a pair. What per cent, of the cost did he gainf ^Ul 132 ARITHMETIC. f). A mnii bouglit a hoisc for Jt^'J-lf) mikI soM liini l"<>i' $ll!)4. VVIiiit per cent, of llio cost tlitl lie f,';iiii.' (i. ir ;i niercluint houj:;lit tc:i at .")(» ct. per Ih. and sold it at 44 ct. pw lb., wliat is his loss ]»('!• cent. .' 7. A workman's wages arc reduced from ^lOawi-ck to fj<7..1(l. Find the per cent, of decrease. H. A collector cliarged t^2').i)2 for collecting ^',^24. What rate percent, did he charge? 9. A man's income is $840 a year and his expenses .toCO. What per cent, of his income does he save? 10. A and B engage in partnership. A invests ifoGOO and U $8400. What per cent, of the capital does each invest? EXERCISE CCX. 1. The aver.age attendance in a school was 5(5; this is 80% of the nnmher enrolled. How many were enrolled? 2. A bookkeeper spends ^WO per year, which is 24% of his salary. Required his salary. 3. I have bought two ]»uilding lots. For the one I paid $.300, which was GO per cent, of what I paid for the other. What did I pay for the latter ? 4. A young farmer owns J520 acres of land, which is 40% of the land his father owns. How mucli has the father* 5. A man had 24 sheep killed ])y dogs, which was 5^% of his flock. How many siieep had he at lii'st? C. A gentlennm pays $49;") for the rent of a hon^;e, which is at the rate of 11 per cent, of the vahie of the house. What is the value of the house? 7. A schoolboy in one week reiid 450 lines of Latin, which was 75% of the number in tiie book. How many lines had he still to read? 8. A clerk spent 00% of his salary for board, 20% of it for clothes, 11% for books, and saved $117. What was his salary? 9. A wool grower sold 3150 head of sheep, and had 30% of his original flock left. How many sheep had he at first? 10. The number of pnpils belonging to a certain school is 48(5, which is 8% more than belonged a year ago. How many belonged to the school a year ago? EXERCISE CCXI. 1. A grain dealer had 7000 busliels of grain; 17% was oats, 30% wheat, and the rest l»arley. How much barley had he? 2. A man bought a horse for $85 and sold him foi' $90.10. What per cent, did he gain? PERCENTAGE. 133 :?. Increase $450 by H% of itself, and decrease $450 l)y S'fr (>r ilselt', and find the difference between tlie I'esults. 4. Find tliu dill'ereuco between 40 ^fc of $12200 and (JO'r of $ir)(H). 5. A farm contains IJilO acres; 15% of it cost $'J<S pei- acre, 2i)'''r' cost $;{5 per acre, and tlie rest $40 per acre. \Vliat was the total cost? G. A f?rocer sells 128% more j^ranulated than loaf su^ar. Ho sells 38275 lb. of loaf sugar in the year. How much granulated sugar does he sell in a year? 7. A music dealer bought ?> pianos at $250 each. He sold one at a gain of 'AQ7o, another at a gain of 40%, and the thir<i at a loss of 20%. What was his net gain? 8. A drover sold cows and sheep for $9180. Ho received for his sh"ep 70% of what he got for his cows. What did he get for the cows? i). A young man having received a fortune deposited 80% of it in a bank. He afterwards drew 20% of his deposit, and then had $57(50 in the bank. What was his entire fortune? 10. I sold my farm for $5000 and made 25%. What per cent. should I have gained, or lost, if I had sold it for $3500 1 EXERCISE CCXII. 1. How many rods are there in 8i% of 121 miles? 2, What ^•um of money, increased by 8]t% of itself, will ii mount to $403? ',',. What is the quantity 71% of which is 12 ounces? 4. A train which runs 45 miles per hour has its rate increased by G;i%. How far will it then run per hour? 5. A library consists of English and classical books. The imniber of English books is 2135, which is 7Gi% of the whole niinilier of books. How many books does the library contain? (). In a r(\giment of 9G0 men of English, Scotch, and Irish (liscent, 40% of the whole are Irish, and3G8^%are Scotch. How ninny are of English descent? 7. The sum of two numbers is 3901 and one of them is 71% more than the other. Find the numbers. S. A nuin owning 75% of a foundry sold 40% of his share to "lie man and 33^% of the foundry to another. What per cent. <it' llii' foundry did he still own? !). Tlif population of a city in 1891 was 15048, being 41% I'loie tnan in 1881. What would have been the population in I'^Ol, if there had been a decrease of 4i%? 10. If water expands 10% when it becomes ice, by what per cent, does ice contract when it b(;comi'S Wiiter? ' ';! CHAPTER IX. APPLICATIONS OF PERCENTAGE. I. TRADE DISCOUNT. ,. Discount is a sum deducted from the face of a bill, debt or note. Trade or Commercial Discount is a sum deduc^ted from the catalogue or list i)rices of goods. The terms Catalogue Price, List Price, Gross Price and Invoice Price all denote the same thing, viz., the price entered in the catalogue of the goods. The Net Price is the List Price diminished by the discount. An Invoice is a bill of goods purchased at one time. EXERCISE CCXIII. 1. Find the discount off the following bills: — Invoice price $i')Q, discount 2')%. Invoice price $570, discount 37i % . 2. Find the net price of goods bought as follows: — Invoice i)rice $'SG'), discount off 20%. Invoice price $756, discount off 33i%. 3. The discount off a bill is $27 ; the rate of discount is 25%. Find the bill. 4. The rate of discount is l(}i% and the discount is $17.50. Find the list price of the goods. 5. The discount off a bill of goads is $45; the rate of dis- count is 20%. Find the net price of the goods. 6. The rate of discount being 33i% and the discount being $75, find the net price of the goods. 7. Find the rate of discount on goods bought as follows: — Invoice price $;)G0, discount allowed $1(!.20. Invoice price $420, discount allowed $157.50. 8. Tlu^ net price of goods is $270. The rate of discount being 25%, lind the list price. i;i4 TRADE DISCOUNT. 135 is(h1 at one tt> of discount 9. A doalor paid fpG20 for goods at 22^% off. Find tlio list ]»ri('(' of the goods. 10. I am eliarged $2.r)0 for a book, wliicli the bool\seller says is '.iVI^'/o less tliau it cost liim. Find tlie cost. EXERCISE .CCXIV. 1. Find tlio net price of goods bouglit as follows: — Invoice price $^75, discount off 20% and 10%. Invoice price $800, discount off 25% and 10%. Invoice price $800, discount off 20%, 10% and r)%. Invoice price $1640, discount off 25%, 10% and 5%. 2. What is the net cost to the purchaser of hardware invoiced at $815 and subject to a discount of 20%, 10% and 5% ? 15. A's list price for pocket-knives is $9 per dozen, 20% anil ')% off. B's list price is $9.50 per dozen, 25% and 10% off. How much will be saved by ordering 24 dozen knives from B rjitlier than from A? 4. At what price must goods l)e marked to sell for $2.72 after allowing 15% discount? 5. At what price are goods listed that sell for $18 after allowing 20 and 10 off? f). If goods cost $3.60, what must be the invoice price to allow discounts of 25%, 20% and 10%? 7. At what price must goods which cost $216 be listed to give 25% gain after allowing 25, 20 and 10 oft'? S, At what price must goods which cost .$1.52 be listed to f.ave 121% gain after deducting discounts of 20%, 10% and 5%? 9. What single discount is equivalent to a discount of 25% ami 10%? 10. What single discount is equivalent to 25%, 20% and 10% off? tXERCISE CCXV. 1 . What is the difference on a bill of $425 between a discount of 50% and a discount of 30% and 20%? 2. A bookseller wishes to mark a book wliich cost $2.00 that he may allow a discount of 25% and still make a profit of 20%. What must be the marked i)rice? .'{. What direct discount is equivalent to a discount of 20% and 10%? 4. A bookseller buys at a discount of 20%, 10% and 5% off, and sells at list prices. What per cent, profit does he make? 5. The selling price of an article was $25 when the rate of ^'aiii was 25%. Find its cost pricef • i. It' $1.40 is gained by selling goods at 25% altove cost, liiid what selling price would make t)u^ rate of gain 35%. i. 'J 136 ARITHMETIC. 7. An invoioo wns $fiK), trsulc dlsooujit 20 ami f) off. Find tli(^ cost ol' tlic j;()»>«ls. S. A dciilci' Ixtu^lii !i l>()<»k, list prico $1 .00, iit n discount of 2i)'/tJ, itiid iit'terwiii'ds sells tlio book jit $1.00. VVh.'it ]>('i' cent, docs lie j^iiin? 9. What is tlic not amount of a bill for $720, discounts being 2'), 10 and ") off? 10. A man jmrchasos goods, list prico $080, discounts being 'S:ik%, Vl}.% and I07r. Find llic not amount of the bill; also, a single discount e(iuivalent to these three. II. PROFIT AND LOSS. Profit and Loss, as a ooinmcrci.'il toi-m, donotes the ^i\u\ or loss ill business tniusac^tioiis. Profit is tlie amount l)y wliieli the sellin<^ pi'iee exceeds the cost price. Loss is the amount by wliicli tlie selling; price falls short of the cost price. The Rate of profit or loss is usually expressed as a certain i)erceutage of the cost pric(\ EXERCISE CCXVI. 1. Find the i)rofit or the loss on the following: — Cost $0, selling i)rice $8; cost $15, selling price $2^. Cost $115, soiling price $113.50; cost $75.50, selling price, $77. 2. Find the gain or the loss per cent, on the following: — Cost $G, selling price $8; cost $80, selling price $125. Cost $7.50, selling price $9; cost $100, selling price $95. 3. Find the profit or the loss in the following: — Cost $100, gain 10"^ ; cost $500, loss 8%. Cost $G5, gain 8% ; cost $450, gain 33^%. 4. Find the selling price iu the following:- - Cost $40, gain 7i% ; cost $80., loss 6i%. Cost $120, loss 15%; cost $75, gain 33^*^. Find the cost price iu the following: — 8elling price $110, gain \0% ; selling price $210, gain 5%. Selling price $40, loss 33i% ; selling price $84, gain l(Sl7o . Helling price $05, gain 8;^% ; selling price $72, loss 25%. Find the cost in the folloAvinji:: — 5. Profit $3, gaiTi 10%; profit $8, gain 5%, Jjoss $5, loss 20% ; loss $50, loss 8%. PROFIT AND LOSS. la? r» off. Find discount of lilt pel' et'iit. :(), discovmtS counts behif? Hi bill; also, ■m, (lonotes (T price falls expressed us X)Y ice $2r>. selling ])net', bllowing:— price $125. ug price $1)5. I<210, gain 5^c. U, gainlG^^o. r2, loss 25':^. I':'! I ■I 7. A iloek of slieep increases from 88 to 110 in a year. What is tlie gain per cent.? H. Bought books for $420, and sold them for $357. Find my loss per cent. [). If Mr. Jones buys a farm for $3875, and sells it for $3720, wiuit per cent, does he losef 10. If I buy i)aper at $3.50 a ream, and sell it at 25c. a (juire, what is the gain per cent.? EXERCISE CCXVil. 1. A merchant sold cloth which cost $1.75 per yard so as to gain H%. Find the selling iirice. 2. Goods which cost $735 ,vere sold at 20% gain. Find the selling price. 3. At what price must goods be sold to lose 12%, if they cost $-13.50. 4. Bought a house for $3500, expended $750 in repairing it, iuitl then sold it so as to lose 15% on the whole cost. What did I receive for it? 5. Sold goods at a loss of 20%, an actual loss of $59.50. What was the selling price? 0. Find the selling price of goods by which there is a loss of 2'r and an actual loss of $55.50. 7. A farmer bought 35 A. of land for $1750, and sold it at 20% gain. How much did he get per acre? 8. Mr. Smith bought a house for $5000 and spent $400 more for repairs. He sold it at 15% gain on the whole cost. What was his profit? 9. A quantity of wheat whieli cost 72 ct. per bu. Wfis sold lit a loss of 20%; the total loss was $1290. How many Imshels were there? 10, A grocer sold potatoes for $10.10, gaining 15%. If he had sold them for $18.20, how much would he have made above the cost price? EXERCISE CCXVIII. 1. A set of jewelry was sold for $140 at a gain of 25%. What did the set cost? 2. A ]>roduco deahn- sold a sliipinciit of wlu^it at a loss of '^'r", realizing as the net proceeds $S170. What was the cost!? •>. A miM'cliant sold rye at 15% gain. His profit was $2(5.70. How much did he receive for the ry»!? 4. A man gained 24% by selling land for $lit5 more than lu) jniid for it, liow much Uiti he receive for the laud? 4 138 AHITHMKTIC. '). TiMi COWS were sold foi- $()!)(), at a ^i\\u of 15^. Fov how mticli per lufiul, oil tlie iivernge, should tliey have Im'cii sod to 6. A merchant lost 25'^ by selling flour at $0 i)er barrel. If he had sold it at $9 per barrel, what would have been tlie gain per cent. ? 7. 1 sold a liorse for $240 and lost 20%. For what should I have sold him to have gained 10%? 8. A building lot was sold for $1840, at an advance of 15% on its cost. What would have }»een the gain per cent, if it had been sold for $2240? D. I bought a lot of goods for 1;")% below market price, and sold them for 15% above market i)rice. What per cent, did I clear? 10. Sold my carriage at 30 per cent, gain, and with the money bought another, which I sold for $182, and lost 12i per cent. How much did each carriage cost me? III. COMMISSIOIN. Cominission is the compensation received by an agent for transacting (pertain kinds of business. It is generallj^ reckoned at a rate per cent, on the money involved. The agent is variously known as Commission Merchant, Broi<er, Collector, Factor, &c. In selling, the Commission is reckoned oh the money received by the agent. In buying, the Commission is reckoned on the money paid by the agent. EXERCISE CCXIX. Find the commission on the following: — 1. $450 at 4% $300 at 2*% $1200 at 4A% $5700 at 3g % Find the commission on the followiiig: — 2. $2500 at i% $044^ at i% $3000 at li% $4800 a" 5% 3. An agent received a consignmeui of flour, .vliich ho sold for $3750. What was his commission at H%? 4. My agent in Chicago has purcliased whert for me to the amount of $7728. What is his commission at 14 per cent. ? $575 at 4J%. $1875 at 4^%. $3000 at i%. $8400 at i%. )r what should I )ned on the COSIMISSION. i;. Find the rate of oo '^**^ ^^^ i^e cVjJ,; *^, ^"^' ^'^eeived ,-, ,^: ;^" '-^Sent sold 'no vd'^nJ''^^ '^''''^- l"^' "Ot proceeds flic™ ""vli;- "f/^' "' 25 at. pe,. Ih „. . 4 Find t, '""'=™"»'»sionf ^ *° "«' <>«■■'«■ *2334.5o: .."-io,, U2i'i STJS: """•"' ^"-i' -ere sold when the com EXtRCISE CCXXI. m 140 AKITIIMETIC. 12. A Hour nn'ivluiiit rcniltM to lils aj^riit in ('hiciif^o $;J71)(i, for tlu' imrcliiisc of j^ijiiu, iiftc^r dediu'tiiij^ the eomiiiissioii at 4"r , How imu'li will tliu Hf^«Mit exptMul for his einployci-, and what will l>o the coininiHsionlf J{. A miller sent liis Montreal apont $9270 to }>e invested in flour, after deductinj* liis eonnnission of ii'/r . What was the conuuission? 4. Hent to my apjent in Boston .$:?8Lir) to l)o invested in French prints at $.15 per yard, after deducting? his commission of '2 % . How many yards shall I receive ? 5. An agent received $2040 to be invested in sugar at .'Ji ct. l>er pound, after deducting his commission of 2%. How many pounds did he buy? (5. What weight of wool at 40 et. a lb. can he bought for $1722 by my agent, after deducting his commission of 5% ? 7. I sent $2G7H to my agent to invest in calico at 5 ct. per yard after deducting his commission at 3%. How many yards did I receive? 8. A si)eculator received $:{290, as the net jiroceeds of a sale, after allowing a commission of 6%. What was the value of the property? 9. A hiwyer collected 75% of a debt of $1200, and charged 5% commission on the sura collected. What did the creditor receive ? 10. I sent a quantity of dry goods into the country to be sold at auction, on commission of v% . What amount of goods must be sold that my agent may buy produce with the net proceeds, to the value of $3500, after retaining his purchase commission of 4%1 IV. IINSURAINCE. Insurance is n contract wliercby one jmrty, in consideration of a certain snm, g-uarantees another party aj?ainst loss by fire or accident. The Premium is the sum paid for the insurance. It is always a certain percentage of the sum insured. The Policy is the written contract, j?iven by the insurer to the insured. EXERCISE CCXKII. Find the premium on the following: — 1. $ 850 at 1% $1200 at f% $ 900 at 1%. $1500 at ?.% $3200 at f% ijiOOOO ?it .70% ijio^OO ut .80% T-. ("-i $8000 at .75 $G(iOO at .()Oii% Vf) , INSURANCE. 141 ;j7<U), for 1 at 4'^. what will ^.est('«l in was tlio vestcfl in )unnissi(m V at 3i <'t- How many l)0uslit for f 5%? vt 5 et. poi" many yavdsJ Is of a sale, ralue of the md charged the creditor 1 to he sold jroods must , proceeds, commission party, in another insnrance. 11 iiisnred. /en by the )0 at S '^r . «)() at .75 % . loo at .U0^%. 2. Kind tlie cost of insurin<? ]>ropt'rty wortli linOOO at },% , if i of the vahu' is insured. ;{. A insured his house for 1 y(Mir for $8000 at the rate of i%, and his furniture for sfHOOO at tlie rate of 1%. W'iuit was the total |>reniiuni? 4. A cotton factory worth $25000, and tlie machinery and stock wortli ifltoOOO, are insured for -i their value, at i%. What is the premium? 5. A cotton factory and its machinery, valued at $75000, are insured at ,-"; per cent. What is the yearly premiuT»'? and if it should be destroyed, what loss would the insurance company sustain? G. What will be the cost of insuring 4000 bu. of wheat worth 75 ct. a bushel, at i% ? 7. The lioyal Insurance Company took a risk of $16000, for a premium of $280. What was the rate of insurance? 8. A company charges $20.25 for $2700 insurance. What is the rate charged? 9. I have goods worth $37560, which I insure for i of their value, paying $262.92. What is the rate? 10. The sum of $280 was i»aid for the insurance at i of its . value of a storehouse worth $40000. What was the rate ciiarged? EXERCISE CCXXIII. 1. At 1^%, how much insurance can be effected upon a store for $128? 2. For what sum was a house insured, if the premium paid was $24 and the rate of insurance ^ % ? 3. A company charged $225 for insuring property at l^% premium. What was the value of the policy? 4. A man pays $87.50 for the insurance of house at |%, and $50 for the insurance of furniture at li%. If both are destroyed by fire, hosv much will he receive? 5. Find the cost of insuring ^ of the value of 6000 bbl. of Hour worth $9.60 a barrel, the insurance being reckoned at |%. 6. A vessel and cargo, valued at $35000, are insured at f per cent. Now, Tf this vessel should be destroyed, what will be the actual loss to the insurance company? 7. I insure a factory for one year, at -ro%, for i of its value. 'J'lie premium is $270. How much is the factory worth? 8. I buy a house for $8000, and get it insured for f of its value, at S-%. If the house is burned, what is my loss? What is the loss of the insurers? 142 AUITIIMKTIC. 9. All insiinmco compiiiiy, Iiaviii;^ taken ii i-isk of $20000 nt 1%, rciiiHured ♦SdOO ut ^'.o with iiiiotlici' (•((inpaiiy, :iihl .f(J()(l() at 'i% with iiiKtthi-r. it' no loss ofcms, wimt docs tlic first company ^'i'" ' 10, A lmii«liiif< wortii $1,10000 is insured in three eonipjiiiies; in tlie lirst for ^UwOOO, in tlie second for $;jr>000, iind in the tiiird for $40000. For what is eaeii company liable in case of damaj,'e to the extent of $10000 f V. TAXES. A Tax is ti sum of niouey levied on the i)ersoii, property or income of iudividiuils for piiblie i)in'poses. Taxes on property or income tire nn^koiied at Ji certain rate per cent, of tlie assessed vtiliie of the property or income, or at Ji certtiin number of mills on the dollar. Taxes are of two kinds: — Direct Taxes jind Indirect Taxes. Direct Taxes are levied by the Province, Town- ship, Town, or City. Indirect Taxes are called Duties and nre levied by the Dominion. Customs Duties are levied on articles imported from other countries. Excise is a duty on articles manufac^tured in tlie country itself. Duties are either Ad Valorem or Specific. An Ad Valorem Duty is reckoned at a certain rate l)er cent, of the cost of the goods in the country from which they have been imported. A Specific Duty is a fixed sum levied on the quantity of goods without regard to their y.ost. EXERCISE CCXXIV. 1. Find the tax on $4500 at 12 mills on the dollar. 12. Find the tax on property assessed at $7r)00 at 2%. 3. Tlie law exempts $700 of income from being taxed. What does A, whose salary is $12000, pay when the rate is 15 mills on the dollar? TAXES. 143 lilt' thinl ^ person, purposes. )1UhI «it Jl ue ot tlio f of luiUt^ axes and ice, Towii- e levied by s imported Hved ill tlie fic. 'ertain rate luutry f I'om ied ou tlie Icost. liar. lat 2%. Ibeing taxed. Ihe rate is 1^^ 4. Kind tlio duty (mi fiiriiitiiir, the invoice prifo ol' which is $l7.")n, :it :i()%. .'». A hMi'dwan* nicnditiiit iniports «'uth'ry to thi- vahic of $1:17'). What duty must he pay at :U)'i i (». What is the duty (»n a case of sardines couXaiMiu^ 410 boxes at 5 et. per box? 7. Kind the duty on KOO Ih. of snfjjar oaiuly worth r» et. i)er Ih., the speeifie duty lieinj,' i et. i>er Ih. and the ad valon-iu duty [iiS % . H. What is the rate of taxation, wlien property assessed for $'J7r)() pays $:{H.r)() tax? 9. Wiuit is the rate of taxation, wlien .+ 1120 is the tax upon $U<)00? 10. Find the rate of taxation, wlien $'J8 is the tax on $1(500. EXERCISE CC\XV. 1. Wliat is the assessed "■itlue of pro])ertv on whieh the tax is $:U.r)0 at lli mills on the dollar? 2. The rate is 16J mills on the dollar. A's income tax is $29.70. What is A's income, $700 of it being exempt? 15. The expense of buildinj? a public bridfjje was $17(58, which was defrayed by a tax upon the proi)erty of th.^ town. Tiie rate of taxation was 3i mills on one dollar. What was the valuation of the property? 4. The duty upon stockings is 35%. What is the invoice cost of stockings upon which $35.56 duty is paid? 5. What is the invoice cost of goods upon which .$025 duty is paid, if the duty is reckoned at 25%? 6. If a tax of $12350 is to be raised, and the collector receives 5% for collecting the taxes, what sum must be levied? 7. What sura must be assessed in order to raise a net amount of $.5501.50, and pay the commission for collecting at 2%? 8. In a certain section a scho ilhouse is to be built at an expense of $9600, to be defrayed by a tax upon property valued at $153(5000. What shall be the rate of taxation? 9. In a school section, a tax of $375 is levied for the sn])port of schools. What is A's tax on a valuation of $4000, the entire valuation of the district being $00000? 10. A town is to be taxed $23200 on an assessed valuation of $2900000. What is A's tax ou au assessed valuation of $14275? [rl "l^Bi 144 AltlTllMRTlC. VI. SIMPLE INTEREST. Interest is imuicv p<'ii<l tor llic iisr of iiHUH-y. Ttie Principal is the smn lor Ihr iis«> of wliicii interest is paid. The Amount is tlic sum of tlii> Principjil mikI Interest. The Rate of Interest is tlie rate per cent, of tlie principal allowed for its use for one year. Interest, is either Simple or Compound. Simple Interest is tlie sum <'liarji:ed foi* the use of the IM'ineipal oidy. Compound Interest is intei*est re(!koued on the principal and mIso on tlu' aeerue(l interest as it falls dut^ from period to period. EXERCISE CCXXVI. 1. Find till! iiitert'st on the following: — $m) at 6% for I yr. if^'JOO at 4% for 1 yr. $ir)() iit 4% for () nio. ^'AH) at ;')% for ;{ mo. IIJ.'jU iit (5% for 4 mo. ^■i')0 ut 4% for (J mo. t>. What will l>e the interest on $;U)0 for 5 mo. at G%? 15. Tf !fi;5r)0() Itorrowed money is re]>aid in 7'A (lays, how much interest should he paid, money being worth HVr ^ 4. Find the simple interest on $4800 for 1 yr. 5 mo. at !S% . n. Find the interest on ^'2i){) for G mo. at 8% . (I. What is the interest on i^HO'.i for J}') days at tho rate of 7% per annum? 7. Find tlie interest on $S7() for 10") days at G%. 8. Find the interest on .$17512 from June '.i to Oct. IG at (>% . 9. What interest is due on $584 from March 7 to August li) at 5%.? 10. Find the interest on $131.40 from Sept. 5, 1899, to March 7, 1900, at 7'^r. EXERCISE CCXXVII. Find the amount of the following: — Principal, Kate. Time. 1. $ 8712 G % 10 mo. 2. $ 9412 G % 15 mo. 3. $]S9(i 7 % 17 mo. 8IM1'I-K INTKKKST. 115 [Mil i>»»(l .('lit. of the ^^^^ i\ (n\ the IS it fulls )r W mo. )v () nio. , how mxich mo . at T) /f • rate of l^c [t. IG Jit (•)%• Ito August 19 [99, to March Ime. mo. mo. mo. 4. n. 0. 7. 8. $511 $408.80 $17'J8 $(iO 7 ^ .liiiH- 'J to Off. 1:.. 5 ^r April I, 1851!), to .hiii. 1^1, liMlO. 7 rf .hily ;{, 18!»!», t(. F«l.. !{, 1!)00. (5K^ 1 yr. 'J 1110. 8 'ir 1 VI'. '.] nu). <>. J. Ay<T li:iM I). How's note Cor !f!l8'jr.. «liit«'(l Dec. L'S), 181M); \lmt in the iimoiint Oct. !», I'XIO, iit (J per cent.* 10. I*. K'vc's his iiot«', Aii^rnst (itii, IS!)!>, lor .flOiC), interest iifc 7^'r; he piiys tlic note iiiid interest May 17lh, I'.MMl, how niucli did he pav? EXERCIS^E CCXXVIII. What is th(» rate jtei' cent, wiieii 1. The interest on $4'yO for 1 y. is ^'27'! 12. The interest on .f!>.")0 for 1() nio. is $88ji ? ;{. Tiie interest on !f!:i80 for 1 yr. 4 nio. is $'J2.80? 4. The interest on Mil for 75 da. is ^^71 5. $480 amounts to l-llO in 1 yr. f (5. .$()00 amounts to $()i;{.75 in 5 nio.f 7. $ll(i8 amounts to .$in»5.()0 in II.") da.? 8. The amount of $1022 for 2(50 days is $10.')4.7r.? 9. The interest on $80:{ from June 10 to Dec. 2 is $2;{.K»? 10. The amount of $87(3 from April 10 to Dee. 1 is $!)0!j.84? EXERCISE CCXXIX. Find the time in wliich 1. Tiie interest on .$45(5 at (]% will be $27.:}(i. 2. The interest on $540 at 4J% will be .$:{(5.45. :i. The interest on $840 at G% will l»e $(5:5.45. 4. The interest on $1.')00 at 7% will lie $4:5.75. 5. The amount of $1(500 at 5i% will be $l()(i(5. G. The amount of $750 at 7% will lie $785. 7. The amount of $2920 at M% will be $2901.40. 8. Tlie interest is ill,, of the jirincipal at 4.1 Cir. 9. The amount of $7:53.(55 will be $751.74 at 0^. 10. A j.rincipal of $i:514, loaned May 12, 1S99, at 5.]^^;, will amount to $1328.85. EXERCISE CCXXX. Find the prineii)al that 1. I'roduces $24.:;0 interest in 1 yr. at 4.?'^. 2. i'rodiices $;;!». :;o interest in I yr. mo. at 4%. :5. Produces $21.25 interest in G mo. at 5%. m -" I IV 146 ARITHMETIC. 4. Produces $22.50 interest in 1 yr. ;it tii%. f). Produces $.56 interest in 1 yr. 4 mo. at ^%. 6. Produces $22.50 interest in 8 mo. at 4i%. 7. Produces $12.96 inte-est in 90 da. at 6%. 8. Produces $56.25 interest in 225 da. at o%. 9. Produces $6.48 interest at 6% from June 5 to Dec. 2. 10. Produces $lu5 interest at 7i% from April 15 to Oct. 7. EXERCISE CCXXXI. Find the pvineipal that 1. Amouiits to $265 in 1 yr. at 0%. 2. Aruounts to $496 in 1 yr. 4 mo. at 5%. Amounts to $596.70 in 1 yr. 6 mo. at 7%. Amounts to $595.40 in 8 mo. ut 6%. Amounts to $li{91.50 in 1 yr. 1 mo. at 5%. Amounts to $424.83 in 9 mo. at 5i%. Amounts to $796| in 1 yr. '.i mo. at 5%. Amounts to $1782.60 in 85 da. at 7i%. 9. Amcant> to $3735.50 from June 3 to Dee. 10 at 4i%. 10 Amounts to $3338.50 from April 17 to Dec. 3 at 6i%. 3. 4. 5. 6. 7. 8. Vli. COMPOUND INTEREST. EXERCISE CCXXXII. Find the compound interest and the amount of 1 . $800 at 5 ^ , compounded annually, for 3 yr. 2. $2500 at G% , com])ounded annually, for 3 yr. 3. $1250 at 4'~r, compounded lialf-yearly, for 18 mo. 4. $8000 at '}9h, compounded iinnually, for 4 yr. 5. $10000 at 12%, comi)Ounded quarterly, for 1 yr. Find the jcineipal which will ])roduce 6. $648.90 interest at 6%,' compounded annually, for 2 yr. 7. $151.32 interest at 5%, compounded annually, 'or 3 yr. 8. $927.27 interest at 6'!^: , j-ompounded half-yearly, for 18 mo. 9. How much j^i'cater is the cf)mpound inicrcst on $1200 foi' 2 yr. Jit 6'^f ,. conipounded yeiirly, tlian the sini])le interest for the same tinu'? 10. ilov niiich juri'ciitcr is the coinpouinl interest on $SO00 for 2 yr. ill, lO'/i, coiniiouiidctl half-yc;ti'Iy, thiin the simple interest for the same time .' BANK DISCOUNT. 147 Dec. 2. to Oct. 7. at 4*^0. 3 at 6i%. 18 mo. a*. fov 2 yv. 'or '^ yv. irly, forlHi'if»- u ;„ $1200 for ilo interest lor it on i^«'"^'^ *''^'; V,uil»»« interest Vm. BANK DISCOUNT. Bank Discount is the charge made by a bank for advaiudng the payment of a note not due. It is equal to tlie simple interest on the face value of the note, for the time between the date of buying the note and iho. time it falls due. The banker deducts the dis- count from the face value of the note and pays the balance, which is called the Proceeds of the Note. A Promissory Note is a promise in writing, made by one person to another, to pay on demand, or at a designated time, a specified sum of money. The Maker of the Note is the person who signs the note. The Payee is the person to whom, or to whose order, the note is made payable. The Holder is the person who has legal possession of the note. The Face of the Note is the sum for which it is given. The Maturity of a note is the time at which it becomes legally due. Days of Grace are three days whi(^h elapse from the time specified in tlu^ note for its payment until it is legally due. The time that elaj^es between the day of discounting the note and the day of maturity, called the term of discount, includes the days of grace. A Negotiable Note is one which is made payable 1<) bearer, or to the order. of the payee. It can be sold to another. If payable to bearer, no endorsement is necessary. If i)ayable to the order of the payee, it must be endorsed by him before being disi)osed of. The Payee endorses the note by writing his name across the back of the note. PROMISSORY NOTE. $;{oo. Toronto, Uay 18, 1900. Sixty (lays aftoi' date I promise to ])ay Xicliolas Walsli, or (irdcf, iJilJOO, value received. John Biuck. Tliere arc three parties to a draft: — The Drawer, the person who makes the di-ai't, — the person who ordei'S the m(Mi(^y to be paid. 1- - 148 ARITHMETIC. The Payee, the person in wliose favor it is drawn. The Drawee, the person on whom it is (h'Hwn. If the draft is ae(;ei)ted, the Drawee l)eeoines the Acceptor. DRAFT. $100. Toronto, Jan. ]5tli, 1900. Ten (liiyH aftoi- sif^ht i)ay to the order of James Mills the sum of one hundred dollars for value received, and charj^e the same to the amount of Thomas Lovkll. To John Smith, Esq., Merchani;, London. In the above draft, Thomas Lovell is the drawer; John Smith, Esq., is the drawee; and James Mills is the payee^ EXERCISE CCXXXill. 1. Draw a note due in 3 months with interest at 0% per ann., (1) payable to John Smith or bearer, (2) payable to John Smith or order, (3) payable to John Smith. 2. Draw a note payable on demand. 3. Write a note for the following: — Face $250; time 3 mo.; interest 4% per ann.; maker James Jones; payee Thomas Harris. 4. Write a note payable at a bank for the following: — Face $.")(); time 3 mo.; interest 5% per ann.; maker Thomas Jones, payee Wm. Meadows. 5. W^iat is the cost of a sight draft in Montreal for $750, at i% premium? 6. What is the face of a draft which can be purchased for $1500, at 1 % premium? 7. Suppose that Porter & Jones of Montreal, owe you $350. Write out a sight draft on them for that sum in favor of the Bank of Commerce. EXERCISE CCXXXIV. Find (1) the day of maturity, (2) the term of discount, and (3) the proceeds of the following: — Date of Note. Face of Note. $657 $803 $182.50 $5021 $511 $) 1(5.80 1. April 17, 1899 2. Oct. 20, 1899 3. Sept. 15, 1899 4. May 11, 1899 5. Aug. 23, 1899 (1. June 20, 1899 Time. Discounted. Kate. 3 mo. May 1 8 %. 4 mo. Dec. 15 7 %. (5 mo. Dec. 28 •5 %. 4 nio. .Inly 31 G %. !>() dii. Oct. 25 r^}<%. (iO da. -lune 28 7li%. • STOCKS AND Dl VI DKNDS, 149 (Iniwu. wu. iiies the », 1900. s the sum tho siuno LiOVKLIi. ver; John at f)'"/" P*^i' ble to John \me 3 nio. ; ree Thomas ins:— Faee Hiias Jones, [for !i;7r)0, at Liehased for ■(> yon $350. It'avor of tUt! tsconiit, and Imtetl. Kate. 1, S '>. 15 7 ^'■. '>S '5 % • 31 %. 25 5i'^. oy 7 i % , 7. Find the face of a note wliieli will realize !f31K.50 when diseonnted 4 mo. Iti^fore maturity at (5%. K. Mr. Jones lias a })iil for $5(58.80 to pay. He f^ives iiis note for 3 mo. whieh discounted at 5% on the day of inaiUiii^ just l>rodiKM*s tliis sum. Find the fae(* of the note. 9. Find tlio proeec'ds of the following notes: — $19()L'i'*,A,. Toronto, July 1>G, 1899. Four months after date I promise to j)ay to the order of James (Jillis one thousand nine hundr<Ml and sixty-two hA, dollars at tin* Ontario Bank, for value received. Discounted Aug. 'J(5, at 7%. John Dkmaukst. 10. .HIOOGiV... Winnipeg, April 19, 1899. Nin(^ty days after date we promise t' pay to the ord(M' of Kiii}^ & bodge one thousand and sixty-six iVo dollars at the ])oiiiinion Harik, for value received. (!ask & Sons. Discounted May 8, at G%. IX. STOCKS AND DIVIDENDS. An Incorporated Company is n iiurn})(a" of per- sons einpovvered by law to act as a sin^lo individual. Stock is the eapitnl of an incorporated company or the money borrowed ))y a government. A Share is one of tlie (Hjnal i)arts into which sl(M'k is divided. Sometimes the share is $200, or $100, or $r)0, etc. Any sum may be agreed upon. When the i)rice is quoted it is always on the })asis of $100 of stock. A Certificate of Stock is a statement showing that th(^ party therein named owns a certain numl)er of shares of the capital. The Par Value of sto(;k is the value nanKul on Ihe face of the certificate. The IVIarket Value of stock at any time is what it can be bought or sold for at that time. Stock is at a Premium, or Above Par, when Hk; mai'ket valu(^ is greater than the i)ai' value. It is at a Discount, or Below Par, when tin; mai'ket value is l<'ss tliau the par value. ^4i a; 150 ARITHMETIC. Dividends jire the profits from tli<^ ))usiTiess oi' compaiiies distributed from time to time amoiijif the stockliolders as percentages upon the par value of the stock. A Bond is an obligation to pay a um of money at a certain time with interest at a fixea rate at stated l)eriods. EXERCISE CCXXXV. Find the value of the following: — 1. $7000 stock in the 4 per cents, at 103. 2. $r^'>00 Bank of Ontario stock at 130. 3. $4850 Bank of Commerce stock at 145. 4. $650 Standard Bank stock at 192. 5. $3400 scock at 78 i. No. of shares. 6. 25 shares Imperial Bank 7. 45 shares Bank of Commerce 8. 75 shares Dominion Bank 9. 40 shares Bank of Montreal 10. 20 shares Ontario Bank EXERCISE CCXXXVI. How much stock can be bought with 1. $588 in the 3 per cents, at 84? 2. $5300 in Imperial Bank stock at 212? 3. $3220 in C.P.R. stock at 92? 4. $5733 in Toronto Railway stock at 102s? 5. $5500 in War Engle stock at 250? How many shares of stock can be bought as follows?— Sum invested. Per value of share. Sellinj; prictj Par value. $100 $50 Sel ing price 190. 145. $50 260. $200 255. $100 130. 6. 7. 8. 9. 10. $650 $5200 $576 $588 $900 $100 $200 $50 $25 $40 130 260 192 84 150 EXERCISE CCXXXVII. VVhiit incotiic is made from investing as follows: — 1. $5200 ill stock at 130, pjiyiiig 5"!^ diviileiid? 2. $5390 in stock at 2694, paying 12% dividend:' STOCKS AND DIVIDENDS. 151 3. $3600 in stock ut 144, paying 8% (livi«l«'iidF 4. $1350 in stock ut 135, payiiif? lOTi dividend? 5. $28(53 in stock at 102i, paying' 4% dividend? What rate of interest is made by investing? as follows: — (5. In British America stock at 125, paying 7% dividend? 7. In Dominion liank stock at 270, payiiifjj 12% dividend? 8. In London Pjiectric stock at 120, paying? (>% dividend? 1). In Traders Bank ^^tock at 112i, paying 6% dividend? EXERCISE CCXXXVIII. What sni. nust })c invested to produce an income of 1. $350 from stock at 130, paying a 5% dividend? 2. $550 from stock at 242, paying a 10% dividend? 3. $500 from stock at 141f, paying a 7% dividend? 4. $720 from stock at 173, paying an 8% dividend? 5. $660 from stock at 104i, paying a 6% dividend? How many sliares of stocl< must l)e bouglit to j>r()duce tiie following incomes: — Par value of stock. Dividend. 50 12%? 400 20%? 40 10%? 50 6%.? EXERCISE CCXXXIX. 1. I received $880 from a 5i per cent, dividend. How much stock do I own? 2. I receive $279 as my share of a 4J% dividend. How iiKiiiy shares^ at $50 each, do I own? 3. A lady receives $1200 dividend at 7%. 'Required th(* uinouiit of stock she owns and the number of shares, valued at $25 each. 4. A owns 85 shares of ruili-oad stock, at $100 a share, attd receives a dividend of $080. What was tiie rate of dividend ? 5. Find tiie rate of dividend ]»aid l)y a railroad when a holder of 240 shares, at $100 a share, receives $1722. (). Mr. .Tones owns 25 sliares, .'it $50 a share, and receives a li;ilf-yearly dividend of $43.75. What was the half-y(^arly rale? 7. A has 40 shares, $50 each, of stock in a bank, wliicii ilfclares a dividend of 5%. What is A's dividend? 8. How much income will be obtained iinnually by investing ■f^iMO in (;% bonds, selling at HI)? !•. Find the sum refjuired tor :in iMV«'stnient in a 4% stock, ;il !>.S.i, to produce iin income of $200 a year. Income 0. $360 7. $5600 8. $880 •J. $1500 \i ■ '?■?■■ 152 ARITHMETIC. EXERCISE CCXL. 1. If money is worth 7%, whut ouglit a stock tlmt regularly pays S% a year to sell for? 2, What must be the price of a T)^ stock in order that a buyer may receive G% on his investment? n. IMoney l»ein,<? worth 41^, what ought to l»e paid for stock that regularly pays 12% per annum ? 4. If an H% stock is wortli ]')0, what rate of interest will a purchaser receive on his money ? 5. How much stock must be sold at V2'.i, brokerage i, to produce $2949? 6. What must l)e paid for 40 shares of stock $25 a sliare, selling at 142i, brokerage!? 7. How many shai'es of stock, $50 a share, at 72|, i% brokerage being paid, can be bought for $1825? 8. What sum must be invested in 6 per cent, gas stock, at 84, to produce an annual income of $2100? 9. The security being equal, which is the better investment — 5 per cent, stock at 125, or 4i per cent, stock at 115? 10. A owns $5000 stock, which pays a dividend of 7%. How much must B invest in a stock which pays 6i% dividend so that his income may be $50 more than A's? X. EQUATION OF PAYMENTS. Equation of Payments is the process of fiiuliiij? the time at which several debts due at different tiiiK^s may be paid without k)ss of i?iterest to either the debtor or the creditor. The Equated Time is the time at whicli the several debts may be caiK^elled by one payment. EXERCISE CCXLI. 1. The interest on $100 for 10 days is equal to the interest on what sum for 1 day? for 2 days? for 5 days? 2. The interest on. $250 for 12 days is equal to the interest on what sum for 1 day? for 2 days? tor 3 days? for 5 days? for 8 days? for 10 days? 3. A loaned me $000 for 10 days. For how long should I allow him the use of $;J75? of $1200? of $1500? of $3000? 4. T borrowed from P> $200 for 4 months, $300 for G montlis, and $400 for 7 months. How long should I lend him $1800 to repiiy the favor? 5. T .7we to A $500, |>;iyjil>Ie in (! moiitlis. and $400, due in 15 mouiUs. When may 1 pay the whole in one payment ? EQUATION OF PAYMENTS. 168 Ito the interest n. I owe to B $80, due in 2 da. ; $60, due in 8 da. ; $40, due in lOda. ; and $100, due i;i 12 da. Find tiie c'(Hiated time of imynieut. 7. A del>t of $200 is due in (50 da.: $r)0 is paid 12 d.-i. Ix'foi'o it is due, and $1(M) is paid 24 da. before it is due. When should the balance be paid? 8. A man bon{?ht a farm on .Ian. 1st, 1900, and is to pay $(500 casli, $000 in 2 mo., $800 in 6 mo., and $1000 in 12 mo. Find the equated time of payment. 0. On Jan. 1st, 1900, a man jijave 3 notes, the first for $r)0(), ])ayable in IJO days; the second for $400, payable in ()(] days; the third for $G00, payable in 90 days. What was the average term of credit? < ( 4 o l\ i|!400, due in EXERCISE CCXLII. 1. Find the averaj?e term of credit for the following l)ills: — (a) $100 due in 2 mo. (/>; $100 due in 1 mo. (c) $700 due in .') mo. ;K)0 " 4 " 200 " 2 " IJaO 200 " 7 " 300 " 3 " 550 400 " 8 " 400 " 4 " 400 2. A grocer buys $400 worth of goods at 90 days, at the end of 00 days he pays $200. Find when the balance should be paid. 3. If I buy goods for $3200 and agree to pay 1 in 3 months and tlie rest in 5 months, but afterwards decide to pay all iu one sum. When should I pay it? 4. A note for $800 is to be paid as follows:— i at once, I in 6 months, and the balance in 8 months. When could it all be piiid together? 5. What is the average date for paying three Vjills due as follows:— March 31st $400, April 30 $300, May 30th $200? G. On Jan. 25th, 1899, a grocer sold goods for $1340, i l>!iyable in 90 days; i in 120 days, and the balance in 150 days. Wiuit was the equated date of payment? 7. I bought goods for $600; i to be paid at once, } in 4 months, and ts in 6 months. At what time may the whole be \KiuU H. A owes a sum of money, of which ^ is payable at 30 days, ■■ at GO days, and the rest at 90 days. What is the equated time tor the payment of the whole? 9. A man purchased real estate, and agreed to pay i of the jivife in 3 months, i in 8 months, and the remainder in 1 year. W^ishing to cancel the whole obligation at a single pay- ment, liow long shall this payment be deferred? <n m !il 1 CHAPTER X, PARTNERSHIP. Partnership is tlie association of two or more persons in business, witli an agreement to share the profits and losses. Partners are tlie persons associated in business. The Association is called a Company, a Firm, or a House. The Capital or Stocic is the money or property invested in the business. '< EXERCISE CCXLIII. 1. B and C gain in business $1050. B's stock was $1500 and C's $2000. What share of the gain should each get? 2. A and B are partners. A furnished $840, and B $1030 capital. Find the share of each of $432 profit. 3. A and B agreed to do a work for $260. A worl<ed 27 days and B 25 days. How should the money be divided? 4. A, B and C rent a pasture field for $275. A puts in 17 horses, B 26 horses, and C 12 '"orses. What share of the. rent should each pay? 5. A, B and C engage in business. A puts in $3600, B $1700, and C $4800, and they gain $2424. What share of the gain should each get? 6. A and B engage in business with a capital of $6000. At the end of the year, ,i. gets $208 and B $272 gain. What was the capital of each? 7. A, B and C enter into partnership. A puts in $2325, B $3250, and C $4625.. A gets $465 for his share of the gain. What should B and C receive respectively? 8. The capital of a firm consists of $40000, of which A contributes $14000, B $17000, and C the rest. Divide $5000 profits among them in proportion to the capital of each. 9. A, B, C and D form a partnership. The capital of each is $4500, $2300, $1900, and $1100 respectively. They lose $1568. What is A's share of the loss? 10. Divide $9282 among A, B, C and D, giving A 10% more than B, B 10% more than C, and C 10% more than D. 154 or property Partnership. EXE.7CISE CCXLIV. 155 7 weeks 'Vi^n^ i'"'" '^ P»«tiJre for .*4/) * , -•• A and B take ., . '"'*''''^ i"'-^ *7;io, be divided ' '" ^'^>'«- ^ovv .iji'.r*" f"/ 10 cows (or mo. How ,.?. , ' • ^' ^" cow, w •, "°- ^ Pi'ls in "o i B ^Jt.^'"™." Partnership. T^ ?'"-■'' "">■' ^- A and B form n * °" "-rtidJ^f »«»« »o-. °^iv? ?S "L1o"'^'h*?S .Ii.l B joi;;" '• ""«' """"y months befJ^e'C: ' ■•«<'™1 """ 9. A and R f >''■'"■ * «'"<» and B $mT " P»rt"erahip for „ y,„, , ^ ^,. CHAPTER XI. IINVOLUTIOIN AND EVOLUTION. I. INVOLUTION. A Power of n iniuilx'i* is tlic product <>l)taiiio(l ])y taking the imnilM'r a number of times us a factor. Involution is \\w proct^ss of raisinj? a iiiurioer to a power. Tlie Index or Exponent of a power is a Hjfun; placed at tlie ri^lit and a little above the iminher to show how many times it is used as a factor; thus, 5", 2 is the exponent. The Square of a number is the product obtained ])y using tlie number twice as a faetor. The Cube of a number is the product obtained by using the number three times as a fac^tor. 4 X 4 = 4** = IG, or, tlie'Jnd power, ors(niiU'('(jt'4. 4X4X4 = 4*^ = ()4, or, the 3rd power, or cul)e of 4. 4X4X4X4 = 4* = 256, or, the 4th power of 4. 4X4X4X4X4 = 4"^ = 1024, or, the nth power of 4. EXERCISE CCXLV. Write tlie following as powers nvl find their vjilues: — 1. 2X2X2 2. r)X5X5 .•J. ixixi 4. 2iX2i 5. .IX.IX.I C. .12X.12X.12 2X2X2X2 5xr>XoX5 ix*x*x* ;jix3ix:{i .03X.03X.0:{ .15X.15X.15 ;}x3x:jx;5x3. 5xr)X 5X5X5. 6 /\ u /N 6 '^ n /^ r. • 4iX4iX4iXv^. .05X.05X.05X.05. 2.5X2.5X2.5X2.5. "Write the factors of the following powers and find their pro- ducts: — 7. 2^ 3* 4^ 8. ar- (f)^ (i)^ 9. i.'^V (.05)- (.001)'' 10. (2i)« iuy (5i)*. 156 INVOLUTION AND EVOLUTION. 157 bXERCISE CCXLVI. .S(|uiir«' llir following iiumber.s: — for. r.bt'i" to a i\imbt'V f<> thus, r>-, t obtuiiuHl t obtained rs(iu!in'of4. or cube of 4. i: 4. f 4. Is : — l5X5X'>. :X4*X'.*. iooX.OoX.O'). .5X2.5X2.5. Ind their pvo- |3 ,5/ .001)'. :5i)*. 1. 19 45 86 93. 2. 101 504 906 708. 3. 75.G 40.8 97.5 7.96. 4. * ♦ i A. 5. 4i 7h 9i V2L ibe the following numbers : — G. 9 19 41 91. 7. 101 110 506 909. 8. 30.5 4.55 78.4 6.97. 9. 1 A H \t. 10. 2i 5i 31 71 EXERCISE CCXLVII. Kiiise the following numbers to the powers indicated: — 1. 9^ 5=' 25^ l6^ 2. (.09)'' (.ir y (2.5)« (.33)3. 3. (t)« (1) I (2i)» (3i)^ Find the value of 4. 452 24 ? 88* (If)". 5. S'-'XS" 7* X7'* 12''X12'^ (i)''x(^)^ 0. 12'' -^12'* a* -H-' J23^2'' 9^-3^ 7. 10^-5' (2 5)«- ■{.IV i^y^av (3.5)«^(.5)» S. What power of )i number is the product of the first power, the second power, and the third powerf 9. If the fifth power of two be multiplied by the third power of two, find the resulting number. 10. What power is the square of the cube of the fourth power? 11. Of what number is 7009 one of the two equal factors? 12. Of what number is 5050 one of the three equal factors? 13. Find the number of which one of its four equal factors is .002. 14. Show that 3G'' = 2*X3^ 15. A field is 48 rods long and 32 rods wide. Fiud the area of a square with an equal perimeter, 168 AUITliMETIO. II. SQUARE ROOT. The Square Root of a numbot' is oik; of its two equal tactors, tlms G is the s(nuir(i root of 36. The stiimn; root of a nuniljcn- is iiidif^attnl by th« radical sujn J, or by tlie fra(!tion A written above and to the right of tlie number. EXERCISE CCXLVIII. Find the square root of the following: — 1. SI i) i:{G9 8. iimi 4. U 5. ni\ 6. .01 7. .061009 121 :ji;{6 98596 .0025 .001225 144 4096 655:36 684 I 1 2 r .0009 .oo:i;u54 225. 6561. 277729. 1 a 2 6 5411. T H (t a • .0S41. .0256. Find the value of the following 8. (144)^ (A)^ Find the following: — I Ki) ^ \^2a) V81 '^ V 1 Off 9. v/9.3025 i/. 010404 /. 326041 >/. 0000316969. Find correct to 3 decimal places the square root of 10. 5 .5 .9 .009. EXERCISE CCXLIX. 1. Find the two equal factors of 240100. 2. What number must be multiplied by itself to produce 2450,Vff. 3. Resolve 10252804 into two equal factors. 4. The area of a square lawn is 576 sq. yd. What is the length of one side? 5. Tlie area of a square is 40 acres. Find tho length of one of the sides in yards. 6. How many rods long must the side of a square field be to contain 250 acres? 7. Find the side of a square equal in area to a rectangle whose sides are 544 ft. and 136 ft. 8. What will it cost to fence a square farm coritainiug 160 (icres at 25 ct, per vo^i OUBK KOOT. ir>j» f its two iO. id by tli« ibove aiul 225. ()')()!. 277729. 1 2 'J 5 6 4 1V T 6 » »^. 10 rt & • .0841. .02r)(5. JW^'J 19B )000:U69(i9. )f .009. [if to produce What is the length of OIK- lare field be to ^0 a rectaiigh' hontainiug lO^J !>. Tin- i«lo of 11 H»|U!ir<> licld is !Mi rods Ion;;. l-'iinl lli«t Iciij^th of i\w si(l(* of II sciuarc (Muitiiiiiiii^ 2i tiiiifs jih iiiiicli. 10. A s<|iiare lnwii contuin.s ll(i(J4 sq. yd. What will it rost to fciK'e it at $.7 > per yd. If EXERCISE ecu 1. A nMtaii>?)iIar KardiMi contains IS7r> h(|. yd., and it is '.i tiiiics as long as it is widi^ Find its length and width. 2. A rectanjfUJMr pird<<n contains 2 acres, atid it is ;') times as long as it is wi(h». Find its Icnj^tli and width in yiirds. 3. A s(iuaro yiird is divided into 57(5 ecjuiil squares. Find tlio length of a side of each. 4. A field is 12 rd. sqiuire. How lotig is the side of another square field containing 1 s<j. rd. more than twice th«» first? 5. Find the number of rails, each 12 ft. lon^, re(|uired to Itnild a straight fence 6 rails high round a s(iiiare lOA. field, allowing the rails to overlap 1 ft. f (). The rroii of a square field is 122i acres. A rectjtngiiliir Held containing the same area is 4 times as long as it is wide. Find the number of rods in the h-ngtii of this field. 7. llaw many yards of fencing are required to enclose a sfpiare farm containing 832A. 105 n(\. rd. ? H. A square bin has a capacity of 1800 cu. ft. and is 8 ft. deep. What is its length? 9. The side of a square field it; 171 yd. loiif; and of another square fiold 140 yd. long. Find the length of the side of a s<|. field as large as both together. 10. The i)erimeter of one square is 3840 yd. and .)f another (i()88 yd. Find the perimeter of a square equal in area to both of them. III. CUBE ROOT. The Cube Root of a iiii]ri])er is one of its three equal factors; thus, 4 is tho cube root i;f 64. T\u' cube root of a number is indicat(!(l by f, or )ty file fraction ^ written abov(i and to tlie rij^lit of tile numl)er. EXERCISE ecu. Resolve the following nnnibers into prime factors, and from these find their cube roots: — 1. 216 512 729 1728. «) 3375 4096 5832 93«1. 3. 15625 13824 21952 35937. 4, 42871^ T17649 166370 175616, 1(50 AUITIIMKTId. Extnu't llio (MiVx' ro(»t of tlu^ follnwlu'': f). 4in;j G. 14,SS77 7. io:j():u)1 S. 3 4 :i "2 1 y 1 9. .001 rji(i7 2or);j79 ];5()7();}i 7 ',' T) « f) .0001210 24:}8!> :5007():! 4S'j()Soa £ 7 4 4 1 1 r> 1 ti ir)GO.S9(5 Find tlio ciihc) root corrc'ct to 'A (liM'iiuul pliicos of 10. .8 .08 .008 jjOCm:}. 3r)7911. G7;")1"J()9. 1 .'i .•! 1 f> a :n 9 • 47832.147, CXERCISE CCLII. Find the followint^: — 1. f'lilG'JS f .Oir)G25 fl.8G08G7 f I012.0480G4. 2. (92G1)^ (8i:W0^ (373i¥5)'' (480it;l)^ 3. Tiu' product of tluvo oqnul fii- 'ors is ,3980.977. Find the factors. 4. Uequirod i\)e rnKn'ru-r of squnro feet in ono faee of a cubical bloelt wliose contents ai-e 40r)224 cu. ft. 5. What is the entire snrftice of a cube whose cnl>ieal coiitents are 912(573 (Mil)ie ft.? G. A cubical cistern liolds 4913 cu. ft. JIow deep is it? 7. The edf?es of a rectanfjjnhir solid are IGO iii., 2;") in., and 54 in. respectively. Find the edj^e of a cube of the same volume. 8. The contents of a cube arc 97.33G cu. in. Find the ed^e ' of a cube that contains 8 times as niucli. 9. A rectanf^ular l)loc]i of stone with a square end is 8 times as long as it is wide and contains 27 cu. ft. Find its length. 10. The contents of two cul)es are respectively 53;')9.37o and 5.3r)937i') cu. in. Find the dilference between the lengths of their edges. 11. Find the total lengtli of the edges of a cube containing 5005)5 cu. inches. 12. What nnist be the edg(^ of a cubical bin that shall contain as many bushels as a bin 10 ft. 5 in. long, 5 ft. 4 in. wide, and 2 ft. 3 in. deep ? 13. Tile product of tliicc numbci's is 2304. The second is twice the first and the third is one-third of the second. Find the first inimlter. 14. A rectangular room "ont.i" -< 13;'<24 cu. ft. Its width is H of its length and its lieiglil is h .' il:; width. Find its length. :.o(»r)3. 3r)7'.)U. G7r)ii:()'J- 1 ;{ :( 1 5 « :t 1 • 47832.147. CHAPTER XIL /1012.0480G4. 480itS)^. 80.977. Find ono faee of a whoHo cul)ical idccp is it? u., 2') in., and of tho same Find the od}?e end is 8 times Id itH lenj?tli. ]y MiVJ.:^.") and tiie lengths ot lube containing lit sliall contain ft. 4 in. wide, Tlic second i^ second. Fi»"' Its widtii is H hiid its length. MENSURATIOIN. A Triangle is a plane figure Ijounded by thivv, straight lines. An Equilateral Triangle is one whieh has its three sides equal to one another. An isosceles Triaiigie is one whieh has two sides ('((ual to eaeh other. A Right Angled Triangle is one which has a riglit angle. The Hypothenuse is the side of a right angled triangle, whieh is opposite to the right angle. The Base and the Perpendicular of a right angled triangle are the sides that (contain the right angle!. A Quadrilateral is a i)lane figure Ixmnded ))y four .<iruiglit lines. A Parallelogram is a qnadi-i lateral, the opposite sides of whieh are i)arallel. A trapezoid is a quadrilateral with oidy two sides ]){irallel. A Rhombus is a (piadrilateral whieh has its four sides ('(pud to one another. A Trapezium is a (quadrilateral, whicdi has none of its sid(\s i)arallel. A Circle is a plane figure bounded l)y a enrved line ealhul the circumference, every point of whi(di is equally distant from a point within called the centre. The Diameter of a (urcle is a straiglit line i)}issing thi'ough the centre and t(!rniinated Ixjth ways l)y the cinnunference. 161 I 162 ARITHMETIC. The Radius ot n ciivle is a straiglit line drawn from the (tcMitre to the eircumfereiice, A Right Cylinder is a solid, bounded by two (eir(;ulai*) plane faees and a eui'ved faee, every part of whieh is the same distanee from a straiglit line joining the eentres ot the plane faees. A Right Pyramid is a solid, bounded by a plane fa(;e enelosed by three or more straight lines, called the bfi^e, and as many triangular plane faees as the base has sides. A Right Cone is a solid, bounded by a circular l)lane faee, (tailed the base, and a cnirved face tapering from the circumference of the base to a point. A Sphere is a solid, bounded by a curved face, every i)art of which is equally distant from a i)oint within it called the centre. EXERCISE CCLIII. 1. Find the area of a square whose side is 39 yd. 2. How many square feet are there in the surface of a table 7 ft. 8 in. long and 3 ft. 10 in. wide? 3. A rectangular grass plot 25 yd. by 20 yd. has a gravel walk 4 ft. wide round it. Find the area of the gravel walk. 4. The sides of a rectangular field are 525 ft. and 84 ft. Find the side of a square of the same area. 5. A rectangular field contains .78 A. It is 3 ch. 25 1. long. Find its width. 6. Find the area of each of the pai'allelograms, one of whose sides and the perpendicular distance between it and the opposite side are respectively as follows: — (a) Side 17 in., perpendicular 131 in. {h) Side 3 ch., perpendicular 1 ch. 80 1. (c) Side 3 yd. 1 ft., perpendicular 2 ft. 8 in. 7. The parallel sides of a trapezoid are 48 in. and 56 in. long respectively, and the perpendicular distance between them is li ft. Express the area in sq. ft. 8. The base of a parallelogram is 75 rods long, and it con- tains 7i acres. Find its width. y. The area of a square field is 40 A. Find it? side. 10. A grass plot in the form of a parallelogram is 125 ft. long and ;$G ft. wide. Find the cost of levelling and sodding it at 10 ct. per sq. yd. MENSURATION. 163 drawn by two ivy part gilt line a plane ;s, called iS as the I ciroAilar ! tapering it. rved f'lce, II a point 1. je of a table lias a gravel .vel walk. . and 84 ft. |i. 25 1. long- )ne of whose the opposite , and 56 in. between them and it con- pide. im is r2r> ft liul sodding it EXERCISE CCLIV. 1. Draw figures repi-esenting the following triangles, and find the area of eacli, the base and perpendicular upon tlio btcx from the opposite angle being rospectivoly : — {a) 24 ft. and 15 ft. G in. (h) 21 yd. 1 ft. 10 in. and li yd. 10 in. ((0 2750 1. and 380 1. (d) 20 ch. and 365 1. 2. The area of a triangle is 875 sq. in. Tlie length of 1!i(? perpendicular from an angle to the opposite side is 3;' !ii. Find the length of this side. 3. The arc^a of a triangle is 34 sq. ft. 63 sq. in.; its base is 14 It. G in. Find the perpendicular from the opposite angle upon the base. 4. A triangular field contains 1 a. 24 sq. per. The per- ]i<'ndi('ular from an angle to the side opposite it is 4 rd. long, llow long is this side? 5. A 3 C D is a ti'apezium. The diagonal, AC, is 100 ft. long. The perpendiculars, frini 1) and B ujon AC, are 30 ft. and 56 ft. respectively. Find the area of the trapezium. 6. In 5, if the diagonal is 65 yd. and tlie two perpendiculars 27i yd. and 38i yd., find the area. 7. The longest diagonal of a quadrilateral is 49 yd. and the perpendiculars let fall on it from the remaining angles are 9 ft. 6 in. and 13 ft. 10 in. Find the area. 8. Draw the trapezoid A B C D, AB and CD being the ]i;irallel sides and being 48 yd. and 56 yd. long respectively. The perpendicular distance botv/een them is 10 yd. 2 ft. Find tlie area of the trapezoid. 9. The parallel sides of a trapezoid are 19 ft, and 23 ft., and the altitude is 9| ft. Find the area. 10. The area of a trapezoid is 1155 sq. ft. One of the parallel sides is 84 ft. long and it is 16i ft. wide. Find the length of the other parallel side. EXERCISE CCLV. Note. — In the following examples tt = 3t. 1 . Find the circumference of circles wliose diameters are ] 1 in. ; 1 ft. 9 in. ; 3 ft. 6 in. ; 5 yd. 1 ft. 4 in. ; 7 yd. 2 ft. 4 in. ; 4 ch. 76 1. 2. Find the diameter of circles whose circumferences are 5 eh. 39 1.; 4 rd. ; 12 rd. 1 ft. 10 in.; 4 ft. 7 in.; 20 yd. 6 in.; i ft. 10 in. 3. A boy can walk round a circle in 1 hr. 17 min. At the same rate, how long will he take to walk along the diameter? 164 ARITHMETIC. 4. Two bicycles liiive wliools 2 ft. 11 in. and .T ft. G in. in diameter respectively. If they start from the same i>lace, and each wheel lias made 1000 revolutions, liow far will one lie ahead of the other f i). A coach wheel turns .330 times in travellinj? one mile. Find the diameter of the wheel. 6. A locomotive is moving at the rate of (50 miles per hour. The diameter of the driving wheel is 4 ft. How many times does it turn in a second? 7. The radius of a circle is 8 ft. Find the perimeter of the semicircle. 8. To enclose a circular garden, there are required 5L*8 yd. of wire fencing. How long is the radius of the garden f 9. The diagonal of a square is 4 ft. 1 in. Find the circum- ference of a circle circumscribed about the square. 10. The radius of a circle is 5 ft. 3 in. Find the length of an arc of 20^: of 30' ; of 50°; of 60°; of 100°; and of 110^ EXERCISE CCLVI. 1. Find the area of each of the following circles : — Diameter, 35 in. ; 42 in. ; 70 in. ; 84 in. ; 105 in. Circumference, 44 in. ; 06 in. ; 77 in. ; 110 in. ; 308 ft. Radius, 7 in. ; 3i ft. ; 4 ft. 8 in. ; 5 ft. 3 in. ; 21 c!'.ains. 2. How many square yards of oilcloth will be required to cover a circular floor 17 ft. 6 in. across? 3. Find the circumference of a circle whose area is 3.85 acres. 4. The radius of a circle is 84 inches. Find the radius of another circle of half the area. 5. Two circles, the radius of each being 7 in., are placed on the surface of a circle whose radius is 14 in. Find the number of square inches not covered. 6. A cow tethered can feed over 2i acx*es of ground. How long is the rope by which she is tied? 7. A circular field contains exactly one acre. Find the lengtli of the fence which encloses it. 8. Find the number of grass sods, each 15 in. by 12 in., that will cover a circular piece of ground 21 ft. in diameter. 9. A circle 18 in. in radius has one 34 in. in diameter inscribed within it. Find the area of the part of the largf circle without the smaller one. 10. Find the cost of making a path 7 ft. wide round ;i circular pond whose perimeter is 352 yd. at $1 per sq. yd. MENSURATION. 165 EXERCISE CCLVII. 1 . b'iiul the hypotl;eiiuso of oucli of tlio following right aiiglfd trituigloH whose base uud perpendicular are respectively :- («) i:i ft., 84 ft. (c) 1032 ft., 574 ft. {b) 408 ft., 500 ft. ((0 598 ft., 300 ft. perpendicular and hypothenuse are respectively:— (a) 40 yd., 530 yd. . (c) 117 ft., 125 ft. (b) 1450 ft., 1900 ft. {(l) 270 yd., 300 yd. 2. Find the bases of the following rigiit angled triangles whose 3. Find the perpendicula- of the following right angled triangles whose base and hypothenuse are respectively:— {a) 050 ft., 794 ft. (c) 50 yd., 394 yd. {b) 240 ft., 818 ft. {(I) 272 ft., 353 ft. 4. A boy is 21 mi. due south from his home; he travels 20 mi. due west. How far is he then from homef 5. A ladder is 37 ft. long and leans against a building with its foot 12 ft. from the wall. How far from the ground will its top rest against the wall? 0. A garden ■ the form of a rectangle is 210 ft. long and 170 ft. wide. How far is it from any corner to the one diagonally opposite it? 7. How far is it from the diagonally opposite corners of a cube 12 in. long? 8. How far is it from the diagonally opposite ©orners of a box 8 ft. long, 6 ft. wide and 5 ft. deep? 9. A ladder 26 ft. long stands upright against a wall. How far must the bottom of It be pulled out so as to lower the top 2 ft.? 10. Find the cost of fencing a field in the form of a right iingled triangle, its base being 105 yd. and the perpendicular 208 yd. long at 10 ct. per yd. EXERCISE CCLVIII. 1. Find the volumes of the cubes whose dimensions are as follows: ik in. ; 3i in. ; 2 ft. 5 in. ; 1 yd. 1 ft. 1 in. 2. Find the surface of each cube in the last example. 3. A rectangular log is 18 ft. long, 18 in. broad, and 14 in. thick, find — (1) its volume, (2) its surface. 4. A block of marble is 10 ft. long, 5 ft. 3 in. broad, and '-i ft. thick. Find — (1) its volume, (2) its surface. 5. The surface of a cube is 2400 sq. in. Find— (1) the Ifiigtli of its side, (2) its volume. (). How much will it cost to excavate the basement of a sclionihouse 27 ft. long, 20 ft. wide and 8i ft. deep at 25 et. l»er eu. yd. iT-T" 166 ARITHMETIC. 7. From the log, in examjde 'S, 2i eu. ft. are cut off. What h^igth of log is left? v S. A room 11 ft. high is half as long again as it is wide, and its cubical space is 47G8i eu. ft. Find its length and breadth. 9. A gallon contains 277.274 cu. in. Find the length of a cubical box that holds 10 bushels. 10. A cubic foot of water weighs 1000 oz. and a gallon 10 lbs. How many gallons are there in a rectangular cistern 6 ft. long, 5i ft. wide, and 8 ft. deep. EXERCISE CCLIX. 1 ■ Find the volume of each of the cylinders whose length and diameter are respectively: — (a) 8 ft. and 14 in. (c) 10 ft. and 7 ft. (6) 12 ft. and 3 ft. G in. {(I) 20 ft. and 2 ft. 11 in. 2. Find the area of the curved surface of each of the cylinders in example 1. '.\. A well is 15 ft. deep and its diameter is 3 ft. (5 in. How many eu. yd. of earth were taken out in digging it? 4. A circular slmft is 90 ft. deep and 3 ft. in diameter. Find the cost of sinking it at $2.80 per cu. yd. 5. Find the total surface of the cylinders in example 1. 6. How much curved heating surface is there in a steam pipe 1 in. in diameter and 350 ft. longf 7. A pillar 21 ft. high and 18 in. in diameter, supporting a building, is to be decorated at 25 et. per sq. ft. Find the cost. 8. A cylinder contains 11 cu. ft. and is 14 ft. long. Find its diameter. 9. It costs $11.88 to paint the curved surface of a pillar 18 ft. high at 63 et. per sq. yd. Find its diameter. 10. Find the number of eu. ft. of iron in a water pipe 12 ft. long and 2 ft. 6 in. in diameter, the iron being 2 in. thick. EXERCISE CCLX. 1. A square pyramid is 16 ft. high, and each side of the base is 4 ft. 6 iui long. Find its volume. 2. A triangular pyramid is 12 in. high, and the sides of the base are 29 in., 52 in. and 69 in. Find its volume. 3. The slant height of a cone is 10 ft., and the circumference of the base is 15 ft. Find the area of the curved surface. 4. A cone is 3i ft. in diameter. Its slant height is 6 ft. Find the area of the lateral surface. 5. The slant height of a conical spire is 45 ft. The circum- ference at the base is 30 ft. Find the cost of painting it at 45 ct. per sq. yd. MISCELLANEOUS EXERCISES. 167 G. Find tlio volnmo of a cone 35 in. in diameter at the base and GO in. in hcij^ht, 7. A cone is 48 ft. lii^li; its volume is 138G en. ft. Find — (I) the area of the basts (2) the eircuniference of the l)ase. 8. JTow many yards of canvas 4 yd. wide will be required for a eonieal tent L51 ft. in diameter ami 15 ft. high? 9. Wliat is the volume of the largest possible cone, cut out of a cubical block whose edge is 7 ft. 10. 'I'he radius of the base of a cone whose height is 5 ft. is 11 in. Find the slant 1; eight. EXERCISE CCLXI. 1. Find the surface of each sphere of the following dimensions: — {a) Kadius, '^i in.; (h) diameter, 3^ in.; (c) circumference, 44 in. ; {d} circumference, 88 in. 2. What will it cost to gild a globe 28 in. in radius iit 3G ct. per sq. ft.f 3. The surface of a sphere contains 24G4 sq. ft. Find its radius. 4. The surface of a sphere contains 5544 sq. ft. Find its circumference. .^». Find the volume of each sphere of the following dimensions: — (a) Radius, Gin.; (6) radius, 12 in.; (c) diameter, 14 in. ; {(I) circumference, 22 in. G. Find the volume of a sphere whose surface is 1386 sq. ft. 7. A cubical block of wood 3 ft. long is formed into the largest globe possible. How much wood is cut away? 8. A solid metal sphere G in. in diameter is melted and formed without loss into a cylinder 3 in. in radius. How long is tlie cylinder? 9. A solid metal sphere 12 in. in diameter is melted and formed without loss into shot i in. in diameter. How many siiot are there? 10. How many balls i in. in diameter can be made from a cubic block of lead 5i in. long? IMISCELLAINEOUS EXERCISES. EXERCISE CCLXII. 1. Each equal side of an isosceles triangle measures twice as much as the base. If the base is 48 ft. long, find the altitude. 2. Find the base of a triangle whose area is 5280 sq. yd. and lieiglit 120 yd. 3. The perimeter of an isosceles triangle is 153 yd. and each "f tlie equal sides is f of the 3rd. Find (1) the base, (2) the iiiea. lOfl AniTIIMRTir, 4. Twfi siilcs of ii Iriiiiifrlc iin> 'J IS It. tiiid 241 ft. loup nnd tli*> iMTiit'iidK iiliii' from tli(> iiii'lii«l<Mi tiii^lo upon tlir llrtl sitlo 'in I'JO ft. I'MikI tli<> :tni si(l«>. 5. Tlic top of a poi<> ih ln'ok(<n olT hikI striUcs tlio ^roiiiid 15 ft. from the foot «^ tlu' polo. V'wul i\w wliolo loii>;tli of tlu' polo supposing ♦' • bi'Oi\( II j>ioco to l»o ;{!► ft. (5. Kiml ,>r< .)f iiii otpiihitoral triimj^lo whoso wido is 10 ft. 7. A stici ft. 1. .i^r pliicod upi-i^ lit in Ww ground is found to Piist )i sluidow 4 ft, ' ni. lon^. V> hut is the hoi^ht of a polo tlnit casts a shadow IJH it. lonj^if 8. A foot jtath fjoos alonj; two adjaoont sid<^s of a I'ocfiinjjio. Ono sido is llMiyd. and tho otiutr 147 yd. lonR. Find tho savinj^ in distan('(« by f^oiii^ iilon^ Uw dia^oiuil instt^ad of tlio sidos. 9. Tho pt»riinotoi' of a s((U!iro is 748 in. and of anolhoi' is '.VM't in. Find tiio poriniotor of anothor o(|inil in area to tlit othor two. 10. There are two rootanf?ular fields of (^qual iirea. Tho adjacent sides of one are 1)45 yd. and IU44 yd. lonj;. Tho lonj^or side of tiie othor is 1KJ4 yd. lonj^. Find tln^ shorter sido. EXERCISE CCLXIII. 1. How long is tho edge of a cube whose surfjico is 11094 sq.ft.? 2. A triangular field contains one acre. A ])eri)endicular drawn from one corner to the side opposite measures 40 yd. Find this side.' 3. The volume of a cube is 37 cu. ft. 64 en. in. Find the cost of painting it at 33^ ct. i)er sq. ft. 4. A has two circular plots of ground 100 ft. and 20 ft. in diameter, respectively. How many times is one as large as the other? 5. What must be the circumference of a circular lake which shall contain nr part as nnich surface as a circular lake I'M miles in circiimference? 6. What is the distance through the opposite corners of a square yard? . 7. Find the perimeter of a rectangular plot of land whose length is 2i times its width, if it contains Oi acres. 8. A ladder 20 ft. long reaches to the top of a wall when the foot is 13 ft. from the wall. How much does the ladder project above the wall, when its foot is 5 ft. from the wall. 9. If a c. ft. of marble weighs 2.71(5 times as much as a en. ft. of water. Find the weight of a rectangular block of marble 9i ft. by 2^ ft. by 2 ft. (A cu. foot of water weighs 1000 oz.) 10. The sides of a triangular field are 350 yd., 440 yd. and 750 yd. in length. It rents for $31.50 per annum. Find the rent V^^' Jicre. MISCELLANEOUS EXERCISES. 169 EXERCISL CCLXIV. Kind tli(^ li'ii^tli !. Tli(f pfrinu'lcr of ii H(ttni(Mr<;lo is 'Mi ft. of tlio (litiiiiotiM*. 'J. VViiioli will carry tin* liirKOKt lunoniit of water two '.i in. tikt or ono 4 in. tile, the speed hc/mf? the same in each ease? ',]. Find the diamet<M' of a eirele ecjual in area to a rectanj^ht whose sides are K)4 ft. by Kl ft. 4. A cireular pond Hli ft. in diameter has a walk 4 ft. wide round it. Find the area of the walk. 5. A tower \i'H ft. hij;h stands in the middle of • stream 144 ft. widen How lon{» is tlie distance from the she t' the foot of the llaj,' staff upon the top of the tower. (5. Find the ar(^a of a trapezoid whose parall. . nidis are 178 ft. and 14(5 ft. and the perpendicular distance between them sri ft. 7. Find the area of a pond whose circumference is 204 ft. H. A H (! 1) is a quadrilatcu-al figure. AB 400 ft. lon^,', liC 'J0:{ ft., CI) '.im ft., DA 195 ft. The anf^ios at A and C are rif^ht aufjfles. Draw tlui figure and find its area. 9. A trapezium is dividcMi into two triangles by a diagonal 40 ft. long. The difference in length of the perpendiculars from the opposite angles on tlio diagonal is 7 ft. Find the difference in area of the triangles? 10. The differetu'o between the circumference and the diameter of a circle is 45 in. Find the area of the circle. EXERCISE CCLXV. 1. ABCI) is a trapezoid. AD and BC are the parallel sides and are '.V2 ft. and 40 ft. long, respectively. AB is 16 ft. long and (M) 18 ft. BA and CD are produced to meet in E. Find th(^ length of EB and EG respectively. 2. Find the aroa of a quadrilateral field wlioso diagonal is 40 rods and the perpendiculars on this diagonal from the opposite angles 14 rods and 2U rods, resi)ectively. .'J. Find the aroa of a trapezium whose diagonal is 108 ft. long, one perpendicular on the diagonal from the opposite angle being 42 ft. long, the other, 50 ft. long. 4. The area of a circle is 44 sq. ft. Find the difference between the areas of the circumscribed and inscribed squares. T). The side of a square field is 40 rods long. Find the li'nii,tii of the side of a square field that contains (I) 4 times as nuu-h land; (2) 9 times as much; {[i) 5 times as much. 0. The perimeter of a rectangle is 104 in. and the difference in length of the two adjacent sides is 22 in. Find the area of the rectangle, 170 AKITIIMKTIO. 7. The Idisc (»r ii friiiiigic is 07 ft. long iiiul i\w <lifT«<rriK'«> in loii^tli of llm oilier two sidcH is li ft. TIk' (listiiiico Itctwt'cn tlio middle of the Imse mid tin- perdciidiciiliir let full from the v«'i*ti- cal allele on Ihe base is ."Ji fl. Find (1) the other sides of the triangle, (2) the length of the perpeiidieiihii'. H. The lieight of a tower on a river bunk is ir)4 ft. Tie length of a line from the top of the tower to tin' opposite bank is 170 ft. Find the breadth ol' the stream. t). Find the surfaces of the cubes whosi* contents are 1)201 cii. in. ttud IDGH.'] e. in. respectively. 10. A man has a circular lawn 75 ft. in diameter. What is the length of a string that as radius would des<'ribe a circle contaiu- iug 9 times as much ground.' EXERCISE CCLXVI. 1. A circular garden contains 24(5400 s((. ft. A pole ])lnced in the centre of tlie garden is broken and the top just reaches the odge of the garden. Find the heiglit of the piece still standing, tlu^ length of the broken part being 287 feet. 2. A cylinder is 14 ft. long and 7 ft. in diameter. Find (1) the area of the curved surface and (2) the area of the entire surface. 3. What is the length of a stone wall that will enclose an acre of land in the form of a circle'/ 4. How many men can stand on an acre of laud allowing 12 sq. ft. to each? 5. What length of wire without loss of metal may be drawn from a globe 6 in. in diameter, the diameter of the wire being iTo of an in.? 6. The area of a rectangular field is 5 acres and the fence that encloses it is 120 rods lung. Find the length of the sides of the field. 7. A stick of square timber 24 ft. long contains 90 e. ft. What must have been the diameter of the tree from which it was hewn? 8. A square tank holding 4500 gal. of water is 5 ft. deep. Find its length. 9. What is the cost of lining a water-cistern .'5 ft. long, 2 ft. deep and 2 ft. in. l)road, with sheet lead of 10 l)>. per square foot at $9.00 per cwt., there l)eing no lid. 10. What is the cost of painting a t'onical spire whose slant height is 120 ft. and circumference at the base GO ft., at 8 c. per sq. yd.? EXERCISE CCLXVII. 1. Three squares contain respectively 36, 04, and 576 sq. ft. Find the length of a side of that square which Juih tin jirop: pqual to four times their sum, MI8(;KIiLANE()UH KXKRCISEH. 171 [•net! in i>en the ,. v»'i'ti- I (it the t. Tie tv bank !)201 en. lilt is the contiiin- ,le placed ,t rcachrrt »iuce Htill Find (1) the entire snelose an llowinj; 12 be drawn ^vire being the fence the sides [s 90 c. ft. which it a ft. deep. lon^^ 2 ft. I per square Lvhose shmt |ft., at 8 c. 57G eq. ft. 2. What in llie h-iiRth of a perin'tHlicuhir I<'t fall from any nnj,'le of an equilateral triangle to its opposite side when this siile is 12 yd. louj^? .'5. How many elmins are there in the side of a field in the torm of an (>(piilateral trianj^le, containing; 24 acres? 4. The len>,'th of a rectangle is 12 chains. What is its In-eadth to contain 4 acres? f). The sides of a i-ectangle are 77 yd. and ;i2 yd. What is the diameter of a circle of ecpial areaf (i. The liase and perpt^jidicular of a right angled triangle are 44 ft. and (>'.i ft. respectively. Find the diameter of u circle of equal area. 7. The l)a«e and i)erpendicular of a right angled triangle are respectively, IIOH ft. and 87") ft. long. Find the diameter of a circle equal in area to the triangle. 8. The side of a square is 15 ft. long. What is the length of the diameter of the circumscribed circle? 9. The length of a stick of timber is 24 ft. ; its breadth is 3 ft. and its thickness 2 ft. 9 in. Find the area of the entire surface. 10. Find the volume of a cylinder 21 inches i i diameter and 20 ft. in length. EXERCISE CCLXVIII. 1. Find the area of the surface of a sphere lii ft. in diameter. 2. The side of a cubical box is 20 in. long. Find the length of its diagonal. ;$. The volume of a cube is 4096 cu. in. Find the length of its diagonal. 4. A room 18 ft. high is quarter as long sigain as it is wide and its cubical contents are 20250 cu. ft. Find its length and breadth. 5. Find the weight of a metal disc 7 ft. in diameter, and li ft. thick, if a cubic foot of this metal weighs 371 lb. 6. How many planks each 13i ft. long and lOi in. wide will cover a platform 54 yd. long and 21 yd. wide? 7. A cii'cular plate- of lead 2 in. in thickness and 8 in. in diameter is converted without loss into spherical shot each of .05 in. in radius. How many shot does it make? 8. If a cube of lead the edge of which is 1 in. long weighs 9 oz., find the weight of a cube of lead whose edge is 3 in. long. 9. A solid sphere of iron 12 in. in diameter is melted and cast into a hollow cylinder 7 in. in radius, Hovv long is the cylinder, the iron being 2 in. thick. 10. A sphere 5 in, in diameter weighs 75 oz. Find the weight of a sphere 4 in. in diameter iP^^i^ ^^ paaterial 2b% heavier than the other, CHAPTER XIII. THE METRIC SYSTEM OF WEIGHTS AIND MEASURES. The Metric System of Wciglits and Measures is ])ase(l upon the deeimal m'n\v of notation. It is used in seientifie treatises, aiul lias heen adoi)ted ))y most of tlie nations of p]uroi>e and South America. Its advantages are: — (I) It is easily applied. All the opera- tions are the same as in simple numbers. ^ (2) It does away with Reduijtion, Addi- 2 tion, Subtraction, Multiplication and Divi- I sion of Compound Numbers. I (3) Its general introduction would g greatly facilitate commerce and exchange, II giving all nations a universal system of g weights and measures. I The fundamental Unit is the Metre, rt From this all the other units of the 1 system are derived, hence the namc^ IVIetrlc 7 System. 2 The principal units of the system are as I follows: — I The unit of Length is the Metre, which ^ is 39.37 inches. The unit of Capacity is the Litre, which is .2201 gallons. The unit of Weight is the Gram, which is 15.43 grains. The unit of Surface is the Are, which is J19.6 so. yd. 173 01 ^ 9 : 01 L Q - ^^ I « : Cl - T^ - CO 1 C4 THE METRIC BY8TEM. 173 \SUBES. liis 1h'<'^^ lio opt-va- ion, A(Wi- and Divi- (^^i would cxcluinKf, svsteiu of Tli(< Metri<; Syslcni is entirely (UmmiiihI. The siib- iniiltiples siiid multiples of the unit tin; denoted l>y the t'oliowinj^ prefixes : — Milli = .001 Ceiiti = .01 Deci = .1 Deka = 10. ^timew, Heeto = 100. Kilo = 1000. Myria = 10000.' a metre. a litre. 1 a gram. [liix aru. LINEAR MEASURE. 10 millimetres (mm.) = 1 centimetre 10 ceiitimetreH (cm.) = 1 decimetre 10 decimetreH (dm.) = 1 metre 10 metres (m.) = 1 dekametre 10 dekametres (Dm.) = 1 hectometre 10 hectometres (Hm.) = 1 kilometre 10 kilometres (Km.) = 1 myriametre Note. — 1 metre = 39^ in. nearly; 70 yd. = G4 metres nearly. 1 kilometre = 1 100yd. nearly ; 8 km. = 5 mi. nearly. .01 metre. .1 1. 10. 100. 1000. 10000. 48.3 mm., (1) as centimetres, (2) as decimetres. EXERCISE CCLXIX. 1. Read the following:— 37.5 m. ; 12.7 cm. 7.H05 Dm. ; 9.7 dm. 2. Express 4560 mm. (;{) as metres. 3. Express 1.87 Dm. — (1) as metres, (2) as millimetres, (3) IIS centimetres. 4. Simplify .789 m. + 78.9 cm. + 7856 mm. + 1897 km. 5. Simplify .845 Km. — 6457 cm.; 6.59 cm. — 54.87mm. 6. Simplify 768.4 cm. X 12; 3.7896 dm. X 789.5. 7. A ]>ook is 3.2 cm. thick. If the average thickness of the leaves is 05 mm., find the number of leaves in the book. 8. Tilt 'Ircumference of a wheel is 6.3 m. in length. How often will such a wheel turn in going 173.88 Km.? 1>. Find the cost of 27.84 m. of cloth at $2.75 per metre. 10. The Mont Ceuis tunnel is about 12.22 Km. long. How iimny miles is this? H. Find the cost of building a railroad 37 Km. 47 m. long at *irtOOO a kilometre. 12. How often will a bicycle wheel 225 cm. in circumference turn in going from Toronto to Hamilton a distance of 63 Km.? 174 ARITHMETIC. SQUARE OR SURFACE MEASURE. 100 sq. millimetres (sq. mm.)- 1 sq. eeiitiiii(>tie=^ .OOdl sq. metre. 100 sq. centimetres (sq. cm.) 1 sq. decimetre == .01 100 sq. decimetres (sq. dm. )--l sq. metre =- 1. " - 1 centare. 100 .sq. metres (sq. m.) 1 sq. dekiiiiietre 100. " =--1 are. 100 sq. dekametres (sq. Dm.)- 1 .sq. liectometre - 10000. "=1 hectare. 100 sq. hectometres (sq. Hm.) -=1 sq. kilometre =1000000. NoTK.— The -ML, ceutiire juid hectare are used only in land measure. The are is slightly less than 4 sq. rods. The hectare is slightly less than I2i acres. EXERCISE CCLXX. 1. Convert 287G345 sq. m. into hectares. 2. How many arts are there in 3.7850 sq. Km.? 3. Write 5.7536 sq. ni. as sq. centimetres; as sq. millimetres. 4. How many sq. metres are there in 2.34' 7 sq. Km.? 5. How many sq. centimetres are there in .0542 sq. m.? 6. Write as one quantity in sq. metres 3 sq. Km. + 3 sq. Hm. -■}- 3 sq. Dm. -f 3 sq, m. 7. How many ares are there in a rectangle 200 metres long and 50 metres wide? 8. How many sq. metres are tliere in a rectangular floor 0.8 m. long and 4.8 m. wide? 9. What will be the cost of 5 sq. m. of sheet tin at 5 mills a sq. decimetre? 10, How many bricks, each 20 em. long and 10 em. wide, will be required to pave a sidewalk 3.3 m. wide and 1.7 Km. long? MEASURES OF CAPACITY. 1000 cu. millimetres (c. mm.)=--l ci. centimetre = .000001 cu. metre. 1000 cii. centimetres (c. cm. )=-l cu. decimetre = .001 " =1 litre. 1000 cu. decimetres (c. dm.)=l cu. metre =1. " =1 stere. Note. — In measuring wood a cul)ic metre, called a stere (st.), is used; 3-0 steres = 1 "ord nearly. In measuring liquids the cubic decimetre, called a litre. In used. In measuring grains, fruits, etc., the hectolitre is r.sed. The numeral preiixes are used with the litre af with tln' metre. EXERCISE C'JLXXI. 1. How many steres of wood are there in a p'ie 29 m. long, 1.25 m. wide, and 2 m. high? 2. What will 17.3 HI. of Wiieat cost at $0 25 a dekalitre? '^HE METRIC SVSTEM. only in land 10 cm. wide, and 1.7 Km. ed a litre, is 175 .01 .1 , '^- 'f^W J.lfUlv )it,.,.w .,„ ., ^' '"ll.-"' i- .i m!'*l„" j"'i "•■; ''l«t will „„ ti,, ,.„,. „f ,. . JO deei^^rams 1]?/) Z J ^^««iS''fim = JO grams ^A^/ ^ .J ff^'fim :^ j .NOTR.--A cubic cenfilT ^'^'^^'^'am == ,000. 1 - am - L,| ^,,.,^j,^g AJ<.,„,.„,„ = ,, ,, ^,„,',>;',;« «™-= 1 o... Avoi... ,.e„W.. K'UO kilograms ^ 22 evvt - w A "tre of water weig],, l" 7uL ""'' ^' "^^*"« to". A eiibie metrfl nC . ^^^'ogram. metie of water weighs looo 1-n J- Write 5 Kg .^ j^''^''''*^^ CCLXXII. 4. Express oT-7" ' "'^ ^^"t'>''am?s.^'' ^ «^nt,grams and 5 . ''■ ^^'^lat is thetl ^'""''' «« f'entigrams ,^;ram.? ''*''*^^««o«tof .67225Kg of o. • ^- ''^ "l"'"" at G2,l et. per ffJ'fun. ^!v*C^ 17G ARITHMETIC. 1). (Jivo llic w»'if,'lit ill milli<j:riuiis of a pill wlion n, mass wcij^liiiij^ 21.7 K- '^ iiiiiclc into 70 pills. 10. Wliiit decinuil is ;") K- '^ <'K- <**^ <>"<' l<iloj?riim? EXERCISE CCLXXIII. Write* tlio following: — 1. {a) Write 7 dekametres, 2 decimetres and f) centimetres as nieti-es. {h) Write H hectolitres, 8 litres and 7 decilitres as litres. ((') Write If) ares, 9 declares and 8 milliares as ares. (d) Write 27 kilograms, ',i decigrams and 7 centigrams as grams. 2. Mercury weighs 115. f) times as much as water. Find the weight of 44 litres of mercury. ;j. Marble weighs 2.7 times as much as water. Find the WH'ight of a rectangular block of marble 2.5 m. long, 1.75 m. wide, and 4 m. thick. 4. If silver weighs 10.5 times as much as water, how many coins, each weighing 5 grams, can be coined from a cubic decimetre of silver? 5. If alcohol is 80% as heavy as water, find the weight of 485 com. of alcohol. 0. How many steres of wood are there in a pile 50 m. long, 1.1 m. wide, and 2 m. high? 7. What is the ])rofit on 75 hectolitres of potatoes, l)ought at 7 francs a hectolitre, and retailed at 1 franc a dekalitre? 8. How many hectolitres of apples, at $1.25 a hectolitre, should be given for 5 dekasteres 5 steres of wood at 75 ct. per stere ? 9. A druggist having .75 Kg. of quinine 'makes up 500 pills containing 2 decigrams of quinine each. How many grams ho,s he left? 10. A farmer, having 4 hectometres of wire fence, uses a portion of it to enclose a field 50 metres square. How many metres has he left? 11. What will be 'the profit on 10 g. of calomel, bought for 50 ct., if sold in powders of 5 dg. at 5 et. each. 12. A train runs 47.5 Km. per hour. How many miles does it go in 6 hr. 24 rnin. i;5. How often can a cup, holding 3 ci., be filled from a- vessel containing 14.:?1 1. of water? 14. How many rolls of wall pjiper, 10 m. long and .5 m wide, are needed to paper the walls of a room, 6.3 m. long, 4.2 m. wide and 3.2 m. high? lien a mass centimetres r. Find the CHAPTER XIV. ^'SCELLANE^ EXERCISES »• CfRCULATrNO DECIMALS Recurring Decimals. '"^'"'*^' Circulatinq o, A Terminating Decimal - '-t I.mited number ornH^^^^^^^ ^^^'^'^^ ^'^^'^'"cls i>*'"'^ as .375, .()()24 ^^''''"^^ ^^•^>"' the DeoimaJ A Circulating Decimal , ''«'"''^n or set of tinn^, /• "' ^" ^^'^^^^'^^ ^h. su,m. same order as ^n'7'7 ' ''''^^^'^^I'dUy reeurs in ,.,.TheRepete„d.«.,,„,eor.,;,«^„.,.,_,„,.,^,_ .^Circulating DeclmaU . ' ■-•^*'** M.xed arc„?atl^g'7?eclmals""""'' " "' ^-^^ ,..,„ '^""'l'"'e tho foil • ^•'^^'*^'SE CCLXXIV. 1. J 3" 4 Si fl H r, Ti r. *. ^\^!'f^ 178 AKITIIMETIC. 5 7 ^r ^ t\ iV n S 1 22 S6 2 8 AV 14T ■1V4 ^VST 4 r, i» 6 111 DOT 14U 8 .Vt o 4 '>. 1 4. i\ 5. I 6. 11 7. H 8. If y. 84 10. 2 88 EXERCISE CCLXXV. Reducn the followiuK to vulgar t'nietions hi their lowest terms:— 1. ' 1 1 J. 1 T 1 • 1 .{ 1 4. 1 1 "44f • 29 Tift. 8 21 . 8 9 1 "17 7 (r . 2 7 7 "I37ff. .5 .17 .;i6 2. .018 .627 .OOU 3. .054 .'h'-i .1376 4. .945 .423 .78;i 5. .9801 .923076 .142857 6. .954 .527 .3si 7. .7852 .103G .01(59 8. .G59(') .00()75 .24376 9. .7954 AWAh 2.297 10. 4.00(i 5.o6() 7.00(5 EXERCISE CCLXXVI. Simplify the following: — 1. .23 + .234 + .2345 + 5.7 + .12345. 2. .1(5 + .792 + .21431 + S)iS + .5(5. 3. 25.12;i — 15.(53; l9.io7 — 5.043. 4. .574 — .2rx; .574 — .25. 5. .754 + .213 — .(5S47 + .45()i — .00(5. G. .(53 X 2.5; 2.15 X 3.204. 7. .1(5 X .72; .75 X .75 X .75. S. .339 - .72; .SI — 2.3. i). 2.7;!<5 — 4.3; 51. SI — 5.18. 1<>. 4.37 X .27 —2.18; .154 — 2 X 11.25. .210. .144. .296. .261. .285714. .24390, .01315. .3857142. 7.675. Ta O 7. «« jrVVv^ <": CIRCULATINO DEC^IMALS. 179 At terms: — )714. m. 6. )7142. 75. |7. EXERCISE CCLXXVII. 1. The product of .9, .19 and a third factor is 2.1. Find the third factor. 2. What must be multiplied by .809523 to produce .liif 3. Without dividiufif, .vrite the decimals equivalent to rooryt 7 1 7L 7.1 7 1 _Xl_ 7_1_- UUU) OUO) UOd> WIMIOJ UOOO) llttUU* 4. What two numbers are those the sum of which is .l!)-i and the greater exceeds the less by .128? "). Without dividing, state what kind of decimal each of the following are e<iuivalent to: — I, ^, n, ^, -i\, v, A, T. G. Simplify .(5518 -^ .140 X .225 + 5 — .15. 7. Simplify .7 of £3 + .2i of 5s. + .:!(') of lid. 8. Simplify .38 of 9 t. + .144 of 37 lb. — .45 of 3cwt. 74 lb. 9. Simplify .375 of 16 mi. + .40 of 198 rd. + .35 of 4^ yd. 10. How many tons, cwt., etc., are there fn .375 of 185 t. ? EXERCISE CCLXXVIII. 1. Describe the vulgar fractions whose equivalent decimals are finite. 2. Why do I, 1, ro, "/o> ¥u, iso and fi i)roduce finite decimals? 3. How many figures will there he in the decimals equivalent to ixij s, :T2? and airo. 4. Why do §, ^, n and ;\^ produce infinite decimals? C-,. How many figures will thcic lie in the non-re|)eating part of the decimals, equivalent to §, j|, jij, H> and ^ff? (). Whether is 7.45()48 more accurately represented by 7.450 or by 7.457? 7. Show that .005 X .005 X .04 X .04 = .0002 X .0002. 8. Show how a numl»er may be multiplied or divided by 10, 100, 1000, etc., by merely shifting the decimal point. 9. Su]»pose unity represents .0015, what decimal will represent .0002? EXERCISE CCLXXIX. 1. A father, dying, left .518 of his property to the elder of his two sons, and .518 of the rest to his younger, and the n'Uiiiinder to his wife. The older son received $1900 more than the y(,nnger. What did the elder son receive? '.'. A reservoir is 03, ;j ft. long and 48.5 ft. wide. How many •'ultf ft it of water must be ]iumped out of it to make the uider sink 3 it.? 180 ARITHMETIC. ;j. Divide $G54.50 amonp A, B and C in proportion to the numbers 1.3, 2.5, and 2.7. 4. A man, after spending .4 of his money, found that .6 of the remainder was $40. How much had he at first? 5. Multiply the sum of 1.5, .6 and .75 by the difference between .26 and .15, and divide the product by 43.5. 6. A man on a journey goes .6 of it by train, .18 of it by street ear and walks the remaining distance in 1.6 hours at the rate of 3 miles an hour. How far is the distance? 7. The area of a square field is 72.9 acres. How long will A require to walk around it at the rate of 3.3 miles per hour? 8. A grocer buys tea at 30c. ; twice as much at 33.3c. ; and three times as ranch at 36. 6e. per lb. He mixes the three kinds tojijuther and sells the mixture at 40c. per lb. Find his gain p( r cent.? 9. Subtract .08 from .08 and divide the remainder by .625. II. PROBLEMS RELATIING TO WORK DONE. EXERCISE CCLXXX. 1 . If A and B cnn do a woik in f of a day, and B alone can do it in 2i days, how much more does A do than B in 1 day? 2. A can do a work in i day; B can do it in i day and C in i day. How long will it take if all begin working together to do the entire work? 3. A can do a work in 4i days; B can do it in 3^ days. Wi^h the help of C the work can be done in li days. In what time can C do the work? 4. A's working power is t of B's working power. How long would A take to do what B dtfes in 12i days? 5. B liikes I of the time that A takes to do a work. What fraction of B's working power is A's working power? 6. A and B take 18 days to do a work, A doing twice as much as B. In what time could each do the work by himself? 7. .V, B, and C can do 5 of a work in 3i days, A doing half as mucli as B and twice as much as C. In what time could each do the woi'c by himself? 8. If 10 men can do a work in 15 days, how soon after cora- meticing v.mst 4 additional men be employed so that the work, may bo done in 12 days? CLOCK PROBLEMS. 181 9. A can do a work in 27 days, and B in 15 days. A works at it alone for 12 days; B then works alone for 5 days; then C finishes the work alone in 4 days. In what time could € do the whole work by himself? 10. If 5 men or IG boys cau do a piece of work in 15 hours, in what time could 3 men and 48 boys do the work ? 11. If the times taken by A, B, and C to do a work are as 1, 2, and 3; and tof^ether they cau do the work in 20 days, in what time could each do it by himself? 12. A does ^ of a piece of work in 12 days. He then calls in B, and they finish the work in li days. How long would B take to do the whole work l>y himself? 13. A and B can together do a work in 14 hr. 56 min. A alone can do it in 28 hr. In what time could B alone do it? 14. A can do a work in 3| hr., B in 2i hr., and C in 3i hr. In what time will it be finished by the three, if B begin i hour after A, and C 22i miu. after B? 15. If 2 liorses do the same work as 3 mules, how many horses along with 7 mules will be required to draw 9i tons the same distance in the same time that G horses and 5 mules cau draw 7 tons? 16. A can do a work in 12 days ; B can do it in 15 days and C in 10 d.iys. They all begin to work together but A stops 2 days and B 1 j days before C who finishes the work. How long does each one work? 17. A can do a piece of work in 7i hr. ; B can do it in 8i hr. If tliey do it together and the work is worth $2.10, what sum ouulit each to receive? III. CLOCK PROBLEMS. EXERCISE CCLXXXI. 1. The hands of clock are together. In what ti' *o will they be 11 minute -spaces apart? 22 minute-spaces apart? 27i minute - spaces apart ? 2. The minute-hand is 16i miiuite-spaces behind the hour- hand. When will they be together? 3. At what time between 3 and 4 o'clock are the hands of a watch together? 4. Find the first time after 6 o'clock tliut the hands of a clock are at riglit angles. 5. The hands of a clock are opposite each other at 6 o'clock. At what time will they l)e togetluM* for the first time? 6. Find the first time after 5 o'clock that the luinds of a clock vviU be 3 minute -spaces apart. 182 ARITHMETIC. 7. Fiiul the times between 6 and 7 o'clock wlien the linnds of u watch are 8 minute-spaces apart. 8. Find the time after 8 o'clock when the hands of a clock are («) together; [h) at right angles; (c) opposite each other. 9. Find the times Lotween 9 and 12 o'clock when the hands of a watch are together. 10. Find the first time after 5 o'clock that the hands of a watch are equally distant from the figure five. EXERCISE CCLXXXII. 1. Find the first time after 4 o'clock that the hands of a watch are 48° opiri. 2. Tlie hands of a watch are 18° ajjart for the second time after 3 o'clock. Find the time. 3. Find the first time after 6 o'clock that the minute-hand is midway between the hour-hand and the figure six. 4. Two clocks are together at 12 o'clock. One loses 8 sec. and the other gains 7 sec. in 24 hours. \Vh('U will one be half an hour ahead of the other and what time will each show? 5. Two clocks are together and show correct time at noon. One loses 5 see. and the other 7 sec. in 12 lir. When will one be 5 minutes faster than the other? 6. A clock loses 5 sec. in 24 min. At 9 p.m. on ^Monday it is 17 min. fast. When will it show cori-ect time? 7. A watch set accurately at 12 o'clock indicates 5 min. to 5 at 5 o'clock. What is the exact time when the watch indicates 5 o'clock. 8. One clock gains 2 min. in 12 hr., and another loses 2 min. in 24 hr. Tliey are set right at noon on Friday. What is the time indicated by each clock when one appears to have gained 8.i minutes on the other? 9. A clock which was 1.4 min. fast at quarter to 11 p.m. on May 2, was 8 min. too slow at 9 a.m. on May 7. When was it exactly right? 10. A watch showing correct time at noon on Tuesday gains 3 min. 40 sec. in 24 hr. What is the correct time on Saturday evening when it is 10 o'clock by the watch. IV. PROBLEIVIS IINVOLVIfNO VELOCITY. EXERCISE CCLXXXIII. 1 . How many feet per second is equal to a rate of 30 miles l)er hour? 2. ITow many miles per hour is equal to a rate of 50 ft. per second? THE SUM AND DIFFKRENCE OK TWO NUMBERS. 183 3. A train 22 rods lonp' i)aHS08 a post in 11 socondH. At wliat ratt< per hour is it moviiif?? 4. How loiif^ will a train GO yd. in length, moving .'JO miles per hour take to pass another 50 yd. long standing on a sidingf 5. A railway train moving at the rate of 49 miles {»er hour goes 7 miles while a coach goes 2 miles. How long will it require the coach to go ;{.36 miles? 6. A is walking 4 miles an hour, and B, who is 4 miles ahojid of him, is walking 3i miles an hour in the same direction as A. How long will it be before A overtakes B? 7. A starts from Sarnia to walk to London, u distance of GO miles. At the same time B starts from Londoti to walk to Sarnia. If A goes 4J miles per hour and B ',ii miles per hour, how far from Sarnia will they meet? 8. In a mile race A can beat B >)y 80 yd. and C by 87 yd. By how much can B beat C in a mile race? 9. In a mile race A can beat B ])y 22 yd. and B can beat C by 11 yd. How many yards start can A give C that there may be a dead heat? 10. If the hands of a clook coincide every G5 minutes, how unich does the clock gain or luse in a day? V. PROBLEMS IINVOLVIINO THE SUM AND DIFFERENCE OF TWO NUMBERS. EXERCISE CCLXXXIV. 1. The sura of two numbers is .'565; their difference is 83. Find the numbers. 2. A man rows at the rate of 7 miles per hour down a stream which flows at the rate of li miles per hour. Find his rate of rowing against the current. 3. A man can row 8 miles down stream in 2 hours, but he takes 3 liours to row back to the starting point. Find the rate of the stream. 4. If a man rows 10 miles in 21 hours against a stream, the rate of \ylnch is U miles per hour, how long will he be in rowing 3 J miles down the stream? 3. A man rows 15 miles down stream in 21 hours and up in 4 hours. Find his rate of rowing in still water. G. A can row a distance down stream in 15 minutes and the same distance up i,i 20 minutes. Wliat is the distance, the rate ot the stream being 1 mile per hour? "• A man rows on the still water of a canal one mile in 15 |iiin. Tie then reaches the river and rows down stream U miles "I the next 15 min. How long will he take to return to the starting-point? !!' 184 ARITHMETIC. H. IIow far can a man who rows 4 miles per hour in still water row up strenm, which Hows nt the rate of 2 miles per hour, so that he may be 2 hours before he returns to the Vioat- house? 9. A crew can row down a stream a eertain distanee in 2 hours and back the same distanee in .1 hours. Comi)are the rate of rowing in still water with the rate of the stream. 10. If A can row (ii^ miles in 2h hours against a strenm flow- ing H miles an hour, how long will it take him to row 12 miles with the current? EXERCISE CCLXXXV. 1. A skated G miles at the rate of 10 miles an hour with the wind and returned against it in 50 minutes. Find tli»' rjito of the wind i)er hour. 2. Two trains moving on parallel traeks in opposite direc-' tions, and respectively 110 yd. and 8s yd. long, pass each other in ;') sec, and, when moving in the same direction, the faster l)asses the other in 45 see. Find their rates in miles per hour. ',]. A train 110 yd. long, moving i mile a minute, meets another on a parallel tiack, moving 40 ft. per see. and passes it in 8 sec. Find the lengtii of the second train. 4. If telegraph poles are 88 yd. apart, and one is observed to pass the window of n r.-iilway car every 4 sec, at what rate pc hour is the train moving? 5. An express train going 57 miles an hour passes a station 5i min. after a freight, going 38 miles an hour. When will the express overtake the freight? 6. A train going 30 miles an hour passes a man walking in the same direction at 3 miles per hour in 10 sec. Find the length of the train. 7. The whole time taken by a train 150 yd. long in crossing a bridge at the rate of 25 mi. per hour was 20 sec Find the length of the bridge. 8. If a train 88 vd. long overtakes a person walking at the rate of 4 miles per hour and passes him in 10 sec, what is the rate of the train in miles per hour? 9. If a train 110 yd. long meets a person walking on the railway at the rate of 5 miles per hour, and passes him in 8 sec, what is the rate of the train in miles per hour? 10. A train 352 ft. long overtakes a man going in the same direction at 4 mi. per hour and ])asses him in 15 sec Shortly after it passes a man walking in the opposite direction in 9 sec. At what rate per hour is the second man walking? 11. A train 88 yd. long takes 10 sec to cross a bridge 44 yd. long. At this rate, how many hours will it take the train to go 180 miles? REVIEW EXERCISES FOR THIRD CLASS. 185 '< ; VI. REVIEW EXERCISES FOR THIRD CLASS. EXtRCISE CCLXXXVI. 1. Two pieces of elotli of the wjuno length cost $r);{.G4 iiml !}!(J9.lL!, respectively. Tlu* price of the hist was !)!i.4y u yiucl. What wjis the price of second per yard? 2. Three l)iif,'s couttiiued 025 nuts. The first bag contained 25 more than the other two together; and the second contained 5U more than the third bag. How many nuts are there in each bag? 3. A man living on $700 a year for 6 years finds that he is exceeding his income and then lives on $500 a year for 4 years and finds he is just out of debt. What was his income? 4. How often can £3 17s. lOid. be subtracted from £288 4s. lid., and what is the last remainder? 5. A boy had the same num])er of five, ten, and twenty-five- cent pieces, and had $6.80 in all. How many pieces of each kind had the boy? <). Find the largest number that will divide '{65, 540, and 1140, leaving as remainders 20, 17, and 13, respectively. 7. A, B and C have JC53 Os. 8d. among them. B and C have £40 2s. 8d. ; A and C have £29 10s. How much has C? 8. How many l)oards 15 ft. long will build a straight fence, (i boards high, around a field 120 rods long and 30 rods wide? 9. A man ploughs a furrow 8 in. wide the whole length of a field in 6 minutes. How many hours will be required to plough a ridge 16 ft. wide? 10. A farmer's wife sold 8 pairs of ducks at 75 ct. a pair and 13 pairs of chickens at 50 ct. a pair and received payment in •sugar at 16 lb. for 1 dollar. How many pounds did she receive? EXERCISE CCLXXXVII. 1. Into a veetangular cistern, the bottom of which is 8'ft. by 6 ft., water is pouring at the I'ate of 500 gal. per hour. How long will it take to fill the cisl rn to a depth of 4 ft.? 2. Divide $25.75 among 10 men, 8 women, and 7 boys, giving each man 50 ct. and each woman 25 ct. more than each boy. 3. A agrees to trade apples at $2.50 per bbl. for cloth at $1.75 per yard. What is the least numbers of barrels that can be exchanged for an integral number of yards? 4. The quotient is 7469; the divisor is 728, and the remainder is 19. If the dividend remains unchanged what divisor would give as quotient 5320 and remainder 411? 5. A and B ran a race. B had a start of 20 yd., but A ran 3 yd. while B ran 2 yd. and won by 5 yd. the race? Find the length of <^. ^^'^'5* o /*>.^. IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I 1^121 12.5 ^ Ufi 11 2.0 1.8 L25 1 M, 1.6 ^ 6" - ► v^ 7: Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 873-4503 ^ .<. Ili 186 ARITHMETIC. U. If 30 men do a piece of work in 24 diiys working 10 hours a day, in bow many days would 25 men do the sunie piece of work, working 9 hours a day? 7. The hind wheel of a wagon is 12 ft. in circumfereneo and turns 7480 times in going from one village to another. How many miles are the two villages apart if 8. A man bought 120 A. of land for $7800. He sold 30 A., gaining $10 per A. and 45 A. at a loss of $15 per A. At what price per A. must he sell the rest to gain $300 in the whole transaction if 9. A farmer sold 250 animals (sheep and pigs) for $1720. He received $8 for each sheep and $6 for each pig. How many were there of each If 10. The cost of 5 coats and 4 vests is $33.25, each coat costing $1.25 more than a vest. Find the cost of a dozen coats. EXERCISE CCLXXXVIII. 1. A bankrupt paid $2.50 out of $4 on one-half his debts and $2 out of $4 on the other half. Altogether he paid away $7200. How much did he owe? 2. A man buys 128 gal. of wine at $1.70 per gal. How much water must be added to gain $33.40 on the outlay by selling the mixture at $1 per gallon? 3. A farmer sells 9 horses and 7 cows for $1200 and 6 horses and 13 cows for the same sum. Find the price of 3 horses and 8 cows at the same price. 4. A person bought 475 apples at 5 for 6 ct. and another lot at 8 for 5 ct. He paid altogether $10.20. How many of the latter kind did he buy? 5. A divided a field 40 rods lon^j .md 24 rods wide into lots, each 165 ft. long and 66 ft. wide and sold all for $1800. Whnt price did A get for each lot? 6. A grocer bought 60 chests of tea weighing 40 lb. each for £280 and sold it at 3s. 6d. per lb. How much did he gain? 7. What is the value of a pile of cord wood 60 ft. long, 8 ft. wide and 8 ft. hi^h at $3.25 per cord? 8. Find the greatest unit of time by means of which 23 hr. 2 min. 36 sec. and 46 hr. 8 min. 55 sec. can both be expressed as integers. 9. Divide $1078 among John, Thomas, and Henry, so that John has 5 times as much as Thomas, and Thomas 8 times as much as Henry. 10. A farmer planted 60 rows of corn. Each row had 240 hills and 5. hills produced one quart. The crop was sold for $50.40. What was the price per bushel? REVIEW EXERCISES FOR FOURTH CLASS. 187 EXERCISE CCLXXXIX. 1. Find the cost of o.irpetinf? a room 18 ft. loiij? iiml 13 ft. G in. wide with carpet 2 ft. 3 in. wide at 75 et. a yard. 2. How much rope will it take to tie a box in the ordinary way, tlie box beinj? 4 ft. by 3 ft. 2 in. by 2 ft. 8 in., allowing? 1 ft. G in. for the knot if 3. The average height of four boys is 4 ft. 7 in.; but if the height of two others be considered, the average height of the six will be 4 ft. 5 in. Find the average height of the other two. 4. If 5 lemons are worth 4 oranges, and 2 oranges are worth 3 apples, find the price of 15 lemons when apples are worth 10 ct. per doz. 5. Find the smallest number of rails of equal length that can be used without cutting to make a straight fence 6 rails high around a rectangular lot 1089 ft. long and 1375 ft. wide. G. The product of four consecutive numbers is 212520. Find the uumbers. 7. On counting out the marbles in a bag by 3 at a time, or by 4 at a time, or by 5 at a time there are always 2 over; but on counting them 7 at a time there are none remaining. Find the least number of marbles there could be in the bag. 8. At 25 et. per sq. yd. find the cost of painting a close board fence G ft. high round a rectangular lot 40 yd. long and 20 yd. wide. 9. How many shingles 4 in. wide and 4 in. exposed to the weather would be required for a roof 35 ft. by 25 ft. ? 10. A bale of hay is 3 ft. long, 2 ft. wide, and 18 in. thick. A car 33 ft. long, 8 ft. wide, andG ft. high requires 2G400 lb. to fill it. Find the weight of one bale? VII. REVIEW EXERCISES FOR FOURTH CLASS. EXERCISE CCXC. 1. A farmer bought two farms of 130 A. each for $19500. What was the cost of an acre of each, if 2 A. in one are worth 3 A. in the other? 2. In going to town the front wheel of a carriage makes 2G4 turns moi^ than the hind one. If the former is 10 ft. and the latter 12 ft. in circumference, how far does the carriage go? 3. A laborer is to receive 95 ct. and his board each day he works, and pay 45 et. for each day he is idle, to pay for his board. At the end of 100 working days he receives $7G.80. How many days did he work? 188 ARITHMETIC. 4. Wliieli is tlie pjreater cost and by how much: — feiieiiig a lot 40 Y(l. long and 30 yd. wide at 1.') ct. a foot or liuildint? a wall< round it 4i ft. wide at 29 et. i)er sq. yd.? 5. A water tanlt without a lid, IG ft. 6 in. long, 7 ft. 6 in. wide, and 7 ft. deep, is lined with zinc weigliing 8 lb. to tlie square yard. Find the cost of the zinc at $4.90 per cwt. 6. Four-fifths of a merchant's goods were destroyed by fire; I of the rest were injured. He sold the injured goods at 1 cost for $840 and the uninjured for $300. There being no insurance, find his loss by the fire. 7. A sum of money in 5 yr. at a certain rate per cent, simple imprest amounts to $1131 and to $1339.80 in 9 yr. Find the sum and the rate per cent. 8. A goldsmith manufactured 2 lb. 3 dwt. 8 gr. of gold into rings, each containing 9 dwt. 16 gr. He sold them for $8.75 each. How much did he gain, gold being worth $18 per oz. ? 9. If 150 men can do a work in 40 days, how soon after ccmmeneing the work must 60 additional men be employed so that the work may be done in 34 days? EXERCISE CCXCI. 1. A legacy of $4500 is left to three persons in the propor- tion of 2, 3, and 4. What should each receive after deducting the legacy duty of 10 % ? 2. A man paid $2580 for 85 head (horses and cattle) , there being t^i Jis many horses as cattle, and the cattle cost $8 less per head than the horses. Find the cost of a horse. 3. A farmer sold a load of barley, weighing 3024 lb., when barley was 46 ct. a bushel. In weighing the ,?rain, the dealer made a mistake and took it as rye, and paid 55 ct. a bushel. How much did the farmer gain or lose by the mistake? 4. A county map is drawn on a scale of 2 in. to the mile and covers a surface 4 ft. by 2i ft. How many acres are there in the county? 5. A rectangular field whose length is to its width as 4 to 3 contains 10 A. 268 sq. rd. Find its dimensions. 6. A bookseller sold a book 16% below cost. Had he received 50 ct. more for it, his gain would have been 4%. Find the cost of the book. 7. A stone wall, under a building 24 ft. longer than wide, contains 8550 eu. ft. This wall is 10 ft. high and 2i ft. thick. Find the dimensions of the building. 8. A father gave his son $128.50. This was 66|%'of what ^he father had left. How much money had the father at first? 9. The amount of a note for 1 yr. 9 mo. at 6% simple interest was $391.17. What was the principal? ( I REVIEW EXERCISES FOR FOURTH CLASS. 189 10. A farmer agreed to pny his hired man 8 sheep and $180 for one year's work. The man quit work at the end of 7 mo., receiving the sheep and $80 as a fair settlement. Find the value of each sheep. EXERCISE CCXCII. 1. A and B earn $4.02 in 7 days; A and C, $7 in 10 days; and B and C, $8.36 in 11 days. How much did each earn per day? 2. A hare is 80 leaps before a hound, and takes 4 leaps while the hound takes 2, but 2 of the hound's leaps equal 5 of the hare's. How many leaps will the hound take to catch the hare? 3. A sells goods to B at a gain of 12%, and B sells the same goods to C at a gain of 15%. C paid $3155.60 for the goods. What did the goods cost A? 4. Find the time a train 184 yd. long, running 21 mi. per hour, will take to pass another on a parallel track 135 yd. long, going in the same direction at the rate of 16 mi. per hour. 5. A hor-^e and lot are together worth $4750. Twice the value of the house is equal to 17 times the value of the lot. Find the value of the lot. 6. If a grain dealer by selling 416 bu. of oats for $277i loses 10%, at what rate per bu. should he have sold the oats to gain 8%? 7. A man mowing gi-ass travelled 4 mi. per hour. In 72 min. he cut 2i-,- A. What width did the machine cut? 8. I bought .2000 lb. of sugar, part at 7 et. and part at 10 ct. per lb. Had I bought all at 8 et. per lb., it would have cost $13 less than it did. How many pounds of each kind did I buy? 9. The area of a rectangular field whose breadth is i of its length is 15376 sq. yd. Find its dimensions. 10. A hall 60 ft. long is to be carpeted. It is found that by stretching the carpet lengthwise any one of 4 pieces — f yd., 1 yd., li yd. and li yd. wide respectively — will exactly fit the hall without cutting anything from th« width of the carpet. Find the cost of carpeting the hall with the narrowest piece at $1.10 per yard. EXERCISE CCXCIII. 1. A train going 30 mi. an hour passes a man going in the same direction at 3 mi. an hour in 10 sec. How long is the train? 2. A and B enter into partnership. A puts in $4900 rnd B $1400. B receives 6% of all the profits for management. The rest is divided in proportion to the capital invested. What is A's share of $450 profit? I 190 ARITHMETIC. 3. In a long division example the dividend is 1768479, and the successive remainders from the first to the last are 127, 180, 166, 28. Find the divisor and the quotient. 4. What is the prime cost of a yard of clotli, if selling it at 1% gain brings $1 more than selling it at 11% loss? 5. Twenty-five animals (cows and calves) cost $427.75, but, if the number of cows and calves is reversed, they would cost $303.50. A calf being worth $5.75, find the cost of a cow. 6. A and B rr . a two mile race; A wins. If B had run one- third faster, he would have won by 22 yd. Compare their rates of running. 7. A can dig 36 post-holes in a day; B, 32; and C, 30. What is the smallest number of post-holes that will furnish an exact number of days' labor for each working alone, for any two, or for all three working together? 8. A, B and C together invest $4860 in wheat. A invests twice as much as B, and C invests twice as much as A and B together. They gain 40% on their investment. What is each person's share of the gain? 9. If my income of $1150 is reduced by taxation to $1063.76, what is the income of another who has $1554 left after paying his taxes? 10. A sold two city lots at the same price. On one he gained 20% and on the other he lost 20%. He lost $30 by the transac- tion. Find the cost of each lot. VIII. REVIEW EXERCISES FOR FIFTH CLASS. EXERCISE CCXCIV. 1. What is the least number by which 2016 must be multi- plied to become a perfect cube? What will be the cube root of this cube? 2. Divide $1650 into two parts such that the simple interest on one of them, at 4i% for 3 yr., would be equal to that on tae other for 2i yr. at 5 % . 3. A man bought a horse and sold him at 10% loss. If he had received $45 more for it, he would have gained 12i%. What did the horse cost? . -,. ... (.201- .102)'^ 4. Simplify ^201)^'- (102)^" 5. A marked goods at an advance of 40%, but in selling them a false b.alauce was used, by means of which he gave 14 oz. to the pound. His total gain being $240, find the cost of the goods. REVIEW EXERCISES FOR FIFTH CLASS. 191 6. The amount of a sum for a certain time at 8% is $336, and at 7i % for the same time it is $330. Find the sum and the time. 7. A solid sphere of iron 12 in. in diameter is melted and oast into a hollow cylinder 6i in. in radius and 8 in. long. Find the thickness of the iron in the cylinder. 8. A hare takes 4 leaps to 3 of a greyhound; but 2 of the hound's are equivalent to 3 of the hare's. The hare has a start of .'iO of its own leaps. How many leaps must the hound take to catch the hare? 9. A clock loses at the rate of 8i see. per hour when the fire is alight and gains at the rate of 5r5 sec. per hour when the fire is not burning. Upon the whole it neither gains nor loses each day. How long in the 24 hours is the fire burning? 10. A walks a distance at a certain rat'*. If he had walked 1 mi. per hour faster, his time would have been f of what it was. If he had walked 1 mi. per hour slower, he would have taken 4 hours longer than he did. Find the distance. EXERCISE CCXCV. 1. A man buys wine at $3.20 per gallon; 20% leaks away. At what price per gallon must he sell the remainder to make 20% on the outlay? 2. A's income is derived from the proceeds of $227.5 at a certain rate per cent, and $2700 at 1% more than the former rate. His total income being $425, find the rates. 3. A grocer has two kinds of tea. By selling the first kind at 45 ct. a pound, he gains 25%, and by selling the second at 42 et. per pound he gains 40%. If he mixes them in equal quantities and sells the mixture at 43i ct. per pound, find his gain per cent. 4. A shipment of wheat was insured at 2#% to cover three- fourths of its value. The premium was $44.07. The wheat being worth 80 ct. per bushel, find the number of bushels there were in the shipment. 5. In a constituency having 3200 voters, A received 23 votes for every 25 votes received by B, and was defeated by 124 votes. How many did not vote? 6. How fast is a locomotive going when the small wheel, which is 4 ft. in diameter, makes 180 revolutions per minute more than the large wheel, which is 7 ft. in diameter? 7. Ten men can do a work in a certain time, but 7 men would require the same time and 7 days more to do the same work. How long did it take the ten men to do it? .1' it' 192 ARITHMETIC. 8. There is a j?ras8 plot in the form of a ciicle 145 yd. in rrjIiiiH and a carriage drive round the outside of it 4 yd. wide, llnvv many cu. yd. of gravel will be required to cover the drive to the depth of 8 inches? 9. A can do a piece of work in 10 days; B, in 12 days; and (% in 15 days. They all begin to work together, but C stops 2 days and B li days before the work is finished. A finishes the work. How long does he work? 10. Divide $2699.10 among A, B, C and D, so that A may have 12% more than B; B, lOVo more than C; and C, 5% more than D. EXERCISE CCXCVI. 1. A farmer raised 3105 bu. of oats in 2 years. He had 30% more the first year than the second year. How many more bushels had he the first than the second year? 2. The breadth of a room is half as much again as the height, and the length is twice the height. It costs $33.60 to paint the walls at 30 ct. per sq. yd. Find the dimensions of t''t-» room. .".. Iron weighs 7.112 times as much as water. How many i" = ft. are there in a ton of iron? 4. A person holding $5000 of 5% stock and $7600 of 6% stock sold the first at 110 and the second at 115, and re-invested the proceeds in 4*% stock at 89. Find the gain or loss in his income? 5. How many oranges must a boy buy and sell to make a profit of $12, if le buys at the rate of 5 for 3 et. and sells at the rate of 4 for 3 ct. ? 6. The price cif gold is £3 17s. lOid. per oz. A compound of gold and silver, weighing 18 lb., is worth £637 78.; but if the proportions r^re reversed, it would be worth £259 Is. Find the value of silver per oz. and the proportion of gold and silver. 7. A drover bought sheep at a certain price per head. He sold I at a gain of 20%, n,- at a gain of 15% and the rest at a loss of 10%, and gained, on the whole $217. How much did he pay for the sheep? 8. A rows 30 mi. and back in 12 hours, and he finds he can row 5 mi. with -e stream in the same time as 3 mi. against it. Find the rate ot the stream. 9. If the time past 3 p.m. is to the time past 1 a.m. as 4 to 1, find the time. 10. The sides of a rectangle are in proportion of 5 to 6, and it contains I A. Find the cost of painting a close board fence 6 ft. high around it at 45 ct. per sq. yd. RRVIKW KXKR(MSK8 FOR FIFTH CLASS. 193 5 yd. in d. wide. ;he drive ays; aud ; stops k. ftuishes it A may 5% more B had 30% lany more lin as the A, $33.60 to aensions of How many 7600 o£ 6% re -invested loss in his to make a md sells at compound 7s. ; but if l9 Is. Find and silver. head. He \\e rest at a luch did he Ifinds he can against it. la.m. as 4 to 5 to 6, and Iboard fence EXERCISE CCXCVII. 1. Find the area of ii sciiiuro inscribed in a circle 48 ft. in diameter. 2. Tlie n«'t proceeds of the sain of 1000 tons of hay at $20 a ton after deducting !t!875 for freiglit, etc., were $18325. What rate of commission was charged? 3. From a cask of wine one-fourth is drawn off, and the cfi' '< is filled up with wat« r: one-fourth of the mixture is then dra off, and tlie cask again lilled up with water; after this process has been repeated four times altogether, what fraction of the original quantity of wine will be left in the cask? 4. A wall whose height is i of its length, and whose thick- ness is i of its height, co.itains 625630/4 eu. in. Find its thickness. 5. Express as a vulgar fraction, and also as a decimal, the difference between 25.135 X 13a-T and 61.375 X b^. 6. Calculate the ratio between the values of gold and silver, if from 2 lb. of standard gold are coined 89 guineas, and from 1 lb. of standard silver GO shillings, y-i of standard gold being alloy, and A of standard silver. 7. A grocer bought 1500 lb. of tea and sold 300 lb. at 45 et. a pound, making 12i% profit. Find the price at which he must sell the remainder per pound to gain 20% on his outlay. 8. A merchant bought 240 yd. of silk. He sold i of it at 2')% gain; i of it at 20% gain; rnd tlie remainder at 15% loss, and received $800 in all. How much did the silk cost him per yard ? 9. How mtich less will it cost to fence a square field of 40 acres than a rectangular one of the same size, 90 rods long, at 81 ct. a rod? 10. By selling $1000 of 3 per cent, stock at 95 and reinvesting the proceeds I increase my income $10 a year. If the dividend on the new investment is at the rate of 8%, what is the price of the stock? EXERCISE CCXCVIII. 1. A rectangulsr field contains 27 A. 48 \\q. rd., and 13 times its length is equal to 21 times. its breadth. How many rods of fencing will be required to enclose it? 2. A buys $18300 of 3% stock at 75 and pays for it with money loaned at 8% per annum. At the end of a year he sells out and his gain is $122. At what price did he sell the stock? 3. A bought cloth at 20 ct. and the same quantity at 30 ct. per yard. He sold all at the same price per yard so as to gain as much per cent, on tlie one kind as he lost on the other kind. Find the selling price and the total gain or loss per cent. 194 ARITHMETIC. 4. The area of the two larger walls of a room is 810 sq. ft.; of the two smaller, 024 sq. it.; and of the floor, 884 sq. ft. Find the dimensions of the room. 5. The road between A and B, distant 15 miles, poes over a hill whose summit is 15 miles from A. Two men set ont at the same time from A and B, the former going 4 miles per hour up hill and 5i down, the latter 3i uj) and 4i down. IIow far will tile slower have to go when the faster reaches B? 0. A pond A. in area is frozen over to a dej>th in. If a cubic fcot of water weighs 1000 oz. and ice is nt »^ heavy as water, find how many tons of ice there are on the pond. 7. A man bought 03 sheep. He sold J of them at 15% gain; y of them at 50% gain; and the rest at 25% loss. His total gain was $15.40. How much did he pay for the sheep? 8. A's present age is to B's as 9 is to 5, and 23 years ago the proportion was 10 to 3. Find the present age of each. 9. If gold can be beaten out so thin that a grain will form a leaf of 50 sq. in., how many of these leaves will be required to make up the thickness of a sheet of paper, the weight of a cu. ft. of gold being 1215 lb. and 400 sheets of paper being 1 in. thick? 10. If 5 men, 4 women, and 3 boys can complete a piece of work in 150 days, what time would it take 9 men, 15 women and 18 boys to do twice as much, the parts done by each in the same time being as 3, 2, and 1, respectively. EXERCISE CCXCIX. 1. The perimeter of a serai'jireular flower-bed is 00 ft. How many plants will it contain, allowing 1 sq. ft. to each plant? 2. A sold a farm to B at 15% Joss; B sold it to C at 10% loss; and C sold it to D for $3786.75 at 10% gain. -How much did the farm cost A? 3. A can row 4i miles an hour in still water and he finds he can row a distance down stream in one-third of the time he can row back again. Find the rate of the stream per hour. 4. How much tea at 48 et. a pound must be mixed with tea at 60 ct. a pound to form a mixture of 180 lb. in which the value of the different teas will be equal? 5. A grocer buys coffee at $34 per ewt. per ewt. He mixes them in proportion of 5 lb. of coffee and sells the mixture to gain i of the cost. much does he charge i)er pound? 6. A town levied a tax for a bridge which cost $2520. Allowing 4% for the cost of collection, wliat sum wa^j levied? and chicory at $10 lb. of chicory to 7 How REVIKW EXERCISES FOB FIFTH CLASS. 195 ) sq. ft. ; 4 sq. ft. es over n ut at the V hoiiv up V fur will in. If a , heavy as id. ].f>% gain; His total p? yoawi ago each. will form a required to lit of a cu. being 1 iu. a piece of 15 women each in the 60 ft. How eh plant? ,0 C at 10% •How much . he finds he time he can _our. xed with tea u which the liicory at $10 chicory to 7 cost. How eost $2520. ;a,.i levied? 7. A merchant's debts amonntrd to $5000. Ono-lialf of liis stock was sold at '.i\i7c discount and tin* rest at 12i% discount. His creditors received G2i% of what was owing them. Find the value of the goods. 8. White cedar weiglis 20 lb. to the cu. foot, while a cu. ft. of water weighs (iiii 11). A kind of iron is 7.492 times as heavy as water. Wliat thickness of iron will be of the same weight as a 9 in. plank of white cedar, their lengths being equal? 9. A cube contains n.']90025 en. in. Find to four places of decimals the differeiice between the lengths of the edge and of the diagonal. 10. Two men formed a partnership. A put in $10000, and B $10000. They lost $2080 and their capitals were reduced accordingly. They then took in (! as partner .ith $18000. They gained $4716. How much should each receive? EXERCISE CCC. 1. A merchant mixes wine at $'i a dozen with wine at $3.60 a dozen. He sells the mixture at $4.32 a dozen at a gain of 26%. In what proportions are the two kinds mixed? 2. It is between 4 and 5 and the hands of a watch form with a line joining their extremities an isosceles triangle, each of whose angles at the base is half the third angle. What is the time? 3. I bought an article and sold it at a loss of 20%. If the cost had been 10% less and the selling price $13 more, I would have gained 25%. Find the cost. 4. The expense of carpeting a room was $45. If the breadth were 1 yd. less the cost would be $36. Find the breadth. 5. Seven pounds of tea being mixed with 4 lb. of a better quality the mixture is worth 88 ct. per pound. What is the value of each kind, the difference of values being 22 et. per pound? 6. I buy two houses for $5850 and sell one at a loss of 8% and the other at a gain of 10% and neither gain nor lose on the whole transaction. How much did each house eost? 7. The sides of two squares are 2321 ft. and 23i ft. respectively. Find the side of a square whose area is equal to the sum of the areas of the other two squares. 8. If 175 men and 240 boys do in 1330 days the same amount of work as 603 men nnd 1005 boys in 350 days, compare the average daily work done by each man with that done by each boy. ill 190 AUITIIMKTIC. !>, Ill tin* ('«'iitrt» of n room 121 ft. sqmirc, thero is ii sqiiiire <'iir|»«*t. 'V\w rt'Ht of the fIor>r is covon'd with oil-cloth. The oirpct mill thf oil-clotli post rcspcctivM'Iy $-.40 and IMi ct. p«'r H(|. .v<l. ; and tln' wliolf cost of carpet iiiul oil-cloth is .fJtO.CiO. FimI the width of the oil -cloth. 10. Tliicc nicrchaiits enter into partnership. I'he fii-st, A, jmts in $W\{) for (5 months; the second, li, a certain snm for 12 months; and the third, (', ff<)40 for ii certain time when the accounts vver* settled. A leceived .$1200 for his stock and j.roHt, H $2400 for his, and C $1040 for his. What was H's Htock and (''s time? EXERCISE CCCI. 1. If tlie telcfjraph poles at the side of a railway are GO yd. apart, what fraction of the true speed will the error bo in rt'ckoninj; the speed of the train to be twice as many miles ptr hour as the train passes poles per minute. 2. A and B f?o to nnirket and biiy tofjfether 80 lb. of meat at 10 ct. per lb. A takes HO lb. and B the rest. Upon examin- ation, they a{?ree that A's meat is worth i ct. per lb. more than B's. How nnich must each pay for the meat. ;{. A merchant borrowed $1300 at .3^% and at the same time $1790 at ^i7r and j)aid both loans when the sum of ])rincipal and interest was $3202.50. How long did he keep the money? 4. Two circular gold plates each 1 in. thick and (5 in. and 8 in. in diameter, respectively, are melted and formed into one j)iate also 1 in. thick. Find its diameter. 5. A merchant sold 400 yd. of cloth, it he gained 10% and r>% on the remainder. S% gain, he would have made $21 more. l)er yard. C. Find the cost price of 3 per cent, stocks, so that if $3(5000 be invested, the income may be $1140 after paying an income tax of 5 ct. on the dollar. 7. If James can do S^ of a work in 8 hr. and John can do f of the remainder in 2 hr. and Charles can finish it in 40 minutes. * What time would all take working together? 8. A piece of metal weighing 1410 lb. has been formed by compounding three metals in quantities which, by measure, are as 5, 3, 2; but the weights of equal volumes of them would be as 7, 11, 13. What weiglitof each of the component metals has been used? 9. Divide $5600 into 4 parts, sucli that the respective interests on the 1st at 2^ per cent, for 4 months, the 2nd at 3 per cent, for 4 months, the 3rd at 4 per cent, for 5 months, and the 4th at 5 per cent, for G months may be the .same. On one -fourth of Had he sold it at Find the cost price REVIKW KXKRCI8ER FOR FIFTH 0LA8S. 197 HOtiare » ct. |»»'r first, A, 11 for VI rhim the :()('k imd was H'H ro GO yd. •or bo iu miles ptr f meat at II examin- more tlian same time f principal he money? ■) in. and 8 into one -fonrth of sold it at cost price it it $:U)000 an income n can do I it in 40 f? formed by easuve, are 1^ ^^•ould be ; metals has respective llie 2nd at 3 iionths, and 10. In a niih' rjH'c, A starts at U70 paccH of 48 inohes ])er minute, and li 'MO paces of 44 inclies per minute. After 4 minut«'s, H (|uickeiiM his pace to II'JO. Siipposiiifi; A eontinueH at his (irij^iniil rate. VVIiich wins, l»y how much, and in what time? EXERCISE CCCII. 1. I'Mnd the dilTerence between the areii of u triaiif^N' wliose sides are IDI ft., -0 ft. and 44 ft., respectively, aiul that of an e(iuilate.'al triangle of the same perimeter. 2. Divide $;r)GO among A, B, (', and 1), giving A 'M% of D's sinire; C, '.M% of A's share; and B as much as A and C toj^ether. :j. A sold a lot which cost $1875 and gained Gi% of the selling price. He sold another which cost $1200 at H% gain on the cost price. His whole gain was $221. Find the selling price of each. 4. A farmer holds two mortgages for $14000 and $34000 rt;spec(ively, which bring in $2000 interest each year. 'V\w rate on the latter is i% higher than that on the former. Find the rates. ii A buys tea at '){)c. per pound and the same quantity of a l»etter quality. He mixes them and selfs the mixture at GGc. l)er pound and thus gains 20% on his outlay. Find the price of the second kind of tea. G. After a certain number of men had been employed on a piece of work 24 days and had half finished it, IG men more were set on and the remaining half was completed in 16 days. How many men were employed at first? 7. A sets out to walk to a town at 3 miles an hour; B on a hicycle sets out with him at 12 miles an hour. On reaching the town B rests half an hour, and after riding 40 minutes on the return journey meets A. How far is the town distant from the starting point? 8. A banker increased his capital 10% per annum and in 4 years, the interest for one year at 4% on the capital he then had was $3GG0.25. Find his original capital. 9. The minute-hand of a town clock is 9 feet long. Find the time after twelve when its extremity has moved over 11 ft. on the dial. 10. If $5 be allowed as discount off a bill of $125 for a certain time, what should be the discount if the bill had twice as long to run, (1) at simple interest, (2) at compound interest? ANSWERS. 10 5. 10 10 4. 9. 4. 9. 4. 9. 10 5. 9. 6. G. Ex. IX. 1. 49 et. S. $47. 3. 209 bu. 4. 87 mi. 5. 124 mi. 945769. 7. 969 yd. 8. 1367 mi. 9. 786. 10. 1668 pages. Ex. XIV. 1. 303. 2. 354 A. 3. 272 marMes. 4. 158 mi. $7353. 6. 1273 animals. 7. 885 trees. 6. MCXVII. .9.46391. . 226. Ex. XV. 1. 40 marbles. ^. $45. 3. 870 pages. 4. 300 mi. 1000 et. G. $1900. 7. $270. S. 98 et. 9. 208 mi. i^. $7856. Ex. XVI. 1. 9054. 2. $9000. 5. 814 baskets. 4. 106 ft. 170 ct. 6. $129. 7. 144 et. 8. 500 ct. 5. 160 A. . 90 sheep ; $389. Ex. XVII. 1. $999:! . 2. $350. 3. 197795. 4. $52948276. 3617 sheep. 6. 510 mi. 7. $100. ^. $120. 9. 195 et. . 3666. Ex. XVIII. 1. 76 mi. 2. 1159620. 3. $45000. • 1171460 oranges. 5. $3811. 6. 78. 7. $31839. ^. $12085. $33820. 10. $33020. Ex. XIX. 1. 1990977. 2. 72720, 147720. 3. $18565. 154 yd. 5. 31136. 6. 131 et. 7. 365 days. 5. 12413. 1832. 10. $140900. Ex. XXI. I.Ul cows. ;?. 40 chickens. 5. $23. 113 pages. 5. 272 gal. 6. $150. 7. 254bbl. ,5. 1232 sheep. 433 A. 10. $1200. Ex. XXVII. 1. 74. 2. 286032. 3. 6319267. 4. 32299. 676. 6. 2714. 7. 526084. 8. 2578. 9. 6667315. 10. 141998. Ex. XXVIII. ^. 89 sheep. ^.$257. 5. $468. '^. 24168 bu. $1779. 6. $2168. 7. $49. .9. 1432 mi. 9. 162482. . 158677 cows. Ex. XXIX. i. $807. ^.39 marbles. 5. 13999 men. 4. $.3816. 351636 min. 6. 439 pages. 7. $21506957, 8. 6300836 ft. 117993. 10. 83849884 lb. Ex. XXX. 1. 27 ct. 2. 288. 3. $11993. 4. $35. 5. 1642. 89 yr. 7. 983 yr. .?. 3688 it. f^. 1325 votes. iO. 3969356. Ex. XXXI. Z. 45. ^.$198. '?. 215bu. 4. $3250. 5. $32. $107950, 7. $7178. 8. 5mi.,13V7'1. 9. 225 mi, 10. 2210. Ex. XXXII. i. $245. 2.1950. 3. Ut7 A. 4. 45 yr., 38 yr. Loss, $2410. 6. Jas. 31, Jno. 26. 7. 4o A. 8. 70 da. 18 marbles. 10. 211V 1, 14896, 18691. 198 ANSWERS. 199 Ex. XXXIII. 1. 6746. 2. 129G8. 5. 1606. 4. 2658225. 5. 6529. 6. 925358. 7. 2534. 8. 73699. 9. 2155. i^A 8453. i/. 23718. 12. 74128. Ex. XXXIX. 1. 1200 mi. ^. $195625. 3. 607488 oz. 4. 1632000 mi. 6. 63168 et. 6. 702 trees. 7. 2920 mi. 8. 95424 hills. 9. $130455. 10. 75087 lemons. Ex. XL. 1. 1530000 ct. 2. 32076 yd. 3. 2368 nails. 4. 62640 mi. 6. 171216 ia. 6. 383600 ct. 7. 482040 ct. 8. $204000. 9. 525600 min. 10. 5285484 papers. Ex. XLI. 1. 43050. 2. $2241190. 3. $5. 4. 553 ct. 5. $516. 6'. Gain, $32. 7. 94720 ct. *. 2472 ct. 9. 1037 mi. i^. Loss, $83. Ex.XLII. i. 172484. ^.233189. 5.1062347. 4.67419143. 5. 15403465. 6. 2016978981. 7. 1123193115. 8. 63096033. 9. 50700. 10. 14254. Ex. XLIII. 1. 55986805. 2. 1516. 3. 62985. 4. 9989001. 5. 7051253. 6. $30613. 7. 57415 ct. 8. 15725910 A. 9. 703 stocks, 8436 sheaves. 10. 99693084. Ex. XLVII. 1. 16, 28, 44, 88 yd. 2. $121. 3. $75. 4. 329 bbl. 5. 142 lb. 6. 524 lb. 7. 15065 lb. 8. 532 pk. 9. $7625. iO. 379 t. Ex. XLVIII. 7. 480 mi. ^. 1760 yd. 5. $13. 4. 13 hr. 5. 30 ct. 6. $32. 7. 57 persons. *. 362 mi. U. 11625000 mi. a min. 10. 5642 pence. Ex.LII. i. 6540. ^.391525. 5.489673. 4.150287. 5.481. 6'. 4798. 7. 61. 8. 378. 9. 9605. 10. 228689. Ex. Llll. 1. 134 da. 2. $2003. 5. 2640. 4. 29603 lb. 5. $658. 6. 160sq. rd. 7. 327 mi. *. 275 persons. 9.168 1b. 10. 9 da. Ex. LIV. 1. 179 mi. 2. 96934 yd. 5. 19 mi. 4. 64 bu. 5. 51 bu. 6. 245 bu. 7. 144. 5. 75 c. yd. 9. 207 bbl. ^<?. 704 cd. Ex. LV. 1. 119. 2. 910. 5. 83. 4. 1331424. 5. 45. C. 27. 7. 14839. .?. 811. 9. 41. iO. 23849. Ex. LVI. 7.7469. ^.23. 5.631229. 4.323603. 5.150321. 0. 66. 7. 245. ,?. 119025. 9. 767561. 20. 336. Ex. LVII. 1. 840 steps. 2. 14668. 5. 2380277. 4. 1249. 5. 962556. 6. 179538. 7. 253440 in. ,S. 20063110804. . 9. 35643910. 10. 40160 ct. Ex. LVIII. 1. 91132497. 2. $288. 3. 1145348. 4. 6029. 5, 30595. 6. 815. 7. 99368. .9. $254. i^. 1420799. 10. 224(1 ct. Ex. LIX. 1. $336. ^. 18 et. 3. $5 each. 4. 2632 ct. 5. 200 ct. 6. $50. 7. $1620. 5. 485 sheep. 9. 11657397. 10. 8 yr. -v^ illl 200 AKITHMKTIC. 6'. C. 6. 4. 8. 6. 5. 10 5. 9. Ex. LX. 960 et. 1. 2552, 7. 72 et. 2. 18480 et. 8, $4800. !K S. 95 et. 4. 42. 113. i<^. 203. 5. 10624. Ex. LXI. i. 27 ct. 2. 10 ct. .■?. 21 mi. 4. $51. 5. $150. 30 yd. 7. 21 dresses. 8. 1728 bu. 9. 11 br. ^6*. 579000 lb. Ex. LXII. i. 21da. ^. 95da. 5. 20 da. ^. 27 da. 5. 18da. 15 men. 7. 45 men. 8. 6 men. 0. 240 men. lU. 225 men. Ex. LXMI. 1. 16, 20. 2. 20, 30. 3. 39 bu., 46 bu. 42 yd., 58 yd. 5. 44, 50. 6. 12 yr., 15 yr. Ill votes, 129 votes. 5. 67 mi., 90 mi. lU Ex. LXIV. 1. 8458. 2. 181357. 3. $3570. $16. 6. 240 ct. 7. $6. *. $135. 9. 170. Ex. LXV. 1. 33148. ^. 5607 ct. 3. 10 ct. 21450 et. 7. 19 gal. ^. $170. 9. 2046 et. Ex. LXVI. 1. 120 pieces. ^. 159 pieces. 1800 ct. G. 11 stacks. 7. 302304 ct. ^. 17 hats. Ex. LXVII. 1. 36405 bu. 2, 202878 ct. Gain, $161. 6'. 38400 lb. 7. 5355 ct. 36 1b. 10. 1953. Ex. LXVIII. 1. 1580712. 7. 19, 28. 192, 195. 4. 264 mi. 10. $46836. 4. 17. 5. 47 ct. 10. $468. 5. 9 et. 4. 21. 500 A. 9. 60 bu. 3. 23 lb. 4. $2028. 8. 4860 et., 90 et. 2. 148 mi. 5. $2277. 4. 1862 et. 5. $2688. 6. 150 boys. 7. $31104. 5. 86 A., $42. 9. 132 head. 10. 114 mi. Ex. LXXIII. 1. £83 12s. 9d. ; £74 18s. lid.; £810 2s. 2. 74 cwt. 64 lb. 3oz. ; 127 t. ewt. 72 lb. ; 56 1. 1 ewt. 281b. 3 oz. 3. 82 yd. 1 ft. 9 in. ; 18 yd. 2 ft. 4 in. ; 58 yd. ft. 9 in. 4. 16 bu. 2 pk. 6 qt. ; 32 bu. 3 pk. 5 qt. 1 pt. ; 133 gal. 2 qt. 1 pt. 5. 38 gal. 3 qt. ; 32 da. 18 hr. 51 min. 56 sec. ; 7 wk. 4 da. 2 hr. 45 min. 3o sec. £3 3s. 9d.: £19 9s. 3d.; 4 cwt. 22 lb. 10 oz. 6. 7. S. 9. 10 t. 15 cwt. 63 lb. ; 3 yd. 1 ft. 5 in. ; 47 yd. 1 ft. 3 8 bu. 3 pk. 6 qt. ; 2 qt. 1 pt. 41 see. ; 1 wk. 5 da. 7 hr. 14 min. yd. 18 e. ft. 1483 c. in.; 51 e. yd in. 45 see. ; 2 e. ft. 28 bu. 1 pk. 7 qt. ; 2 da. 18 hr. 8 min. 6° 50' 39". 10. 30° 53' 49"; 31 c. 1488 e. in. Ex. LXXIV. 1. £66 9s. 2d. ; £454 14s. ; 136 ewt. 67 lb. 1 oz. 2. 61- 1. 13 ewt. 31 lb. 8 oz. ; 211 yd. 2 ft. ; 967 yd. ft. 3 in. 3. 23 bu. pk. 1 qt. 1 pt. ; 95 bu. 3 pk. 2 qt. ; 34 gal. qt. 1 pt. 4. 187 gal. 2 qt.; I.i9 da. 11 hr. 33min. ; 46 da. 13 hr. 34 min. 56 sec. 5. 123° 53' 39"; 422° 17' 20"; 86 c. yd. 22 e. ft. 967 e. in. 6. £20 98. 5d. ; £5 3s. lid. ; 7 ewt. 85 lb. 14 oz. 7. 2 t. 10 cwt. 64 lb. 9 oz. ; 12 yd. 1 ft. 11 in. ; 9 yd. ft. 11 in. 8. 4 bu. 3 pk. 6 qt. 1 pt. ; 8bu. Opk. 1 gal. 1 qt. ; 15 gal. 2qt. Ipt. .9. 4 gal. 1 qt. 1 pt. ; 164 hr. 26 min. 24 see.; 187 da. 21 hr. 55 min. 57 see. 10. 19° 15' 42"; 125° 9' 24"; 19 e. yd. 22 e. ft. 969 e. in. ANSWERS. 201 Ex. LXXV. 1. 13; 32. 2. 400; 35. 3. 49; 42. 4. 77; 720. .5. 325; 64. 6, 1856; 375. 7. 90; 35. 8. 2880; 156. .'>. 78; 1680. 10. 1120; 303. Ex. LXXVI. i. 4 ft. 8 in. ;g. 504pt. 5. 744hr. 4. 131,36oz. 5. £116 168. 3d. 6. £54 13s. 4d. 7. 11 ft. 6 in. ; 6 ft. 6 in. S. 107° 40' 38". 9, 353. 10. $529.20. Ex. LAXVII. i. $27. 2. 1301. 5. $104. 4. 3080 yd. 5. $164475. 6. 342 min. 7. 37 lb. 14 oz. ,S. 15 t. 9. 3000 gal. 10. $551760. Ex. LXXVIII. i. 45t. ^. 60 spoons. 5.108. -^.15 pages. 5. 42 mi. 60 rd. 6. £110 10s. 7. £9 78. 6d. .S. $54.92. 9. 60 yd. iO. 15 ct. Ex. LXXIX. 1. 95 gal. 2 qt. 1 pt. ;g. 12 gal. 2 qt. 1 pt. S. 278 bu. 36 lb. 4. 23 bu. 13 lb. 5. 5 min. 15 see. past 8. 6'. 4 lb. 4 oz. 16 dwt. 7. £3 17s. lO^d. 8. 288 lb. 9. $2919. 26*. 15 lb. Ex. LXXX. 1. $44.70. 2. $153. 5. $8778.50. 4. $134.09. 5. $297.45. 6. $153.27. 7. $17.81. ^. $49.97. 9. $2.56. i(?. $58.95. Ex. LXXXI. 1. $290. ^. $2.79. S. $7.25. 4. $311.48. .5. $221.81. 6. $5.32. 7. $21.80. 8. $42.70. 5. $13.94. iO. $71.91. 11. $13.54. Ex. LXXXII. 1. 10 in. ; 14 in. ; 22 in. ; 16 in. 2. 56 ft. -:?. $45. 4. 250 boards* 5. $3.40. 6. $700. 7. $256. S. 14080 yd. 5. $1440. 10. 120 ft., 40 ft. Ex. LXXXIII. 1. 1224 sq. ft.; 1216 sq. ft.; 5616 sq. ft. ^. 9 A. ; 10 A. ; 15 A. ; 42 A. ; 15 A. ; 19 A. S. 18 sq. ft. 4. 11 sq. yd. 5. 2304 sq. yd. 6. 200 sq. yd. 7. 112 sq. in. 8. 1056 sq. ft. 9. 2000 sq. ft. 10. 24 sq. ft. Ex. LXXXIV. 1. 18 ft. 2. 54 ft. S. 40 rd. 4. $290. 0. $150. 6. 500. 7. 72 ft. 8. $940. i>. 360 ft. 10. $660. Ex. LXXXV. 1. 40 yd. ,?. 60 yd. S. 32 yd. 4. 70 yd. 5. 196 yd. C. $57.60. ' 7. $13. 8. $130. y. $24. if. $12.60. Ex. LXXXVI. ?. 6; 9. ^.8. .?. 16. ^.8. 5.10. 6.72 yd. /'.48 yd. .§.$58.80. r>. $88. iC. $110. Ex. LXXXVII. 7. 80 sq. yd. 2. 168 sq. yd. S. 224 sq. yd. 4. $9.12. 5. $40.02. 6. 82 sq. yd. ; 91 sq. yd. ' 7. $23.60 ; $26.20. <V. $21; $23. 9. $:59; $41 ..'50. if. $70.20; $76.14. Ex. LXXXVIII. 1. 160 yd. 2. 288 yd. .^. 448 yd. 4. 96 yd. J. 348 yd. C. 82 yd. 7.396 yd. 5.144 yd. .^>. $5.85. if . $16.25. Ex. LXXXIX. 1. 9 ft. ; 24 ft. ; 24 ft. ; 24 ft. ; 40 ft. ; 24 ft. ; 12 ft. 2. 3300 ft. S. 4200 ft. 4. 2220 ft. 5. 7680 ft. 6'. 768 ft. 7. 1650 ft. 8, 10000 ft. 9, $300, 10. $540. 202 ARITHMETIC. Ex. XC. 1. 2880 c. ft. 2. 210 c. ft. 3. 60 c. yd. 4. 210 c. yd. 5. 4032 lb. 6. $40.50. 7. 13600 c. yd. v 8. 109 e. yd. 1 c. ft. 9. 2376 c. ft. 10. $1380. Ex. XCI. 1. 30 cd. 2. 63 ed. 3. 30 cd. 4. $84. 6. $216. 6'. $75.25. 7. 80 ft. ,S. 5 ft. D. 8 ft. id?. 224 ft. Ex. XCII. 1. 7 ft. 2. 11 ft. S. 24 ft. 4. 3 ft. 6. 112 ft. 6. 18144. 7. 192 ft. «. 40 ft. 9. 30 in. 10. 17 ft. Ex. XCIII. 1. 32 ft. ^. $40.25. 3. $1080. 4. 1120 lb. 5. 32 t. 6. 48 t. 7. 1760 c. yd. 8. $792. 9. $1440. i<?. $72. Ex. XCIV. 1. $32.64. 2. 220 yd. 5. 3600 sods. 4. 3 ft. 5. 90 c. ft. 6. 33 mi. 7. 15 ft. 5. 9 ft. 9. 36 8q.yd. 10. 5 ft. Ex. XCV. 1. $17; $23. 2. 19 yd.; 30 yd. 3. 36; 48. 4. $48.75; $50.25. 5. $27000; $23000. r>. $215; $160. 7. $425; $371. 8. 271 mi.; 237 mi. 9. yu5; 361. iO. $4500; $1250. EX.XCVI. 7. $5120; $1280. ^. 2064 bu. ; 2311 bu. 5. $2726. 4. 361 yd.; 242 yd. 5. 297; 315. 6. 462; 534. 7. 24 ed. 39 e. ft. : 27 cd. 89 c. ft. 8. 9 A. 115 rd. ; 10 A. 45 id. 9. 4 mi. 275 rd. 10. 1 t. 8 ewt. ; 2 t. Ex. XCVII. 1. 30; 90. 2. 254; 508. 3. 23 yd.; 92 yd. 4. $2450; $9800. 5. $75; $168. 6. $145; 462. 7. $3450; $10500. 5. 30 rd.; 90 rd. 9. $126. 10. 1240; 3737. Ex. XCVIII. 1. $36; $48. ^. 60 bu. oats; 150 bu. peas. 3. 17. 4. $7800; $11700. 5. 275; 330. 6. $20; $40; $60. 7. 30; 45; 75. 8. 6. 9. $420; $140; $560. 10. $10940; $3020; $2450. Ex. XCIX. 1. $8; $10; $13. 2. 170 lb.; 152 lb.; 134 lb. 3. 150 yd. ; 125 yd. ; 169 yd. 4. 2400 lb. ; 2200 lb. ; 1800 lb. 5. 127 lb.; 100 lb.; 175 lb. 6. 60 mi. ; 25 mi.; 40 mi. 7. 81 rd. ; 45 rd. ; 123 rd. 8. 256; 378; 452. 9. $450; $531 ; $612. 10. 180 bu. ; 233 bu. ; 160 bu. 11. 32 et. 12. 87 red, 94 blue, 105 white. Ex. C. 1. 1975. 2. 3683. 3. 184019. 4. 7, 10, 9. 5. 14, 11. 6. 43, 16. 7. 14 lb. 8. 48 yr. 9. $119. 10. $7095. Ex. CI. 1. 6.59 lb. 13 oz. 2. 256 mi. 160 rds. 3. $204.75. 4. $17.82. 5. 35 ewt. 25 lb. 6. 12 lb. 9 oz. 7. 33 mi. 96 rd. 8. 45. 9. $75. iO. 24 lb. 10 oz. Ex. Cll. i. qj32. ;?. 7 ct. ,?. 15 carats. 4. 40 ct. 5. 6 et. 6. 200 bu. at 75 ct., 300 bu. at 70 ct. 7. 4 ft. 3 in. 8. 139 lb. 9. Is. 7d. 10. 4s. 9d. Ex. cm. i. 272 lb., 2448 lb. ;g. $570940. 5. 2oz. 4. 35et. 5. 22 yr. 6. $25. 7. 7 ct. 8. •*6 ct. 5. $6.60. 10. 12 carats. ii A17SWERS. 203 [. 6. $216. 5. 112 ft. 1120 lb. :0. 10. $72. . 4. 3 ft. yd. 10. 5 ft. 16 ; 48. L60. bu. 5. $2726. ; 10A.45rd. . ; 92 yd. 3450; $10500. bu. peas. 0; $60. lb. ; 134 lb. .. ; 1800 lb. mi. i; $531; $612. 9. 5. 14, 11. 3. $204.75. mi. 96 rd. et. 5. 6 ct. 8. 139 lb. loz. 4. 35 ct. 10. 12 carats. Ex. CIV. 1. 2, 2, 3; 2, 2, 2, 7; 2, 2, 3, 7; 2, 3, 5. ;?. 2, 2, 7, 7; 3, 7, 11; 2, 2, 3, 3, 7; 2, 2, 2, 2, 2, 2, 2, 3. S. 2, 2, 3, 73; 2, 2, 3, 79; 2, 2, 263; 3, 353. i. 3, 5, 73; 3, 7, 53; 7, 7, 23; 2, 2, 17, 17. 5. 2, 601; 2, 607; 2, 3, 7, 29; 5, 311. 6. 797, 821. 7. 1187. ^. 2543, 2521. 9. 2273, 2339, 2417. 10. 3119. Ex. CV. 7. 2, 5; 5, 7. ^. 3, 7; 11, 13. 5. 7, 17; 2, 2, 3. 4. 2, 2; 2, 2, 3, 3, 3. 5. 2, 2; 5. ^. 30; 25; 275; 193; 443. 0. 2, 3, 5; 3, 5, 7; 5, 7, 11; 7, 11, 13; 11, 17, 19. Ex. CVI. 1. 180. 2. 5. 5. 6. 4. 120. 5. 4. 6. 1008. 7. 2400. ^. 900 bu. 9. 75 yd. iO. 40 da. Ex, evil. 1. 14; 16; 13. 2. 35; 46; 42. 3. 72; 32; 4. 4. 9; 16; 7. 5. 25; 42; 42. C. 9; 4; 73. 7. 73; 32; 11. 5. 9; 8; 13. 9. 32; 110; 14. iO. 91; 143; 323. Ex. CVIII. 1. 14 ft. 2. 17 in. 3. 15. 4. 7 ft. 5. 2 ft. 3 in. G. 13 ft. 7. 63 bu. 8. $1, $2, $5, $10, or $50. 9. $124. 10. 26880 rails. Ex. CIX. i. 18; 7; 251. 2. 107, 311, 103. 3. 52, Prime, 601. 4. 31, 947, 233. 5. Prime, 47, 811. 6. 8, 616, 884. 7. 1188, 13, 13. 8. 46, 21, 9. 9. 897, 1323, 1429. 10. 315, 19. Ex. ex. 1. 105; 3, 5, 7, 15, 21, 35, 105. 2. 2 da. 5 hr. 3. 1 mi. 37 yd. 4. 3 gal. 5. 117. 6. 29. 7. 25. 5. 19 men. 9. 7 oz. iO. 126. Ex. eXI. 1. 24; 120; 120. 2. 75; 600; 720. , 3. 315; 2652; 3705. 4. 360; 1260; 504. 5. 576; 600; 27720. 6. 1260; 8415; 16546530. 7. 10890; 17160; 205205. 8. 14280; 166320; 22770. 9. 1190595; 27945372; 885989. 10. 12018233514; 110250; 620310. Ex. eXII. 1. 120. 2. 360. 3. 85085. 4. 6435. 5. 48. 6. 143. 7. 1526. 8. 90. 9. 120 ft. iO. 60 gal. Ex. eXIII. 1. $20. '2. 141 lb. 5. 94 lb. 4. 30. 5. 30 mi. 6.365. 7.62,122,182. 5.600 bu. 9.13,14,15,16. i<?. 1008000 gr. 51 r). 7. 8. 9. 10 s. 5. 7. .9. Ex. CXV. 1. f; V-; V; V- -2- V; l V;-V-; ff; %¥. 4. V; V; ¥; ^F 4JLQ . 508.23 3.S2T3 /? 8449. 4 41 8 30 ^. ^9. 4^^ TT : -ff-; T5"; i^T- n. --^s- 519L. 68861. 36449. 19126 13 33 1. 44 3 99. 5.9881. 1.60689 1.102 2. 71041. 18 3 821. 101001 .2 8 114 1. 49880 3. 288161. 110 8 61 > 46664 . 84 80 Ex. exvii. i. oi. 7,1!; 5; 51*4; 5A. 4. 9A; 5fA; 4iAA; 6,¥,-; 13f:^. 6 34 ; 2. (9 17. oB , ^- 16M: 33i§; .35^. 4,^^a„-; 260|i; 16-3¥3 ;. 1-,W:< 20h-§; 9f|f; Sfltf ; 342^2^^. 8. 334^3; lOOrg-; lOeVy ; lO^^u '>'^M; 45f gal.; 53f da. 50* lb 10. 7M mi. ; 24f? cd. ; 2lH yd. ; 63^ oz. 204 ARITHMETIC. Ex. CXVIII. 1. $4i. 2. 92i bu. 3. 4i mi. i. 16.V lb 6. 321* bu. 6. Latter by ij^ lb. 7. li in.; 7 lb.; 25 oz. S. 7i gal. y. 20 ft. ; 16 ft. 10.. $19.75. Ex. CXXII. i. i; I; f; i. ^. A; /s; I. 4. J; l;il; i^. 3. 0. &. 10. 2. 3. 4. 5. 6. 7. 8. 9. 6 . iVr; i; /s; I AV; 11; I; " ^1; i; I; 4. J; 5 3 9 8jir; ij. 13. 829 gCr; T33T A; 3 . 6» 'y 8.89. ' • 9 ; jt; i^. A; H; 5. 841 . 68T; 1 . 4 s; 1 1 . 3; e; II. 6 fi 3 9 T29 6 5. V, 63 13 «. i. Ex. CXXIV. 12 6 2 4 3 6_ . TSO", TS^T, T60 > 8 4 2 3 3, liii lir, T¥4> 2 16 14 1 8 0, 2 5 3» 8Jf3» ^5? 8 0^ 6 2, ]8 8ff, J 8 TTf, 39 . 15 "A; Tg 110 1 1 9 0-, f f , I 42 ¥8, 3 6. ■98» 8 A2 600 64 84 Tffff, ^/l 22 10. ^9, 4P fl, fl, !l, II; il, H-, h, -It " 102 HI, Hi Mi If. 86 18 10 3 0_ 14 — TTT? 4*0.. 8 8_ 10 8 19 2 66 . log. TffF; T?o, rrff, rrs, yrs" 6. 3 .120 198. 3 2 4. 99, ff9 , ¥9"; 4 5(r, f3 ITT, ¥^¥, 10 TUTT, tVtt, 1 2 1 626 96 TSTF. 1 32 Tff"8, 84 39 3150 ¥30". 9 Ex. CXXV. i^. I; 3 ro i; h 5. 1: 2; 13.1 li.3 It; i2r«. "30' d. 36 1 4> 13 «? 91 25. 29'-^ 23f. ft A. 5. 6. 6. 4' mi. /. •T2 0. <*• 35» iZ Q 71 30- ^' S1)0« 9. 114/2- gal. 8. t\' Ex. CXX^^I. .?. h ; Ex. CXXVII. 4. 2; 1; 2. 7. IH; li^.; 2A< ^0. im;2A^o; iS-t^ Ex. CCXIX. l.\\l. i 6. 24t. 7. 35i^. ,?. 17^0. Ex. CXXX. 1 6. 178/„. 7. f.}. Ex. CXXXIII. & 'T kl. O 5 4' ' • 1 2 O • O Ex. CXXXIV. "2 8 , UjjHU. 14f; 23 ,i,; 20,^, 9. 17f|; m?-, 31M. i<? Ex. CXXXV. /. m gal. i?. 13f yd. 5. $95f^-. (;. l.>9^i}A. 7. $68f. .?. 13,\. Ex. CXXXVI. 1. U; lA. 2. 3i; SH. 4. 6; 9/s. 5. 4|; 5^1. 6. 1-|?; 34§. 7. «. 2H; 7i^9. 9^ 10; llA. i<9. 8^; in^. Ex. CXXXVII. i. 97M lb. ^. 16i gal. 6. 33i miles. 6. Gained $la%. 7. $23j. iO. 37M yd. iO. 6. 288, 1024. 1^9, 2r2. 2.> O 119, oli. . ol-^£ y. T»?; •isi; ^440. 1 73 4 1 S 36 • * • 10. 26i§. llll^ lb *3B0» ^' O li!7 73 20- '8 , jlB •Jl 1 •'1 3« 59 200' 7 ^)» 23 60 . 4. 10. 132i mi 5 11 5.H too- f; 1 4 ^^3- • 4. ft . 4 *• «>17 , ti 1 ? '^i 3' 7. 1 48 . 5 39 , OQ '-3 . 5. 133 21 14 , 17 144- 13 . 10^5^1 84 » i"l 40 10-A_. 1-143 , 6 13 ^-A Ol 7 . 12 63. -2T, 1288' ^. 2G*-i; 2011 ; lOy^. T5- 16i" .9. «4 mi. 6 Yb- a IQl. <5 • I 1 O 1 111; 27H 4. -m. \'^n. lO.lQii} 4i. 3. 54 lb. 5. $94H. 4. 9. 193H. 18i vd. ANSWERS. 205 i- lb. oz. 6 3, h- 2i?t 40» 8, 1024. 5. -jSTbo- 7 3 |«-< i 2 O • \2i mi foo* 5.i 11 ?oM; iOt^. 4. 30ft. :?0. 164s}t. |4i. 4. 193H- 9. 18i yd. 4. H. 3. 0. 9. .«.. . 1 1 . 1,1 1 > ■'■To > T'f' Ex. CXL. i. 4; 9; 8. 2. tI; ^r; M. 5. |t; H; M- m-, i%. 6. A; f ; 4i. 6. ^; Gl; 5f. 7. -h: I; H. i'. 8; f; n. 10. h T%; 35. Ex. CXLI, 1. l»Oi; 30fV; 5GA. ^. 30*: 42^; 72H. 42^; 5(iA; 15ttU. 4. i; t^; A. 5. 15; l(i*; 9*. U; 11; 20. 7. U; 195; 16i. 5. 31i; 2A; 1. $1^; $i; i>55 mi. 10. $558; 324 oz. ; 3 hi*. Ex. CXLII. 1. $39i^. 2. $159lt. ^. 71|c. 4. 8i mi. $13i. 6. 12k^ bu. 7. $1733i. ^. 36 bu. 9. 47 A. i<?. $4. Ex. CXLIII. 1. $1.68. 2. $30000. 5. 85 mi. 4. 37^^ ft. 385 mi. 6'. $105000. 7. 257|. .S. 39100 men. 9. 210 pages. $65600. Ex. CXI IV. 1. 21; 24i. 2. 18; U. 3. 17ir; 7. 4. 3^1 U. 5. ,J\; 3^ G. 7; 20. 7. 10; 40. 8. 2f; tV. y. 3i4; i. ic^. 1; 2i^. Exc CXLV. 1. 1851 mi. 2. $1012. 5. 59|. 4. 32H bu. 10 5. $170861. G. 10. 7, 37 im- ^. $3125. 9. $43i. iO. Gain, $12. Ex. CXLVI. 1. 14, 16, 15. 2. 36, 55, 44. 3. 8f, 14|, 24f. 4. 171. 31i, 30f. 5. 4f, 5.^4, 6^. C. 6||, 1^%, llf}. 7. 5i 4, 7i. .Sf. la-o, laS, it- 9. ih, 2i, If. ^ 3, i, U. Ex. CXLVI I. 7.11; TT> 111 <? 1 1 IB. S. y 1 1 11 1 a 2if, 12. 4. ^. 231, 16. 9. h ^' 5) »■, T" i'" ii> It* k). G. 3i8» It, l54» 7. 2i, 6, 8. ^. 31, h, 3i. 5. 1|§, t, 2. ii^. 7f, A, 5i. Ex. CXLVIIi. .*. 37* yd. 2. 8| mi. .9. $26i. 4 5. 10 bags. G. 12i et. 7. 28| hr. 8. 8M. 9. 217i A. 10. 370i A. ii. 15i ct. 12. 32 da. 13. $3.60. i4. 20. Ex. CXLIX. 1. 7^, 4. :^. 3J, 3f r ol 2.5 /I 5. 4>a6 w jl _S,_ •-'• "T, aaa. o. 7, -sT. /• *1i> ii5» Ex. CL. 1. 1^, 3i i^' H(H «4« 'J' 10) *jT« Ex. CLI. 7. 5f, i. 2. n, U. /; 11 3 /; 1 14. /y 9I .jA o Ex. CLII. /. 144§. 2. 2. 5. 17f mi. 2H. 1 1 6 O > 1 « • 2. 3i, 30. 3. 54, 66J. 4. 6, 7. i, 5i. ,?. lOA, f. 9. 5H, *. IB. 1 ra> li. •^^ 2 1 » 3 13 7 -1 7. 15i. V?. 43 1^ Ex. CLIII. 7. 101. ,?. U. 9 Ex. CLIV. 7. 9. h. \h. 9. 11, 40. ' 10. 4, I. 5. 7i. C. 4x^„. 2. 1 11 i. TJ. ^. 10. 4. -36 • lUi. 1» 6 r3 3B ; 30 fj T3» >* 4. 5. 6H. 2 1 6 J •- iB 7_ . 21 T3i5 > 4, ^0. 5. 2. 10. f. 4^5 ; 60. e. 35. 4. 2h ft. 5. 5tft.; 19. G. 60. 7. $112i. 8. 3S bu., 51 bags. 9. 59. 10. 6| da; A, 10 times; B, 15 times; C, 8 times. Ex. CLV. 1. 16s., 3M., 4id. 2. 87i et., 80 ct., 75 ct. 3. 17 cwt. 50 lb., 7 lb. 8 oz., 14 oz. 4. 213 rd. 1 yd. 2 ft. 6 in., 3 yd. 2 in., 2 ft. 6 in, 5. 128 sq. rd., 22 sq. yd., 2 sq. ft. 117 sq. in. y"' 2Qe ARITHMKTIC. 6. 96 e. ft,, 11 e. ft., 432 c. in., r)04 c. in. 7. 2 pk. 1 gal., 1 K'll- H qt., 'A (jt. if. 3 qt. 1 pt., li pt., 3i- qt. .'/. 4 da. 21 hr. 'Mi niin., 7 lir., 2.') min. 10. 40, 288 , 16'' 40". Ex. CLVI. 1. 444.')4() in., 12(5744 in. ^. 1 mi. i:{l rd. 4 yd. 2 it. G in., 1 mi. 179 rd. 1 ft. 6 in. 3. 237600 in. luuOi in. 4. 31637628 aq. in., 3860136 sq. in. 5. 1 A. 52 Hq. rd. 19 sq. yd. 8 sq. ft., 2 A. 47 sq. rd. 9 sq. yd. 3 sq. ft. 36 »q. in. 6'. 16727040 sq. in., 131868 .sq. in. 7. 9600 lb., 3800 oz. 8. 14") rd. 2 yd. 1 ft. 6 in., 93 sq. yd., 10 sq. vd. 108 sq. in. !). 9 A. 120 sq. rd. 22 sq. yd., 1 A. 16 sq. rd. 9 sq. yd., 3 sq. ft. 10. 200 gul., 35 t. Ex. CLVII. /. ,$82.11, $28.80. ;?. £1 Hs. 3id., £1 2s. 8d. 3. 3 t. 12 ewt. 4 lb., 1 t. 11 cvt. 48 \h. 4. 2 mi. 197 rd. 5 yd. 9 in., 2 mi. 270 rd. 4^ in. 5. 1 A. 135 rd. 22 yd. 8 ft. 51 in., 2 A. 16 rd. a. 2 ed.59eu.ft., 10 ed. 60<?.ft. 7. 3 bu. ^gjil., 2 bu. pk. 4 qt. 8. 5 gal.,, 13 gal. 1 pt. 9. 23 lu-. 20 min., 5 hr. 26 min. 40 see. 10. W 30' 12", 14" 30' 30". Ex. CLVIII. 1. tItt owt. 2. &A-S. 3. iV Ini. i. A i'<^. •^. liir i"<l. A. 10. { ft. 0. 1 1>I. 7. i oz. .S. U. Ex. CLIX. 1. ^ 11). iW. 6. A on. yd. 2. lb. /-. lit. .7. m iiii. 4. T*J c'v. I mi. .'y. ^^^ 557561. 10. $300. $3.84. i>. $21.51. 5. 10. i\ A. Ex. CLX. 1. 34940585. 2. 525 lb. 3. 169 qt. 4 5. 4320. 6. 5940. 7. $251.25. 8. $1837.J. i>. $44.20. Ex. CLXI. 1. 118188 lb. 3. 31 i cd. -■?. $150. 4 5. $633.60. 6. 267 d. 7. 129600 min. ,?. 1440 min. 10. 2024 poleo. Ex.CLXII. i. 471b. ^. 36112 pt. 5. 5392oz. 4. 31t.5ewt. 5.1800. 6'. $499.95. 7. 1248oz. A'. 40et. 5.189. id>. 467721b. Ex. CLXIII. ^. 22506 gr. 5. 161 gr. S.ohho?.. 4. 5184gr. /J. 11088 gr. C. 10 D). 1 oz. 12 dwt. 8 gr. 7. 25. 8. 37i lb. y. 701 lb. 6 oz. 6 dwt. 5 gr. 10. 114|| lb. Ex. CLXIV. 1. 63360 in. 2. 8064 in. 3. 2 ml. 4. $462. 5. $428.40. 6. $500. 7. 10 hr. 17 min. 8. 1584000 in. 0. 506898 in. 10. 440 mi. Ex. CLXV. ?. $72. .?. $31..50. ,?. $1.95. ^. 438 baskets. 5. 335pt. 6. $1.05. 7.4. .S'. $510.30. .9. 2 qt. iO. $13T.74i. Ex. CLXVI. 1. 32 da. 2. 264 ft. 5. 9. 4. 44 ft. 5. 9 mi. G. 320 hr. 7. 500 da. cV. $57.24. .9. $47.25. 10. $19.44. Ex. CLXVII. 1. 68 et. 5. 5 ft. 3. 8184. ^. 15. 5. 43 mi. G. 48 hr. 7. 4620 paces. 8. 43. .9. 24320. 70. 8f| mi. VNSWERS. 2U7 pt., 3i- qt. 16'Uo". i in. sq. in. . 1) sq. yil. oz. < sq. in. I., 3 sq.ft. ;i 28. 8d. i.0pk.4qt. [iiin. 40 sec. bu. 4. T5' 144 4. 55756^ 0. ^6*. $300. 4. $3.84. . iy. $21. ni. 31t.5ewt. JO. 467721b. 4. 5184 gr. h*?. 37i lb. 4. $462. in. basliets. to. $137,741. It. 5. 9 mi. 519.44. 5. 43 mi. 1 4 mi' 4. 6(5 mi. 9. .■?. 12 hr. Ex. CLXVIII. 1. 6 lb. 4 oz. H dwt. 12 gr. 2. £200. 5. 10 cwt. 80 lb. 1 oz. 4. 24 ft. J. 990 yd. 6'. 4 min. 16 sec; 980 yd. 7. 32 yd. *. 54. 9. 989 1b. 70. 1271. Ex. CLXIX. 1. 84 in. ;.^ 7 da. 5. 506 da. 5. 75 ct. 6. $8050.50. 7. 49| yd. ,y. 60 et. !K 12 da. 20 hr. 20 min. 10. 4 yd, 1 ft. -i in. Ex. CLXX. 1. 3 lb. 11 oz. 11 dwt. 6 g. i 4. 110 da. 5. 36 hr. 6\ 42. 7. 92928. ,!;. 12 spoons. .9. 5/a mi. iO. £43 Is. 3d. ; £6 8s. 9d. Ex. CLXXI. /. 209 bii. 1 pit. 3 qt. S. 1569 bbl. 3. A, 131 yd.; R, 19i vd. 4. 36 mi. 298 rd. 1 ft. 6 in. 5. 48 rd. 6. 8f yd. 7. $62. ,?. $13.50. 9. $432. iO. Hi t. Ex. CLXXI I. ./.s-7.50. iJ. $1.76. 5. $96. -^ $49. 5. $19.12. 6. 27i yd. /". 27 lb. 8. 1.0 hr. 9. $8. 92 J. 10. $94.40, $660.80. Ex. CLXXIII. /. 48, 8 lb. 2. 32 lb. 3. 42 mi. 4. 24 yd. 5. 450sheep. 6.176ft. 7. 58|A. ^. 60ct. .9. $12000. 10. U A. Ex. CLXXIV. /. 288. 2.$:]H. 5. 160| bu., 32U bu. -^. $20J. 5. $6000. 6. 8i ft,., 2079U gal. 7. $23.76. ^.100 A. 9. $4070. 10. $0250. Ex. CLXXV. /. 50 A. 156 rd. 2. 7 ft. 9 in. 3. 8f ft. 4. 3 doz. .5. 181iJ A., 203^5 A. 6. 38 A. 91i rd. 7. 42240. ^. :-!;6C.01. .9. 396 lots. iO. $13459.56; Jamr*' $3364.89; William, S»}4486.52; daughter, $1121.63; wife, $4486.52. Ex.CLXXVI. 7. all. ^. -i\. 5. l^da. 4. 36da. 5. 16^ da. 6. 41ida. 7. 10 da. 8. Uf da. 0. 2h da. 10. l|f da. 11. 21^ da. 12. £J hr. 13. 28f hr. 7-^. 6^,^ da. 75. 2^ da. 16. 3^ da. Ex. CLXXXI. 1. 282.405 A. 5. 307222.086446. 3. 363.536487. 4. 115.8125 yd. 5. 24.2675 t. 6. 25269.111505. 7. .42951303. 8. 6.5 t. .9. 138.122427. 10. 48095.139833. Ex. CLXXXIV. 1. 72.927. 2. .1993. 3. 364.9953. 4. 6999.9996045. 5. 999999.999999. 6. .017481. 7.2999999.900001. .?. .000999. .9.43.08997. 70.6929.95993. Ex. CLXXXV. 7. .30.280965. 2. 75.0665. 3. 15.635563. 4. 16.()799884. 5. 49.1.56. d. 4.152. 7. 81.143. 8. 9.7597. .9. 80.025. 10. 9.0897. Ex. CLXXXVI. 7. 228.475 A. ^. $.327,065. 3. 199.35 mi. ^.$963.68. 5. 262.35 A. 6. .08 in. 7. $111.58. 5. 29569.92 A. 9. 123.325 lb. 10. 73.73 ft. 77. .3. 12. 30.338 in. Ex. CLXXXVIII. 7. .435; .0676. ^. 506.4463; 35.4367519. -'?. .013272: 32.5779. 4. 36.9; 1.7005. 5. 3.8; 1860.867. 6. 525; 92.;. 7. 11221.1; 54.706. 5. 9.06453; 279.29475. 9. .000000027; 4.8. 70. .1728; .032. Ex. CLXXXIX. 7. 12.34.i56, 12.345.6, 12.3456. 2. 33.5175. 3. .000019737. 4. .00.365. 5. 005162. G. 45; 450; 4.500; 45000. 7. 421000. 8. 1144.90001605. 9. .68785. 70. .0000000000884. 208 AKITHMETIC. 4. .V. 6. 8. 4. 9. 3. 4. 6. G. 7. 8. !). 10 3. 9. 4. 8. 6. 8. 5. 10 4. 7. 11 9. Ex. CXC. J. 204.375 mi. il. 4'y'.i A'2') lb. 3. $7000. 270.40.) ft. 5. H64.H() ft. 6. 23. (52.') yr. 7. 4:{(}247.424 ^r. r)yO.U28 mi. 9. 993.12;') gal. JO. 2y7.2r)37r). Ex. CXCIII. /. ir>.24. ;.\ 3r)0000. 3. .413. 4. 330000. .024. 6'. 647r)3(;t)0000. 7. 12.34r), 1.234.^), .12345, .012345. 10.5. 9. 127.4. 10. .075, .0075, .00075. Ex. CXCIV. /. (5.165 nl. 2. 320 rd. 3. 42 bu. 144 bbl. 5. 87.5 bbl. 0. $128.50. 7. $27.5. 8. $10800. 15.75 bu. 10. 5.2 hr. Ex. CXCVII. /. I.^s. 9fd.; 15h. 3|(1.; £1 16s. 2id. 83 lb. 4 oz. ; 1 cwt. 74 lb. 14.4 oz. ; 3 t. 17 cvvt. 95 lb. 252 rd.; 80 rd. 4 yd. 1.2 ft.; 21 mi. 118 rd. 145 sq. rd. 6 sq. yd. 64.8 sq. in. ; 141 sq. rd. ; 13 A. 70 sq. id. 25 eii. ft. 540 eu. in.; 7d. 112 cu. ft.; 9 eu. yd. 20 cu. ft. 432 cu. in. 3 i>k. 1 gal.; 2 bu. 1 pk. 1 gal.; 5 bu. 1 pk. 1 gal. 3.2 qt. 3 qt. 1 pt. ; 5 gal. 1.4 pt. ; 7 gal. 3 qt. 11 hr. 52 min. 48 sec. ; 7 wk. 6 da. 3 hr. ; 9 wk. 6 da. 15 hr. 36 min. 58' .30"; 2" 5C' 51"; 17° 23' 15". . 3 ft. 9 in. ; 17 rra. 17 qr. 12 sh. ; 7 gro. 9 doz. Ex. CXCVIII. 1. £1..')25, £7.68125. 2. 9.854 t., 5.70375 t. 7.1109375 mi., 6.089 mi. 4. 9.3 A., 7.283 A. 7.875 cd., 7.0875 cu. yd. 6. 7.8125 l.u., 5.890625 bu. 27.875 gal., 14.375 gal. 8. 3.55875 da., 2.7725 wk. 3.8775% 17.12375°. 10. 5.8875 rm., 24.75 grs. Ex. CXCIX. 1. $.3380. 2. 10.3826 ft. 3. $59,375. The latter, 8.875 cu. in. 5. 3.2 lb. G. $24.80. 7. 83.75 yd. $322.28. 9. 199218.75 oz. 10. $186.15. Ex. CC. 1. $414. 2. $109.0625. 3. 75 sheep. 4. $161.6.')5. 50. 6'. $492.01875. 7.3720. A\ $53.25. 9. $i. i6^. 13.378A. Ex. CCI. 1. 67.75 A. 2. 28 vr. 3. $26484. 4. 7.39, 8.95. $10.32. 6'. Gain, $846,875, $12.50. 7. A., $75.87; B., $57.39. 16.5. 9. 1585584 cu. ft. 10. 8.6328 mi., 9.1872 mi. Ex. ecu. 1. $5. 2. $96,768. 3. 29.83 in. 4. 2.7 ft. 2.2968. 6. .5625, 33.75. 7. 15360. 8. 58 lb. 9. $24.60. . $192.78. Ex. CCIII. 1. 42.34. 2. 17.3. 3. 8.45, 5.65. 26.1 cd.. 24.65 ed. 5. 64 mi., 56.25 mi. 6. $340.05. $18.8325. S. .7875. 9. 4 ft. 3.2 in. 10. 92.4 vd. , $181.50, $77, $44. i^. 660 ft. ^5. 2446.875 lb. i4. 4A da. Ex. CCVII. 1. 444 sheep. 2. $103. 3. 225 bales. 288 boxes. 5. $216. G. 480 A. 7. 120 lb. 8. 200 A. 300. 10. 30 bu. ANSWERS. 209 td. )5lb. \. 70 sq. . 20 cu. 1(1 ft 1. 3.2 qt. da. 1;-) hi Ex. CCVIII. /. $1400. 2. $77(50. S. 120 A. 4. $:j:175. 6. $29500. 6. 4930 sheep. 7. 231 girls. 8. 20277. U. $717.25. lU. 73%, 876 sheep. Ex. CCIX. /. 061%. 2. 98%. S. 80%. 4. 50%. 5. '20%. 0. 12%. 7. 25%. H. 8%. y. 33i%. 10. 40%, 60%. Ex. CCX. 1. 70. ;^. $2500. 5. $500. 4. 800 A. 5. 450 sheep. 6'. $4500. 7. 150 Hues. ^. $1300. 9. 4500 sheep. i(>. 450 pupils. Ex. CCXI. /. 3290 bu. .^6%. 5. $72. ^.$20. 5. $12932.50. 6'. 48992 lb. 7. $125. H. $5400. U. $9000. 2(^. Lost, 12i%. Ex. CCXII. 1. 330 rd. 2. $372. 5. 10 lb. 4. 48 mi. 5. 2800 books. 6'. 224 men. 7. 1880, 2021. 8. 11|%. f^. 13752. 10. 9A%. Ex. CCXIIl. 7. $112.50; $216. 2. $292: $504. 5. $108. 4. $105. 5. $180. 6. $150 7. 4i%;374%. ^. $360. 9. $800. i6^. $3.75. Ex. CCXIV. 1. $270, $540, $547.20, $1051.65. 2. $557.46. 3. $10.26. 4. $3.20. 5. $25. 6". $6g. 7. $500. 5. $2.50. 9. 32i%. iO. 46%. Ex. CCXV. 1. $25.50. ^. $3.20. ,?. 28%. 4. 46.19%. 5. $20. 6. $7.56. 7. $850. .!?. $33i%. 9. $461.70. 10. $357, 47i%. Ex. CCXVI. 7. 25%. «. 15%. 9. 4%. iO. 42f. Ex. CCXVII. 1. $1.89. ^. $926.10. 3. $.38.28. 4. $3612.50. 5. $238. 6. $2719.50. 7. $60. 8. $900. 5. 9000 bu. 10. $4.20. Ex. CCXVIII. 1. $112. ;g. $8600. 5. $204.70. 4. $1007.50. 5. $75. 6. 12*%. 7. $330. .^. 40%. 9. 35^. i<?. $160, $208. Ex. CCXIX. 3. $168.75. 4. $115.92. 5. $12.50. (. $19.38. 7. $13.50. .?. 3%. 5. U%. iO. 3|%. Ex. CCXX. /. 3%. 2. 2\%. 3. 3*%. 4. $14400. 5. $8400. 6. $2592.80. 7. 84ct. 5. $7200, $216. 9. 156 members. 10. $3264. Ex. CCXXI. 1. $150. ^. $3650, $146. 3. $270. •^. 25000 yd. 5. 6000 lb. 6. 4100 lb. 7. 52000 yd. 8. $3500. ». $897.75. iO. $4000. Ex. CCXXII. 2. $80. 3. $66.25. 4. $225. 5. $675, $74325. 6. $22.50. 7. 11%. 8. %%. 9. i%. 10. |%. Ex. CCXXIII. 1. $16000. ;^. $3000. 3. $20000. i/. $14000. 6. $420. 6. $34737. .50. 7. $40000. 8. $2040, $5960. y. $75. 10. $2500, $3500, $4000. 210 AKITHMETIU. Ex. CCXXIV. /. i|i.'>4. 2. $150. .?. |19.r>0. /. !fir)23. 5. $tjr)2.50. a. $22. 7. $1H. J^. 14 milln. 'J. 12i mills. i^>. 17 J inlllH. Ex. CCXXV. /. $2800. ;-'. $2500. .i. $.544000. 4. $101. fiO. 6. $".)00. a. $13000. 7. $5075. 8. 6i inillH. U. $25. 10. $114.20. Ex. CCXXVI. 1. $0, $8, $.'{, $7, $7, $9. 2. $9. ./. $50. 4. $:i40. 6. $10. 6'. $5.39. 7. $15.12. 8. $38.88. f>. $13.20. 10. $4.0110. Ex. CCXXVII. /. $915.00. ii. $1012.05. 3. $2084.02. 4. $074.01. 6. $531.65. 6'. $425,050. 7. $1859.04. 8. $66. 0. $1910.20. 10. $1154.04. Ex. CCXXVIII. l.(S%. 2.1%. 3.H%. 4.61%. 6. Oi%. 6. 5i%. 7. 7i%. 8. 4i%. 0. 6%. iO. 6%. Ex. CCXXIX. i. 1 yr. 2. li yr. .?. li yr. 4. 5 mo. 6. 9 mo. 6*. 8 mo. 7. 115 da. *. li yr. 9. 150 da. 10. 75 da. Ex. CCXXX. 1. $540. i2. $055. 5. $850. 4. $360. 5. $840. 6. $750. 7. $876. *. $1825. 0. $219. 26?. $2920. Ex. CCXXXI. /. $2.50. 2. $405. 3. $540. 4. $572.50. 6. $1320. 6. $408. 7. $750. 8. $1742. f>. $.3050. 10. $.3212, Ex. CCXXXII. i. $126.10, $920.10. 2. $477.54, $2977.54. 5. $70.51, $1320.51. 4. $1724.05, $9724.05. 6. $112.55.09. 6. $5250. 7. $900. 8. $10000. 0. $4.32. 10. $124.05. Ex. CCXXXIil. 5. $751,875. 6. $1485.15. Ex. CCXXXIV. 1. $645.48. 2. $792.22. S. $180..50. 4. $.5579.42. 5. $508.69. 6. $115.48. 7. $325. 8. $570. 9. $1920.70. 10. $1053.77. Ex. CCXXXV. 1. $7828. 2. $6760. S. $7032.50. 4. $1248. 5. $2669. 6. $4750. 7. $3262.50. 8. $9750. 9. $20400. 10. $2,600. Ex. CCXXXVI. 1. $700. ;g. $2500. .9. $3500. 4. $.5600. 5. $2200. 6. 5. 7. 10. /?. 6. 9. 28. /fl. 15. Ex. CCXXXVII. 1. $200. ;2. $240. 3. $200. 4. $100. 5. $112. 6. 5^%. 7. 4^%. ^. 5%. 5. 5i%. Ex. CCXXXVIII. 1. $9100. «. $13310. 3. $11340. 4. $15570. 5. $11495. C. 60. 7. 70. 8. 220. 9. 500. Ex. CCXXXIX. 1. $10000. ;?. 124. 3. $18000; 720. 4. %%. 6. 1%. 6. 3i%. 7. $100. *. $540. 9. $4925. Ex. CCXL. 2. lUf. ;2. 83i. 5. 20Gf. 4. 5*%. 5. $2400. C. $1420i. 7. 50. 5. $29400. 9. 5%. 2^;. !!;)!00, Ex. CCXLI. 4. 3 inc. 5. 10 mo. C. 8 da. 7. 60 days after the debt is due. 8. 6 mo. 9. 02 du. ANSWERS. 211 ^2i. i, $101.60. 15. .h $56. 184.02. 8. $66. . 6%. 5 mo. da. JS360. iO. $2920. $572.50. 10. $:J212, p4, $2977.54. 2.55.09. 24.05. 80.. 50. ?. $576. 50. ;9750. 4. $.5600. U. $100. I340. I. 500. 720. |$4925. 10. t'WOQ. Ex. CCXLII. 1. 6 mo., 3 mo., 4 mo. 2. 120 da. S. 4 mo. 4. 5 mo. 5. Ap. 23. 6. Il2i dii. 7. 3* mo. ,y. 70 da. 0, H mo. Ex. CCXLIII. 1. B, $450; A, $600. 2. A, $189; B, $243. 3. A, $135; B, $125. 4. A, $85; B, $130; C, $60. 5. A. $864; B, $408; C, $1152. 0. A, $2600; B, $3400. 7. B, $650; V, $925. ^. A, $1750; B, $2125; C, $1125. !). $720. /^. A, $2662; B, $2420; C, $2200; D, $2000. Ex. CCXUV. 1. A, $17.50; B, $22.50. 5. A, $285; B, $150. ^- A, $25; B, $21; C, $54. 4. A, $75; B, $175; C, $330. 5. Equally. 6. A, $2200; B, $3000. 7. A, $1225; B. $875; C, $1050. *. 4 mo. 9. $1480. /^. A, $8445.94; B, $4054.05. It. $1800. 12. C, $16051^; 1), $1544^^; K, $1050. Ex. CCXLVII. 7. 80; 15625; .512; 343. 8. 6th. .9. 256. 10. 24th. 11. 49126081. 13. 128787625000. 13. .000000000016. 15. 10 A. Ex. CCXLVIII. 9. 3.05; .102; .571; .00563. W. 2.236; .707; .948; .094. Ex. CCXLIX. 1. 400. 2. 49j. S. 3202. ^. 24 yd. 5. 440 yd. 6. 200 rd. 7. 272 ft. 8. $160. .9. 144 id. 10. $324. Ex. CCL. 1. 75 vd., 25 yd. e. 220 yd., 44 yd. .9. H in. •/. 17 rd. 5. 1440 mils. 6. 280 rd. 7. 8030 yd. S. 15 ft. .'>. 221 yd. 10. 7712 yd. Ex. ecu. 9. .1; .06; 11.6; 36.3. 10. .928; .4308; .2; 1.709. Ex. CCLII. 3. 35.3. 4. 5476 sq. ft. 5. 564.")4 sq. ft. 0. 17 ft. 7. 60 in. cV. 9.2 in. 9. 12 ft. ^^. 15.75 in. 11. 37 ft. 12. 5 ft. i5. 12. 14. 36 ft. Ex. CCLIII. 1. 1521 sq. yd. ^. 29 sq. ft. 56 sq. in. 3. 1144 sq. ft. 4. 210 ft. 5. 2 ch. 40 1. 6". {(i) 229i sq. in. (/>) .54 A. (c) 20| sq. ft. 7. 5A' sq. ft. 5. 16 rd. 9. 80 rd. 10. $50. Ex. CCLIV. i. {a) 186 sq. ft. (^) 318^ sq. ft. (c) 5-A A. id) 7A A. i?. 50 in. 3. 57 in. 4. 92 rd. 5. 4300 sq. ft. G. 2145 sq. yd. 7. 1715 sq. ft. 8. .5541 sq. yd. .9. 203 sq. ft. 10. 56 ft. Ex. CCLV. 1. 44 in.; 66 in.; 11 ft.; 51* ft.; 73i ft.; 14 eh. 961. 2. 7 in.; 17i in.; 19J ft.; 1 ch. 7U 1.; 7 vd.; 21 vd. 7 in. ^>. 24i min. 4. Ill rd. 1 ft. 10 in. 5. 5 ft. G. 72. 7. 4lf ft. 8. 84 yd. 9. 12 ft. 10 in. 10. 22 in.; 33 in.; 55 in.; 06 in.; 110 in.; 121 in. 212 ARITHMETIC. Ex. CCLVI. 1. 9()2i Hq, in.; 138(5 sq. in.; 3850 sq. in. 5544 sq. in.; 8(502^ sq. in.; 154 sq. in.; 346i sq. in. 471f sq. in.; J)62i sq. in.; 7546 sq. ft.; 154 sq. in. 38i sq. ft. ; G8^ sq. ft. ; 861 sq. ft. ; 1386 sq. eh. 2. 26M sq. yd. 3. 88 rd. 4. 59.4 in. 5. 308 sq. in. 6. 62.04 yd. 7. 246.66 yd. cS'. 277.^:. U. 110 sq. in. 10. $838^ Ex. CCLVII. 1. («, 85; (/>) 650; (f) 1730; {d) 698. 2. (a) 528; (/>) 1230; (c) 44; (r/) 144. 5. (a) 456; (/>) 782; (c) 390; (<0 225. 4. 29 mi. 5. 35 ft. 6.274 ft. 7. 20.7J^in. ,?. 11.18 ft. .9.10 ft. i^>. $54.60. Ex. CCLVISI. 1. 9H eu. in.; 34fi cii. in.; 14 cu. ft.; 197 cu. in.; 68 cu. ft.; 145 cu. iu. 2. 121i sq. in.; 63| sq. in.; 35a-4 sq. ft.; lOOA sq. ft. S. 311 cu. ft.; 99^ sq. ft. 4. 131i eu. ft.; 18U sq. ft. 5. 20 in.; 4^f eu. ft. 6'. $41i. 7. 16| ft. 8. 25i ft.; 17 ft. 9. 28.09 in. 10. 1650 gul. Ex. CCLIX. 1. {a) 8f eu. ft.; (ft) 115i eu. ft.; (c) 385 cu. ft.;. ((0 13311 cu. ft. 2. {a) 29* sq. ft.; (/>) 132 sq. ft.; (c) 220 sq. ft.; (^0 183* sq. ft. 5. 5f^ cu. yd. 4. $66. 5. {a) 31^ sq. ft.; (6) 15U sq. ft.; (c) 297 sq. ft. ; {d) 196 sq. ft. 101 sq. in. 6. 91^ sq.ft.. 7. $24.75. <f^. 1 ft. .9.1yd. i^. 14|cu.ft. Ex. CCLX. 1. 108 eu. ft. 2760 eu. in. 3. 75 sq. ft. :>. 89^ eu. ft. 4. 33 sq. ft. 5. $33.75. 6. 19250 cu. in. 7. (1) 861 sq. ft.; (2) 33 ft. 8. 89.51 yd. 10. 61 in. Ex. CCLXI. i. (a) 154 sq. in. (/>) 38i sq. in. (c) 616 sq. in. id) 2464 sq. iu. 2. $24.64. ^. 14 ft. 4. 132 ft. 5. (a) 905|eu. iu. {b) 3620teu. in. (c) 1437ieu. in. (d) 179lreu. in. C. 4851 cu. ft. 7. 14f eu. ft. 8. 4 in. 5. 110592. 10. 2541. Ex. CCLXII. J?. 92.9 ft. 2. 88 yd. 3. 68 yd.; 867 sq. yd. 4. 391 ft. 5. 75 ft. 6. 43.3 sq. ft. 7. 32 ft. 8. 98 yd. 9. 820 in. 10. 1120 yd. Ex. CCLXI 1 1. 1. 43 ft. ,?. 242 yd. 3. 5. M mi. 6. 4.24 ft. 7. 140 rd. 8. 4 ft. i(^. $3.30. Ex. CCLXIV. 1. U ft. 2. 3 in. tiles. 4. 704 sq. ft. 5. 170 ft. 6'. 14175 sq. ft. $22f. 4. 25. 9. 8063i lb. 3. 126 ft. 7. 5544 sq. ft. 8. 79194 sq. ft. 9. 140 sq. ft. 10. 3461 sq. in. /. 80 ft. 90 ft. 2. 5 A. 3. 8232 sq. ft. 89.44 rd. 0. 1560 sq. in. Ex. CCLXV. 4. 28 sq. ft. 5 7. 65 ft., 68 ft.; 60 ft 10. 1121 ft. 80 rd.; 120 rd. 8. 72 ft. 9. 2646 S(i. in.; 4376 sq. in. sq. in-; H sq. in.; 4 sq. ill-; h. 'lO. $838 J. 198. 5. 35 ft. $54.60. -u. ft.; 197 ft. ft. ft. ; 17 ft. (c) 385 cu. 132 sq. ft. ; L51i sq. ft. ; lieu. ft. rS sq. ft. oil. ft. ;) 616 sq. in. I) 179"ncn . 10. 2 . in 541 ; 867 sq. 98 yd. yd 4. 25. 3i lb. ft. sq. ft. sq. ft. |)0 sq. in. 4376 sq. in. ANSWERS. 213 Ex. CCLXVI. 1. 63 ft. 2. 308 sq. ft. ; 385 sq. ft. S. 246.66 yd. 4. 3630 men. 5. 4800 ft. 6". 40 rd. 20 rd. 7. 2.18 ft. 8. 12 ft. 9. $28.32. 10. $32. Ex. CCLXVII. 1. 52 ft. 2. 10.39 yd. S. 23.54 ch. 4. 'ih eh. 5. 56 yd. 6'. 42 ft. 7. 414.12 ft. 8. 21.213 ft. 5. 292i sq. ft. 10. 48i c. ft. 1. 38i sq. ft. 2. 34.64 in. 5. 27.71 in, 5. 1925 lb. 6'. 864. 7. 192000 shot. Ex. CCLXVIII. 4. 37i It. ; 30 ft. 8. 243 doz. a. 12 in. i^. 48 oz. Ex. CCLXIX. ;g. (1) 456 cm., (2) 45.60 dm., (3) 4,560 ni. ,9. (!) 18.7 m., (2) 18700 mm., (3) 1870 cm. 4. 1897009.434 ni. 5. 780.43 m. ; 11.03 mm. 6. 92.208 m. ; 299.18892 m. 7. 640 leaves. 8. 27600 times. 9. $76.56. 10. 7.6375 m'. 11, $555705. 12. 28000 times. Ex. CCLXX. 1. 287.6.345 hectares. 2. 37856 ares. 3. 57536 sq. cm. ; 5753600 sq. mm. 4. 2341700 sq. m. 5. 542 sq. em. 6. 3030303 sq. m. 7. 112 ares. 8. 32.64 sq. m. 9. $2.50. 10. 280500 bricks. Ex. CCLXXI. 1. 72.5 st. 2. $432.50. 3. 25800 1. ^. 23.375 c. m. 5. 2.604 m. G. 1.40 c. m. 7. 30 em. 8. 300 HI. 9. $275.31. 10. 8 ct. Ex. CCLXXII. 1. 5037 j?. ; 503.7 Dj?. ;?. 3075 mg. ; 30.75 (Ijr. 5. 8070006.5 eg. 4. 2.756 Kg. ; 275600 eg. 5. 7.28 1. 6. $750. 7. 264.6 Kg. 8. $420.15625. 9. 310 mg. 10. .00504. Ex. CCLXXIII. 1. (a) 70.25 m. (6) 808.7 1. (c) 15.908 a. ((0 27000.37 g. 2. 594 Kg. 5, 47250 Kg. 4. 2100 coins. 5. 388 g. «. 110 st. 7. 225 francs. 5. 33 HI. 9. 650 g. /^. 200 m. 11. 50 ct. 12. 190 mi. iJ. 477 times. 14. 13.44 rolls. Ex. CCLXXIV. 1. .3, .45, .96, .765. 2. .4, .142857, .285714, .42857i. 3. .571428, .714285, .857142, .076923. 4. .230769, .384615, .692307, .63. 5. .83, .583, .9318, .9287514. 6'. .9428571, .954, .89285714, .15990. 7. .7083, .4196428571, .54861, .164772. .S'. .44230769, .72li53846, .1392045, .3809523. .'>. .20238095, .8270, .14076.5, .505067'* 10. .170138, .686789772, .35267857142, .20145. 214 ARITHMETIC. 1 1 16 1 n , 3r, TIT, 1 1 1 Ex. CCLXXV. i . § , H , T I , f 1 . ^ o2 1810 8 ^35 47 S9 89 «3- 3T> 5T, i?, ?7. 4. ]JT, Til, 5T, 111 r9»1218 /J81198110 5. TIFT, TI, T, T. O. 8 2, 36, tz, 4 1. ^ 583 61 14 41 o 89 1 389 81 7- Tffff, 360", ^25, SffOTT. o. 44, T4g, iJSff, '10. o 36 43 Oil 735 7/1 /|1- f^l 72 r;5 ^- 44, "SSff, -^Jf, 'IT- -tl'- "ITSO, JT63, '353^, «^1S. Ex. CCLXXVI. i. 0.60244. 2. 2.3060941229258. 3. 9.4H69; 14.0636727. 4. .32457; .32147. 5. .73231777. 6. 1.590; 6.893. 7. 339; .429. 8. .4675; .350649. D. 63; 10. 10. .54175; 7.805. Ex. CCLXXVII. 1. 10.5. i?. .42. 4. .161; .03. 6. 33.142857.7, £2 Os. 8|. 6'. 3 t. 8 cwt. 35.3 lb. 9. 6 mi. 92 rd. 1.6 yd. 10. 69 t. 888.8 lb. Ex. CCLXXVIII. 6. 7.456. 9. 13. Ex. CCLXXIX. 1. $3780. S. 9215 cii. ft. 3. $132, $247.50, $275. 4. $100. 5. .0078125. 6. 33 mi. 7. .405 hr. 8. W-A'^n. 9. .00129. Ex. CCLXXX. 1. A. 2. h dii. S. 3* da. •^. 14.7 da. 5. L 6. A 27 da., B. 54 da. 7. A 19^ da., B 9|da., C 39ida. 8. 4i da; 9. 18 da. 10. 4i hr. 11. A 361 da.; B 73i da.; C 110 da. 13. 15 da. IS. 32 hr. i4. li hr. ^5. 8 horses. 16. A 3A da.; B 3^^ da.; C 5h da. 17. A $1.10; B $1. Ex. CCLXXXI. 1. 12imn.; 24.min. ; 30 min. ^. 18 min. 3. 16ri min. past 3. 4. Wrx min. past 6. 5. 32 1\ min. past 6. 6. 24 min. past 6. 7. 24 min. past 6 and 41n- min. past 6. .9. (a)43i^i min. past 8, (?>)27A min. past 8, (c) lOi? min. past 8. 9. 49n min. past 9; 541*1 min. past 10; 12 o'clock. 10. 23 ra min. past 5. • Ex. CCLXXXII. 1. 13A- min. past 4. 2. 19fi- min. past 3. 3. 3I2-3 min. past 3. 4. 120 da. ; 44 min. past 11 ; 14 min. pnst 12. 5. 75 da. 6. 36 min. past 6 a.m., Friday. 7. 5A min. past 5. 8. 5i min. past 9 p.m. on Tnesday, and 57i min. past 8 p.m. 9. 3 p.m.. May 3. 10. 43MH- min. past 9 p.m. Ex. CCLXXXIII. 5. 14 min. 24 see. 10. Gains 10/.,% min. Ex. CCLXXXIV. 1. 44 ft. S. 34 A- mi. 3. 22h 4. 0. 8 lir. 7. 33: mi. 8. 7h yd. 9. i'l sec. t J M ~ 5. 41 mi. 0, nil. /. 224. 141. 2. 4 mi. ,1. J mi. ^. i hr. 7. 45 iiiiii. 6'. 3 mi. .V. 5tol. tO. '2k hr. ANSWERS. 215 1 1 6 riT, T 1 1 n 5 1777. 14.7 da. .,C 39^ilii. 3. 32 hr. ; C oh dii. 2. 18 mill. mill, past 8. lin. past '.5. nil. pjist 12. |min. past 5. ist 8 p.m. 4. 7i sec. li. 4. i liv, to. 2i hr, Ex. CCLXXXV. 1. l! mi. 3. 45 mi., 36 mi. 3. 114 yd. 4. 45 mi. 5. 11 min. 6. 396 ft. 7. 94^ yd. .?. 22 mi. 9. 23i mi. 10. G'i mi. ii. 6| hr. Ex. CCLXXXVI. 1. $1.92. 3. 325, 175, 125. 5. $620. 4. 74; 3s. 8jd. 5. 17. 6. 23. 7. £16 6s. ,S. 1980. 9. 2 hr. 24 min. it*. 200 lb. Ex. CCLXXXVII. 1. 144 min. 2. Men, $12.50; women, $8; boys,$5.25. 5. 7bbl. /. 1022. 5.75yd. 6'. 32da. 7. 17 mi. 8. $80. 9. 110 sheep, 140 pigs. 10. $51. Ex. CCLXXXVIII. 1. $12800. 3. 123 gal. 5. $672. 4. 720 apples. 5. $75. 6. £140. 7. $97.50. 8. 223 sec. •O. John, $880; Thomas, $176; Henry, $22. 10. 56 et. Ex. CCLXXX!X. /. $27. 3. 26 ft. 6 in. 3. 4 ft. 1 in. 4. 15 ct. 5. 2C88 rails. 6. 20, 21, 22, 23. 7. 182. 5. $60. ,9. 7875 shingles. 10. 150 lb. Ex.CCXC. i. $90,$60. 2.3m\. 5. 87 da. 4. Latter, 51 ct. 5. $20.0246. 6'. $8460. 7. $870, 6%. ,?. $2.50. 5. 19 da. Ex. CCXCI. 1. $900, $1350, $1800. 2. $36. 3. Gain, 72 ct. ^.230400 A. 5. 49.90 rd, 37.43 rd. 6. $2.50. 7. 100 ft. by 76 ft. 8. $321.25. 9. $354. 10. $7.50. Ex. CCXCII. 1. A, 30 ct. ; B, 36 ct. ; C, 40 et. 2. 160 leaps. •S. $2450. 4. vm see. 5. $500. 6. 80c. 7. U yd. 8. 900 lb. at 7 ct. ; 1100 at 10 ct. 9. 248 yd., 62 yd. 10. $440. Ex. CCXCIII. /. .396 ft. 2. $329. 3. Divisor, 547; Qiiot., 3233. 4. $4J-. .5. $23.50. 6'. A's rate is to B's as 79 to 60. 7. 409036320 post-holes. 8. A, $432; B, 216; C, $1296. 0. $1680. 10. $300; $450. Ex. CCXCIV. 1. 294; 84. 2. $900, $750. 3. $200. 4. ,^,?, . •5. $400. 6. $240, 5yr. 7. 2i in. ,?. 300 leaps. 9.9hv. 10. 2imi. Ex. CCXCV. 1. $4.80. 2. 8%, 9%. 3. 31^-%. 4. 3060,^j bn. 5. 224. 6. 60 mi. per hr. 7. 16j da. 10. A, $776.16; B, $693; C, $630; 8. 813i cu. yd. 9. 4fo da. D, $600. Ex. CCXCVI. 1. 405 bu. 2. 24 ft. by 18 ft. by 12 ft. .?. 4.5eii.ft. 4. Gain, $14. 5. 8000 oranges. 6. 5Jts. ; 56 oz. gold; 160 oz. silver. 7. $2480. 5 U mi. per hv. 9. 20 min. past 4 a.m. 10. $217.80. Ex.CCXCVII. /. 1152 sq.ft. :?. 4%. 3. -i^^. ^.14.625 in. 5. I?; 675. G. 14.288 to 1. 7. 48jct. <S'. $3i. i?. $1.80. 10. 190. Ex. CCXCVIII. i. 272 rd. 2. 111. 3. 24 ct. ; loss, A% . 4. Length, .34 ft.; width, 26 ft.; height, 12 ft. 5. 4^ mi. 6. 3G75§ t. 7. $441. 8. 63 yr. ; 35 yr. 9. 567 leaves. 10. 104 da. 216 ARITHMETIC. Ex. CCXCIX. /. 213 plants. ;2. $4500. 3.2imi. 4.1001b. 5. 28 ct. 6. $2625. 7. $4000. 8. .384 In. (Note, their length and width being equal.) 9. 164.7114 in. 10. A, $1035; B, $1656; C, $2025. Ex. CCC. 1. 2 to 5. 2. 13tV niin. past 4, or 30 min. past 4. 3. $40. 4. 5 yd. 3. $1.02, 80 ct. 6". $3250; $2600. 7. 233H ft. 8. 3 to 2. f?. 2i ft. iO. $1600; 15 mo. Ex. CCCI. 1. A-. 2. A, $2,901; B, $5.09f. 3. 10 mo. 4. 10 in. 5. $3. 6.90. 7. 3 hr. ,?. 5251b., 4951b., 3901b. 9. $2100, $1750, $1050, $700. 10. B, by 50 yd. in 4i min. Ex. CCCII. 1. 141.4 sq. ft. 2. A, $600; B, $780; C, $180; D, $2000. 5. $2000; $1296. 4. 4%;4i%. 5. 60et. 6. 32 men. 7. 15i mi. 8. $62500. 9. 11 J min. past 12. 10. $9r3 ; $9|. The End. 4. 1001b. a.) min. past 4. 7. 233H ft. 10 mo. , 390 lb. I min. ; C, $180; 6. 32 men. >r3-; $9^.