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JOHN, N.B.; FOR SALE BY T. A. HALL. 1861. fcV,.- A^ 1* ;ii J.w. Lawrence coi lection PREFACE. L.w: The ibUowing little work has been prepared, tinder the direction of the Board of Education, by a committee of the teachers of the St. John County Institute, with a view to meet the want arising out of the adoption of the Decimal System of Computation in the Province. From the familiarity of teachers with the general arrangements of the small Arithmetic of thd Board, that volume has been made the founda^ tion of this; but; besides its adaptation to the altered currency, some new and original ques- tions have been substituted for those considered of less practical value, by which arrangement, it is hoped, the work has been somewhat im- proved, while no addition has been made to its bulk or price. Great care has been taken to keep it fre^ from typographical and other errors. John Bennet, Chi^SupL Education Offiob, Fredsbioton, 1861. 8 CONTENTS. V I i *- PAOI Signs used in Arithmetic. 5 Addition Table 5 Multiplication Table ....... 6 Money Table 7 Table of Weights and Measures, Ac 7 Notation and Numera- tion 10 Simple Addition 13 Simple Subtraction 18 [ Mixed Questions in Addi- I Uon antl Subtraction . «2 I Simple Multiplication 23 :' Simple Division 28 New Brunswick Currency 34 ! Beduction 35 Compound Addition 39 Compound Subtraction 42 Compound Multiplication 44 Compound Division 47 i Mixed Questions on the ^ Compound Rules 50 Simple Proportion 51 * Compound Proportion 57 ^ Bills of Parcels 59 s Bills of Book Debts 60 Practice 61 Simple Interest 62 Compoiind Interest 65 Discount 66 4 P*«B Commission, Brokerage, Insurance, Buying and Selling Stocks 68" Barter .,.. 70 - Profit and Loss... 71 Partnership, , or Company Business.... ^'..... 73 ExchaiiE^e 75 Vulgar Fre^tions 77 Reduction.., 78 Addition.... 82 Subtraction .1 83 Multiplication 83 Division..... 84 Reduction — continued 84 Decimals 88 Addition 89 Subtraction....... 89 Multiplication..... 89 Division..... 91 Redukiou.. 92 Involution.' 95 Evolution . I.. 95 Extraction of the Se- cond or Square Root 95 Extraction of the Third or Cube Root 97 Duodecimal Multiplication 98 Answers to all the Ques- tions 100 ira oun .8pou 4 qua 20huii 14 poundG 112 poundE This weij general, I Wool is 1 ■r lamiHllVi,! illftlliVnilrtilii rrr V » ' impp^^^*^ TABLES. 7 lONBT. r 1 penny. — 1 shilling. =r 1 crown. = 1 pound. '^ == 1 guinea. Qgs, and d. pence. >r one quarter of any thing, or a half of any thing, -gs, or three quarters of any thing. BRUNSWICK MONET. cents = 1 dollar, — $. * OR UNITED STATES MONET. marked nills (m.) = 1 cent. et. 'cents = 1 dime. d, J dimes = 1 dollar. $ ^ 10 dollars = 1 eagle. JE. • AVOIRDUPOIS OR QROGBRS' WEIGHT. marked irams (dr.) = 1 ounce. oz, ounces =1 pound. lb. .8 pounds =1 quarter. gr, 4 quarters, or 112 lb. = 1 hundredweight, cwt 20 hundredweight = 1 ton. T. 14 pounds make one stone, and 8 stone 1 hundredweight. 112 pounds make one quintal of dried fish. . This weight is used for bread, meat, groceries, for goods |a general, and for all the metals exoiept gold and silver. Wool is bought and sold by this weight. TROT OR goldsmiths' WEIGHT. « marked 24 grains (^r.) = 1 pennyweight, dwt. 20 pennyweights = 1 ounce. oz. 12 ounces = 1 pound. lb. !piis weight is used for gold, silver, jewels, and liquors. \\ ■i 1 * ' I'iMlilMriTiifiliirii ■MMMta I iiiiwia^i Ti'-i"" ^._ci!.w.,...-L»i;...-^- ,, — -.,. "•^T" t A&ITHM apothboabiib' <^ 20 grains z= . 8 Borupleit z^ 1 8 drams = 1 12 ounces = 1 1. Apoiheoaries «« this weight but they buy and sell by ayoirdi LOirO MSASUI I ' ;;♦ ^ 12 lines 12 inches > 8 feet 6^ yards V 40 perishes ^ 8 furlongs 8 miles 60 geographical miles» or \ 69^ British miles / 860 degrees lin Ifoc 1 yar 1 perc 1 furlo 1 mile. 1 league. 1 degree. the earth's ci An inch if supposed to be equal to three ba in length. Four inches make one hand, usea suring horses. / CTLOttt MSASUBB. marked ^l tnohes ^= 1 nail. nl. • 4 nails =2= 1 quai^er. qr, 4' q«n»ters^aa 1 yard. ffd. The Flemish ell is 8 quarters of a yard; the DngUj ( ell, 5. quarters of a yard; and the French ell, 6 quartej ' of a yfurd. SAtTAR^ OR LAN1> HBA8UBB. 1 square foot. 1 square yard. 144 square inches 9 square feet = 1 square yard. ♦ S0\ square yards = 1 sq. perch, pole pr rod. 40 square perches = 1 rood. 4 roods 640 aores^ 1 acre. 1 square mile. markM "sq. ft 9q. y< aq. pi rd. ac. • ■ ttewri^niilifi^iiiiiiMl r ithiii ARITHMETICAL TABUE8. ir re rlo Lie. , ague. 1 gree. earth's 01 to three ba hand, usea marked nl, BT. qr. a yard; the t!ng£i renoh ell, 6 quartc L8UBB. market "tq. ft, 9q. y< »ole or rod. tq. pt .. rd, ac. \ 1728 eubio inches 27 oubio feet The square of any number is obtained by multiplying it by itself. 12 multiplied by 12 = 144, the square of 12. OUBIO OB SOLID MBASUBB. = 1 cubio foot. = 1 oubio yard. 40 oubio feet of rough timber, or \ m ±^„ , i . j 60 cubio feet of hewn timber / =* ***"*' **' *®**' 42 oubio feet =1 ton of shipping. 128 oubio feet = 1 <^ord of wood.* Cubes are solid figures, similar to dioe, and have six equal sides. The oube of jtny number is obtained by multiplying it twioe by itself; thus, 12 X 12 X 12 = 1728, the oube of 12. MBASUBB or OAPAOITT. marked 4 gills = 1 pint. pt, 2 pints = 1 quart. qt. 4 quarts =: 1 gallon. yal. 2 gallons = 1 peck. pk. 4 peeks = 1 bushel, btuh, ' 86 bushels = 1 chaldron, chald. The gill, pint, quart, and gallon are used for liquids. The peck and bushel are used for pojtatoes, oats, salt, &o. The chaldron is only used for coal. The gallon contains 277.274 cubio inches. TIMB. 60 seconds ('^) 60 minutes 24 hours 7 days 12 months, or 62 weeks and 1 day, or 866 days Every fourth year contains 866 days, and is called leap-year. marked 1 minute. mm. 1 hour. kr. 1 day. da. 1 week. wk. ]- 1 year. yr. • The legal oord in this Province is 8 X 4 X 4i ^^t or 188} enbio jMt. l<^ NOTATION AMD NUMEBATION. DATS Ur 1X08 MONTH. Thirty days hath September, April, June, and November ; All the rest have thirty-one, February twenty-eight alone. But in Leap- Year twenty-nine. DIVISIONS or TUB OIBOLB. marked 60 seconds (/^) = 1 minute min. or ' 60 minutes = 1 degree. deff. or ^ 80 degrees = 1 sign. S. 12 signs = 1 circle of the zodlfto. 0» , QUANTITIES. msrked 12 articles = 1 dozen. doz. 20 articles = 1 score. *e. 144 articles = 1 gross. gr. 24 sheets paper — 1 quire. gr. 20 quires = 1 ream. Tm, 196 pounds = 1 barrel of flour. 200 pounds = 1 barrel of pork { [)r beef. /. f' ^ I; n' NOTATION AND NUMERATION. Notation is the expressing of numbers by cer- tain characters. Numeration is the reading of these characters. There are two systems of Notation in use* among us, — viz. the Roman and the Arabic. By the Roman Notation, numbers are expressed by seven capital letters, — viz. I, V, X,.L, C, D, M; the re- lative values of which are, — I = one, V = five, X = ten, L = fifty, C = one hundred, D = five hundred, and M == one thousand. NOTATION AND IIVMKBATION. n The Arabic Notation uies ten jBgtiTeB, and is the method in common use. The figures are f, 2, 8^ 4, 6, 6, 7, 8, 0, 0. The value of these figures depends upon two things : firstf what the figure itself expresses ; and, titondy what position it is placed in with respect to a certain point ex- pressed or understood to evi^i'y number^ In reading figures, we group them into periods of three figures, (one for units, one for tens, and one> for hun- dreds,) and we give each period or group of them a sepa- rate name ; thus,-— r WHOLB KUMB1B8. Increasing to the left. MBOIKAtS. M Period, lilUloni. 3d Period. Tbovwnd*. lit Period, QnlU. f. Jl^^Becreasing to the right. lit Period, 3d Period, 8d Period, • .TkMiftndtbe. MUllontbs. BllliouUii. ! : : s \ \ : 1 5 2 8 5 5 2 : 4 6 8 6 4 2 2 7 6 6 8 6 4 8 7 9 6 ,67046 4 6 6 8 6 4 6 7 8 4 : 6 : 7 2 6 8 8 7 6 8 6 6 7 8 6 2 8 6 4 6 9 8 6 4 2 6 8 4 2 8 4 9 7 7 8 8 7 68 6 246784 . 42 6 04878^ ^ Let the pupil be required to read and write this exer- cise in as many different ways 4ts the figures can be read uid written, the teacher Ulustrating on the black-board, especially with reference ^ the decimals. BXXBOISSS IN NUMSBATION. Ready or write down in wordSf the numbers tignified by the follomng figures : 1. 1, 2, 8, 4, 5, 6, 7, 8, 9, 0. • 2. 10, 11, 14, 16, 19, 20, 42, 18, 17. 12 8. 4. 6. 6. 7. 8. 9. 10. 11. 12. 18. 14; 16. 16. 17. 18. NOTATION AND NUMERATION. 200, 420, 607, 886, 478, 247, 864. 9i2, 874, 788, 660, 202, 604. 610. 4000, 2700, 8601, 7036, 2101, 1060. 1010, 7080, 4600, 9111, 4076, 6870. 26012, 70101, 4S100, 86100, 90201. 700000i 701020, 9264.27, 104.206, 9000000, 9764.268; 8202100, 6023.067. 2600060, 4101010, 2004000, 14021.49. 40000000, 2960.28o7» 6002.6017, 167.002. 9412.68767, 267602.r>07, 401467680. 2960.26876, 710020010, 270603060. 14028.6074, 8460760010, 4023.601497. 704260.8714, 6079607.906, 1704070600. 81462306012, 4600768. V681, 94086121360. 14028641201, 20860002001, 400020.00202. 907060.206204, 240026.100201, 690960126020. SXEB0I8ES IN NOTATION. Express hy figures th&follotcing numbers. 1 . Six, — seyen, — nine, — eight, — five, — ten, — twelver*- fourteen, — sixteen,— -eighteen, — twenty, — nineteen. 2. Seventy-four, — twenty-six, — ^thirty-one, — forty-nine, — fif*y-eight, — sixty-two, — seventy-six, ■— seventy-seven, — r t'xety-seven, — eighty-four, — fifty-five,— ninety-nine. r. One hundred, — one hundred and four, — two hundred and I'orty-four, — six hundred and ninety-one, — seven hun- drec' and fif>j' -Dine hundred and nine, — nine hundred and iiU7ety-»iiii*.. -^ight hundred and two. 4. Foui t?iW5and, — ^our thousand two hundred, — nve thou3a< < $18.15o. $40.26o. $181,190. 628.143 63.26 73.84 284.82 486.821 41.76 28.61 667.66 673.460 82.12 84.62 842.24 519.875 166.27 226.73 1946.40 2807.799 $64.28c. $48.61o. $624.48o. 864.21 98.63 64.28 446.30 78.346 83.41 91.46 679.84 264.7 64.24 84.25 821.76 405.638 ^ (^^ (2) ^ (3) (4) $412,030. 246 $623,290. 854 846.68 326 . 146.03 236 427.76 678 (6) 460 679.42 875 • 264.64 547.804 il 368.003 407 653.673 479 762.74 679 866.407 627 866.696 636 (10) 467 276.306 894 (9) $246,730. $47.61o. (i|) 78.21 608 . 602.84 70 604.48 92 68.25 926 40.30 400 720.36 47 7.91 78 (14) 79.24 5 (13) 6129 (15) * (^^) 4268.342 8687 $2407.600. 7142 2426.208 ' 4215 798.24 9687 4276.46 708 . 46.38 4312 8607.2 9362 7083.07 8687 2390.4146 96 579.15 16 NoTB.— In adding or subtracting decimaln, tho fignres must be pnf down BO that tlie decimal points shall stand diructly under each other. 16 07) 6126 1472 6826 9687 2764 4279 42674 84126 68768 28642 65768 74387 96728 (22) 24786.48 66843.242 26879.66 43663.219 68764.846 66287.36 66423.142 SIMPLE ADDITION. 2427 768 9412 893 4026 475 >036 784 6070 85 7507 687 (23) $48763.140. 86270.26 4687.38 678.24 49060.66 18709.67 70471.38 r80 6708 1070 687 5368 769 (24) 46637 54263 43986 6079 81 641 98076 . 26. How many do 7 and 4 and 8 and 24 and 62 m^.ke ? 26. How many are 42 and 64 and 40 and 68 and 79 ? 27. How many do 67 and 79 and 93 and 104 and 65 make? 28. How many do 426 and 67 and 240 and 742 make ? 29. Add together 6479 and 846 and 70 and 667 and 7426. 30. Add 742c. -f 64c. -I- 80.+ 341o.+ 804c. + eOo.-f 643c. -f 790c. -h 806c. 31. Add $7260 + $1404 +$8496 -|-$2413 -f- $46 -j-$4786 -f$3326. 82. Add $4126 + $27804 -f $2687 + $426 + $846846 + $746897. . 33. Add $76876 -f- $20464-$896874+$6876874 + $4268 +$4276. 34. Add 367068c. + 64708c. + 94687c. + 6870c. + 2489c. + 264c. 36. What is the amount of four hundred and sixty- three, — five thousand and sixty-four, — seventy thousand and ninety-eight, — and fifty ? L^«E, SIMPLE ADDITION. 17 ^6. Add together seyen hundred and ninetjr-siz, — ^five thousand four hundred and forty, — nine hundred and eight, — five thousand four hundred and nine, — two hun- dred and two thousand and fifty, — ^ninety-six thousand an*^ nine, — four hundred and one. ' 87. How much do the following sums of money amount to, when added together? $79.66,-|-$86.40,4- $4.60,4- $20. 48,+$468.97. 88. I saw four large baskets full of apples ; in one of the baskets there were four hundred and ninety-four apples, in another three hundred and sixty-eight, in another nine hundred and eighty, and in another four hundred and four ; fiow many apples were there in the four baskets ? 89. I gave John 12 apples, James 15, Patrick 20, and I had still 25 remaining ; how many apples had I at first ? 40. If you buy a yoke of oxen for 75 dollars, a caTrt for 57, thrde cows for 88, and a plough for 10, how much must you pay for the whole ? 41. A merchant owes one man in Dalhousle 975 dollars, one in Woodstock 483.25, another in Fredericton 237.15, one in St. Andrews 87, and another in St. John 689 ; what is the amount of his debts ? 42. If your debts to different persons are as follow, 2756 dollars, 1000 dollars, 75 dollars, 467 dollars, 895 dollars, and 5832 dollars, how much is the whole that you owe ? 48. A fruiterer bought six chests of oranges. In the first chest there were 468 oranges ; in the second 679 ; in the third 804; in the fourth 979; in the fifth 104^; in the sixth 1709 ; how many oranges were there in all the chests ? 44. A gentleman planted on his property 478 oaks, 748 beeches, 64027 firs, 409 apple-trees, 1764 pear-trees, 878 cherry-trees, and 87 peach-trees ; how many trees did he plant in all ? 45. In a' house there were nine windows in front, and each window had twelve panes of glass. In the rear 2* 18 SIMPLE SUBTRACTION. M ' ' l' there were six windows, and each of these windows had nine panes of glass ; how man;^ panes of glass were there in all the windows ? 46. If a boy receive a present every New Year's day of $125, how much money will he possess when he is twenty-one years of age ? 47. A linendraper sold 46 yards of cloth on Monday ; 78 on Tuesday ; 65 on Wednesday ; the same quantity on Thursday; 64 on Friday; and 97 on Saturday; how many yards of cloth did he seU during the week ? 48. A grocer received for goods sold on Monday $16; on Tuesday $24; on Wednesday $4P; on Thursday $36; on Friday $52 ; and on Saturday as much as he had re- ceived all the former days of the week ; how much did he receive during the week for goods ? SIMPLE SUBTRACTION. SuBTARCTiON is the method of finding the dif- ference between two numbers. MENTAL EXERCISES. 1. Tom had 16 marbles, and gave Dick 7 of them ; how many had he left ? 2. A man bought a cow for 12 dollars, and sold her for 21 dollars ; what was his gain ? 8. A boy has 5 nuts in one pocket and 8 in another ; how many more has he in one pocket than in the other, and how many in both ? 4. John is 18 years old, and George is only 6; how many years older is John than George ? 6. A man owing 48 dollars paid 19; what had he to pay? SIMPLE SUBTRACTION. 19 From 6237 take 4895. KuLE WITH Example. — Place the less number under the greater, so that units may stand under 6237 units,- tens under tens, &c. Draw a line under 4895 them. Begin at the units' place, that is, at the 5. Take 5 from 7, an^i 2 remain. Put down the 2 under 1 342 the 5. Oo on to the next figure, which is 9. Take 9 from 3 ; this cannot be done ; when this is the case, add 10 to the upper figure, which will make it 18. Take 9 from 18, and 4 remain. Put down the 4. Whenever 10 has been added, as it was to the 8, 1 is to be added to the next figure. Thus, add 1 to 8, which makes 9. Take 9 from 2 ; it cannot be done; then, as before, add 10 to the ^. Now take 9 from 12, and 3 remain. ]?ut down the 3. Add 1 to 4, it will make 5. Take 5 from 6, and 1 remains. Put down the 1. The number 1 342 is called the Remaindety the Difference, or the Excess. The number from which the subtraction is made, viz. 6237, is called the Minuend, The number- which is subtracted, viz. 4895, is called the Subtrahend, EXERCISES. $426.20c. 647 754.382 827 $968.40o. 214.17 212.03 423 621.176 403 224 133.206 424 412.26 556.14 643.621 498 $783.72o. 869 548.460 411.348 132 172.35 217 232.278 866 611.37 652 213.263 335.197 $423.50c. 742 $834.67o. 546 $643.44o. 269.28 154.22 489 478.49 298 278 (?) 253 856.18 248 (2) i?) (4) 169.19 474.25 (5) $623,810. 821 $602,230. 714 147.94 (7) 479 (?) 146.71 $643,250. 741 $610.17c \u 178 (10) 268.12 278 79.09 $101. 40o 11.52 20 01) 42654 26479 (16) 74603.684 87684.267 (19). 42681 19697 SIMPLE SUBTRACTION. (12) (13) 86871 78268 17928 47296 (16) 91020 12647 m) 41021.14 768.36 (20) $42890. 62o. 27601.48 (21) 81000 2641 (23) 741026831 27^904896 861264981.346 248600989.679 614102013 178906844 921002461.482 198007019.847 98648 27896 (18) 40000 :i00i $46801.200. 20009.05 (25) 148120718 74198648 (28) 181201041.46 89890122.618 29. 741826421741 80. 841298471312 81. 812014001018 82. 431701468642 83. 614214687648 84. 419000100014 427984642814 71489641264 107987862141 7126142687 196412741689 2120101706 85. From seven hundred and nine thousand four hun- dred and twenty-seven take two hundred and fifty-one thousand eight hundred and seventy-two. 86. From two millions two hundred and two thousand and two, take nine hundred and ninety-six thousand and seven. o7. "\yhat is the diflference between six millions five hundred thousand and four, and two millions nine hun- dred thousand seven hundred and sixty ? , 88. How much does sixty-four thousand two hundred nnd four exceed six thousand two hundred and forty- nine ? SIMPLE SUBTRACTION. 21 39. John lent James $9071 ; of this sum he has re- ceived baok $999; how much has James yet to pay? 40. On a cherry-tree there were 2046 cherries ; of these 1875 were gathered ; how many remained ? 41. Columbus discovered America in the year 1492; how many years is it from that time to 1861 ? 42. In a certain school there are 486 boys; of these only 264 can write ; how many are unable to write ? 43. The parliaments of England and Scotland were united in 1706; that of Ireland was joined to them in 1800-; how many years between these dates ? 44. John had 202 nuts in his pocket, but, there being a hole in it, he lost 96 nuts ; how many had he remaining ? 45. On an apple-tree there were 165 apples; the wind blew o£f two dozen and a half ; how many were left ? 46. A draper bought 4786 yards of cloth, and sold 8987 yards ; how many yards has he unsold ? 47. What sum added to sixty-five thousand seven hun- dred and ninety-six, will make one million four hundred and fifty-two thousand three hundred and thirteen ? 48. I was born in the year 1828 ; how old shall I be in the year 1861 ? 49. Ireland is about 800 miles in length, and 170 miles in breadth ; how much greater is the length than the breadth? * . \ 50. Ben Nevis in Scotland, the highest mountain in the British Islands, is 4350 feet above the level of the sea ; the summit of Magillicuddy's Reeks, the highest point in Ireland, is 3610 ; what is the difference in height between these two mountains ? 51. The Shannon, the largest river in the British Isles, has a course of about 170 miles. The Amazon, in South America, has a course of about 3000 miles. What is the difference in the length of their course ? 52. The diameter of the Sun is about 888246 miles ; that of the Earth, about 7912; what is the difference between the diameter of the Sun and that of the Earth ? 22 SIMPLE SUBTRACTION. 63. The surface of the earth ijs nearly 200 millions of square miles ; of this it is probable that 60 millions are land ; how maay more square miles of water than of land are there in the earth's surface ? 54. The population of London being about 2,776,656, and the population of New Brunswick being about 283,652, how many more people are there in London than in New Brunswick ? 65. Mont Blanc, in Switzerland, is the highest mountain in Europe, being 15,680 feet above the level of the sea. Chimborazo, the highest mountain in America, is about 21,000 feet in height. What is the difference in height between these two mountains ? 66. Sir Isaac Newton was bom a.d. 1642, and died 1727 ; how old was he when he died? 67. The art of printing was discovered about the year 1449; hbw long is it from that time to the year 1861 ? 68. At her accession to the throne in 1837, Queen Victoria was in the 19th year of her age. In what year was she born? and how long had she reigned on the 20th June, 1860, the anniversary of her accession ? 59. Between the landing of the Loyalists in 1783, and the visit of the Prince of Wales in 1860, how many years had elapsed ? ^ MIXED QUESTIONS. vl. Tom had 264 marbles; he gave 64 to James, 75 to William, and 42 to John ; how many had he left ? 2. A merchant had 4268 yards of cloth ; on Monday he sold 146 yards, on Tuesday 97, on Wednesday 246, on Thursday 198, on Friday 364, on Saturday 497; how much cloth had he remaining ? 3. Three regiments went to battle; in the first there were 968 soldiers, in the second 769, and in the third 84'i. There were 248 men killed in the first regiment, 368 in the second, and when the regiments returned there were oniy 436 men in the third ; how many returned from the battle I mm SIMPLE^ MULTIPLICATION. 23 4. A man had a journey of 298 miles to make ; the first day he walked 42 miles, the second 36 miles, the third 81 miles, the fourth 27 miles ; how much farther had he to go? 6. Three vessels sailed to America with emigrants ; in the firRt vessel there were 126 men, 96 women, and 42 children ; in the second vessel there were 93 men, 87 women, and 26 children ; in the third vessel there were 43 men, 2 ( women, and 8 children. In the first vessel 8 persons died ; in the second 2 were washed overboard; the third vessel was wrecked, and all on board perished; how pany got safe to America? 6. A little boy went to the Zoological Gardens to see the animals ; he laid his hat on the ground, which con- tained 264 nuts; while his attention was engaged, the monkey stole 27 of his nuts ; while he was pursuing the monkey, a squirrel made off with 16 more; how many had he remaining ? 7. The population of Fredericton is assumed to be 6224, of MoiiCton 1738, of Woodstock 4978, of St. An- drews 4166 ; by how much does the population of St. John exceed all these towns, its population being estimated at 86,894? 8. Received on Monday 247Z. ; paid away on Tuesday 196^ ; received on Wednesday 349^. ; paid away on Thursday 4021. ; received on Friday 687Z. ; paid away on Saturday 398/. ; what money had I still remaining ? SIMPLE MULTIPLICATION. Multiplication teaches us to find what a number will amount to when it is repeated a number of times. MENTAL EXERCISES. 1. At 7 cents apiece, what will 9 copy-books cost? 2. What is the price of 13 yards of cloth at 3 dollars a yard? / 24 SIMPLE MULTIPLICATION. 8. What cost 17 barrels of cider at 2 dollars a barrel ? 4. I bought 8 pieces of cloth; each piece was 15 yards, and I gav« 4 dollars a yard for it. What was the price of each piece ? and of the whole ? Case I. — ]Vhen the Multiplier doea not exceed 12. Multiply 58 by 7. RuLB WITH Example. — Place the number by which you are to multiply under the number to be multiplied; then say, 7 times 8 make 21. Put do^n the 1 under thS 7. Then, 7 times 5 make 85, and the 2 of the 21 make 87. Put down the 87. The 58 is called the Multiplicand; the 7 is called the Multiplier; and the 371 is called the Product. The mul- tiplicand and the multiplier taken together are called the Factors ; thus, 58 and 7 are factors. 58 7 871 , EXERCISES. 659 ' 2 427 2 642 2 748 2 896 2 1818 854 1284 1496 792 $ c. *486.75 8 968 8 • 687 4 $ c. 983.42 6 758 5 * The product must have as many decimals as there are in both factors. Tf, for instance, there are 4 in the multiplicand, and 3 in the multiplier, then the product mus have 7. If there should not be as many figures in the product as are iiccessary to make the required number of deci- mals, as many ciphers must be prefixed as are necessary to make up the required number. If, fur instance, the number of decimals in both factors is 7, and there are only 6 figures in the product, then two ciphers must be prefixed. EzAMPiJi:— .00074 .30 444 222 .0002664 Here there arc only four; so three ciphers are prefixe^. Mi •" * aUfPL^ MULTIPLICATION. 26 $4: $ 0. 896.64 6 4483.20 276.170. 798 6 $ 0. 878.26 7 696 8 $ 0. 974.68 9 4768 2647.76 4768 $67287.26 $8646d.64o. 2 6 8771.67 268. 06o. 8 $7626( 68.828 84076. 9468.828 7 $4561 i87.16o. 84076.646 8 (10) "4.120. $3685 11 12 48256.889 9 $68875.310. 9 74879 10 a^^' 889 12 13. Multiply 87646 by 14. — 16. . — 16. — 17. -. 18. 19. 20. 21. 4 7 — 9 — 6 — 8 — 6 t-10 — 11 — 12 22. Multiply 988.27 by 2 28. — 7 24. — 4 25. — 8 26. — 6 27. — 6 28. — 9 29. — 12 80. — 11 Gasb II.- • When the Multiplier it a eompoeite number,* Multiply 486 by 82. Bulb with Example. — Tlie multiplier, yiz. 32, is formed by the two factors 4 and 8 ; therefore, instead of multiplying by 32, you may multiply by 4> and obtain the product 1744. Multiply this product by the other factoir, 8, and you obtain 13952, the product of the 436 multiplied by 32. 486 4 1744 8 18962 * A composite number is the product of two factors; thus, 16 is a com- posite number, because formed of the factors 2 and 8, or 4 and 4; 2l is formed of 3 and 7 ; 27 of 3 and 9; 36 of 4 and 9, or 6 and 6, or 3 and 12. 3 / ; * III 26 8IMPII: MULTIPLI^TION. 81. 82. 83. 84. 86. 86. $ c. 4264.78 X 16 7436.87X18 9687.48 X 24 6748.67 X 27 6430.67 X 36 4264.66 X 49 87. 38. 89. 40. 41. 42. $ 0. 8687.46 2468.76 7849.78 2040.74 4368.76 4968.76 X 54 X 66 X 72 X108 X132 X144 Case III. — When the Multiplier exceeds 12. Multiply 3426 by 342. Rule with F^a.mple. — Place the multiplier under the multiplicand, units under ^nits, &c. Multiply by the figure in the lowest place of the multiplier, viz. 2. Then multiply by the next figure of the multiplier, viz. 4; thus, 4 'times 6 3426 342 6862 13704 make 24; but take notice that you are to place 10278 the 4 of the 24 directly under that figure of the multiplier by which you are multiplying. Pro- 1171692 ceed in the same manner with the figure 3 of the multiplier. Then o^dd together the products obtained. Multiply 6487 by 230 2ao 194610 12974 • 1492010 43. Mult. 98.476 by 6.42 44. — 76.8 45. — 296 46. — .496 47. — 86.7 48. — 4S.68 49. — 7.896 bO. — 36.64 Multiply $64. 87c. by .203 .203 19461 129740 $13. 16861c.* 61. Mult. 66839 by 958 62. — 627 63. — 3.69 64. — 426 55. — 704 56. —8.743 67. — .6007 68. — 9864 "^e 16-handredths represent cents, the other figures are parts of a MkMl SIMPLE MULTIPLICATION. 27 59. Multiply sixty-foar thousand eight hundred and fifty-two, by nine hundred and eighty-seven. 60. Multiply four hundred and fifty-eight thousand six hundred and ninety-four, by eight thousand and seventy- six. 61. Multiply nine hundred and eight^^-six thousand seven hundred and forty, by four hundred and nine. 62. There are 8766 hours in the year ; how many hours are there in 20 years ? 63. A grocer sells goods to the amount of $382.40c. per week ; how much does he sell during the year ? 64. In a flock of 648 sheep, how many feet were there ? 65. Suppose the page of a boolr to contain 49 lines, and each line 47 letters ; how many leilers does the whole page contain ? ' , 66. In 264 dozen of wine, how many bottles are there ? 67. A gentleman dying gave orders in his will that his fortune should be equally divided among his five chil- dren; each ' received $648; how much money did he leave? 68. Suppose that there were in the parish 896 houses, and that each house in the parish contained 5 persons ; what would be the population of that parish ? • 69. How many miles will a person travel in 34 years, supposing he travels 9 miles per day, and there are 365 days in the year ? 70. There were in a garden 8 trees, and upon each tree there were 268 apples ; how many apples were there upon all the trees ? 71. There were 4768 geese plucked, and 17 quills got from each goose ; how many quills were got from all ? 72. There were 27 desks to be made for the school, and each desk required 29 nails; how many nails were re- quired for all the desks ? ' \ 28 .^IMPLE DIVISION. 73. In a school, there were 6 windows in the boys' room, and 4 in the g*rls' room; in each window thv.re were 8 panes of glass ; how many panes of glass were there in all ? 74. I knew two boys ; one of them was lazy and lay in bed till 9, the other was an active little fellow who rose every morning at 6 ; how many hours did the active boy gain in a year that the other lost ? 75. How often does a clock strike in a year, at the rate of 156 times a day ? 76. How many pins may a boy point in 6 days who works 8 hours a day, and points 16,000 pins in an hour ? SIMPLE DIVISION. Division is the method of finding how often one number is contained in another. MENTAL EXEBCISES. 1. How many pine-apples, at 8 cents each, can be ob- tained for 40 cents ? for 56 cents ? 2. What will 13 yards of silk cost, if 5 yards cost 45 dimes ? 3. A man bought 4 barrels of flour for 20 dollars, and gave 3 of them for cider, at 3 dollars a barrel ; how many barrels of cider did he get ? 4. In how many days can 15 men earn as much as 3 men can in 25 days ? 6. If 1 man can ride 1 mile for 4 cents, how far can 2 men ride for 80 cents ? \ SIMPLE DIVISION. 29 Case I. — When the Divisor does not exceed 12. Divide 252 by 6. Rule wi'th Example. — Put the numbers down according to the annexed example. Find how 6)252 often the figure by which you are to divide — viz. 6 — is contained in the first, or first and second 42 figures : thus, 6 in 2, there are none, then 6 in 25 ; there are 4 sixes in 25, and 1 over. Put down the 4 under the 5. Suppose the 1 placed before the 2, which '' would make it 12. Say, 6 in 12. There are 2 sixes in 12. Put the 2 under the 2. The number 6 is called the Divisor; 252, the Dividend; and 42, the Quotient. EXERCISES. 2)4628 2)6824 3)6039 4)8408 2314 3412 2013 2102 $ c. * 2)476.58 3)76389 $ 0. 4)857.36 $214.^4 6)76590 $238.29 25463 12765 (1) 4)27645 $ (2) c. 6)687.64 (3) 6)79687 $ (4) c. 7)806.20 $(5)c. (6) $(7)c. (8) 8)764.26 9)28676 10)642.68 11)46267 (9) 12)76426872 $(10) c. 8)426876.42 (11) 7)96402687 ♦ When there are decimals, point oflf from the right of the quotient as many for decinmla as the decimnla in the dividend exceed those in the divisor. For instance, if the dividend has three and the divisor one, point of. two, &c. . 8* 80 19. i'O. 21. 22. 23. 24. 25. 26. 27. 28. $(12) c. 9)642687.02 $ c. 6)760020.41 SIMPLE DIVISION. $(18) 0. 12)468768.76 $ (16) c. 9)43026.01 (14) 8)46876400 n7) 2006 7)41200602 18. Divide 56472689 by 2 c. — 3 — 4 — 6 — 6 — 7 — 8 — 9 — 10 — 11 — 12 29. Divide 749680.23 by 2 80. 31. 32. 33. 34. 35. 36. 37. 38. 39. 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10 — 11 — 12 'L— Case II. — When the Divisor exceeds 12, and is a composite number. Divide 6789 b> 28. Rule with Example.-— The two factors that produce 28 are 4 and 7 ; divide them by 4 and by 7, as in the example. The quotient found is 242, but with two re- mainders, viz. 3 and 1. To ob- tain the complete remainder, mul- tiply the first divisor, viz. 4, by the last remainder, viz. 3, and to the product add the first remainder, viz. 1 ; thus, 4X8 + 1 = 1 ^> *^® *^r^® remainder. f 4)6789 284 ( 7)1697 remains 1 242 remains 3 40. 41. 42. 43. 44. 46. 426478 •743687 968748 674867 643067 45>6456 16 18 24 27 36 49 46. 868745 -?- 54 47. 246876 -^ 56 48. 784978 -5- 72 49. 204076 -}- 108 60. 436876 -f. 132 61. 496876 ; 144 SIMPLE DIVISION. 31 Casb III. — When the Divisor contains several figures. Divide 431769 by 528. 628)4317,69(817 quotient. 4224 ^"936 528 4089 8696 893 remainder. KuLE WITH Example. — Put down the sum in this form. Consider whether the divisor, viz. 528, is contained in the first three figures of the divi- dend, viz. 431 ; you see at once that it is hot ; mark off then four figures, viz. 4317. You are now to find how often 528 is contained in 4317 ; for this purpose find how often the first figure of the divisor, viz. 5, is contained in the first two figures of the dividend, viz. 43. It is contained 8 times ; put the 8 on the opposite side of the dividend from the divisor. Multiply 528 by 8, and put the product under the 4317; subtract, and there remains 93; bring to this the next figure of the dividend, viz. 6. You are now to find how often the divisor, 528, is contained in your new dividend, 936; find, as you did before, how often the first figure of the divisor, 5, is contained in the first figure of the dividend, 9. It is contained once ; put the 1 beside the 8 ; multiply 528 by 1, and place the pro- duct under the 936 ; subtract, and you obtain 408 ; bring to this the next figure of the dividend, 9. Find, as be- fore, how often 528 is contained in 4089. Because 5 is contained 8 times in 40, you will be inclined to try 8. Do it, and you will find that you obtain the product 4224, but this is greater than the 4089 from which you have to subtract it ; when this is the case, you must try / a smaller figure : in this case take 7. 52. Divide 74236 by 42 6.3. 43 64. 44 65. 45 56. Divide 74236 by 46 57. 689 68. 799 69. 410 I ; 32 SIMPLE DIVISION. 60. Divide 87403 by 611 62. 63. 64. 65. 66. 67. 68. 312 584 708 246 867 428 502 618 69. 70. 71. 72. 73. 74. 76. 76. 77. 842.786 976842 4201.076 6416879 286.4976 2876.407 6412930 980.0147 4078948 78 946 4.38 648 39.6 410.7 7481 30.76 4278 If the decimals in the dividend exceed those in the divisor, point off from the quotient as many as the decimals in the dividend exceed those in the divisor. That is, for iQstance, if the divisor has three and the dividend three, from the quotient p6int oflF none. If the divisor has four and the dividend two, add two to the dividend to make them equal, and point off none. If the divisor hfts two and the dividend five, point off thbee. 78. 4078948 H- .0008 79. 7198641 --.2864 80. 864.1201-^.1407 81. 248070.8 -5- .2600 82. 78.64126-5- 7410 83. 8002602 -<- .8000 84. 402026.4 -f- .0069 86. 9687600 -*- .4300 86. Divide six millions seven hundred and ninety-four thousandths, by four hundred and eighty thousand six hundred a^id nine millionths. 87. What is the ninth of $6037.45 ? 88. A ship sailed in four weeks 1262 miles ; how much is that per day ? 89. If a vessel contains 648 gallons of water, how long will it take to discharge it all, at the rate of .18 of a gallon a minute ? 90. The population of Ireland is about eight millions, and there are about 30,000 square miles of surface ; how many persons to each mile ? 91. The Earth ip about 96 millions of miles distant from the Sun; how many days would a horse take in reaching the Sun, supposing he went at the rate of 45 miles per day ? 92. The rays of light come from the Sun to the Earth SIMPLE DIVISION. 88 s in S\ minutes, or 495 seconds ; at what rate does light move per second, the distance from .the Sun to the Earth being 96173000 miles? 93. The circumference of the Earth is about 25000 miles ; how many days would a man take to walk round it at the rate of 27 miles per day ? Case IV. — When a Multiplier has a fraction. Rule with Example. — Place the multi- plier under the multiplicand, as usual, then multiply by the upper figure of the fraction and divide by the under. Pro- ceed with the other part of the multiplier as if there was no fraction there, placing units under units, &c. Add the quotient in with the others when summing up. 68340 6| 4)205020 51255 341700 892955 94. Multiply 7346 b.v 3^. 95. 86214 i( 6f 96. 9567 (( 34 i. 97. 3278654 it 680f. 98. 7268 (( 17f 99. 2897 (< 19f. 100. 462 (< 325f 101, 601834 <( eb^. 102. 10837464 (( 94f 103. 9746 i( 13jV. Case V. — When a Divisor has a fraction. Rttlb with Example. — Multiply the divisor by the under figure of the fraction, adding in the upper, and multiply the dividend also by the under figure ; then divide by sl^ort or long division as the case may require. 104. Divide 8245 by 105. " 678 11 / 67846 4 271384 24671,|?r (t 2|. / 84 NEW BRUNSWICK CURRENCY. 106. Divide 486213 by 7f * _ ' 107. 98464 " lOA. 108. «« 8826 " 4|y 109. « 2424 " 1 . 110. " 38466 " 2 . 111. " 6794 " 13^. " 261. 112. « 463820 113. " 978654 1 " 134A. NEW BBUNSWICK CURRENCY. ' ADDITION • $563.52 $29.32 $0.32 '$1.00 45.65 6.53 1.06 0.37 9.05 18.09 3.03 0.62 283.26 4.28 90.02 5.00 9.00 2.60 1.06 4.36 $908.48 SUBTRACTION. $8765.32 $432.53 $16.05 $7.19 387.62 187.60 t 8.39 1.65 8377 JO *' MULTIPLICATION. $768.54 $527.59 $687.35 $28.05 2 3 4 5 $1637.08 $ $ $ • DIVISION t 9)$8406.45 3)$980.10 6)$27.65 6)$8654.04 934.06 \ \ REDUCTION. 35 1. Add the following sums: $1.05, $0.66, $2.63, $4.06, $7.85, $60.30. 2. James owed John $800.00; he has paid him $175.55; what does he still owe him? 8. (f 1 barrel flour cost $6.25, what will 6 barrels cost ? at the sanxe rate, what will 25 barrels cost ? 4. If $972 is to be divided'^between 108 men, what does each m&n receive ? 5. What is the sixth part of $836.34 ? 6. What will eight barrels of potatoes cost at $1.25 each? 7. What is the diflFerence between $60.00 and $49.99? 8. How many dollars in 6534 cts., and how many cents over ? 9. What will 235 grammars cost at 83 cts. apiece? Express the answer in dollars and cents. REDUCTION. REDUCTidN IS the bringing of one denomination another without altering its value. Case I. — ^To bring from a higher to a lower, i Rule with Example. — Multiply by as many of the lower as make one of the higher. Thus, to bring 2Z. to shillings, multiply 2 by 20, because there are 20«. in a pound. £2 20 40*. Case II. — To bring a lower to a higher. Rule with Example. — Divide by as ». ' many of the lower as make one of the 2,0)4,0 higher. Thus, to bring 40 shillings to pounds, divide by 20, because there are £2 20 shillings in a pound. / 36 REDUCTION. Bring M 9«. 6^d, to farthings. Multiply the 4 by 20, and add the 9«. to the product ; this will give the number of shillings, 89«. Multiply then by 12, adding 6 pence ; this will give the number of pence, 1074d. Multiply by 4, and add the two farthings to the product ; this will give the number of farthings in 41. 9«. 6^(/. £ «. 4 9 20 89 12 1074 4 d. 4298 Bring 4298 farthings to pounds. Divide the farthings by 4 ; this will give 4)4298 1074 pence and 2 farthings. Divide this by 12, and 88 shillings and sixpence is 12)1074-^ obtained. Divide by 20, and the quotient is 4 pounds 9 shillings, in all M 9«. 6^d. 2,0) 8,9 6 £4 9 6^ MENTAL EXEBCISKS. 1. How many shillings are there in £Z 10s. ? in £4 59. ? in £6 18«. ? 2. How many pence are there in 1«. Sd. ? in 2«. 6d'. ? in 16s. ? 8. How many pounds are there in 7&s. ? in 163«. ^ in 194».^? 4. In four miles how many furlongs are there ? 6. How many rods are there in one mile ? 6. How many hours are there in a week ? EXERCISES. STEBLINQ MONET. 1. How many farthings are there in 12^. 7s. 6J 8 1 19 4 2 27 8 1 13 d. 41 6 4 5| (7) £ s. 623 16 846 14 764 12 276 11 876 10 798 4 10 473 16 Hi (10) ac. rd. per. 46 3 27 12 2 16 61 84 4*6 8 17 ctut. qrs. lbs, 4 2 12 2 3 14 6 17 3 2 24 17 2 1 (2) ^ £ s. d. ■5 12 4 72 17 6| 13 8 i\ lii 14 %\ 72 12 4J (5) ' joer. yc?. ft. 16 3 2 17 4 1 24 6 23 2 2 (8) £ s. d. 264 16 6 146 17 8J 869 19 7{ 796 18 210 6 4 407 2 2f 864 17 6| (lA) /wr. joer. ya. 7 22 2 6 22 4 9 16' 3 6 14 6 ac. rd. per. 32 3 16 16 2 21 76 1 13 24 2 27 150 1 37 (3) ^ £ s. d. 86 13 4J 12 8 6|- 11 19 10| 17 14 8| 28 12 6f (6) qrs. lbs. oz. 1 14 12 2 24 15 3 13 7 2 17 13 £ s. d. 560 16 9^ 216 14 4 378 13 8| 924 17 1 623 9 4 146 16 7J 876 31 10| (12) ac. rd. per. B7 2 12 41 3 21 62 1 17 47 2 34 COMPOUND ADDITION. 41 & 8. d. For paving yard.... 4 7 — new-laying floor 2 6 6 1000 bricks 1 16 For mortar 14 6 — hair 2 6 £ a. d. 40 copy-books 14 100 slates 10 6 100 slate-pencils.... 8 8 qrs. of paper.. 9 4 600 quills 7 7 16. A merchant, the first year he was in business, sold goods to the amount of 476Z. 18s. Id. ? the second year 678Z. 14». Q^d. ; the third year 878Z. 7.'. O^d. ; the fourth year 91 7Z. 18«. Id. ; the fifth year 1312Z. lOs. ^d. ; what was the amount of goods sold during the five years ? 16. A silversmith matie three dozen spoons, weighing 6 lb. 9 oz. 8 dwt. ; a teapot, weighing 3 lb. 2 oz. 16 dwt. 16 grs. ; two pair silver candlesticks, weighing 41b. 6 oz. 17 dwt. ; a dozen silver forks, weighing 1 lb. 8 oz. 19 dwt. 22 grs. ; what was the weight of all the articles t 17. A person went to market and laid out on the pur- chase of tea 2Z. 165. Id. ; on coffee 21. 7s. S^d. ; on sugar SI. lis. ; on beef 21. 16s. Qd. ; on mutton 37s. ; on veal 95. 7^d. ; on various other articles 3Z. 15*. 7|df. ; how much was laid out in all ? 18. The bricklayers were engaged about a house 23 weeks, 4 days, and 8 hours ; the carpenters 14 weeks, 6 days, and 9 hours ; the painters 12 weeks, 6 days, 7 hours, and 84 minutes ; the upholsterer 6 weeks, 10 hours, and 42 minutes ; how long were these different workmen en- '^aged about the house ? 19. The expenses of building a house were as follows : — architect 198Z. ; bricklayer 4762Z. ; mason 2141Z. I65. 6c?. ; carpenter 2768Z. 175. 9d. ; plumber 396Z. 145. ; glazier 478Z. I65. Qd. ; painter 421Z. I85. ll^d. ; and paper-hanger 243Z. I85. 7d. ; what was the amount ? 20. A man rode 36 miles, 2 furlongs, 34 perches ; walked 24 miles, 6 furlongs, 26 perches, 2 yards ; then rode again 42 miles, 7 furlongs, 4 yards ; then walked again 16 miles, 4 furlongs, 38 perches, 3 yards ; what was the length of his journey? 4* \ jZ — = 42 COMPOUND SUBTRACTION. 21. I bought four fields ; in the first there were 6 acres, 8 roods, 12 perches ; in the second 7 acres, 2 roods ; in the third 9 acres and 13 perches ; in the fourth 6 acres, 2 roods, 36 perches. How much in all ? COMPOUND SUBTRACTION. This is finding the difference between numbers baying different denominations. BuLE. — Place the less number under the greater, having figures of the same name directly under each other. Begin at the right hand or lowest denomination, subtract the under from the upper, and write the remainder directly below. If the under figure is greater than the figure above, add to the upper figure as many of the same as it takes to make one of the next higher, then subtract the lower figure and set down the remainder. Carry one to the next number of the subtrahend. £ s. 49 17 17 14 d. ^ 2J ml. fur. per. 4 6 20 1 7 35 yrs. wks. 43 4 24 6 dys 2 5 32 3 2 6 25 18 49 4 £ s. 78 14 29 17 d. £ 9. d' 47 16 8J 28 17 6} r3) £ s. 86 17 27 19 d 4 Of £ s. 68 13 28 16 d. 7 10} £ 8. d. 94 24 17 ^ £ s. 83 17 47 d Of COMPOUND SUBTRACTION. 43 (7) ac. rd. per. 42 1 25 17 2 35 (8) dys. hrs. min. 47 12 10 17 20 40 (9) per. yd. ft. 16 2 *1 12 4 2 (10) £ «. >I«(W«^^wrt,.. COMPOUND MULTIPLICATION. 45 lbs. oz. dwt. 24 3 12 8 yds. qrs. j 36 2 lis. 3 9 \ (3) cy)t. qrs. lbs. 6 2 18 7 £ s. d. 78 16 7| ll| (5) & s. d. 69 19 7 12^ £ s. d. 67 16 10| 9 7. A mail-coach travelled at the rate of 7 miles, 6 fur- longs, 25 perches, per hour ; how far would it go in twelve hours ? 8. Eight men cut down a field of hay ; each man cut 3 acres, 2 roods, 27 perches. How much was mown ? 9. Sold eight silver teapots, each weighing 3 lb. 9 oz. 18 dwt. 13 grs. ; how much did they all weigh ? 10. A farmer bought 12 cows ; they cost him 91. 12s. 6d. each ; how much did they all come to ? 11. Bought 11 barrels of herrings at 11. 8s. 7Jc?. each; what did the whole cost? • I Case II. — When (Tie Multiplier exceeds 12. Multiply ^£4 6«. dd. by 23. Rule with Example. — When the mul- tiplier, viz. 23, is under a hundred, multi- ply the multiplicand, 41. Gs. 3c?., by one ten, and the product, 43Z. 2s. 6c?., by the number of tens, 2 ; then multiply the top line, viz. 41. 6s. Sd.y by the number of units, 3 ; add this to the amount obtained by multiply- • ing by the number of tens, 2, and the sum required is obtained, viz. 99Z. Ss. dd. £ 4 s. 6 d. 3X3 10 43 2 6 2 86 12 6 18 9 .a £99 3 9 46 COMPOUND MULTIPLICATION. r. £ 8. d. 4 6 3X3 10 43 2 6X2 10 431 5 4 1725 86 5 12 18 9 Multiply 41. 6«. Sd. by 423. When Uie multiplier, 423, is a hundred, or above it, multiply the multiplicand, 41. 68. 3d, twice by 10, and the product, 4312. 65., by the number of hundreds, 4 ; then multiply the product of the first 10, 432. 2«.'6d, by the number of i^ens, 2 ; and place it un^er the product of the 4, under 17252. 0^. Od. ; mul- tiply now the first line, 42. 6«. 3c?., by the number of units, viz. 3 ; put the product obtained under the product of the tens, 1725 and add the products of the hundreds, the tens, and the units together for the an- swer. — For thousands, multiply by four tens, and fr.oceed in the same manner. 1824 3 9 12. Multiply £64 IQs. 7^rf. by 68. 13. Multiply 17 lbs. 7 oz. 14 dwts. by 478. 14. Mifltiply £476 15«. Sd. by 647. 15. Multiply 4 mis. 6 fur. 20 per. by 7426. 16. What is the weight of 36 hhds. of tobacco, each hhd. weighing 5 cwt. 3 qrs. 14 lbs. 13 oz. f 17. Eow much molasses is contained in 25 hhd., each hhd. having 61 gal. 1 qt. 1 pt. ? 18. A farmer has 18 lots, and each lot contains 41 a. 2 r. 11 p. ; how many acres does he own ? 19. If a railroad-car goes 21 m. 2 fur. 10 r. per hour, how far will it go in 16 hours ? 20. How much cloth will i'c take to make the clothes for a regiment of soldiers containing 1143 men, if each suit requires 7 yds. 3 qrs. 2 nls. 1 in. ? 21. If a steamship in going round the world travel 211 m. 4 fur. 3^ per. a day, how far will she go in 367 djJys ? 'imimr^'-*' COMPOUND DIVISION. 47 22. In 27 barrels there was on an average in each, 29 gallons, 3 quarts^ 1 pint; how much in all? 23. I can go to a certain town by the railway in nine hours, 26 minutes, and 30 seconds ; it would take me, at least, five times as long to go by the stage-coach ; how long would the coach take ? 24. How much water will be contained in 96 hogs- heads, each containing 62 gal. 1 qt. 1 pt. 1 gl. ? 25. A gentleman spends, per day, 11. Is. 6d. ; how much does he spend in a year ? 26. If one spoon weigh 8 oz. 5 dwt. 15 grs., what is the weight of 120 spoons ? 27. A person spent 12*. Qd. per day, and found that at the end of the year he had saved 25 guineas ; what was his annual income ? 28. A farmer bought 568 sheep ; he paid for them 1^. 12s. Qd. each ; how much did the whole flock cost him ? COMPOUND DIVISION. Compound Division is wheu the dividend con- sists of several denominations. KuLE. — Divide the highest denomination by the quan- tity, and if any thing remains mul^ply it by as mainy of the next lower as it takes to make one of the same, add- ing in the given number of the next lower. Divide the number thus obtained by the divisor, as before ; and so on. Proceed by long or short division, as the case may require. 48 COMPOUND DIVISION. £) 8. d. 2)74 16 8J £37 8 4^ yds. qrs. nls. 4)26 3 2 6 1 3| (1) cwt. qrs. lbs. 6)14 2 17 !•! 7 <^) , yds. qrs. nls. 7)64 2 3 (5) ^ Zo«. 02. dwt. 4)67 8 17 £ s. d. £ s. d. 6)8 12 7J 47)64 7 8^(1 £1 8 9J cw<. g'r*. lbs. 6 2 12 9)36 dwt 47 17 20 3)19 3 8 47)347(7 329 18 12 (2) . qrs. lbs. oz. 47)224(4 9)19 11 13 188 86 (4) yds. qrs. nls. 47)146(3 141 oz. dwt. grs. 5 remain. (7) dys. hrs. min. 7)43 16 22 8)36 17 6 8. Divide 19 cwt. 3 qrs. 8 lbs. by 3. 9. Divide 18 lbs. 6 oz. 14 dwts. by 17. 10. Divide 16 per. 2 yds. 1 ft. by 9. 11. Divide 64 yds. 2 qrs. 3 nls. by 42. 1%. Divide 36 acr. 3 rd. 27 per. by 31. 13. A tradesman had in the savings-bank 96?. 16.?. M. ; tills sum he had savea in 5 year/" ; how much did he save on an average each year ? 14. Ten men rented a house at 46?. 14«. 8rf. ; how much had each to pay ? COMPOUND DIVISION. • 49 15. A father left 426Z. 16*. 6rf. to be divided equally among his eight children ; how much did each get ? 16. Twelve persons subscribed 2Sl. 16s. 6rf. per annum for the support of a school; how much did each subscribe? 17. A piece of cloth containing nine yards was bought for 41. 16«. 8c?. ; how much was that per yard ? 18. Ten sacks of potatoes weighed 19 cwt. 3 qrs. 13 lbs. 14 oz. ; what was the weight of each sack ? 19. How many parcels, each containing 4j^ lbs., can be made out of 2 cwt. 2 qrs. 23 lbs. ? 20. If 36 bags of cotton weighed 49 cwt. 8 qrs. 13 lbs., how much did one weigh ? 21. A surveyor, who had 19 miles, 7 fur., 36 perches of road to keep in repair, appointed 12 men to the work ; what length of road had each to attend to ? 22. A man travelled in nine days 160 miles, 4 furlongs, 18 perches, 3 yards ; how much did he travel per day on an average ? . 23. Bought sixty-five yards of cloth, for which I paid 721. 14«. 4fc?. ; what did it cost per yard ? 24. A rich man divided 168 bu. 1 pk. 6 qt. of corn among thirty-six poor men ; how much did each receive ? 25. If in 30 days a man travels 746 ml. 5 fur., travel- ling the same distance each day, what is the length of each day's journey ? 26. A farmer rents a farm at 596?. IQs. Qd. per annum; i wishes to lay past as much every week as may pay the i 3iit ; how much must he save each week ? 27. A gentleman had an estate of 3468 acres, for which he received per annum 879?. 16«. 8d. ; how much was it let for per acre ? 28. A tax-gatherer colljcted 747?. 15i^Kf. per month the first six months of the year, and w^. lis. Sd. per 50 COMPOUND DIVISION. N' r \ I f^ • month the last six months of the year ; how much did he oolleot daily on an average for the whole year ? 29. In a savings-bank in a village there was de- posited 268/. 17«. Sd.f and there were 66 depositors, or people who had placed money in the bank ; how much had each depositor on an average ? MIXED QUESTIONS ON THE OOMFOUND RULEd. 1. What is the weight of the sugar in 4 hogshe6.ds, when each weighs 13 cwt. 3 qrs. 14 lbs. ; the empty hogs- heads weigh 1 qr. 10 lbs. ? 2. What is the net weight of 9 chests of tea, each weighing 6 cwt. 2 qrs. 19 lbs. ; empty chests weigh 18 lbs. ? 8. How many hogsheads of sugar, each containing 13 cwt. 2 qrs. 14 lbs., may be put on board a ship of 324 tons burden ? 4. St. Paul's bell, in London, weighs 5 tons 2 cwt. 1 qr. 22 lbs. ; by how much does the great bell of Moscow ex- ceed it, which weighs 198 tons 2 cwt. 1 qr. ? 5. In 27 barrels there was on an average in each, 29 gallons, 3 quarts, 1 pint ; how much in all ? 6. If it take 5 yds. 2 qrs. 3 nls. to make a suit of clothes, how many suits can be made from 182 yards ? 7. I have a field of corn, consisting of 123 rows, and each row contains 78 hills, and each hill has 4 ears of corn ; now, if it take 8 ears of corn to make a quart, how many bushels does the field contain ? 8. How many steps, 2 ft. 8 in., will a man take in walking 15 miles ? 9. A man, on being asked his age, said he had spent the first 19 years of his life in England, the next 9 in America ; durmg 27 following, 6 years, 11 months, 3 weeks, 6 days, were fNnt in France, 16 years, 4 months, 3 days in the United States, and the remainder in his native J.W. l/.Vvi;E.XE Co- lECTION SIMPLE PROPORTION. 51 country ; how old was he, and in which land had he lived the longest ? 10. A man has 3 farms ; the first contains lOOac. 8 ro. 15 rds. ; the second, 161 ac. 2 ro. 28 rds. ; the third, 860 ac. 3 ro. 5 rds. He gave his oldest son a farm of 112 ao. 8 ro. 80 rds. ; his second, a farm of 316 ac. 1 ro. 18 rds. ; his youngest, a farm of 168 ac. 8 ro. 18 rds. ; and sold the remainder of his land at $1.35 a rod. To what did it amount ? 11. A farmer has two meadows, one containing 9 a. 8 r. 87 p., the other contains 10 a. 2 r. ^ p. ; also three pas- tures, the first containing 12 a. 1 r. 1 p., the second con- taining 13 a. 8 r., and the third 6 a. 1 r. 89 p. ; by how many acres does the pasture exceed the, meadow land? 12. Divide $462 among 5 men and 6 women, giving to each man thrice the share of a woman. 13. If 8 qrs. 16 lbs. of silk is sufficient for a thread of 100 miles in length, what length of a similar size will 5 oz. spin? 14. If one man consumes in a week 7 lbs. 12 oz. 3 drams of bread, how many men will consume 13 cwt. 2 qrs. t5 lbs. 6 oz. in the same time ? 15. Bought 60 casks of molasses, each containing 58 gals. 3 qts., at 50 cts. per gal. ; afterwards 215 gals. 2 qts. leaked out, and the remainder was sold at 64 cents per gal. ; what was the result of the operation ? SIMPLE PROPORTION. When we have three numbers given, this rule teaches how to find a fourth number, which may have the same proportion to the third number that the second has to the first. 52 SIMPLE PROPORTION. ;( Thus, if the three given numbers be 1, 2, 3, it is re- quired to find a fourth number which will have the same proportion to the 8 that the 2 has to 1. Now, the 2 is double the 1 ; therefore the required number must be double of the 3, that is, 6. To express proportion, the numbers are put down thus, 1 : 2 : : 8 : 0, and are read thus, 1 is to 2 as 3 is to 6. Casb I. — To find out a fourth proportional to three given numbers. Find a fourth proportional to the numbers 4, 8, 6. Rule with Example. — Place them thus, 4:8: and multiply the second and third numbers C together, and divide by the first ; the quo- tient is 12, which bears the same proper- 4) 48 tion to 6 that 8 does to 4. — 12 \ Ans. 24. Ans. 4. Ans. 16. Ans. 8. 6 To 3, 6, 12, find a fourth proportional. To 6, 8, 3, find a fourth proportional. To 3, 6, 8, find a fourth proportional. To 6, 12, 4, find a fourth proportional. To 10, 160, 68, find a fourth proportional. Ans. 1020. Find a fourth proportional to 1020, 68, 150. Ans. 10. Find a fourth proportional to 150, 10, 1020. Ans. 68. Find a fourth proportional to 68, 1020, 10. Ans. 150. Find a fourth proportional to the following numbers : — To 2 tons, 17 tons, and 25^. Ans. 212Z. 10s. To 10 lbs., 150 lbs., and 6«. Ans. 76s. To 9 yds., 36 yds., and I85. Ans. 72s. To 5 lbs., 1 lb., and 15*. Ans. Ss. To 4 yds., 18 yds., and 2^. Ans. 9s. To 1 cwt., 215 cwt, and 60s. Ans. 107505. To 6 tons, 60 tone, and 271. Ans. 2701. it is re- he same the 2 is must be ion, the are read ree given 8,6. 8 : : 6 : G 18 L2 \ 14. 18. 1020. \.ns. 10. Vns. 68. IS. 150. Ibers : — J SIMPLE PROPORTION. A 53 Case II. — When the two first terms are oj^d^^ftm denomi' nations y reduce them to the same. To 3 oz., 112 lbs., and 2«., find a fourth proportional. Rule with Example. — Multiply the oz. lbs. ». 112 lbs. by 16, to bring them to the same 8 : 112 : 2 as the first term, — viz. to ounces. When 16 this is done, the numbers stand thus, — " 3 oz., 1702 oz., 23. 672 112 1792 2 3)8584 1194,2 Find the fourth proportional to the following numbers: To 2 qrs., 240 yds., V2s. Ans. 5760*. To 5«., SOL, 1 yd. Ans. 320 yds. . To 5 cwt., 6000 lbs., Ss. Ans. 855., 600 remains. To 55. 6d.f 140«., 2 yds. Ans. 60 yds., 60 remains. To Ss. 4c?., 11. 10s., 1 yd. Ans. 9 yds. Case III. — When the third term is of different denomina- tions, reduce it to the lowest. To 2 lbs., 112 lbs., and 5s. Qd., find a fourth proportional. Rule with Example. — Multiply lbs. lbs. s. d. the 6». by 12, adding the M. It 2 ; 112 : : 6 6 : then stands thus,— 2 lbs., 112 lbs., 66 12 66c?. Proceed as formerly. , 672 672 66 *♦ 2)7b?2 8696 pence. ,/,-•' I I i ^ i I ^s \i ] ^i 54 k SIMPLE PROPORTION. lbs. Z6«. £ s. 24 :3: : 1 20 28 8 8 1 2)84 Find the ^Bn proportional to the following numbers : — To 2 tons, 14 tons, 2Sl. lOs. Ans. 3990*. To 5 brls., 100 brls., I85. 6c?. Ans. UiOd.' To 4 lbs., 112 lbs., ^d. Ans. 688 farthingu. If 24 lbs. of butter cost £1 Ss., what is the price of 8 lbs.? Rule with Example. — In this ques- tion there are two things mentioned — butter and money. Is the answer to the question to be given in butter or money ? You see at once it is to be given in money. Put down the money, 1/. 85., for the third term. Having done this, you have now to consider where you are to place the 24 lbs. and the 3 lbs. Read 24 over the question, and you will see that j 12)42 the answer must be less than the third term ; for 3 lbs. will not cost so much Ss. Gd. as 24 lbs. If, then, the answer is to be less*, put the less number for the -second term, and the greater for the first. In all questions let the third term, be the same as the answer ; and if the answer is to be greater than the third term, put the.ffreaier second; if it is to be less, put the less second. 1. If 2 lbs. of tea cost 9s., what will 24 lbs. cost? 2. Bought 2 oz. tea for 10 cents ; what is that per lb. ? 3. For 6 pairs of gloves, a lady paid $4.45; what cost 11 pairs? 4. Bought 65 barrels of flour for $422.50 ; what is the price tf one barrel ? 5. If 11 tons of hay cost $212.50, what will 1 ton cost? 1 . - 6. For 45 acres of land a farmer paid $500; what cost 150 acres ? 7. When $60 are paid for 96 arithmetic-books, what will 87 dozen cost ? \s SIMPLE PROPORTION. 55 8. Gave $5.68 for 9 bushels of potatoes; what will 43 bushels cost? 9. Bought five tons of hay for eighty-five dollars ; what would a single ton cost ? 10. A merchant sold 509 chaldrons of coals at $5.50 per chaldroci ; what money was received for the whole ? Hi A gentleman gave $450 for 300 square feet of land, that he wanted for building ; what would an acre cost at that rate ? 12. A bankrupt owes $4968, but he has only money sufficient to pay Sf ^ents for every dollar he owes ; how much money has he to pay his debts ? 13. If 24 yds. cost 3^. 14a. Id., how much must I give for 1 yd. 3 qrs. 2 nls. ? 14. JVhat cost 6 hogsheads of sugar, each weighing 14 cwt. 2 qrs. 24 lbs., at 21. IZs. 6c?. per cwt. ? 15. If. for 7s. Sd. I can buy 9 lbs. of raisins, how much can I purchase for 56^. 16a. ? 16. A grocer bought 6 cwt. 3 qrs. 26 lbs. of sugar, for which he paid 2il. 16a. Sd. ; at what rate per pound must he sell it to gain 42. 10a. 4c?. on the whole ? 17. A person reaches a certain place in 18 days oy walking 8 hours a day ; what number of days would he have. taken had he walked 12 hours a day ? 18. If 14 men could make a ditch in 18 days, in what time could 34 men do it ' 19. A ship was provisioned for a crew of 40 for 3 months; how long would these provisions last, if the crew were reduced to 32 men ? 20. If 8 houses can subsist on a certain quantity of hay for 2 months, how long would 12 horses subsist on the same quantity ? ' , 21. A field 'of corn was to be cut down b;^ 40 men in 10 days; ten of the men, however, did not make their appearance ; in what ti^ie would the field be cut down ? 22. A pole 6 feet high throws a shadow of 5 feet 8 i y"" I / 56 SIMPLE PROPORTION. i I'i inches; what is the height of a spire which throws a •shadow of 166 feet? 23. If 54 men can build a house in 90 days, how many men would be required to do it in 12 days ? 24. Paid $136.50 for wood, at $3.25 per cord; how many cords did I buy ^ 25. If a bushel of turni^^s cost 28 cents, what will 59 bushels cost ? 26. Sold 169 pine logs, for $1.30 each ; what did the whole sell for ? 27. I gave $60 for some refuse boards, at the rate of $1.10 for a thousand feet; how many feet were there in the pile ? 28. A tailor purchased a bale of cloth containing 83 yds. for $415.45, and sells it by the yard at $6.86 j how much does he make on the whole ? » 29. Bought in London 57 yards of broadcloth for 49 guineas ; what did it cost per ell English ? 30. If the penny loaf weighs 7 oz. when flour is $8 er barrel, how much should it weigh when flour is 7.50? 31. If a certain vessel has provisions sufficient to last a crew of 10 men 45 days, how long would the provisions last if the vessel were to ship 5 new hands ? MENTAL EXERCISES 1. If 5 quintals of codfish cost $15, what would be the price of 20 ? 2. If 12 yards of cloth cost $48, what will 15 yards cost? 3. What is the price of three barrels of flour when two cost 13 dollars? 4. If 17 lb. of sugar cost $1.19, what is the price of 3651b.? .5. If 2 cords of wood cost $11.60, what will 18 cords cost? COMPOUND PROPORTION. 57 ows a , how ; how nil 59 [id the rate of lere in ing 83 >j how for 49 18 .our is last a risions lid be yards jn two price cords COMPOUND PEOPORTION. When, in order to find a fourth proportional, several circumstances require to be considered, it is called Compound Proportion. If 14 horses eat 56 bushels of oats in 16 days, how many bushels will be required for 20 horses for 24 days? bush. horses 14 days 16 224 : 20 : 24 480 66 2880 2400 56 224)26880(120 bus. 224 448 448 Rule with Example. — Write down for the third term tha* number which is of the ^ajae kind with the ansv/er required — 66 bush- els. Then take two num- bers of the same kind — 14 horses and 20 horses — and consider, as in Simple Pro- portion, whether, from the nature of the question, the greater or less "is to be put in the first or second term. Here it is obvious that the greater must be in the , second term, as 20 horses will eat more than 14 horses. Take the other two terms, and proceed in the same manner. After all the terms have been put down, multi- ply the two first terms, 14 and 16, together ; do the same with the two second terms, 20 and 24, and proceed as in Simple Proportion. Contraction. — Let the question be the same as in the last example. After the terms have been pro- perly arranged, the operation may often be greatly shortened by using the following method : Draw a line, and place the first terms, 14 and 16, under it, and tlie second and ^^ X )I0 third terms, 20, 24, and 56, above J| 5} it ; then divide any number above 4 10 3 ^ ?!0 X?^X^j3 58 COMPOUND PROPORTION. Kl\ hi the line and any below by any number which will divide both without leaving a remainder. Thus, 14 below and 66 above may both be divided by 7; divide by it, and place the numbers obtained below and above the 14 and 66, drawing your pencil at the same time through the 14 and 66. Again, you see that 16 and 24 may be divided by 8; draw your pencil through tbem, and write the numbers above and below, then cancel the 20 and the 2 ; then the 8 and the other 2. . Multiply all the numbers that remain above the line, and divide the product by the product of all the numbers under the line, if any, for the answer ; thus, 10 X 3 X ^ = 120. This is the answer, as there is nothing below the line by which to divide. *1. If 15 men build 37 roods of wall in 27 days, how many roods will 74 men build in 63 days ? 2. If 8 men for 6 days' work get $40, how much ought 32 men to get for 24 days' work ? 3. If 4 men can mow 20 acres of grass in 7 days, how many acres can 12 men mow in 28 days ? 4. If 6 tailors can make 10 suits of clothes in 4 days, how many suits can 20 make in 7 days ? 5. A wall, 28 feet in height, was built in 15 days by 68 men; how many men, working at the same rate, could build a wall 32 feet high in 8 days ? 6. If 12 horses in 5 days draw 44 tons of stones from a quarry, how many horses would it require to draw 132 tons in 18 days ? 7. A garrison of 1500 men has provisions for 12 weeks, at the rate of 20 ounces per day to each man ; how many men will the same provisions maintain for 20 weeks, allowing each man only 8 oz. per day ? 8. If 50 men can do a piece of work in 100 days, working 8 hours per day, in what time will 120 men do it, working 6 hours per day ? 9. If 4 men receive $20 for 5 days' work, how much would 8 men receive for 15 days* work? 10. If 25 men can dig a trench 86 feet long, 12 feet broad, BILLS OF PARCELS. 59 in 9 days, in how many days would 15 men dig a trench of the same depth, but 48 feet long and only 8 feet broad ? 11. If 20 girls in a factory can do as much work as 15 boys, and 60 boys as much, as 25 men, how many girls would accomplish as much as 250 men ? 12. If a pasture of 12 acres will feed 8 horses 4 months, how many acres will feed 12 horses for 6 months? BILLS OF PARCELS. A Bill is a written account of goods purchased, or work performed. A Bill op Parcels is that which is delivered with the goods at the time of purchase. booeseller's bill. Mr. Thomas Bobebtson 1861. Bought of J. & A. McMillan. June 3. Ingram's Mathematics $1.45 White's Universal History 1.76 Cruise of the Betsey 1.25 Worcester's Dictionary 7.50 Macaulay's History, 5 vols 5.50 $ hosier's bill. Mrs. Young 1861. Bought of John M^'Donald. May 4. 5 pairs of Worsted Stockings @ 62 cts. '^ pair. 6 yards of Flannel "34" "yard. 4 pairs of Gloves '* 56 ** "pair. 8 pairs of Thread Stockings " 48 " ** " 6 pairs of Cotton " " 44 " " *< 60 BILLS OF BOOK DEBTS. OBOOS&'S BILL. . Mrs. YouNa , Bought of John Dickson. 1861. July 16. 12 lbs. of Loaf Sugar, @ 17 cts. •^Ib. 9 lbs. of Green Tea, " 64 ♦« C( • '>, 6 lbs. of Turkey Coflfee, *' 26 " 8 lbs. of Hy sou Tea, " 60 " 16 lbs. of Brown Sugar, f* 9 '* 14 lbs. of Rice, " 6 " <( f 16 lbs. of Currants, " 17 *' 4 # $ BILLS OF BOOK DEBTS. A Bill op Book Debts is a statement of debts formerly contracted. The following is the man- ner in which it ought to be copied from the tradesman's books : — , wine-mebchant's bill. . Mr. Thos. Bobinson 1861. May 24. To 4 dozen Port, ♦* 28. — 3J " Sherry, June 13. — 3 ** Claret, July 19. — 4 J " Burgundy, " 24. — 1 " Champagne, " Sept. 19. — 4 gals. Brandy, " " 27.-3 «« Hollands, " To Wm. Andebson. $9.00*^ doz. '* 9.35 " 11.22 « 12.60 " 7.00 " 3. 10*^ gal. 1.70 i( (( 21 $ di is w th hi fo lb 2 itE (( $ \ • PRACTICE. 61 CKSON. if debts man- m the )EBSON. PRACTICE. Practice is a short method of doing questions in Simple Proportion, by the aid of fractional parts. A less number is said to be the Miquot part of a greater, when the less number is contained in the greater any number of times without leaving any remainder : thus, 3 is an aliquot part of 9 or of 15, and 4 of 16 or of 20. TABLE OF ALIQUOT PARTS. Of a Ton. cwt: 10 is ^ 5 - I Of a Cwt, qrs. lbs. 2 is 1 — Of a Quarter 14 is \ 7 - i 4 - i 1 -^ 16 — 14 — 8 — 7 — i 4 - \ 2 -^ 1 -i^ EuLE. — Multiply i\i% price by the highest name in the quantity, and take parts for the rest of the quantity. Example. -Bought 2qrs.=J)$16.50 29 cwt. 2 qrs. 14 lb. at ^ 29 $16.50 per cwt. ; what did I pay? Here $16.50 1485Q is multiplied by the 29, 33QQ which gives the price of the cwt. 2 qrs., being 473.60 price of cwt. half a cwt., gives $8.25 141b. =^) 8.25 - qrs. for Its price, when 14 - 2.06.25 «' lb. lb., being the quarter of 2 qrs., gives $2.06 as its price = ^ of $8.25. $488.81.25 pr. of whole. 1. 24 cwt. 2 qrs. 7 lb. @ $12.80 per cwt. 2. 14 '* 1 " 8 " '* 16.60 " 3. 7 " 3 " 6 *' *' 24.40 " 6 62 SIMPLE INTEREST. 4. 16 cwt. 2 qrs. 181b. @ $30.20 per cwt 6. 27 1 16 " 48.48 6. 32 2 14 " 6.30 7. 86 1 8 « 22.72 8. 45 1 14 " 7.36 9. 48 2 4 " 18.24 • 10. 40 -* 9 " 20.20 fM' SIMPLE INTEREST. Interest is money paid for the loan of money. The Principal is the sum of mouey lent. The Rate per cent, is the sum to be given for the loan of a hundred. The Amount is the principal and interest added together. Thus, if I get Arom a banker $100 at 5 per cent, I must pay him back at the end of the year the principal, viz. $100, and the interest, viz. $5. The principal and in- terest, viz. $105, is the amount. Note. — Any of the following examples, or others similar, may be used for Mental Exercises. Case I. — To find the interest of any sum for one or more years. What is the interest of $106 at 6 per cent, per $106 annum, for three years ? 5 Rule with Example. — Multiply the principal, $100, by the rate, 6, and divide the jiroduct 630 6.30 by 100, which is done by simply pointing off 3 the tens and units. The quotient, $5.30, is the interest for one year; this multiplied by the 15.90 number of years, 3, will give the interest for . the number of years, which in this instance is $16.90. SIMPLE INTEREST. 68 1. What is the interest of $78 for 1 year (^ 6 per cent. ? 2. What is r.he interest of $675 for 2 years @ 5 per cent. ? 3. What is the interest of $260 for 4 years @ 4 per cent. ? 4. What is the interest of $480 for 2J years @ 6 per cent.? 5. What is the interest of $575 for 10 years @ 6 per cent. ? 6. What is the interest of $60 for 12| years @ 6 per cent. ? 7. What is the interest of $84 ,for 7 years @ 3 per cent. ? 8. What is the interest of $95 for 8 years @ 4} per cent. ? 9. What is the interest of $760 for 15 years @ 6 per cent. ? 10. What is thfi interest of $1000 for 10 years @ 1 J per cent. ? boused 5.30 3 5.90 Case II. — To find the interest for weeks and days. What is the interest of $400 for $400 10 weeks and 3 days at 4 per cent. 4 per annum ? Rule with Example. — By Case I., the interest of $400 for one year at 4 per cent, is $16. Mul- tiply it by the number of days, which is 73, =10 weeks and 3 days, and divide by the number of days 865)ii68.00($3.20 m a year. The quotient, $3.20, is 1095 the interest for 73 days. 16.00 78 4800 11200 < ' ' 730 730 64 SIMPLE INTEREST. 11. What is tho interest of $42G fcr weeks and -4 clays at 6 per cent, per annum? 12. What is tho interest of $7G4 for 9 weeks and 3 days at 4 per cent, per annum? 13. What JD the interesL of $376 for 240 days at 4J per cent, per ann im ? ^ 14. What is the amount of $718 for 120 days at 3J per cent, per annum? 15. What ii? the interest of $860 for 6 years, 8 veeks, and 4 days at 2^ per cent, per annum? 16. What is the amount of $978 for 3 yeurs and 136 days at 4 J per cent, per annum? • * 17. What is the interest of $7462 for 9 years and 6 weeky at 3} per cent, per annum ? 18. What is the amc rat of $836 for 12 yoars and 93 days at 4 1 per cent, per annum ? 19. What is the interest of $764 for 5 weeks and 6 days at 3J^ per cent, per annum ? 20. What is the amount of $9804 for 10 years, 7 weeks, and 4 days at 4| per cent, per annum ? 21. Required the interest of $460 for 2 yeui 3, 4 months, and a day, at 5 per cent, per annum. 22. Required the interest of $326 for 8 weeks and 6 days at 4 per cent, per annum. 23. What. is the amount of $864 for 120 days at 4| per cent, per annum ? 24. Required the amount of $246 for 3 years, 6 weeks, and 4 days at 2^ per cent, per annum. Case III. — To find the interest for months at 6 pe^ cent. What is the interest of $308 for 8 months at 6 per cent. ? Rule with Example. — Six per cent, for a year 368 is h per cent, for a month, and 4 for eight monthr. 4 Hence the rule, Multiply by half the number of months, and divide by 100. $14.72 COMPOUND INTEREST. 65 4.72 , r 25. What is the 26. What is the 27. What is the 28. What is the 29. What is the 80. What is the 81. What is the 82. What is the NoiJB.— In New interest of $637 for 10 months ? interest of $61.18 for 16 months? interest of $11.89 for 19 months? interest of $1671. r2 i'or 14 months? interest of $819.75 for 11 months? interest of $3671.25 for 18 months? interest of $9.08 for 23 months ? interest of $167.18 for 50 months? Brunswick the legal interest is 6 per cent. ' COMPOUND INTEREST. Compound Interest is interest, not only for the use of the sum borrowed, but also for the use of the interest, if it be not paid at the end of a year. Thus, if I borrow $100 at 5 per cent., I owe at the end of the year $105. If I wish to pay oflF the debt, I pay $106. If I wish merely to pay the interest, I pay $5, and still owe $100. If, ho soever, I do neither, it is ob- vious that at the end of the second year I must pay inte- rest, not upon $100, but upon $105. What is the compound interest of $240 for 8 years at 6 per cent. ? 1st year's prin. 1st year's int. 252 2d year's prin. add 12.60 2d year's int. Rule with Example. — 240 Find the interest upon the add 12 principal fori year at 5 per cent., viz. $12, and add it to the principal. At the be- ginning of the second year the principal is $252 ; find the interest upon this for 1 year at 5 per cent., add it, and so on for any number 277.83 Amt. in 3 yrs. of years. $277.83 is what subtract 240 Principal. $240 amounts to in 3 years. The compound interest 87.83 Comp. int. is found by taking the in 3 years. 6* 264.60 3d year's prin. add 13.23 3d year's int. C6 DISCOUNT. original principal, $240, from the amount in 8 years, $277.83, and what remains, $37.83, is the compound interest on $240 for 3 years. 1. Required the compound interest on $420 for 3 years at 5 per cent. 2. Required the amount of $G40 for 4 years at 3 per cent., compound interest. 8. What will $436 amount to in 3 years at 4J per cent., compound interest? ■ 4. What is the compound interest on $078.80 for 6 years at 3 J per cent per annum ? 5. What will $764 amount to in 4 years at 6 per cent., compound interest? 6. What is the compound interest on $786.10 for 6 years at 4^ per cent, per annum ? 7. Required the amount of $16.50 in 10 years at per cent., compound interest. DISCOUNT. Discount is an allowance made for the payment of money before it is due. Thus, if a person gave me his note for $100, to be paid at the end of a year, and I wished money immediately, I might take it to a banker, who, if he was sure of getting the money at the end of the year, would give me $94, keeping $6 to himself for the interest of the money he had given me. The $6 is called discount, and the $94 is called tho present worth of $100 a year hence at 6 per cent. Rule. — Fine the interest of the sum of the note or debt at the given rate and for the given time, which is called the discount, and subtract it from the sum for the present worth. DISCOUNT. 67 paid |eiy, I itting $94, |ey he >l^4is |6 per te 01* Ich is Ir the What is the present value of $250 due in two years at 6 per cent. ? Example.— Hevo $15 is the interest of $250 $250 for 1 year, and $30 for 2. Subtract 6 the $80 from the $250, and $220 is the ' present value. 15.00 2 $250 30 $30.00 $220 1. What is the present value of $640 due 8 years hence at 6 per cent ? 2. What is the discount on $736 due 9 months hence at 6 per cent. ? 3. What is the discount on $370 due 100 days hence at 4 per cent. ? 4. What is the present worth of $245.50 on March 26, when the note is payable on June 23, three days* grace being allowed, at legal interest ? 5. What is the value on May 1 of a note for $300, which was drawn on January 1, payable in a year at 6 per cent., the three days' grace being allowed ? 6. What is the disco'int on $381.15 due 4 months hence at 5 per cent. ? 7. A merchant bought 450 quintals of fish at $3.50 (^ash, and sold them immediately for $4.00 on 6 months* credit, for which he received a notte. If he should get this discounted at a bank, what will he gain on the fish? Jg!^*" The rule- given above is that which is always employed in actual practice. It gives the discount too large, and consequently the present value too small. The coBKECi 1. c'Le.— As the amount of $100 for the given time and at Lhe rate is to the debt, so is $100 to the present worth of the note or "^.ebt." 68 COMMISSION, BROKERAGE, INSURANCE. Taking the previous example, 12 is the interest of $100 for 2 years at 6 per cent. : so we add the $12 to the $100 for the first term, take the amount of the note or debt for the second, and the $100, being the present value of $112, for the third, and work out the pro- portion. The answers to the exercises are given both ways to a cent. 112: 250:: 100 100 112) 25000 223.21 COMMISSION, BROKERAGE, INSURANCE, BUYING AND SELLING STOCKS. Commission is an allowance given to an agent or factor for buying or selling goods, negotiating bills, &c. Brokerage is an allowance to a broker for pro- curing sales, transfers of property, &c. Insurance is an allowance, called premium, given to persons who engage to make good the loss of ships, merchandise, houses, &c. that may be lost or damaged by storms, fire &c. Stock is the debt owing by government, or it is the capital of any trading company. Any questions in these rules may be performed by the rules for Simple Interest. 1. What is 2 per cent, of $335 ? 2. What is 5 per cent, of $594? 8. A man received a legacy of $10,000, but he lost 25 per cent, of it in speculation ; how much remained ? 4. Bought 25 shares of the stock of the Bank of New Brunswick, at $100 each ; but scon after I sold them at 11 per cent, premium; what was the gain? .0::100 100 )000 223.21 ays to a BUYING AND SELLING STOCKS. 69 ANCE, S. n agent otiating for pro- 'emium, Ithe loss be lost or it is by the lost 25 I of New them at 5. What is the commission on the sale of a quantity of goods valued at $4820, at 2 per cent. ? G. An auctioneer sells goods to the amount of $789 at 2 per cent.; what is his commission? 7. My factor advises me that he has purchased on my account 97 bales of cloth at $25.50 per bale ; what is his commission at 2^ per cent. ? 8. A broker in Montreal exchanged $46256 on the St. Stephen's Bank, at ^ per cent. ; what did he receive for his trouble ? 9. What must be given for 75 shares of bank-stock, at- 25 per cent, premium, the original shares being $100 each? 10. A stockholder in a railway sells his right of pur- chase on 5 shares of $100 each, at 12 per cent, advance ; what is the premium ? ^.^ 11. Bought 84 shares in a certain joint-stock company, at 12 per cent, below par, and sold the same at 17 2^ per cent, above par ; what sum did I gain, the original shares bqing $175 each? 12. What is the premium of insurance on $8G8, at 12 per cent. ? 13. What is the insurance upon a property valued 'at $17498, at 4 per cent. ? 14. A house, which was valued at $5904, was insured at 1| per cent. ; what was the premium? 15. A bark and her freight, rated at $45,000, are in- sured at 3f per cent. ; now, in the event of the vessel and cargo being destroyed, what will be the actual loss to the insurance company ? 16. My agent in London has purchased goods for me to the amount of £4755, at 3 per cent. ; what is the com- misfeion ? 17. What is the purchase of $5000 railway-stock, at 76^ per cent. ? If m 70 BARTER. m 18. What is the price of $28709 bank-stock, at 168 per cent. ? 19. What is the expense incurred in insuring a ship and cargo, at 3.75 per cent., the ship being worth $9878 and the cargo worth $3497 ? 20. If a broker disposes of woollen goods to the amount of $6050, muslin to $5406, and hardware, $3515, what will his commission amount to, at 2^ per cent. ? 21. A broker negotiates a bill of exchange of $2500, at ^ per cent, commission ; what is his commission ? 22. My agent at Savannah informs me that he has dis- posed of 500 barrels of herrings, at $7.60 per barrel, 88 barrels of apples, at $2.76 per barrel, and 66 cwt. of cheese, at $10.60 per cwt. ; what is his commission, at 2^ per cent. ? BARTER. Barter is the exchanging of goods of one kind for goods of another kind, either at the market value of each, or at prices mutually arranged by the parties who barter. How many yards of cloth, at $2 per yard, ought I to get for 98 lbs. tea, at 50 cts. per lb. ? Rule with Example. — Find the value of the goods given. In this example, the value of the tea is found to be $49 ; you have, there- fore, to consider how many yards of cloth you ought to receive for $49.00, the value of one yard being $2.00. All the questions in this Rule may be solved by Simple Proportion. 1. How many pairs of boots, at $3.50 per pair, should be exchanged for 206 pairs of stockings, at 40 cts. per pair ? tbs, 98 60 2)49. 00 24^ yds. PROFIT AND LOSS. 71 168 per I a ship h $9878 amount 15, what 12500, at has dis- ' barrel, ) cwt. of 3sion, at 2. How much patty, at 10 cts. per lb., ought I to re- ceive for 18 p»irs of gloves, at $1.05 per pair? 3. How much coflFee, at 20 cts. per lb., should I receive for a chest of tea, containing 55 lbs., at 50 cts. per lb. ? 4. A wine-merchant bartered 94 gals, of wine, at $4.00 per gal., for Jamaica rum at $1.75 per gal. How much ought he to receive ? 5. How much silk, at $3.50 per yard, should be ex- changed for 90 barrels of apples, at $2.25 per bl. ? 6. A tallow-chandler gave 100 boxes of candles, at $3.75 per box, for 22 cwt. 3 qrs. 16 lbs. tallow; what did the tallow cost per lb. ? 7. How much iron, at 5 cts. per lb., ought a nailer to receive for 10,000 nails, at 9 cts. per hundred ? 8. How much tobacco, at $25 per cwt., must be bar- tered for 6 cwt. 1 qr. 14 lbs. of snuflf, at 90 cts per lb. ? He kind market by the ght I to i^ds. should ets. per PKOFIT AND LOSS. This Rule is used for the pv .pose of discovering what* is lost or gained in the purchase or sale of goods. Case I. — ITie prime cost and selling price being giveUf to find the entire gain or loss on any quantity of goods. Bought^ yards of silk, at $2.50 per yard, and sold it for $3.15 ; what did I gain upon the whole ? Rule with Example. — Subtract the cost price, $2.50, from the selling price, $3.15, and multiply the gain upon a yard, 65 cts., by the number of yards bought, 9. The product, $5.85, is the gain on the 9 yards. $3.15 2.50 65 9 $5.85 i'Ji PROFIT AND LOSS. 1. Bought 256 yards ribbon, at 9 cts. per yard, and sold it for 11 cts. ; what did I gain upon tire whole ? 2. Bought 106 logs, at $3.95 each, and sold them for $8.41 ; what did I ^ain upon the jv^hole? 3. Bought 506 lbs. cheese, at 16 cts. per lb., and sold it at 19 cts. ; what was the amount of profit ? 4. Purchased 208 lbs. butter, at 24 cts. per lb., and sold it for 22^ cts. ; what was the whole loss ? 6. A fruit-dealer bought 12 chests of oranges for $35.00 ; whether did he lose or gain by selling them at $3.15? Case II. — The prime cost and the selling price being given, to find the gain per cent. Bought velvet at $4.50 per yard, and .^old for $5.05; what was the gain per cent. ? Rule with Example. — Find the gain or loss by the former case ; then say, as the cost price, $4.50, is to $100, so is the gain, 55 cts., to the gain or loss per cent. $5.05 4.50 4.50 : 100 55 100 4.50)5500.00 1222f 1. If a pound of sugar be bought for 9 cts. and sold for 11 cts., how much gain per cent. ? 2. When a pound of tea is bought for $0.55 and sold for $0.02, what is the gain per cent. ? 3. If a ham be bought for $3.87 and sold for $2.53, what is the loss per cent. ? 4. When molasses is purchased for $0.30 per gallon and sold for $0.34, how much is the gain per cent. ? 5. Bought a quantity of goods for $1005.00, but sold' them for $9075.00; required the gain per cent. PARTNERSHIP; OR COMPANY BUSINESS. 73 rd, and lem for nd sold b., and $35.00; 15? \g given, $5.05 ; 105 50 55 100 5500.00 1222f id sold id sold $2.53, gallon it sold PARTNERSHIP, OR COMPANY BUSINESS. Partnership is the connection of two or more persons in business transactions. Such a union is called a Company or Firm. The profits or losses (as the case may be) are shared by each person, in proportion to the capital each puts into the com- mon ^nd or joint stock. Rule with Example. — As the whole stock, or fund, is to each partner's share of such stock, so is the whole profit or loss to his share of the profit or loss. X, Y, and Z, whose stocks in trade are respectively $300.00, $450.00, and $676.00, have to share a gain of $650.00 ; what is the share of each partner ? X's stock = $300 Y»s do. =$450 Z's do. =$676 Whole stock = 1425 As 1425 : 300 : : 650 : $136.84^f X's share of gain. As 1425 : 460 : ; 650 : $206.26|i Y's do. do. As 1426 : 675 : : 660 : $807.89|^ Z's do. do. Proof' $660.00 1. Two merchants engage in business; A put into the business $500.00, B $2500.00; the gain was $6500.00; what is the share of each ? 2. A, B, G, and B purcliase a ship ; A pays for 6 shares, B for 5 shares, C for 8 shares, and D for 4 shares. They receiv'j of net freight, for a voyage to Pernambuco and I^io Janeiro, $866. How much of this sum ought each to receive ? 3. James Williams, John Sm^ton, and William Win- stanley engage ia business, under the style of Smeaton, Winstanley & Co. They gain the first year they are in business $950.00. Their shares in the joint stock were r I 74 partnership; OR company business. respectively $250.00, $450.00, and $726.00. What was ' the share of each of the amount gained ? 4. E and F enter into partnership; E puts in $4000.00 and F $2000.00; what wa& each man's share of the $670 which they gained ? Case II. — Partnership with time. BniE. — Multiply each person's money by the time it continued in the business, a^d proceed as in Case I. Example.— A and B enter into partnership; A had a capital of $400, which was employed 6 months, and B a capital of $450, which was employed 8 months. They gained $120. What was the share of each? Am. A's $48, B's$72. Capital. $ $ A 400 X 6 = 2400 As 6000 : 2400 : : 120 : 48 A's share. B 450 X 8 = 3600 As 6000 : 3600 : : 120 : 72 B's share. 6000 ^ Charles Jones, Henry Adams, and John Stephens formed a company, under the name of H. Adams & Co., and commenced business, 1st June, on $2000.00 put in by Jones ; the 1st August, Adams put in $3000.00, and 1st September Stephens put in $4000.00. At the end of that year they had gained $1600; what was each partner's share ? 6. A, B, and C trade in company. A put in $700.00 for 5 months; B put in $800.00 for 6 months ; and C put in $500.00 for 10 months. They gain $899.00 ; what is eacu trader's share of the gain ? 7. H, I, J, and K transact business in company ; H puts into the joint capital the suiu of $326 for 3 months ; I the sum of $460 for 4 months ; J $676 for 6 months, and K $600 for 6 months ; their profits were $4999 ; what "w as their share of the gain ? 8. Four men hired a pasture for $60. A put in 5 EXCHANGE. 75 horses for 4 weeks ; B put in 6 horses for 8 weeks ; C put in 12 oxen for 5 weeks, calling 3 oxen ec«r8 to improper fractions. Having done this, bring tbem to '% common denominator. Add all the numerators together, and place, under the result, the common denominator. If the answer be an improper fraction, bring if to a mixed number. Add together the following fractions, f , |, and 4^. Here the mixed number 4^ is first brought to the improper fraction |, and then all the frac- tions are brought to a common denominator. 30 IX f= H W = 6M Add together the following fractions and . _^ed numbers. 1. I + I + *• 2. f + A + if . 3. * + ii +:if. 4. J + if + il + A. 6. A + ii + A + if. 6. f i + li + li + 7- f off + A + foff 8. ^-f ^yof^f + |of5^. 9. ^fof7 + |of9 + fofl4. 10. M + iiof2f + iof6|. 11. i^of|fofl7f-t-f ofl2. 12. if + i|of9f + iiof8f VULGAE FRACTIONS. 83 I a com>. b will be lave the and ^V , SUBTRACTION. RuLE.^Reduoe the fractions to common denominators, as in additioa. Find the difference of the numerjators, under which write the common denominator. * From ^ take f . Here the fractions are first 10 w 7 jjl brought to a common denomina tor, then the 60 taken from the 84, and the common denominator written under the difference. = ^ What is the difference between the following fractions ? •actions, ng done i all the ult, the nproper = m imbers. ^^' ^of 14. f6f. fl2. f8f f-f A. 1. 2. 4- ^j — xV 6. 41 -.^. 6. 5f - V. 7. 3f — 2|. 8. 9^^ -. 6f 9. ^^ — ^ of 4. 10. ii - 3^ of |. 11. 169 -- 14f 12. 76J — I of 19. MULTIPLICATION. Rule. — Reduce the mixed numbers to improper frac- tions, and compound fractions to simple ones ; after this has been done, multiply all the numerators together for the numerator of the product, and all t jie denominators together for its denominator. Multiply6f byf of J. 6f=!V>andfofJ = it thenVXM=¥^-8n Ans. Here the mixed number 6| is con- verted into the im proper fraction ^, and the compound fraction | of | into the simple fraction A|. The numerators and denomina- tors being multipliea, produce the improper fraction W, which being reduced to a mixed number gives 344 = 3|. 84. VULGAR FRACTIONS. Multiply together the following fractions. 1. f X f . 2. i X A- 8. A X H. 4. AX A. 6. 8f X A- 6. 7 X A. 7. 6f X Hi. 8. 3f X 4f . 9. 8f Xfoff 10. 16 X ^ of ^^. 11. 17| XHofTf 12. 24A X if of 9^. DIVISION. BuLE. — Prepare the fractions as in multiplication ; then invert the divisor and proceed as in multiplication. 4 V 6 = 20 Divide f by f ^ -^ | inverted thus, y w g ^ 21 1. Divide V by H- 2. U A- 4. M f «• ih A- 7. Divide 5f by f 9. 3^ 9^. 10. 9| I of 7. 11. 116^ iof5^. 12. J of I i of |. REDUCTION, Continued. Case VI. — To reduce fractions from one denomination to another. Rule. — ^If from a lower name to a higher, multiply the denominator, as in reduction of integers. If from a higher name to a lower, multiply the numeratorf as in reduction of integers. Reduce f of a farthing to the fraction of a pound. Here the denomi- 2 2 1 nator is multiplied, 3 v 4 X 12 X 20 = 2880 '' as it IS to be brought ^^ ^^ ^^ to a higher name. 1440 VULGAR FRACTIONS. 85 then Beduoe f of a pound to the fraotion of a penny. Here the numerator is mnl- 8 X 20 X 12 = 720 tiplied^ as it is to be brought g *"T~" = to a lower name. 1. Reduce ^ of a farthing to the fraotion of a pound, 2. Beduce f of a pound to the fraction of a penny. 8. Reduce f of a shilling to the fraction of a guinea. 4. Beduce f of a shilling to the fraction of a farthing. 5. Beduce ^^^ of a day to the fraction of a week. 6. Beduce | of a week to the fraction of an hour. 7. Beduce f of a nail to the fraction of a yard. 8. Beduce | of a cwt. to the fraction of a dram. 9. Beduce f of a yard to the fraction of a mile. 144 T 1440 Case VII. — To express any given quantity as a fraction of another quantity y considered as an integer. BuLE. — Reduce both quantities to one denomination; then make the reduced integer the denominator, and the other quantity the numerator. What part of XI is 13». 4c?. ? Here both quantities, the £1 and the 13*. 4c?., are reduced to pence; the pence in the integer, 240, is made the denominator, and the pence in the other quantity is made the nume- rator; the fraotion ||^ of a pound is, when brought to its lowest terms, equal to f of a pound. 10. Beduce 14«. 6«?. to the fraction of a pound. li. Reduce lis. id. to the fraction of a pound. 8 £ t. d 1 20 13 4 — 12 20 12 160 240 then ^1^ : = iAns i86 yULOAB FRACTIONS. 12. Bedaoe 13. Reiduoe 14. Reduce 16., Reauce 16. Reduce 17. Reduce ounce . • 18. Reduce 19. Reduce day. 6s* 8\d. to the fraction of a pound. 17«. 9 a nd ta ke f of a shilling. 8. From -rV <>^^ 3> shilling take f of | of a penny. 4. W^afcijii i ' va^e of j yard of cloth at J£|^f. per yard? -j* , ^,-- - '._*w>--- 5. What is the value of ^ oz. of silver at £^ per lb. i 6. If 8^ yards of clotli cost 49|«., what is the price per yard? 7. What is ihe price per yard, when 8 pieces of cloth, each 12f yards, cost i^46f ? 8. What is the di:^rence between f of a league and f of a niile ? 9. y/hat is the sum of f of a cwt., 7} lbs., and 4| oz.'? 10. From | of a guinea take f of a pound. 11. How much is 8 times {^ of a yard ? 12. How much is -^ of f of a pound sterling ? 13. A yard of ribbon cost 17d. ; what is the price of ^ of ^ of a yard? 14. If ^ of a yard cost £^, what ought to be paid for 6f yaifs? 15. If 2| yards of flannel cost 3|«., what is the price of 4i yards ? 88 DECIMALS. 16. If ^ of a ship cost £273}, what is ^ of her worth ? 17. If f of a cwt. cost £i^y what will i^ lbs. cost? 18. If 1 lb. of coffee cost 2|«., how many pounds can I have for 38^. ? 19. If 7f yards cost £7 18s. id., how much did 49,11^ yards come to ? , 2Q. What cost V^^ quintals offish at $4.75 per quintal? 21. What cost J of a cord of wood at $6.75 a cord? _ 1_ DECIMALS. A Decimal Fraction is a fraction whose de- nominator is 10, 100, 1000, &c., or a uni. with as many ciphers annexed to it as there are places in the equivalent decim-?^. Thus, y%, -^^^y iViftyj ^^^ decimal fractions, and are equivalent to .5, ,25, .325, whicl are decing^als, u point being placf d at the left-hand side of the latter, to distinguish them from integers. In reading the^ decimals, the first is called 5-tenths, the second 25-hundredtLs, and the third 325-thousanfl'hs. When there are not so many figures in the numerator as there are places iu the equivalent decimal, as many ciphers as are necessary must be prefixed : — thus, y J^ = .03, and y^^^j ^ = .003. Ciphers on the left hand of a decimal decrease its value tenfold : thus, .5 is 5-tenths, .05 is 5-hun- dredths, and .005 is 5-thousandths. Ciphers on the right do not alter the value ; for .5, .50| .500, are the same as f\j, /g^, y^q, and these are of equal value. DECIMALS. 89 worth ? ost? ads can id 49^^. ][uintal? ord? ADDITION; Bttlb. — Place the numbers to be added so that the decimal points be directly under each other, and add as in Simple Addition. Insert the point in the ans'^er. directly under the other points. Add together the following numbers : (1) (2) 2.13 43.27 .426 21.2 7.63 640.072 9.042 712.417 41.007 .962 820.71 2.006 84.243 217.C72 9.841 i 3se de- v^ith as aces in h> are 5, .25, Xf d at 1 them le first s, and n the valent ust be 3. crease 5-hun- )n the 0, are equal 4. Add 4.231, 72.32, 920.74, .9374, 376.05. 6. Add 723.312, 91.0006, 2.0251, 8724.7, .00007. 6. Add 37.214, .736, 7213.04, 123.476, 21.6743. 7. Add 800.273, 498.0009, .296, .0071, 4266.008. 8. Add 320.492, .23687, 970.0083, 9.086, 41.762. SUBTRACTION. KuLE. — Place the numbers as hi Simple Numbers, and insert points. in addition; subtract as the point under the other 1. Ft&m 72.378. take 2. From 9.007 take 8. From 41.217 take 4. From 298.01^ take 6. From 840.001 take 6. From 279.712 take 7. From 72.0076 take 8. From 900.005 take 9. From 243.21 take 10. From 462.0068 take 4.861 .962 7.0968 .9999 170.98 97.0076 1.973 89.1171 .964213 134.791 MULTIPLICATION. Rule. — Arrange the factors and multiply as In integers. Reckon the number of decimals in both factors, and point 8* 90 DECIMALS. off as many from the right of the product. When the number of figures in the product is not so great as the number of decimal places in both factors, as many ciphers as may be necessary to make up the deficiency must be placed at the left of the product. Multiply 7.4 by .86 7.4 .85 870 222 2.590 In the above example there are three decimal places in the multiplicand and multiplier; therefore three figures are pointed off from the right of the product. 'ultiply .045 by .03 .045 .03 .00136 In the above example there are five decimal places in the factors, and only three figures in the product ; therefore two ciphers are placed at the left of the pro* duct to make the number of decimal places in the pro- duct equal to that in the factors. * 1. 2. 8. 4. 6. 6.* % 8. 9. 10. 11. 1^ Multiply .27 by .27 4.21 — 8.41 97.04— 80.03 .4102— .t004 .7 — .806 .879 — 10 2*00.7— 48.003 - 704.23— .0007 .786 — 100 4.862 — .75 200.03— .002 .00076— 1000 11 * In order to multiply a decimoJ by 10, remove the point one to the right ; if by 100, remove it two places ; and ao on. • DECIMALS. DIVISION. 91 RniB. — Divide as in integers. Point off aiLmany de- oimal places in tlie quotient as the diyiden.y 2.84 .496 .278 7.6 -_ .734 7.28 __ 4.06 .024 __ .001 29.6 ._ 10 724.1 ._ 88.07 82.08 __ 9.0002 7.624 ._ 2.001 .5213 _ .24121 31 ___ .124689 3468.9 — 1000 * To divide by 10, 100, Sec., remove the decimal place of the dividend as many places to the l^t as there are ciphers. , / >. / Vi 92 DECIMALS. < fi REDUCTION. GasiJ. — To reduce a vulvar fraetion to a decimal, BuLB.-Jjivide the numerator by the denominator; annexing as many ciphers to the numerator as may be necessary. Point off as many decimal places in the quotient as there were ciphers annexed to tiie numerator. Reduce^ to a decimal. 2)10 .6 Aru. 1. Reduce | to a decimal. 2. — i 8. I 4. i 6. — * 6. i Reduce f to a decimal. 4)800 .76 Afu. 7. Reduce ^ to a decimal. 8- — T^ »• — H 10. — A "• — mt 12. tM Case II. — To reduce a, decimal to a vn^ar fraction. . Rule. — Make the given decimal the numerator, and place under it, for a denominator, a unit, with as many ciphers as there are places in the decimal. Reduce .6 to a Tulgar frac- tion. ^Ana. R.educe .078 to a vulgar fraction. jii^ Ana. 1. Reduce .25 to a vulgar fraction. 2. .625 8. .875 4. .006 6. .01 6. .001 7. .41 8. .021 9. .007 10. .019 w- DECIMALS. 93 ator; ay be 1 the rator. al. mal. and [uany ulgar Casi III.— 7b reduce -numbers of a tower denomination to the decimal of a higher. Rule. — ^Write the given numbet>8, if more than one, directly under each other, beginning with the lowest, md divide by as many of the lower as make one of the higher, annexing ciphers if necessary. Reduce 12«. Zd. to the decimal of a pound. • 12) 8.00 20)12.250 .6125 Ana. Here the shillings and pence are placed under each other, beginning with the lower, and each di- vided by as many of the lower as make one of the higher. Reduce 16«. 6|(f. to the decimal of a pound. • 4) 8.00 12) 6.7500 20)16.56250 .828125 Ans. Here the farthings, pence, and shillings are placed under each other, begin- ning with the lowest ; each is then divided by as many of the lower as make one of the higher. 1. Reduce 2. Reduce 8. Reduce 4. Reduce 5. Reduce 6. Reduce 7. Reduce 8. Reduce 9. Reduce 10. Reduce 11. Reduce acre. 19«. 6^d, to the .decimal of a pound. 15«. 9|(^. to the decimal of a pound. 13«. id. to the decimal of a pound. 9d. to the decimal of a pound. 3 owt. 2 qrs. 8 lbs. to the decimal of a cwt. 4 feet 3 inches to the decimal of a yard. 26 min. 84 sec. to the decimal of a week. 5 furlongs 8 poles to the /lecimal of a mile. 4|(f. to the decimal of a guinea. 5 dwt. 12 grs. to the decimal of an ounce. 2 roods 12 perches to the decimal of an ii ^ .^^ii^< IMAGE EVALUATION TEST TARGET (MT-3) A ^ T/. ^ 1.0 I.I 11.25 S lia II 2 V] ■^r ^? > ^^^y %^* > 7 % *> > J^'^4 Photographic Sciences Corporation m V 4^ is. ;\ is \ fv 23 WEST MAIN STREET WEBSTER, N.Y. MS80 (716) 873-4503 i % >, 94 DECIMALS. 12. Beduoct 17 yards, 1 foot, 6 inches, to the deoimal of a mile. Cass lV,~^To find the value of a decimal. Bulb. — Multiply the decimal by as many of the next lower denomination as make one of the giyen denomi- nation. Point off from the product as . many decimal places as are in the given decimal. Prcceed thus to the lowest denomination. The figures on the Idft of the points are the value of the decimal. What is the value of .427 of a pound? .427 20 What is the value of .243 of a day? .248 24 8.540 12 6.832 60 6.480 4 49.920 60 1.920 Am. Ss. 6ld, 55.200 Am. 6 hrs. 49 min. 65 sec. 1. What is the value of £.7634? 2. What is the value of £.3412 ? 3. What is the value of £.0076 ? 4. What is the value of .764 cwt. ? 5. What is the value of .936 lbs. avoirdupois ? , 6. What is the value of .007 ton r 7. What is the value of .732 shilling ? 8. What is the value x)f .9218 day ? 9. What is the value of .496 yard ? 10. What is the value of .0796 mile? | 11. What is the value of ."J •321b. troy? INVOLUTION. 95 Imal of 12. What is the value of .987 oz. avoirdupois ? 13. W^iat is the value of .987 oz. troy ? 14. What is the value of .779 lbs. avoirdupois ? lie next lenomi- decimal ,6 to the of the of .248 55 see. INVOLUTION. When a number is multiplied by itself, tb« pro- duct is called a power, and the uumber multiplied, the root. Thus, 2X^ = 4: here 4 is the square or second power of the root 2. Again, 2 X ^ X ^ "== ^ : ^^^^ ^ ^ ^l^e oube or third power of the root 2. Again, 2X2X2X2== 16 : here 16 is the fourth power of the rooi 2. 1. Fi|id the second power pf 8. 2. B^quired the third power of 18. 8^ Biise 82 to the fourth power. 4. Involve 19 to the fifth power. * 5. Involve 38 to the sixth power. 6. What is the seventh power ot 5 ? 7. What is the twelfth power of 7 ? 8. Involve 8 to its eiglith power. EVOLUTION. Evolution is the method of finding the roots of numbers. EXTRACTION OF THE SECOND OR SQUARE ROOT. To extract the square root of any given number is to find a number which, when multiplied by itself, will produce the given number. / 96 EVOLUTION. 106929(327 62) 169 124 647) 4629 4529 What is the square root of 106929 ? Bulb with ExAMPLB.-rDivide the given number into periods of two figures each, by placing a point over the unit figure, and over every al- ternate figure towards the left. Find the square root, 8, of the first period, 10, and place it in the quotient. Sub- tract the square of it, 9, from the first period, and to the remainder annex the next period, 69, for a dividend. Double 3, the root already found, for 'a divisor, and supposing the unit figure, 9, omitted, find how often it, viz. 6, is contained in the dividend. It is contained 2 times ; place the 2 then both in the quotient and the divisor. Multiply the divisor, 62, b^ the 2, and subtract the product, 124, from the dividend. Bring down another period, and proceed thus till all the periods are brought down. If there be a remainder after all the periods are used, periods of ciphers may be annexed f when the result will be decimals. Should there be decimals in the given number, still the pointing is to begin from the unit's place of the inteffers, and a point to be placed over every alternate figure both right and left. The square root of a fraction is found by extracting the square root of the numerator for a new numerator, and the square root of the denominator for a new denominator : if, however, this cannot be done, let the fraction be re- duced to a decimal, and the root extracted as before. 1. What 2. What 8. What 4. What 5. What 6. What 7. What 8. What is the is the is the is the is the is the is the is the square root of 30976 ? square root of 1234321 1 square root of 2052.09 ? square root of 4795.25731 ? square root of 24674.1264? square root of ^j ? square root of -^^ ? square root of 60^ ? EVOLUTION, 97 )(327 . )ntaiiied ;e the 2 Liply tlie 24, from proceed f ods are e resuU le given unit's er every ting the tor, and ainator : a be re- »re. EXTRACTION OP THE THIRD OR CUBE ROOT. ' To extract the cube root of any giycn number is to find a number which, when multiplied twice by itself, will produce the given number. Find the cube root of 12812904. 12812904(234 4812 645904 Rule WITH Ex- . ^ AMPLE. — ' Divide the given num- ber into periods of three places, 2X2=4X 30O:::=1200 beginning at the 2X3.=0X 80= 180 place of units. 8X3 =9 Place the cube " ' root of the first 1389X3=4167 period, 2, in the quotient, and sub- tract its cube, 8,*23«X300 ^=: 158700 from the first pe- 23 X4X30= 2760 riod, and bring 4* = 16 . down the next period Cor a di- 161476X4 vidend, which . ' makes 4812. To find a divisor, multiply the square of the figure placed in the quotient by 300, = 1200; find how often this is contained in the dividend, viz. 8 times; place the 3 in the quotient for the second figure of the root. Multiply the part of the root formerly found, viz. 2, by the last figure placed in the root, viz. 8,. and the product by 30, = 180 ; add this and the square of the last figure placed in the root to the divisor, viz. 1200 ; multiply the sum of these, 1389, by the last figure placed in the root, 3, and subtract the product, 4167, from the dividend, 4812; bring down another period for a new dividend, and proceed in the same manner. 9 645904 98 DUODECIMAL MULTIPLICATION. 1. Of 378248. 6. Of 2. — 64872. 7. — 8. — 889017. 8. — 4. — 1092727. 9. — 5. — 84604519. 10. — In order to extraot the cube root of a yulgar fraction, reduce it to a decimal, and then extract the root. In mixed numbers, reduce the fractional part to a decimal. Find the cube root of the following numbers r-^ 62734.375. 7834.8748. .053157376. h. . DUODECIMAL MULTIPLICATION. This rule is made use of by artificers in measur- ing their woik. The dimensions are taken in feet, inches, and parts. The foot is divided into 12 parts called inches ; the inch into 12 parts called seconds; the second into 12 parts called thirds; and the third into 12 parts called fourths. Three seconds are marked thus, 3"; thirds thus, 3'"; and fourths thus, 3"". Multiply 7 feet 6| inches by 2 feet 6| inches. Rule with Example. — Place the multiplier under the multiplicand, feet under feet, inches under inches, &o. Multiply the multiplicand, be- ginning at the lowest term, 9, by the highest term in the multiplier, 2, carrying by 12 ; then multiply by the next lower term in the multi- plier, viz. 6 inches, taking care, however, to put the picduot o^e place towards the right hand. Do the same with the next lower term, and so on. Add the different products together. Jt. 7 2 in, ff 6 9* 6 3 16 3 1 6 19 9 1 10 8 3 18 6 Vf h^ff^'f' * Instead of f inches, 0" are put down, because they are equivalent. The same is done with the i inch. DUODECIMAL MULTIPLICATION. 99 1. Multiply 7 feet 9 inches, by 6 feet 6 inches. 2. Multiply 9 feet 5 inches 8^^ by 4 feet 8 inches 6^^. 8. Multiply 12 feet 8 inches V, by 8 feet 4 inches V', . 4. Multiply 46 feet 11 inches 8'^ by 12 feet V', 5. Multiply 87 feet 9} inches, by 11 feet 10|^ inches. 6. Multiply 678 feet 1\ inches, by 24 feet 10^ inches. To find the auperficial content, multiply the length by the breadth, 7. Find the content of a board 8 feet 4 inches long, and 8 feet 4 inches broad. ^ 8. Find the area of a tabled feet 9 inches long, and 6 feet 4 inches broad. 9. What is the priee of a marble slab, the length of which is 6 feet 4 inches, the breadth 8 foet 2 inches, at 7t. per foot? 10. Required the area of a square, the side of it being 23 feet 9 inches. 11. A grave-stone was charged at $1.04 per foot; what was the price of it, the length of it being 7 feet 2 inches, the breadth 8 feet 6 inches ? 12. How much will it cost to plank a court-yard at 17cts. per foot, the length of it being 26 feet 9 inches, the breadth 12 feet 4 inches ? To find the solid content, multiply the length, breadth, and thickness together, 18. What is the solid content of a block of marble 9 feet 2 inches long, 6 feet 8 inches broad, and 2 feet 3 inches thick ? 14. Required the solid content of a box 6^ feet long, 4f feet broad, and 3| feet deep. 15. A log of mahogany is 72 feet 7^ inches long, 5 feet 6^ inches broad, and 8 feet 6J inches thick. Required its solid content. 16. What would it cost to have a cellar dug 18 feet 4 inches long, 12 feet 9 inches broad, and 9 feet 6 inches deep, at 18 ots. per solid yard ? 17. Required the solid content of a log of beech 27 feet 6 inches long, 2 feet 6 inches broad, and 1 foot 2 inches thick. 18. What is the value of a block of granite 8 feet 9 inches long, 8 feet 7 inches broad, and 4 feet 2 inches thick, at $1.50 the solid foot? vs ANSWERS. NUliERATION. 1. One—Two— Three — Four-rFive — Six— Seven— Eight — Nine — Naught. 2. Ten — Eleven — Fourteen — Sixteen — Nineteen — Twenty • — Forty-two — ^Eighteen — Seventeen. 8. Two hundred — Four hundred and twenty — Six hun- dred and seven — Nine hundred and eighty-six — Four hundred and seventy-three — Two hundred and forty- seven — Three hundred and sixty-four. 4. Nine hundred and twelve — Eight hundred and seventy- four — Seven hundred and eighty-three — Six hundred and fifty — Two hundred and two— Six hundred and four — Five hundred and ten. 5. Four thousand — Two thousand seven hundred — ^Eight thousand six hundred and one — Seven thousand and thirty-six — Two thousand one hundred and one — One thousand and sixty. 6. One thousand and ten — Seven thousand and thirty — Four thousand six hundred — Nine thousand one hun- dred and eleven — Four thousand and seventy-six — Five thousand eight hundred and seventy. 7. Twenty-six thousand and twelve — Seventy thousand one hundred and one — Forty-two thousand one hun- dred — Thirty-six thousand one hundred — Ninety thousand two hundred and one. 8. Seven hundred thousand — Seven hundred and one thou- sand and twenty — Nine thousand two hundred and 100 ANSWERS — NUMERATION. 101 -Eight Cwenty K hun- — Four I forty- jventy- undred ed and -Eight ad and —One lirty— e hun- -six — usand 3 hun- !^inety ft thou- Id and ■ sixty-four and two hundred and seyenty thousandths — One hundred and four and two hundred and six thousandths. 9. Nine millions — Nine tl|ousand seven hundred and sixty-four and two hundred and sixty-eight thou- sandths — ^Eight millions two hundred and two thou- sand one hundred — Five thousand and twenty-three and sixty-seven thousandths. 10. Two millions six hundred thousand and sixty — Four millions one hundred and one thousand and ten — Two millions four thousand — Fourteen thousand twenty-one and four hundred and ninety thou- sandths. 11. Forty millions — Two thousand nine hundred and sixty and two hundred and sixty-eight thousandths seven hundred millionths — Five thousand and two and six hundred and one thousandths seven hun- dred millionths — One hundred and sixty-seven and two thousandths. 12. ^ine thousand four hundred and twelve and six hun- dred and eighty-seven thousandths and six hundred 'and seventy millionths-^Two hundred and sixty- seven thousand six hundred and two and six hun- dred and seven thousandths — Four hundred and one million four hundred and sixty-seven thousand six hundred and eighty. 18. Two thousand nine hundred and sixi^y and two hun- dred and sixty-eight thousandths seven hundred and sixty millionths — Seven hundred and ten mil- lions twenty thousand and ten — Two hundred and seventy millions six hundred and three thousand and fifty. 14. Fourteen thousand and twenty-three and six hundred and seven thousandths four hundred millionths — Three billions four hundred and sixty millions seven hundred and sixty thousand and ten — Four thousand and twenty-three and six hundred and one thou- sandths four hundred and ninety-seven millionths. 9* 102 ANSWERS — NOTATION. 16. Seven hundred and four thousand two hundred and sixtv and three hundred and seventy-one thou- sandths and four hundred millionths — Five millions seventy-nine -thousand six hundred and seven and nine hundred and s^x thousandths — One billion seven hundred and four millions seventy thousand six hundred. 16. Eighty-one billions four hundred and dixty-two mil- lions three hundred and six thousand and twelve- Four millions six hundred thousand seven hundred and sixty-eight and seven hundred and sixty-eight thousandths and one hundred millionths — Ninety- four billions eighty-six millions four hundred and twenty-one thousand three hundred and sixty. 17. Fourteen billions twenty-three millions six hundred and foriy-one thousand two hundred and one — Twenty billions eight hundred and sixty millions two thousand and one — Four hundred thousand and twenty and two thousandths and twenty millionths. 18., Nine hundred and seven thousaAd and sixty an^two hundred and six thousandths two hundred and four millionths — Two hundred and forty thousand and twenty-six and one hundred thousandths two hun- dred and one millionths — ^Five hundred and ninety billions nine hundred and sixty millions one hun- dred and twenty-six thousand and twenty. 1.] 6—7—9—8—5- .NOTATION. .10-.12— 14— 16— 18— 20— 19. 2.] 74—26—31—49—58—62—76—77—97—84—66—99. 8.] 100—104—244—691—760—909—999-802. 4.] 4000—4200—6352—6705—7050—9002—8080—6707. 5.] 10000 — 15560 — 19019 — 266^5 — 38038 — 40040 — 66.825—168.6. ANSWERS — SIMPLE ADDITION. 108 6.] 400000— 400040— 600707—980000— 256975— 8891.25 14782.04—458215.678. 7.] 6000000—5498000—8040402—7498766—10010010— 20240606—58058058—87800010.005— 14014014.014014. SIMPLE ADDITION. MBMTA] L EXBB0I8BS. 17. 80164 1. 22 cents. 18. 18001 2. 21 dollars. 19. 20169 8. 18 20. 14872 4. 85 21. 411093 6. 13 22. 861626.939 23. 278540.63 BLATB EXERCI8B8. 24. 248663 1. $1186.870. * 25. . 105 2. 1248 26. 293 8. $1848.740. 27. 408 4. 1465 28. 1476 6. 2250.979 29. 16888 6. 2072 80. 4258c. 7. 2348.190 81. $24781 8. 2856.000 82. 1824286 9. $977,680. 83. 7861214 10. 1635 84. 5361460. 11. $1518.800. 85. 75675 12. 1056 86. 811013 18. 84957 87. $660.11 14. 21868.6246 88. 2246 15. 18068 89. 72 16. $10914.440. 40. 230 104 ANSWERS — SIMPLE SUBTRACTION. 41. 42. 48. 44. $2471.40 $10626 6681 68891 46. 46. 47. 48. 162 $2626 415 880 SIMPLE SUBTRACTION. MINIMAL IXIBOISIS. ! 1. 2. 91 8. 8 4. •' 7 5. 29 6LATB IXBB0I8ES. 1. 184 2. $476.87 8. 842 4. $466.62 5. 686 6. $876.18 7. 468 8. $581.08 9. 96 10. $89.88 11. 16176 12. 18948 18. 26972 14. 70747 15. 86919.427 16. 78878 17. 40262.79 18. 88999 19. 22984 20. $16289.09 21. 78869 22. 26292.15 28. 462121985 24. 436196169 26. 78922070 26. 612668991.767 27. 722996412.185 is. 91810918.882 29. 818841778927 80. 769808880048 81. 704026188872 82. 424676826966 88. 417801946969 84. 416879998308 85. 467666 86. 1206996 87. 8699244 88. 67956 89. $8072 40. 171 ! ANSWERS — SIMPLE MULTIPLICATION. 105 162 ^2626 415 880 41. 869 61. 2880 42. 172 62. 876884 48. 94 68. 140 millions. 44. 106 64. 2542904 46. 185 66. 6820 ft. 46. 799 66. SSyrs. 47. 1886517 57. 412 yrs. 48. 88 68. 18l9 and 23 49. 180 69. 77 60. 740 • MIXED QUESTIONS IN ADDITION AND subtbaotionJ 1. 83 5. 415 2. 2720 6. 221 8. 1667 7. 19789 4. 162 8. £287 SIMPLE MULTIPLICATION. MENTAL EXBB0I8E8. 5. . 66278.296 1. 63 cents. 6. 672618.16 2. 89 dollars. 7. 889307.501 8. 84 8. 748790 4. 60 and 180 9. . $502558.76 10. $1162249.44 SLATE BXEBOISES. 11. $574877.79 1. $17104.68 12. 668668 2. $134674.52 18. 850184 8. $432268.20 14. 612822 4. $225804.18 15. 787914 106 ANSWERS— SIiu72V5 MULTIPUOATION. \S-i'- <^ 16. 626276 17. 262688 18. 487780 !i9. 875460 20, 968006 21. 1060662 22. $1966.64 23„ ^ $6882.89 24. $8983.08 26. $7866.16 26. $6899.62 27. $4916.86 28. $8849.48 29. $11799.24 80. $10816.97 81. $68236.48 82. $183868.66 83. $232499.52 84. $182214.09 85. $281604.12 86. $208968.44 87. $199122.80 88. $188260.56 39. $665184.16 40. $220899.92 41. $676676.82 42. $716501.44 48. 682.21592 44. 7464.4808 45. 29050.420 46. 48.844096 47. 8439.8932 48. 4301.43168 49. 777.666496 60. 8598.31804 61. 68073762 52. 41281053 63. 242945.91 64. 28047414 66. 46350656 66. 6V5630.377 5r. 89549.4873 58. 649435896 59. 64008924 60. 8704412744 61. 403576660 62. 176320 63. $19884.80 64. 2592 66. 2303 66. 8168 67. $3240 68. 4480 69. 1H690 70. 2144 71. 81056 72. 783 73. 80 V4. 1095 75. 66940 76. 768000 ?ION. ANSWERS — 8IMPLE DIVISION. 107 8439.8982 1801.43168 777.666496 3698.81804 68078762 41281068 242946.91 28047414 46860666 6V6680.377 B9649.4873 649486896 64008924 J704412744 408676660 176820 $19884.80 2692 2308 8168 $3240 4480 111690 2144 81056 783 80 1095 66940 768000 SIMPLE DIVISION. MENTAL EXEBCISES. 1. 6 and 7 2. $11.70 d. 6 4. 6 5. 10 SLATE EXERCISES. 1. 6911i 2. $137.52^ 8. 13281J 4. $116.17^ 5. $96.68f 6. $8186f 7. , $64.26A 8. 420Q^ 9. 6868906 10. $63359.66f 11. 18771812f 12. $71409.78f 18. 89064.06^ 14. 6869550 16. 126670.06f 16. $4780.66^ 17. 5885800f 18. 28236344^ 19. 18824229f 20. 14118172-^ 21. 112945371 22. 9412114f 23. 8067527 24. 7069086J 25. 6274743$ 26. 5647268^ 27. 6183880^f 28. 4706067^^ 29. $374840.11^ 80. $249893.41 81. $187420.061 82. $149936.041 88. $124946.70| 84. $107097.17^ 86. $93710.02J 36. $83297.80f 37. $74968.02^ 38. $68152.74^^ 89. $62473.85^ 40. 26654—14 41. 41316—17 42. 40364—12 48. 24995 2 44. 17862—35 46. 8703—9 46. 6828—38 47. 4408—28 48. 10902—34 49. 1889—64 60. 3309—88 61. 8450—76 52. 1767-^2 108 ANSWERS — SIMPLE DIVISION. If ' 58. 1726 18 84. 58264695—45 64. 1687 8 85. 22529802 1400 55. 1646—81 86. 12-240000786692 ^6. 1618 38 87. $670.82—7 57. 107 613 88. 46—2 58. 92—728 89. 8600 minutes. 59. 181—26 90. 266—20000 60. 143 30 91. 2111111 5 61. * 280 43 92. 192268—840 62. 149 387 98. 925—26 68. 123—819 94. 26711 64. 355 73 95. 546022 65. 244—296 96. 829378f 66. 1 204—91 97. 22819437101 67. 174—55 98. 129612^1 68. 141—265 99. 57618^ 69. 10.804—74 100. 160427^ 70. 1032 570 101. 89173922,«r 71, 959.1—218 102. 1022785665 72. 9902 383 103. 12751635^ 78.^ 7.234—312 104. 29983^^ 74. 7.00—1607 106. 452 75. 857—1713 306. 61881—86 76. 81.86 11 107. 9670—64 77. » 953 2014 108. 882 9 78. 5098686000 109. 2154-6 79. 25134919—1984 110. 14^24—3 80. 2587—1292 111. 518 224 81. 954118 1200 112. 18138—38 82. ,01061—2110 113. 7296—1606 88. 8763262—4000 • •\ ANSWERS — ^REDUCTION. 109 NEW BRUNSWICK CURRENCY. 1. $76.4^ 5. $139.89 2. $124.45 6. $10.00 f $31.25 ^' I $156.25 7. $10.01 8. 55 dollars and 84 cents. 4. $9.00 9. $77.66 * f KEDUCTION. MENTAL EXERCISES. 13. 118067 fourpences. 1. 70«. 85». and 133*. 14. 9880 crowns. 2. 20rf. 30rf. and ISOd. 16. £4884 10«. 3. £B 15s., £8 Zs., and 16. 4947*. 6rf. 1 £9 Us. 17. 873740 threepences. 1 4. 82 furlongs. 18. 67662 fivepences. | 6. 820 rods. 19. 9621 fourpences 1 Ji. 1 6. 168 hours. 20. 31932080 sixpences. I \ t 21. 33466cr. 3». SLATE EXERCISES. 22. 118801^ seven shil- 1. 11882 farthings. lings. 2. 63478 pence. • 3. 350160 farthings. AVOIBDUPOIS WEIGHT. * 4. 131825 halfpence. 23. 864 lb. 6. 69552 pence. • 24. 1564 oz. 6. 71520 farthings. 25. 89 lb. 3 oz. 7. 87552 farthings. 26. 70321b. ^ 27. 812 parcels. • ^ 8. 10692 pence. 9. £3394 10a. 10. £444 13*. 3rf. TEOY WEIGHT. 11. 1751<7». 18a. 28.,5760dwt. 12. 1146cr. 2*. lOd. 29. 6 02. 2 dwt. 20 gr. 10 110 ANSWSBS— COMPOUND ADDITION. 80. 6184 gr. 81. 6 spoons — 77 82. 1 lb. 11 oz. 2 dwt. 88. 21 spoons — 8. APOTHBOABIBS' WEIGHT. 84. 27160 grains. 85. 6 oz. 1 dr. 1 scr. 7 gr. 86. 186 scruples. 87. 252 days. LONa MEASURE. 88. 24560 Jierches. 89. 1332 yds. 1 ft. 4 in. 40. 200640 yards. 41. 57200 times. 42. 39600 times. CLOTH MEASURE. 4ap 3936 nails. 44. 299 yds. 2 nis. 45. 8 shirts— 8. 46. 7 suits— 8. MEASURES OP CAPACITY. 47. 197 pints. 48. 585 gal. 3 qts. 1 pt. 49. 3479 pecks. 50. 1199 bushels. 61. 2016 gills. TIME. 52. 1094 hours. 53. 51dy8.20hrs. 57min. 54. 5316480 minutes. 55. 341640 times. COMPOUND ADDITION. 1. ' • £328 10*. Od. 2. £241 5». 7d. 8. £107 9*. Old. 4. 29 cwt. i qr. 19 lb. 6. 82 per. 4 yds. 2 ft. 6. 10 qrs. 14 lb. 15 oz. *7. £4660 7«. 0| 1^ 17. 18. 19. € cwt. 2 qr. 11 lb. 7 qrs. 23 lb. 14 oz. 8 cwt. 2 qrs. 27 lb. 112 ANSWERS — COMPOUND MULTIPLICATION. 2a 21. #22. 28. 24. 26. 26. 27- 28. 81b. 11 oz. lldwt. 6gr. £U 1*. 2|rf. 4 miles 5 fur. 5 per. 436 bush. 2 pk. 6 qt. 1 pt. 10 yd. 1 qr. 1 nl. 65 ao. rd. 88 per. £21529 Us. Qd. 13 gal. 2 qts. 1 pt. 8 gills. 2 wks. days. 19 hrs. • COMPOUND MULTIPLICATION. 1. 194 lb. 4 oz. 16 dwt. 2. 830 yd. qr. 8 nl. 8. 46 owt. 2 qr. 14 lb. 4. £906 11«. 6^. J. 6. £764 16». 2}rf.~| 6. £610 11». 8K 7. 92 miles 3 fur. 20 per. 8. 29 ac. 1 rd. 16 per. 9. 801b. 7oz. 8 dwt. 8 gr. 10. £115 10«. 11. £15 14«. 10J