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Mapa, piatea, charta, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one expoaura are filmed beginning in the upper left hand corner, left to right and top to bottom, aa many framea aa required. The following diagrama iiiuatrata the method: Lea cartea, pianchea, tableaux, etc., peuvent Atre filmia i dea taux da rMuction diffirents. Lorsque Ie document est trop grand pour fttra reproduit en un aeui ciichA, ii eat filmi A partir de Tangle aup4rieur geuche, de gauche k droite, et de haut an baa, an prenant la nombre d'imagea nAcaaaaire. Les diagrammes suivants iiluatrant la mAthoda. 1 2 3 1 2 3 4 5 6 1 m- I Former COMPLETE SYSTEM OF PRACTICAL ARITHMETIC, FOR Tllr: USE OF SCHOOLS IN BRITISH AMERICA. TO WHICH ARE ADDED, f A SET OF BOOK-KEEPING BY SINGLE ENTRY ; AND A PRACTICAL ILLUSTRATION OF MENTAL ARITHMETIC, VEDBIAL MONET, RECEIPTS, BILLS OF EXCHANGE, INLAND AND • • • FOREIGN, EXPLANATION OF COMMERCIAL , ' . ' TRRJIS, ETC. The whole adapted to the business of real life, to the circumstancs of this Country, and to the present improved state of Commerce. BY G. & J. GOUINLOCK, Formerly Britith Teaekert of long experienet and exttnaive fractiee. HAMILTON: PRINTED, PUBLISHED & SOLD, WHOLESALE ^ RETAIL, BY J. RUTHVEN, BOOKSELLER &, STATIONER. 1842. (Priet, Boundf Two SkilUngi and Nin$pnu9t Currtney.) ■fcl II f r. .iJiiilWrf 0. /Ol Wi Entered according to Act of the Provincial Legislature, in the Year One Thousand Eight Hundred and Forty.two, by G. & J. Gouinloox, in the Office of the Registrar of the Pi^pvince of Canada. y HAMILTOH : J. HVTBrBH, rKIRTIR. 3 '5'?/' ADVERTISEMENT. Year One NLOOK, in The object tlie Compilers of the following treatise had in view was, to supply the Provinces of British America with a good Text-book for the use of Schools, comprising a full course of Arithmetical instruction ; aUke remote from the puerile and obsolete matter abounding in some works of the kind, and the abstruse and fanciful perplexities contained in others. Ac- cordingly, in this will be found a great variety of exercises conveying pertinent information, adapted to the business of real life, and the present improved state of Commerce. Great care has been taken to have the rules concise and perspicuous, and also appropriate exercises for their elucida- tion : hence the pupil is led on step by step, from what is easy to what is more difficult, without any thing that has a tenden- cy to perplex or discourage him in his progress. But, as every practical Teacher knows well, it is comparatively easy to tench children certain rules, but to make them comprehend the various uses and applications of these rules to the every, day business of life, is very difficult. With a view to assist in overcoming this difficulty, and to excite the pupils to exert their ingenuity and exercise their reasoning faculties, a copious collection of miscellaneous questions is given at the end of every part. This, it is presumed, is the best exercise for their becoming acquainted with the meanings reason^ and xise of the different rules. This Arithmetic, is the first of a seriesy which the Compi. lers intend to publish for the use of Schools, as speedily as possible. They have ready for printing, — A Pronouncing and Explanatory Vocabulary ; First, Second, and Third Rea- ding Books : — also, a Geography, in a forward state of pre- paration. OO" A Key for this Arithmetic is in course of preparation. n \h r !■ u CONTENTS. PARTI. - Page. Arithmetical Tables, 5 Definitions, &c 10 Numeration and Notation, 10 Simple Addition,.. • 11 " Subtraction, 14 ^ Multiplication^ IG " Division 18 Promiscuous Exercises, 23 Questions for Examination, 24 . " PART II. Compound Addition, • 25 <* Subtraction,... 28 '< Multiplication 30 «* Division, 33 Miscellaneous Exercises, 38 Bills of Parcels, or Invoices, 41 Reduction,. 45 Compound rules of Weights and Measures, 49 Miscellaneous Exercises,, ,•.......«•«..,•.««....«.. 50 Questions for Examination, • 52 PART III. Simple Proportion,. • 53 Compound Proportion, 59 Distributive Proportion, or partnership, 62 Rules of Practice,. •«.......«« « 65 Commercial Allowances on Goods, n 73 Simple Interest, 75 Compound Interest, 80 Commission, Brokerage, and Insurance,. . . ,.. 81 Buying and selling Stocks, <•..... • 83 Discount, True and Common methods,. . . ^ 85 Equation of Payments, • 67 Barter, * 87 Profit and Loss, 89 Miacellaneous Exercises, .•.••.••.«•»••.•••»• 01 Questions for Examinationi <«,.••,••«•••••««<< 9^ I ■ 1 ■; CONTENTS. 4 PART IV. Page. Vulgar Fractions, Definitions, &c 97 Reduction of Vulgar Fractions, 98 Addition « 104 Subtraction « 105 Multiplication » >.... 106 Division « 107 Proportion « 107 Decimal Fractions, Definitions, &c 106 Addition of Decimals,. 109 Subtraction " 110 Multiplication ^* •• 111 Division " Ill Reduction " 112 Circulating " 115 Miscellaneous Exercises, in V. & D. Fractions, i)6v> Questions for Examination, 124 PART V. British Exchange of Monies — with Holland, Germany, France, Spain, Portugal, Italy, Denmark, Norway and Sweden, Russia, Prussia and Poland, W. Indies, Uni- ted States, Canada, E. Indies, and Canton in China,.. 125 Alligation, Medial and Alternate, 135 Involution, 137 Evolution. — Square Root, 138 « Cube " 142 Position, Single and Double, • 145 Progression, Arithmetical & Geometrical,. •••••• 148 Duodecimal Multiplication, 152 Exercises in Artificers* Measuring, ^ - . • 155 Tonnage of Ships, .••...» 156 Permutation, • • 157 Miscellaneous Questions, », 157 Questions for Examination, 160 APPENDIX. No. I. — Book-keeping by Single Entry, 161 No. II.— Mental Arithmetic, 193 No. Ill — Federal Money, &c 198 No. IV.— Forms of Receipts, Bills, &c 206 No. V. — Explanation of Commercial Terms, . . • 211 .•:9'- if ¥ f .^fj'-.ii" •:'!';• ARITHMETICAL TABLES. ( 'i Units,. Teiuj,. NUMERATION TABLE. 1 21 Hundreds, 321 Thousands, 4,321 Tens of Thousands, 54,321 Hundreds of Thousands, 654,321 MiUionB, , 7,654,321 Tons of Millions, 87,654,321 Hundreds of MUiions, 987,651,321 Thousands of Millions,. 1,316,038,426 Tens of Thousands of Millions, 27,608,507,080 Hundreds of Thousands of Millions, 360,750,900,504 BilUons , 4,516,328,471,951 ROMAN NOTATION. The Romans expressed numbers by means of the seven following cap* ital letters of the alphabet. Numbers, I. V, X. L, C. D. M. ; dv Value, 1, 5, 10. 50. 100. 500. 1000. ' ' And by repeating and combining these, any of the intermediate or higher numbers were denoted as follows : — Numbers, II. III. IIII. XX. CC. CCC. MM. ' . Value, 2, 3, 4, 20, 200. 300, 2000. Also, annexing a letter, or letters, of a lower Value to one of a higher, denotes their sum : — As, VI. VIII. XII. XV. XVII. LXX. DC. -f Value, 6. 8. 12. 15. 17. 70. 600. And if a letter of a lower value be prefixed to one of a higher, it denotes their difference : — As, IV. IX. XIX. XL. XC. CD. r r. ft* Value, 4. 9. 19. 40. 90. 400. >^ The character for 500 is Iq, or under an abbreviated form D ; its value is doubled, or becomes 1000, by prefixing a C to if, as in CIq ; 5000 is denoted by Iqq, and 10,000 by CCIqq ; and the value becomes increa. aed in a decuple proportion, by the successive addition of pairs of C, on each side of the hne I ; thus, 100,000 is denoted by CCCIqqq ; 1,000,- 000 by CCCCIoaoo. Though 6 is usually denoted VI, yet in some inscriptions it is express. ed by six lines ; V. and L. are never repeated, and X. and C. never more than four times. By placing a line over these numeral characters, their values are increased one thousand fold ; thus I. is 1000, V. is 5000, X. is 10,000, L. 50,000, C. 100,000 ; 2000 is usually denoted by CI^CIq, or MM, but sometimes also by IICI^, or IIM ; and in the same manner 4000 is sometimes represented by JVCIq, 7000 by VIICIq, and similar, ly in other cases. : » ARlTlIMETICAt rASLfiS. 6 s 1 21 321 ... 4,321 .. 54,321 654,321 r,654,321 7,654,321 7,651,321 6,038,426 3,507,080 0,900,504 8,471,951 twing cap- 'f }00. e or higher IM. 900. a higher, DC. 600. it denotes ; its value ) ; 5000 is (les increa- 8 of C, on 3 ; 1,000,- is express, lever more jters, their 000, X. is Ij)CIo. or e manner nd similar. q The writer of the article Arithmetic, in the Ericyclopeclia Metropplitana^ makes the following remark, afte^ giving an accv n.o.i: ARITHMETIC. PART I. Abithmetic is the science of numbers ; it expltuns their properties, and the art of computing by them. All numbers are expressed by the ten following figures : 1, one, or unit ; 2, two ; 3, three ; 4, four ; 5, five ; 6, six ; 7, seven ; 8, eight ; 9, nine ; 0, cipher, or nought. Number is one or manift a unit or collection of units ; as 1. 0, 15. Unit or unity is the number one. ' ■'' A Whole Number consists of one or more units ; as 1, 3, 8, A Fraction consists of one or more parts of a unit ; as i, f . An Integer is a whole number^as distinguished from a frac- tion. An even number can be divided by 2 without a remainder ; as 4, 6, 8. An odd number cannot be divided by 2 without a remainder ; as 3, 5, 7. An abstract number denotes a number of things generally, without a name ; as 2, 7, 16. A concrete number mentions the name ; as 2 men» 7 miles, 16 shillings. A simple number is a number of one name or denomination, as pounds, £5. A compound number is a number of different names or de* nominations ; as pounds, shillings, and pence ; £5 6 3. A composite number is the product of two or more other numbers ; as 24 ; which is the product of 4 and 6 ; hence 4 and 6 are called the component partJi of 24. The fundamental rules of Arithmetic are Addition, Subtrac- UoUi Multiplication, and Division, NUMERATION Is the art of reading a number expressed in figures. Quintillions. Quadrillions. Trillions. Billions. Millions. UniU. 438,759 274,165 341,789 429,561 752,948 756,342 Scxtillions, Septillions, Octillions, Nonillions, follow. I 11 NOTATION. I Read, or write in words, the following numbers :-— 48 — 103—570—2,600—3,1 10—4,062 —25,874—90,206—74,023 —615,490—308,201—4,720,586—81,504,900—420,607,058, —14,270,053,409—306,058,400,740—8,052,604,170,683. NOTATION 1 3 the art of expressing any given number in figures. Express in figures the following numbers : seventy-five — one hundred and forty-six — three hundred and two — four hun- dred and seventy — five thousand eight hundred and twenty- three — six thousand four hundred and ninety — nine thousand and nine — fifty thousand and seventy — one hundred and eighty thousand and twenty-five — six hundred and four thousand nine hundred — three millions eighty thousand and forty — sixty mil- lions four hundred and two thousand and twenty-one — three hundred and forty millions five hundred thousand — fifty thou- sand two hundred millions sixty thousand five hundred and three — six billions forty thousand nine hundred millions seven- ty thousand and eighty. SIMPLE ADDITION • Is the method of finding a number equal to several numbers taken together. The number found is called the sum or amount. Rule. — Write the given numbers under each other ; units under units, tens under tens, &c. ; draw a line below them ; add up the units column, put down the right hand figure, and carry the rest to the next ; continue doing so with each col- umn to the last, under which place the whole sum. t — EXAMPLES. 4 25 436 5274 2436 43058 41 274 1063 7052 7015 36 510 8920 847 74820 14 125 4318 5309 475 52 603 6205 61 95146 63 789 .3742 7538 8563 n 231 2737 29522 23243 229677 If 306 231 2301 2737 24248 20807 186019 m 29522 23243 229677 ral numbers the sum or 34 52 16 73 48 (•) 426 703 180 317 651 ilPLE ADDITION. rz 4326 63207 n C) ;*?«;• 574625 1780 21894 705194 3408 37050 652307 9854 45618 168072 7065 74362 831936 ^ ■ ,1. " •. -- • 37486 o 43875 > ■ I n 63854 54963 , ' n ■ 48378 71630 76031 35469 . 87052 • 31702 85019 14708 70387 15804 67495 46754 51684 69536 ' 93891 85264 20583 85460 94720 26370 58036 98307 67259 52016 74855 75941 (") 74958 57428 25876 38204 n 85615 68174 31072 74054 •61093 38094 43643 16945 51720 47182 50718 5159G 83604 36209 86340 63260 27435 62750 17481 20475 47907 84269 20857 40318 75264 15381 13702 98310 t»634 14571 95249 n 47384 74156 46835 ; 63816 n 16378 71005 10943 76018 17052 80741 26192 87405 90802 84708 38072 5C410 24870 471«6 35640 01408 18089 48269 29573 ' 20938 27890 00945 38052 02704 70183 54374 54256 61738 12845 4724 02581 34371 96321 84934 r 6875 17483 1< ll SiMPtB ADDITION. n 43836 (") 74958 54886 738569 56492 38594 785d 7098 75649 93625 40 42 89758 89764 87508 57807 36285 45839 98796 586 64937 74383 372 943750 95476 69658 • 4865 8374 (") 38546 n 85496 n 74939 (") 3854 74953 54967 788 796 9538a 96763 9478 98347 38546 75384 83245 854765 85469 58479 74 T3 46932 84796 8697 675938 93274 79654 348 4897 32747 96548 6569 976 U What isthesumof 634+8050+78+95800+4619+85 + 766? 2. What is the sum of 8425+170+95836 + 47+708+ 84392 + 5654 + 389? J^. What is the sum of 70,560+839+561,428 + 74,807 + 84 + 7540625 + 7276 + 542 ? 4. What isthesumof 9,482+39,867 + 80+48927 + 854+ .>27:J + 9S + 7000+80172+19+8467 ? 5. Add together, — Twenty-seven thousand eight hundred and lorty-nine, — thirty-six, — eight thousand and nine, — twelve thou- H'lnd nine hundred and sixty-three, — five thousand and forty, — five hundred and seventy-eight thousand and forty-six, — four jjundrcd and sixty, — forty thousand eight hundred and seven? 6. Find the sum of — Six millions eight hundred and seven thousand nine hundred and two, — fifty thousand and seventeen, — ninety-six millions eight hundred and five thousand six hun- dred, — nineteen thousand and four,— ^ight millions six hun- dred and ninety thousand eight hundred and forty, — five hun- dred and sixty-nine millions fifty-five thousand and sixty-three, — four hundred and three thousand seven hundred, — four hun- dred and nine. 7. A. borrowed from B. at one time J6348, at another time ^£73, at another £157, at another ^96 ; how much did he bor- row in ail? SIMPLE SUBTRACTION. 14 8. A gentleman planted upon his estate 846 elm trees, 7350 fir trees, 578 ash trees, 14282 oak trees, 389 birch trees, and 94 beech trees ; how many did he plant in all ? 9. A farmer has 14 horses, 19 cows, 36 young cattle, 25 calves, 500 sheep, 21 goats, and 18 pigs ; what is the number of his live stock ? 10. From the Creation to the departure from Egypt was 2513 years ; from thence to the building of Solomon's Temple 437 ; to the Jewish captivity 398 ; to Alexander's conquest of Persia 273 ; to the Christian era 333 ; to the present year 1842 ; required the time from the creation ? 11 Mary's fortune is £215, Margaret's £174, Eliza's £342, Jane's £269 ; how much is their brother John's fortune, who has as much as all his four sisters ? 12. In the year 1830, the population of London was 1,474,. 009 ; of Dublin, 265,316 ; of Edinburgh & Leith, 162,156 ; of Glasgow, 202,426 ; of Liverpool, 189,242 ; of Birmingham, 146,986 ; of Manchester, 237,832 ; of Norwich,61110 ; of Bris- tol. 117,016 ; and of Leeds, 123,393 ; required the amount of the whole ? C) 109932. C) 195621. (») 8256161. (*) 200239. (») 673210 (") 681832535. C) 674. («) 23539. (") 633. {'') 5846. (") 1000. (") 2979546. SIMPLE SUBTRACTION Is the method of finding the difference between two given numbers. The greater is called the miAuend, the less the sub. trahend. The number found is called the remainder or differ, cncc. Rule. Write the less number under the greater, — ^units under units, tens under tens, &c. Begin at the units, and take eacli figure in the subtrahend from the figure above it in the min- uend, and set down the remainder; but if any figure in the subtrahend be greater than the figure above it, add ten to the upper : subtract as before, and carry one to the under figure, — proceed in the same manner to the end. EXAMPLES. Minuend 87493652 From 74385921 Subtrahend 36033531 Take 47840136 Difference 51460121 Diff. 26530785 Proof 87403652 Proof 74886021 ? 15 SIMPLE SUBTRACTION. C) D , (•) 853947689 710948564 74925869 310442552 617290413 28470316 !! I )i . ^!1 1 11 ;■ It n 651940851 . 156073474 809431789 216438274 n 43709528 38072974 n 90038593 60084608 n 581302970 131207874 809080700 62109201 30498132 926139 • n 80003947 8092 51800934 999085 71324900 329603 n 71009425 90478 60034166 34167 n 4000000 3999999 n 63849673 6295618 n 70938266 7086368 What is the difference between 8390000 & 901239 ? What is the difference between 499679 & 1030547 1 What is the difference between 90188 & 210043 t How much does 8540317200 exceed 8997485 ? How much does 99999 want of 1000000 ? From 8314050 subtract 748392+68396. From 7000000 take 99999+777777. From 63014+8579 take 14680+6495. From 7408612 + 9483 take 2498768. ' ' 10. Subtract 12346678 from 100 millions. 11. A man born in 1716^ died in 1798, what was his age 7 12. A man was 98 years old in ISSS, when was he born ? 1. 2. 3. 4. 6. 6. 7. 8. 9. pos •ST SIMPLE MULTIPLICATION. 16 1869 )316 9528 2974 80700 09201 )0934 )9085 n 4156 4157 n 8265 186368 9012391 L030647 1 L0043 1 18 his age T he bora t 13. America was discovered in 1492, how long is it since ? 14. Gunpowder was invented in 1400, how long is it since ? 15. A. borrowed from B. £1000 of which he has since paid JS419 how much remains unpaid ? 16. D. borrowed 150jC, but paid £75 of it at one time, and £38 at another, how much remains unpaid ? SIMPLE MULTIPLICATION Is a short method of performing addition : the number to be multiplied is called the multiplicand ; the number multiplied by is called the multiplier ; the result is called the product : — the multiplier and multiplicand are sometimes calledyhc^or*. Rule I . When the multiplier does not exceed 12, begin at the units place and multiply each figure of the multiplicand by the multiplier, carrying by tens as in addition. 1 '• examples. 1935862 2 , 48529763 9 84952765 4 149871724 145589289 339811060 Multiplicand 785649 Multiplier 5 Product 3928245 Multiply By 874956 6 Product 5249736 Multiply 837429156 ; by 2,3,4,5,6,7,8,9,10,11,12. Multiply 837429156 ; by 3,2,5,4,8,7,6,12,11,9,10. 74963854 X 60 53689472 X 80 4854293 X 500 72954386 X 400. 38396857 X 7000. 95827694 X 90000. Rule II. When the multiplier is greater than 12, but a com- posite number ; multiply by its component parts. Mult. 74867384 by 14 2 Mult. 49526378 by 24 4 149734768 7 1048143876 198105512 6 Product 1188688072 •^.ij' r '1 17 SIMPLE MULTIPLICATION. I* 1 |. . f n- •1 1. 748391576 2. 563427905 3. 479360587 4. 394857324 5. 684937246 6. 751385794 7. 429536287 8. 570854838 9. 749385627 10. 563728564 11. 748526395 12. 351965748 13. 648374829 14. 574926385 X 18 X 32 X 36 X 42 X 48 X 54 X 63 X 72 X 84 X 96 X 108 X 121 X 132 X 144 13471048368. 18029692960. 17256981132. 16584007608. 32876987808. 40574832876. 27060786081. 41101548336. 62948392668. 54117942144. 80840850660. 42587855508. 85585477428. 82789399440. Rule III. When the multiplier is not a composite number, or consists of several figures, multiply by each figure separately, taking care to place the first figui-e of each product directly un- der the figure you multiply by, then add the products. Mult. 3210421765 by 235. Mult. 4876948600 by 407500. . 235 Proof. 407500 Proof. 4 4 10052108825 ,-y^ , 243847430 9631265295 6420843530 754449114775 1. 74851963 X 2. 38274539 X 3. 38056918 X 4. 91847364 X 5. 48514967 X 6. 57493685 X 7. 7846529 X 8. 5319476 X 9. 8736582 X 10. 4517847 X 11. 6085700 X 12. 3916000 X 13. 8450549 X 14. 5195463 X 1. How many stones, 40 feet long and 82 feet 2. My income is 29jS lX4 4 341386402 195077944 4 1987356554500000 43 = 3218634409. 57 = 2181648723. 238 = 9057546484. 905 = 83121864420. 870 = 42208021290. 642 = 36910945770. 4372 = 34305024788. 8006 = 42587724856. 70500 = 616929031000. 394000 = 1780031718000. 90580 = 551242706000. 2700500 = 10575158000000. 15463 = 130670889187. 600080 = 3117693487040. each a foot square, will pare a floor broad? per week, what is that per annum ? Is in to SIMPLE DIVISION* 16 3. How many letters in a volume of 436 pages, each page 39 lines, and each line 52 letters ? 4. PT parishes are each assessed jB37, what is the whole assessment ? 5. How many sheaves in a field containing 3276 shocks, each 12 sheaves ? 6. Ninety-six persons have a legacy divided among them, and the share of each is £354 ; what was the legacy 1 7. How many grains of wheat will fill 987 bushels, when one bushel contains 675,000 grains? 8. If the number of students at the College of Edinburgh be on an average 1856, and each expend £30 for his main, tenance, besides £12 for class-fees and books; how much money is thus circulated in Edinburgh ? 9. If the number of newspapers published each week in Great Britain be 578, and of each on an average 1145 copies are sold, how many are sold in a year ? 10. If the number of hackney-coaches in London be 1200, and each earns 13 shillings per day, how many shillings will they earn in a year of 365 days ? 11. A gentleman gave his daughter a scrutoire, in which were 12 drawers, each having six divisions, and in each divi- sion £134 ; what was the lady's fortune ? 12. How many miles will a man walk in 56 years, tuppos- ing him to travel 6 miles per day, and that every year con- sists of 365 days ? ■ (') 1280. O £1508. (») 884208. (*) £'3219. (') 39312. f ) £33984. C) 666225000. (') £77952. (') 34414120. (") 5694000.S. (") £9648. (") 122640. SIMPLE DIVISION Is the method of finding how often one number is containeti in another. The number we divide by is called the divisor, the number* to be divided, the dividend, and the result, the quotievt. Rule I. — When the divisor is not greater than 12, divide mentally. Dividend. ^ Dividend. Divisor. 2)46283274 Divisor. 3)47286492 Quotient. 23141637 2 Quotient. 15762164 Proof. 46283274 Proof. 47286492 . •iSMieBaHi 19 SIMPLE DIVISION. r 1. 852956150746 2. 573860941258 3. 945172384963 2,3,4,5,6,7,8,9,10,11,12. 2,3,4,5,6,7,8,9,10,11,12. 4,3,8,2,9,6,5,7,12,11,10. Rule II. — When the divisor is a composite number, divide by its component parts. — NotCt to find the true remainder, multiply the last remainder by the first divisor, to this add the first remainder. 14 2)74263849-1-14 7)37131924—1 i Quot. 5304560 — 4) Rem. 4X2-M=9 20 4)27548634 -r 20 14 5) 6887158—2 Quot. 1377431—3 if Rem. 3X4-1-2=14 1. 7438952617 2. 8507281935 3. 5194637084 4. 9305263820 5. 6714832156 6. 3750984719 7. 1938527492 8. 5409182561 9. 4738509127 10. 7294850642 11. 3710538274 12. 8593250750 13. 5148365083 14. 6039147815 15. 4718052938 16. 9403678195 18 24 28 35 42 54 63 72 81 84 96 99 108 110 132 144 413275145VV 354470080if 185522753 265864680f^ 159876956,!^ 96462679ff 30770277fi 7512753541 58500112ff 86843460/y 38651440ff 86800512ff 47670047^1^ 54901343yV^ 35742825yV2 653033201^ Rule III. — When the divisor is not a composite number — Draw a curve on each side of the dividend, and place the divisor on tlie left of it. — Take the least number of figures on the left of the dividend, that will contain the divisor ; find how many times they contain it, and place the number in the quo- ticnt on the right of the dividend. Multiply the divisor by the figure placed in the quotient, subtract the product from the assumed figures, and to the re- mainder annex the next figure of the dividend. — Divide thf number thus obtained in the same manner, and so on till all the figures of the dividend are used. SIMPLE DIVISION. 20 12. ■■ 12. 10. mber, divide } remainder, D this add the Divisor. Dividend. Quot. 7486)487698472(65148 44916 65148 7^4.^ Ans. 7486 5f8 3 'H 7 2 55.5. "8 I )-5- ^9 6 25.2. *9 9 7-1- ' 1 8 ■^1 1 "^ 3JL "T3 2 "l44 nposite number , and place the )er of figures on ivisor; find how nber in the quo- in the quotient, s, and to the re- ind.— Divide the and so on till all 1 38538 391432 i ' 37430 521184 1 ProoH 260592 456036 11084 1 7X6 7486 1 487RQ«/tTQ P•.r.r^f 1 35987 29944 m I •±t7 f -* 1 60435 - 1 5988^ 2 Proof. ^ 31 > 1 Remainder 54^^ I ' 48769847 1 58396274 - 1883750^4. 1 *^* 60837425 - r- 46 — ' 1322552|f m ^' 27419538 - f- 53 = 517349|i m 4. 40381694 - f- 67 — 6027114^ 1 5. 19507431 - r- 74 263613fa 1 6. 34182947 - r 85 : 402152fi m '^* 70546152 - r 97 : — 727279ff fl d. 174963081 - f- 217 806281^^4 M ^' 410589475 - - 308 133382|if m 10. 764127542 - - 470 1625803^VV m 11* 519380257 - ■- 526 = 987414^1^ 1 12. 873154963 - r 691 1263610H^ S 13. 249375016 - ■- 705 = 353723f^i 1 14. 931842790 - - 852 1093712/JL. fl 15. 838140819 - - 4081 = 205376yi|^ % 16. 481093600 - - .5830 82520m 1 ^^' 743725482 - - 7153 -rr-. 103973ffif 1 ^®' 619430528 - - 9007 — 68772iifi 1 19. 951653000 - - 8700 =r I069385|i 20. 765419364 - - 43742 — 17498i^f2A i 21. 919008500 - - 708000 — - 1298xH6 i 22. 674851680 - - 81030 = 8328fi^i 1 23. 752087000 - - 66500 — T 11309tV3 l| 24. 548300000 -: - 53080 = 10329V3Vt 1 25. 390542000 -. - 427000 ~— 914H4 . I M iV '■ \ I \ i 21 8T7PPL1MBNT TO MULTIPLICATION AND DIVISION. 1. My yearly income is j£3648, what is that per week ? 2. If a floor 40 feet long require 1280 stones, each a square foot, to pave it, what is its length? 3. The number of letters in a quarto volume which con- tained 4465 in a page, were 3,393,400 ; how many pages and sheets were in it ? 4. Great Britain and Ireland contain a population of 27,. 000,000, and their surface is 117,670 square miles, how many inhabitants is that on an average to the square mile ? 5. France contains a population of 32,800,000, at the rate of 160 to the square mile, how many square miles does France contain ? 6. A multiplier is 789, and product 6,678,885; required the multiplicand ? 7. If the hackney coaches of Edinburgh earn 985,500 shil- lings a year, at the rate of 15s each per day, what is the num- ber of coaches ? 8. If a pigeon fly at the rate of 56 miles an hour, what time would it take between Edinburgh and the cape of Good Hope, a distance of 5544 miles ? 9. A captain, mate, and 56 men, take a prize worth £40,- 020, how much will every one receive, supposing them all to share alike ? 10. How many miles is a person living in Edinburgh car- ried eastward in an hour, in consequence of the earth's diur- nal revolution; supposing it performed in 24 hours, and that the parallel of Edinburgh is 13,990 miles? (») £70t2j. C) 32. C) 760p. or 95s. (*) 230 nearly. (') 205000. C) 8465. C) 180. («) 99. (») £690. (") 582ii SUPPLEMENT TO MULTIPLICATION & DIVISION. I. When the multiplier contains a fraction. Rule. — First multiply by the upper figure of the fraction, and divide the product by the under figure ; then multiply by the integer, and add the product to the quotient. Mult. 6487536 by 8f Mult. 588267 by 406f H 406f 5)19462608 3892521^ 51900288 56792809f Prod. 6)2691335 3364161 3929602 2153068 2188728181 Prod. 8VPPLKMBNT TO MULTIPLICATION AND DIVISION. 32 me which con- •w many pages pulation of 27,. niles, how many 3 mile ? 000, at the rate ies does France ?,885; required rn 985,500 shil- ivhat is the num- 3 an hour, what e cape of Good ize worth £40,- ising them all to Edinburgh car. he earth's diur- hours, and that 1. d880086 X .-H =c 26275887. 2. 7183673 X n ^ 55673465|. 3. 4920527 X 6| ::=•. 328035131. 4. 2176498 X f r= 1360308J. 6. 8431956 X 10^ :^ 891378204. 6. 3066472 X 12tV nz; 37092211^. 7. 4936582 X fj — — 2879672jJ. 8. 3405274 X 50f — 171236686^f, 9. 7580924 X 61 4f = 46613266444. 10. 4718360 X 302^ =r 1425781 113f 11. 9374250 X 540f| — 5068969450. 12. 1852148 X 800^f =r 14827216461 II. When the divisor contains a fraction. Rule. — ^Multiply both the dividend and the divisor by the ider figure of the fraction, taking in the upper figure to the >roduct of the divisor ; then divide. Divide 467654 by 3| 3|) 487654 5 5 16 C 2)2438270 ( 8)1219135 1523911 Quot. Divide 7458 by 8| H) 6 7458 6 Quot. 53) 44748(844|f 424 234 212 228 212 16 Rem. of the fraction, | len multiply by | 1. 7493185 2. 2704526 8. 8571492 4. 5149300 5. 6381753 6. 1437016 7. 4913628 8. 5174095 9. 7438624 10. 3751393 .11. 6407430 Id. #7340«8 4* 8| m I2f 34f 524f 800^7, 780f| 274H 1665152f. 309088f|. 803677f. 6436625. 505485WV 15807176. I42719||f 86091^1 14175HH 4685f|§4 = 10768^ = 24540|f:| WW ml 2(3 PROMISCXfoltS EXERCISES IN THE SIMPLE BULES^. i I ■( ,r PROMISCUOUS^XERCISES IN THE SIMPLE RULES. 1. Lent to A. £30, to B. £48, to C. £120, to D. £209, to E. £44, to F. £1340, how much have I lent in all ? Ans, £1791. 2. A gentleman has £40 per week, how much is that per year? Ans. £2080. 3. Sir Isaac Newton was born in 1642, and died in 1727 ; what was his age ? Ans, 85. 4. A plantation consists of 10,656 trees, planted in 96 rows, how many trees does each row contain? Ans, 111. 5. A person whose fortune was £5000, gave his eldest son £909, his second son £808, and each of his other 3 sons £625 ; how much has he left ? Ans. £1408. 6. 7412 eggs were packed in 34 casks, how many did each cask contain ? Ans. 218. 7. How many stones, each a foot square, will pave a court, measuring 99 feet by 49 ? Ans. 4851. 8. A man born in 1829, when will he be 68 years of age ? Ans. 1897. 9. A field contained 32 acres, and produced 1664 bushels of grain ; how much was that per acre ? Ans. 52 bush. 10. My farm, last year, produced 526 bushels of wheat, 147 bushels of barley, 78 of beans, 100 of pease, 274 of oats ; how many bushels had I in all ? Ans, 1125. 11. A certain county contains 124,440 acres, and 20,740 in> habitants, how many acres are there to each ? Ans, 6. 12. What number divided by 27, will have for quotient 1111? -4»w. 29997. 13. If a man walk every day 2 hours, at 3 miles an hour, how many miles will he walk in a year ? Ans, 2190. 14. Borrowed from A. sixty -three pounds, from B. twenty- nine, from C. three hundred and forty-eight, and from D. one thousand and four; how much did I borrow in all? Ans, £1444. 15. How many days are in the 12 calendar months? Ans, 365. 16. What is the difference between twice 5 + 20, and twice 20 + 5? ^iw. 15. 17. Three boys, A. B. and C. won together 97 marbles at play ; now, if the number of marbles B. won be added to the number C. won, they will make 60 ; and, if the number A. won be added to the number B. won, thev will make 02 : how many marbles did each boy win separately ? * Ans. A. 37, B. 25, C. 36. IB. Surnames were first authoris9d to be used in Scotland by a parliannont hek) at Forfar in 1001 ; how long is it since? this being 184:2. 781 Ans, years. i RULES». fPLE RULES. JO, to D. £209, Ltinall? Ans, £1791. luch is that per Ans, £2080. d died in 1727 ; Ans. 85. ated in 96 rows, Ans, 111. ^e his eldest son [lis other 3 sons Ans. £1408. 7 many did each Ans, 218. ill pave a court, Ans, 4851. »8 years of age ? Ans, 1897. 3d 1664 hushels Ans, 52 hush. s of wheat, 147 74 of oats ; how Ans, 1125. , and 20,740 in. Ans,fi, quotient 1111? Ans, 29997. miles an hour, Ans, 2190. rom B. twenty- nd from D. one 1? Ans, £1444. nths? Ans, 365. f 20, and twice Ans, 15. 97 marbles at }e added to the the number A. make 02: how , B. 25, C. 36. ed in Scotland ong is it since? 31 Ans, years. QUESTIONS AND EXAMINATIONS. 24 19. A merchant has 960 pieces of cotton, containing 26^ yards each ; how many yards has he ? Ans, 25680. 20. A gentleman's income is £2000 per year, how much may he spend pqr day, and save £540 at the year's end ? r Ans, £4. 21. The figures now used in arithmetic were brought into Europe by the Saracens, from Arabia in 991, and Lord Napier I invented Logarithms in 1594 ; how many years intervened ? , Ans, 603. J 22. What is the difference between six dozen of dozens, and ihalfa dozen of dozens? Ans, 192. I 23. The sun's diameter is 890,000 miles, and the earth's 1 7970 ; required the difference? Ans, 882,030. , 24. Ho,w many seeds were produced by a bean which had 14 {Stems, each stem 19 pods, and each pod 6 seeds? Ans. 1590. ^ 25. What is the dilference between the area of a floor 50 ^feet by 34, and the joint areas of two floors, each one half of * these dimensions ? Ans, 850 feet. 26. What is the annual number of deaths in the world, sup- posing its population to be twelve hundred millions, and t|iat every year one out of 33 dies ? Ans, 36,363,636 /y. I ,27. A ship bound to a port 860 miles distant, after sailing for- ward 256 miles, is driven back 58 miles: she then gets for- ^ward 156, and is driven back 180 miles ; again she gets for- ; ward 680, and is driven back 58 : how far is she distant from her port ? Ans, 02 miles. 28. How much is 1 billion greater than 197,840,e05? ilns." 999,802,159,395. 29. The sum of £5000 is to be raised from 12 counties, in each county are 6 townships ; how much must each township contribute \ Ans, £96A. 30. How many pins will a boy point in a week, who works 8 hours per day, and points 16000 pins in an hour ? ; Ans. 768,000. ' 31. The art of printing was discovered in the year 1449, Miow long is it since, this being 1842 ? Ans. 393 years. 32. How many strokes does the hammor of a clock strike in . a day, and how many in a year of 305 days ? Ans, 156 per day, 56940 per year. QUESTIONS FOR EXAMINATION. What is Arithmetic? By what are all numbers expressed- What do you moan by number? What is the meaning of unit or unity? What is a whole number? Of what does a fraction s 1 U i'» Hi COMPOfTND ADDITION. consist? What is meant by an integer? What is an even number? What is an odd number? What is an abstract num- ber? What is a concrete number? What is a simple num. ber? What is a compound number? What is a composite number? What are the fundamental rules of arithmetic? What is meant by Numeration? What do you mean by No- tation? What is simple Addition? How should the numbers be placed? What is the number found called? What is sim- pie Stibtraction? What is the greater number called? What is the less number called? How do you place the numbers in subtraction? What is simple Multiplication? What is the number to be multiplied called? What is the number you multiply by called? What is the number arising from the o- peration called? What are the multiplicand and multiplier sometimes called? How do you multiply when the multiplier does not exceed 12? How do you multiply when the multipli-. er exceeds 12, but is found in the multiplication table? When the multiplier is not in the table, or consists of several figures, how do you proceed? How do you multiply when there is a fraction in the multiplier? What is simple Division? What is the number to be divided called? What is the number you divide by called? What is the result of the operation called? How do you divide when the divisor does not exceed 12? How (io you divide whon the divisor exceeds 12, but is a composite number? How do you divide when there is a fraction in the divisor? ' PART II. COMPOUND ADDITION Is the operation of adduig two or more numbers of difibrent denominations. ' * Rule. — Write numbers of the same denomination under oach other ; find the sum of the right hand column, which di- vide by us many of that name as make one of the next higher ; pi&cc the remainder, if any, below the column added, and car- ry the quotient to the next. Proceed in the same manner with the remaining denomina- tions to the last, which add as abstract numbers. Hi COMPOUND ADDITION. 26 ^hat is an even an abstract num- i a simple num. : is a composite s of arithmetic? ou mean by No- 3uld the numbers 1? What is sim. er called? What ;e the numbers in n? What is the the number you ising from the o- d and multiplier len the multiplier vhen the multipli-. on table? When )f several figures, when there is a Division? What the number you operation called? pxceed 12? How ut is a composite a fraction in the £ s. d. £ 8, d. £ s. d. 247 10 11 J 410 19 e% 246 11 n 381 17 6| 794 13 11 371 16 ^ 148 12 9i 421 12 n 713 10 111 412 16 n 876 17 10| 465 17 10^ 319 11 in 768 18 4 654 13 91 470 19 n 216 16 4| 892 16 11 I It- ^4 1981 9 8i 1733 18 9 1981 9 8i 3489 18 8| 3345 7 6^ 3078 19 3098 15 11^ 8i 3489 18 8| 3345 7 6^ n £ s, d. 54 17 8| 67 12 10 54 18 7i 19 9 6i 95 10 4 47 18 IH (•) £ s, d, 17 13 6i 80 19 7i 56 8 10 63 15 8| 49 7 3 95 14 9^ i (•) •3 17 6| |0 6 11 |3 18 5i to 15 8i 04 9 10 )5 13 4i fO 12 8| 34 12 7| 8 17 8-i 95 6 11 7 14 6i 80 10 41 6 10 74 15 3i C) 81 16 37 14 70 15 48 17 54 13 45 17 63 12 n 6i 9i 8i tbers of difibrent omination under olumn, which di- the next higher ; 1 added, and car- lining denomina- irs. 847 16 r63 14 \\B 15 190 10 K06 18 )41 13 178 17 n d, £ a, d, 8i 584 17 6i 6;^ 419 15 7^ 7| 372 8 11 3 106 14 3| ^ 890 16 8i 9 247 9 4i 4i 671 11 10 n £ s. d, 473 15 10 616 8 7i 190 14 el 740 17 8i 805 9 4) 864 18 lli 252 6 C) £ s. d, 43 14 Hi 96 17 64 57 16 7| 75 13 5^ 58 19 lOi 84 15 81 14 12 4i 75 8 11 9 15 Si 63 7 5 8 16 7| 81 9 10 9 13 6^ n £ a. d. 160 15 8| 906 11 2\ 3d4 7 9i 841 16 4 426 8 7i 273 10 8| 789 14 11 !• If^ k. ij 27 n 758 15 190 13 614 17 423 18 271 11 542 14 305 13 824 16 COMPOTTin) ADDITION. n ^ n 426 10 ^ 581 16 4i 103 10 10 874 16 7$ 240 17 3 718 13 6i 361 14 6i 718 18 11 (") 547 13 670 14 418 10 385 18 886 13 203 19 784 14 351 17 6 8i U 5i 2 H 44 748 15 160 10 848 18 520 17 473 14 968 19 8| ^ 44 3i 255 10 10| 847 18 8| n 749 14 8^ 420 IT 5| 368 10 7i 573 18 4 149 15 3t 954 17 104 507 13 dl 475 19 n 374 14 3^ 857 16 el 260 17 11 538 13 74 741 8 lOi 479 15 4| 152 19 64 604 7 6 n 748 13 7i 409 7 10 83 14 6f 950 8 11 16 19 2^ 662 6 5 45 10 8^ 531 5 4 71 n 304 16 62 5 4 740 12 83 16 8 5 853 17 3^ 74 6 10 523 10 7^ 65 9 6 £ 4385 504 86470 79 95314 851 M 74300 162 n s, d. 16 7 10 8i 8 a 15 10 6 5J 17 3 4i 18 6 5 11^ £ 347 7802 90 18417 281 65164 58 7630 25 n s, d. 14 8 8 H 15 7i 6 3i 17 10 9 4i 13 64 8 If 14 11 £ 74931 180 19 38674 3150 406 48385 20 4817 n s, d. 12 4 7 6i 14 11 6 64 17 5 8| 12 3 10 7i 4 10 ii 1. What is the sum of £43 17 4^, £817 6 I04, £6 12 Oi £610 8 6, £73 17 5^, £18 10 llf, £425 18 7^ ? Atu, £1806 11 10| 2. What is the sum of £516 14 I04, £90 8 51, £8 7 3 £3710 5 6, £436 10i» £16 10 4, £7 6 6^ 7 Atu, £4785 2 10 3. Add £4 13 6, £73 9 11^, £7 18, £0 15 6|, £46 9 Hi . £5 11 0|, £20 10, £8 10 74. Ans. £168 7 74. (") 748 15 8i \ 169 10 ^ t 848 18 44 I 520 17 ^ \ 473 14 H 968 19 ^ \ 255 10 101 \ 847 16 85 ^"^ n \ 304 16 7| 82 5 4 1 740 12 83 16 8 5 h 853 17 H 74 6 10 h 523 10 ^ 65 9 6 tJOMPOTIND SUBTRACTION. 28 n £ s. d. r4931 12 4 180 ? eh 19 14 11 J8574 6 54 3150 17 9 406 5 81 18385 12 3 20 10 n 4817 4 10 8 104, £6 12 Oj 8 7i? . £1896 11 101 00 8 5g, £8 7 3 *? fw. £4786 2 10 5 61, £46 9 Hi Ans, £168 7 74. 4. Add £436 15 8^, £75 7 10, £4 6^, £1630 12, £45 17 04, £500, £68 14 3i, £5 8 10. Ans. £2766 16 3. 5. Find the sum of £90 12 64, £8 19 llf, £67 8 4, |£26 16 lOf, £9 12 84, £63 13 11, £8 8 9, £81 12 6^ Ans. £357 5 7^. 1 6. What do these three sums of money amount to, the 1st %s £11 19 6, the 2d is 21 guineas, the 3d is three half-guineas and a crown? Ans. £36 17. I 7. A servant went to market and laid out on tea £1 14 8^ ; |on cofiee 18s. 6d. ; on sugar £2 6 ; on beef 2Ts. ; on mutton S36s. ; on veal 9. Z^d. ; on various other articles 25s. ; how ruch did he lay out in all ? Ans. £9 11. 8. A man lent his friend at different times these several |iums, viz : £25 15, £8 7 6, £36 14 10, and fourscore and iiineteen pounds, half a guinea, and a shilling, how much did jie lend in all ? Ans. £170 8 10. 9. Paid for ground to build a house £200, mason's bill 324 17 6, carpenter's £483 8 9, slater's £98 13 4, smith's 10 18 9, glazier's £48 7 10, at what must I sell it to gain 100 ? Ans. £1266 6 2. 10. A clerk, having been sent out for the payment of some J)ills, received from A. £23 12 6, from B. £31 17 10, from om F. £15 15 ; how much did he receive in all ? Ans. £156 8. COMPOUND SUBTRACTION lis the method of finding the difference between two com- ^ound numbers. ,' Rule. Write like names under one another. B'^gin at the flight hand and subtract each number of the subtrahend from that of the like name in the minuend ; but if the under num- )er be greater, subtract it from the value of the next higher mme, add the remainder to the upper number, and write the mm below •, but in this case carry 1 to the under figure of fthe next name. f Minuend. 27 18 11^ From 88 10 44 372 14 64 j Subtrahend. 19 17 ll| Take 27 li ll^ 178 16 8| i I Difference. 8 11| Dlff. 10 18 4| 198 17 9^ .Proof. 27 18 Hi Proof. 88 10 44 872 14 64 29 n £ s. 73 18 27 5 d. COMPOUND SUBTEACnON. £ s, d, 43 8 2^ 17 11 9| £ s, d, 685 13 Oi 419 15 3| £ s, d. 814 19 3 45 8 6i n \- I f'f I \.§ 85 10 3i 19 10 10^ 90 5 10 55 13 H n 10 U 1 15 2| (") 04 13 5^ 28 16 81 70 40 H (•) C) 70 3 Oi 714 6 3 8 14 8| 190 11 10| 53 19 2 17 3 11^ 631 11 7i 236 15 8i 600 10 11^ 419 17 4| n 24 19 9 5 li n 560 96 4 914 6 3 615 11 4i 708 199 19 Of 65 14 7^ 16 17 9| 874 17 8i 489 18 11^ n 80 19 19 Of n 500 90 11^ n 563 17 7i 278 17 8i n 700 9 19 llf ^ft ■11 54 13 6 48 14 9j r) 30 10 5^ 9 12 10^ n 705 17 8i 418 6 10| n ( 82 11 Hi 95 11 11 lli 5 10 0| 1 10 400 ( 1 n 914 11 8i 219 18 8| 600 10 Oi 09 9 9i ^ n n 1 £ s. d. N ^^K* 814 19 3 H 45 8 H m - S COMPOUND MULTIPLICATION. 90 (") 600 10 Hi 419 17 4| 914 6 3 615 11 4i 708 199 19 Of 1. What is the diiTercnce between £589 15 8^, and je748 13 6i? 2. What is the difTerence between £35 19 Hi, and 35 19 2i ? 3. From £1, subtract 1 1^. 4. Borrowed £10, of which I have paid £3 3 3^, how uch am I still in debt ? 5. How much is the sum of £11 11 \\\ less than £12 ? 6. £1000— £135 15 + £74 8 7i + £209 12 11^. 7. £43 4 8f + £78 12 4— £100 16 9i + £8 7 8^. 8. What sum added to £83 13 4i will make £100? 9. A horse in his harness is worth £30 10, out of it 5E19 19 9, what is the value of the harness ? 10. I lent a friend £100 ; and have received from him in sh £43 17 6, in goods £46 2 8^, how much does he ve me? 11. Borrowed from a neighbour at one lime £27 16 6, at nother time £6 12 ; but I have since paid him twice the mount of the latter sum, and £10 besides, how much do I till owe him ? 12. A gentleman's yearly income is £500 ; — his household ixpences £294 13 7|, rent £54 13 6, taxes £20 11 8^, ser, ant's wages £25 17 11, tradesmen's accounts £52 11 7^, .nd incidental expences £24 17 11^; how much does he ave ? Ans, £26 13 8. 563 17 278 17 700 9 19 \\\ 914 11 8i 219 18 81 690 10 90 9 9i COMPOUND MULTIPLICATION 18 the operation of multiplying a compound quantity by a |imple number. ' , ,, , Rule I. When the multiplier does not exceed 12, place it inder the lowest denomination of the multiplicand, then muU [iply, and carry as in compound addition. (ult. £ 74 18 t £ 38 9 5i 4 £ 658 s. d. 12 10 i Ans. 149 17 3^ 153 17 9 4611 11 1| I 1. Multiply £678 17 8^ by 4, 2, 7, 3, 5, 8, 6, 10, 9, 12, 11. 2. 945 8 7J — 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, Rule II. When the multiplier is a composite number, mul- lliply by its component parts. 1^' ! I •11 ■ I, I 1:' r • 14 20 yds. moleskin, (a> 4 21 Quires paper, (S) 1 22 yds. calico, (S) 1 24 Pairs boots, (S) 13 25 Bushels oats, , • fa) 1 27 Ounces bark, (S) 28 Quarto volumes,. . . .© 1 12 30 Pairs shoes, ^ 8 32 Bushels wheat, ^ 5 .33 Days' wages,. , (a> 4 . 35 yds. linen, ^ 2 36 Horses, © 14 17 .40 yds. ribbon (S) 42 Sheep, (S) 1 2 44 Pairs stockings, (a) 3 45 yds. silk, (a> «5 48 Gallons brandy,. . . .© 16 49 lb. tobacco,. ....... ® 1 50 lb. sugar, (a> 54 Maps, (3> 17 56 cwt. sugar, fS) 4 13 60 Norwich shawls,. ...'«) 11 63 yds. silk, (S) 4 64 Barrels beer,.. (3> 1 8 66 Arithmetics, (S) 1 70 lbs. tea, (S> 4 72 Acres land, ^ 2 17 77 pairs shoes, 'S) 9 80 Quarts rum,. ....... rs) 1 84 Hats, (^ 18 88 lbs. cloves, "3) 2 00 Bottles wine, ^ 2 d. £ «. d. 9 Aws !. 1 18 6 r 71 « 1 4 4i 8 « 6 2 8 9 " 13 5 6 ; if 9 « 4 15 "i 2^ « 1 5 -41 1 3i « 1 7 IH 4 6 « 16 4 4| « 1 14 lOf % H « 12 H M 10 « 45 19 4 w 91 « 13 3 9 M 3 « 8 8 M 7i « 7 11 IH ■m 11 " 5 2 1 8 « 535 16 M 9| « 1 12 6 M 3 « 46 14 G M H" 6 17 6 M 10 ^* 13 2 6 'M 7 « 39 16 ,'h 5i « 3 10 H ■1 8% « 1 16 ^ 6 " 47 5 M 6 « 261 16 M 4Jt " 34 2 6 ■f 10 « 15 4 6 - 1 « 89 12 •1 8| « 5 14 H If 41 " 15 6 3 :i.> 6 " 207 3i " 35 13 10* M 111 " 7 18 4 9 " 78 15 4^^B 5^ " 10 16 4 ■ 7i « 11 14 4^ (:,y 4^ Uy 3;> 5 in 3 lOi Ans. £ Ans. 1 « 1 6 13 (( 4 1 1 16 1 s, 18 4 2 5 15 5 7 4 14 12 45 19 13 3 8 8 7 11 5 2 " 535 16 « 1 12 46 14 6 17 13 2 39 16 3 10 1 16 47 5 " 261 16 " 34 2 15 4 89 12 5 14 15 6 207 u tt It « « u tt tt tt tt tt tt tt tt tt it tt tt tt tt d. 6 41 8 6 4^ 10£ H 4 9 Hi 1 6 6 6 H 6 6 U 3 COMPOUND MULTIPLICATION. 32 '67, 96 yds. broad cloth,....© 1 5 3 « 121 4 38. 100 Watches, ® 4 IT 8 "488 6 8 39. 108 Deals © 1 2| " 6 12 9 40. 120 Oxen © 9 13 5 "1160 10 41. 110 Firkins butter, © 2 8 10 " 268 II 8 42. 121 Ewes, ® 17 11 " 108 7 11 43. 132 Stones beef, © 3 4^ « 22 5 < [44. 144 Dozens eggs, © 7i « 4 7 Rule III. When the multiplier is not a composite number; mltiply by the component parts of the number nearest to it, id the multiplicand by what the given number is greater or iss, and add or subtract accordingly. Mult. 2 14 7^ by 38 or thus.- I 2 14 7^ X 2 2 14 7^ X 2 tt 35 13 m tt 7 18 4 tt 78 15 tl 10 16 4 tt 11 14 4^ 16 7 9 6 98 6 5 9 6 3 \ns. 103 15 9 10 18 6 10 ! add 109 5 5 9 i\ sub't. Ans. 103 15 9 1. 17 rs) 5 4 Ans. 4 10 8 2. 31 (a) 10 •71 (( 16 9 41 3. 39 (a) 2 15 6 tt 108 ,4 6 4. 47 rs) 17 10 tt 41 18 2 5. 58 (S ^ it 1 16 3 6. 67 (S) 3 4 tt 214 8 7. 73 (a) 2 114 tt 149 8 51 8. 78 (5) 3 10 it 14 19 9. 85 (a) 7 11 It 30 5 71 10. 97 (a> 8 9:: tt 42 10 91 11. 102 (5> 1 9 tt 8 18 6 12. 107 (S> 15 OJ it 80 11 81 13. 113 (S) 5 6 3 tt 600 6 3 14. 122 (S> H tt 1 13 01 15. 128 (a) 1 6 tt 131 4 16. 134 (a> 1 61 tt 9 15 5 17. 140 (S> 3 H it 23 3 9 18. 146 (a> 3 10 1 it 511 12 2 19. 150 © 17 8 n 132 10 20. 153 (S> 6 10 tt 52 5 6 Note. — Multiplication by large numbers can also be per- )rmed, but such questions are more easily solved by practice. f. M :h' :1., ■ ■ I; il:: i .«; 'fi- t : I ^Wh COMPOUND DlVISIOlf. 563 yds. at 15 7 per yd. *. d. t, 16 7X3 I 10 6248 yds. ® 3 5 per yd. s* d, 3 5X8 10 7 15 10X6 10 . 1 14 2X4 10 77 18 4 5 17 1 8X2 10 ■ t<- ■ i 389 11 8 price of 500 46 15 price of 60 2 6 9 price of 3 438 13 5 price of 563 170 16 8 6 1025 price of 6000 34 3 4 price of 200 6 16 8 price of 40 17 4 price of 8 £8 16 5 X 435 10 7 4^ X 174 4 12 10 X 847 5 8 3^ X 3740 2 15 8 X 6054 6 14 9 X 1507 1067 7 4 price of 6248 = JB1662 1 3 = 1804 3 S = 3931 9 10 A = 20250 10 10 = 16850 6 = 10153 8 8 COMPOUND DIVISION' * Is the operation of dividing a compound quantity by a simple number, &c. Rule I. — ^Divide the highest denomination of the dividend by the divisor, and reduce the remainder, if any, to the next inferior denomination, adding the given number of that name ; divide this as before, and procoed in the same manner to the lowest denomination. Divide £547 13 6^ by 4 Divide £5149 13 8^ by 7 £ 8, d, £ s, d, 4 )547 13 6^ 7 )5149 13 8^ 136 18 A^—j Ans. 735 13 4^— ^ Ans. Divide £7493 17 5^ by 2, 3, 4, 6, 6, 7; 8, 9, 10, 11, 12, Divide £91075 8 8| by 4, 3, 2, 8, 7, 6, 5, 12, 11, 9, 10. Rule II. When the divisor is a composite number, divide by its component j^aits. ti -*rirf^*.* ■ .\} 3 5 per yd. ix8 » tX4 ) 3X2 ) price of 6000 4 price of 200 B price of 40 4 price of 8 4 price of 6248 1 3 3 3 10 ^0 10 6 8 8 tity by a simple of the dividend iny, to the next !!• of that name ; manner to the 9 13 8| by 7 . 3 8t 3 4|— ^ Ans. 9, 10, 11, 12, 12, 11, 9, 10. number, divide 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 8 ^ i 6 Th llf 1 3 30 COMPOUND DIVISION. JE375 16 8 -^ 25 =£15 816 13 7i -T- 36 = 22 13 493 17 6f -^ 45 = 10 19 904 9 3 -f- 54 = 16 14 562 15 8i -r 60 = 9 7 7 100 7 -^ 63 = 1 11 101 I 750 10 -r 70 = 10 14 54 417 9 8 ~ 72 = 5 15 IH f 5173 14 7^ -^ 77 = 67 3 9f ^ 4805 8 9 -f- 81 = 59 6 1364 13 6f -r 90 = 15 3 8550 ^ 99 = 86 7 31 j\ 3256 18 -r 110 = 29 12 1$ H 9037 15 8 r 121 = 74 13 10 j\ 7830 -r 132 = 59 6 5107 16 -^ 144 = 35 9 U 6J- i Q 1 7 ^ 30 ^4 I I 5 17. If 30 yards of cloth cost £37 15, what is the price of yard? Ans. £l 5 2. 18. If 36 lb. tea cost £9 1 6, what is the price of 1 lb ? Ans. 5s. O^d. 19. If 42 yards linen cost £5 7J , what is the price of 1 ^ard ? " Ans. 2s. 4^d. 20. Divide £25 10 5 equally among 50 persons. Ans, 10s. ^^d. M 21. Bought 63 yards silk for £17 6 6, what is that per l^ard? Ans. 5s. 6d. f 22. Bought 72 cwt. sugai for £243 18,' what is that per ^^wt. ? Ans, £3 7 9. j 23. Sold 84 yards calico for £5 8 6, how much is that per yard? Ans. Is. 3^d. 24. Sold 96 sheep for £84 16, at what was that a piece ? Ans. 17s. 8d. 25. Sold 100 acres land for £252 10, what was that per fere ? Ans. £2 10 6. I 26. What is the price of 1 yd. when 120 cost £21 15 ? ;| Ans. 3. 7id. . I 27. What is the value of 1 gallon rum at £58 6 for 132 |als? Ans, 8s. lOd. 28. What is the price of sugar per lb. at £4 10 for 144 lb ? Ans, 7Jd. Note. — When the divisor is not a composite number, di- b^ide as in long division. S / I f'i ■'V # ■! ' t...;r ^ 4 .■:l ";s I ml. > .1 li '"^ 'it'; 35 COMPOUND DIVISION. Divide £27 13 7^ by 17. Divide J6452 8 lOi by 74. £ s. d. £ B. d. £ 8. d. jS s. d. 17)27 13 7i(l 12 e^tVans. 74)452 8 10^(6 2 3i3»ans. 17 444 8 20 168 148 9 12 115 102 13 4 54 51 3 • 1. £743 16 51 -i 23 -£32 6 9Hf 2. 514 13 7i H 37 — 13 18 ^u 9. 180 6 4 -. 43 — 4 3 lOifl 4. 879 15 6 -i 52 16 18 4i ,t(.-. 'B*- 426 11 3 -. 65 — 6 11 3 -^1* 960 9 H -"' 76 — 12 12 9 ^8 7. 290 14 10 - 83 — 3 10 om 8. 704 12 3f - 97 , — 7 5 3H? 9. 6538 10 9 - - 131 — 49 18 3 10. 4063 9 11 H - 165 — 24 12 ^T\% 11. 1952 H - - 247 — 7 18 Oifif 1 12. 8169 18 4 - - 365 — 22 7 8 13. 7619 8 - - 416 — 18 6 3^/3 14. 5371 16 9 - r 508 10 11 H tVt 15. 3675 1 H - 'r 629 — ' 5 16 lOi i6. 8050 9 2 - - 760 — ' 10 11 m 17. 5913 15 6| - - 809 — 7 6 2i m y 18. 4184 8 - - 951 — 4 8 ■<'l ^ COKPOimD BIYISION. 90 2 8 lOi by 74. M 19. £2700 19 11 j&s. d. M 20. 9067 9 7 W 2 3i?» ans, 1 ^^* 6543 15 7| 'S 22. 1800 ' 1 23. 7195 7 10 'fl 24. 3714 19 • '^S 25. 2088 4 2 ^m 26. 9154 12 ■■ 27. 6307 15 4^ ^B 28. 8(28 9 1 6 18 3 18 11 12 10 5 18 12 18 7 6 11 16 11 6 8 9i if 2H4 lOHl 3 9 "2 8 3 3H^ _IL 38 I a 5 J 34? 8 lOi lOi 2i m 1 13 6|iWr 2 16 7 1 12 i^W 6 3i IHf 1 2 9i llfi 10 HHI 4 H 15 2 2 5| ^jW^ 1 Hi [30. -r- 1609 = -r- 3206 = -r 4070 = -^ 5708 = ^ 6315 = -T- 7000 = .-7- 8716 = -7- 12072 = -r 50800 = -7- 83014 = [29. What is cloth per yard, when 78 yds. cost £92 12 6 ? Ans. £1 3 9. What is wheat per quarter, when 85 qrs. cost jte25 12 6 ? Ans. £2 13 1 j\ 31. Divide a prize of £2011 9 equally among 98 sailors. .^* Ans. £20 10 6 32. If I spend £70 4 in 2 years, how much is that per jek? Ans. 13s. 6d. ■ 33. If you earn £47 2 11 in a year, wha^ is that per day ? Ans. 2s. .7d. 34. Sold 119 gallons beer for £9 18 4, what was that per gallon? Ans. Is. 8d. ,, 35. My yearly rent is £75, how much is that per week ? H Ans. £1 8 10 -5% 36. How much must I spend per day, to spend £300 rear? Ans. lOs. 5:^d.7|^. [37. Bought 470 lambs for £180, how much is that a piece ? Ans. 7s. 7^d.^| -i|38. Divide £100 equally among 375 poor people. I Ans. 5s. 4d. 39. Bought I cwt. of tea for £30, what is that per lb. ? m Ans. 5s. 4^ |d. 1 40. Sold 745 acres of wild land for £651 17 6, what was It per acre ? Ans. 17s. 6d. jRuLE in. When the divisor is also a compound number, wduce both the (^i^ ' or and dividend to the lowest name IMi^ntioned, and (V u is in simple division. 37 COMPOUND DIVISION. Divide £6 8 3 by 3s. ^d, Divide £99 8 H by £1 11 6| s. d, £ s, d. £ s. d, £ s» d. 3 4^) 6 8 3 1 11 6^) 99 8 5i 12 20 20 20 ■I s. jv ■II ' '^i' ' m !| 4i 40 4 162 128 12 ans. 31 12 378 4 1515 1988 12 1539 4 23861 4 162)6156(38 486 )95445(63 ans 9090 1296 1296 4545 4545 1. £113 12 6 H - £2 10 6 = 45 ans. 2. 52 18 6 - - 12 2 = 87 " 3. 11 5 - - 14^= 163fT " 4. 45 11 ^ - - 3 7^= 250 5. 815 10 6 - -876= 97tVVV « 6. 32 3 li - 17 6 = 36| 7. How much cloth at 153. ejd. per yard can I buy for £95 11 7i? Ans. 123 ydaA 8. How many dozens of wine at £2 2 6 per doz. can be bought for £297 10 ? Ans, 140 doz, 9. How many gallons of brandy may be purchased foi £625 19 6 at 18s. 3d. per gallon ? Ans, 686 gals, 10. The revenues of an hospital amount to £1807 ^ yearly, how many boys will it maintain, if each boy cos £18 16 Oi ? Ans» 96 boys 11. A gentleman distributed £19 14 6 among some pooi people, giving each 10s. ll^d., how many poor were there? Ans. 86 12. If a man gain 2s. 6d. per day, and spend Is. lO^d. Jiow many days must he labour to pay a debt of £11 7 6 Ans, 364, Note. — In Compound Multiplication and Division, whe: the multiplier or divisor contains a fraction, the rules are tli .same, as those given for Simple Multiplication and Division. iigi MISCELLANEOUS EXERCISES IN THE COMPOUND RULES. 38 It by £1 11 6| £ s, d. 99 8 H 20 95445(63 ans. }090 4545 4545 ans. (( (( <( L5 37 53fT 50 rd can I buy for Ans. 123 yd3> *" per doz. can h Ans. 140 doz. )e purchased fo! Ans. 686 gals, tunt to £1807 f if each boy cos Ans. 96 boys among some pooi oor were thero ? Ans. 36 \ spend Is. lO^d. icbt of £11 7 6 Ans, 304, d Division, wher , the rules are thi )n and Division. 1. £748 13 7^ X 8^ 2. 817 14 9| X 12i 3. 58 15 10 X 36f 4. 160 9 6i X 70f 5. 94 12 8 X 84V'2 6. 503 8 9f X llOf 7. 80 16 10 X 1441 8. 953 11 5i - •:- eh 9. 74 7 H - ■- m 10. 817 15 8 - - 23f 11. 62 10 10 - - 65f 12. 1760 17 4i H - 81t'2 13. 48 9 7 -. - 137J 14. 506 11 11 - - 308tV £6363 15 10358 2160 11 11333 13 7988 12 55756 11711 18 146 14 6 6 34 13 16 21 14 7 1 12 9^ m lOi loii V 11^ i 8^ lOiiVV AV 4 m J. ¥ i I - • , MISCELLANEOUS EXERCISES IN THE COMPOUND RULES. 1. A person's income is £96 a-year, and he spends on an iverage £1 3 3| per week ; how much does he save yearly ? fi Ans. £35 7 9. 4 2. How much will the wages of 13 men amount to in 7 f weeks, at Is. lOd. per day each? Ans. £50 1. ^ 3. If scissors are bought at 4s. 9d. per dozen, and retailed #it 6^d. per pair, how much is gained on 5 dozen ? Ans. 8s. 9d. 4. C. borrowed from D. £120, of which he has paid at )ne time £40, at another time £19 19 6, at another )16 8 4, at another £6 17 4, and at another £30, how mch has he paid in all, and what remains to pay ? Ans. £113 5 2 paid, £6 14 10 to pay. .;^ 5. Divide £3 10 among 5 men and 6 womeni and give itach man thrice the share of a woman. Ans, A man's share 10s. a woman's 3s. 4d. 6. A piece of cloth at 8s. 4d. per yard cost £18 15 ; how mny yards were in it ? Ans, 45 yds. fi 7. What cost 9^ gallons, at 19s. 7id. per gallon ? Ans. £9 3 11^. 8. A gentleman's income is £960 ; what should bo his 'daily expenses to save £150 per annum 7 Ana, £2 4 i^^^, 9. A gentleman gave £5 13 4 among some poor people, {iving each 6s. 8d. ; how many were there ? Ans. 17. 10. A workman earned on Monday 48. 7d., on Tuesday Ids. lOd., on Wednesday 6s. 4d., on Thursday 28. 6d., on Friday Os. 2d., and on Saturday Ss. 6d,» what did his week's wages amount to ? An$, £1 6 1. I* . it J'f* '1 ■ !• 1.- h • I I* i :S if •I' 39 MiaCELLANfiOUS EXEftGISES IN THE COMPOUND RULES. 11. A labourer earns 16s. 6d. per week; how much should ho spend per week, lo save £11 for his house rent and clothes? Ans, lis. Sd.y^j,- 12. A servant having contracted a debt of £2 6 8^, allows d^d. of his wages to lie in his master's hands every week for the payment of it ; in what time will this liquidate the debt ? Ans. 59 weeks. 13. fn 48 purses, each containing a Joannes, a moidore, a half.guinea, and a half-crown, how many pounds ? Ans. JB182 8. 14. If ld% yards cloth cost £8 17 7^, what is that per yard? Ans. 12s. lid, 15. Divide £394 117 among 5 men and a boy, and give the boy half of a man's share ? Ans. A man's share £71 14 10, the boy's £35 17 5 16. A labourer's house-rent is £3 13 9 yearly ; how much must ho lay by weekly in order to pay it ? Ans. Is. 5J^d. 17. Lent £105, and received £66 14 8 ; how much is yet duo to me ? Ans. £38 5 4. 18. What is tlie price of 83 yards of India nankeen, at Is. 9^d. per yard ? Ans. £7 10 5i. 19. A servant went lo market with a ten.pound note, and bought as follows : beef 19s. 5d., mutton 7s. 6d., lamb 25s. 4d., vegetables 2s. 3d., eggs 33. 4d., butter 14s. 8d., cheese 3l8. 4d., how much did she bring 'lome ? Ans, £4 16 2. 20. Bought 06 pairs of stockings for £19 10 ; at what rate must I sell them per prtir, to gain £4 4 6 by them? Ans, 4s. Hi id. 31. Paid £88 13 for a lot of cioth measuring 69^ yards ; at what rate did I buy it per yard? Ans. £1 5 6tVV' 22. A certain person said if ho were to present each of his ^rand-children with throe half-crowns, he should expend ex- actly £24 15 ; how many hud he ? Ans. 66. 28. A banlvrupt compounds with his creditors at 13s, 6d. per £ J how much will W. receive, to whom ho owes £425 ? '"- . Ans. £286 17 6. 24. A person who spent at an average 18s. 4^d, per day, aaved £52 10 last year ; required his income. Ans. £387 16 10^. '25. At a public dinhcr, the bill amounted to £16 10, oach periwn paying 6s* 6d., how many dined ? An^. 60. 26. A piece of linen containing 25^ yards, Wud bought for £4 9 3, what was that per yard ? Ans. ^n, 6d. ■ ' ^7. A Hlk^chant sold 50 yards linen at 3s. 9d., but allowed til llULJES. MISCELLANEOUS EXERCISES IN THE COMPOUND RULES. 40 how much ise rent and lis. Sd.VV £2 6 8i, Imnds every ns liquidule ?. 59 weeks. I moidore, a IS. £182 8. t is that per s. 12s. lid. oy, and give s£35 17 5 early ; how it? •V^d. much s. Is. ow s, £38 5 is 4. nankeen, at £7 10 5i. id note, and , lamb 25s. 8d., cheese 5. £4 16 2. 10 ; at what yrthem? 4s. Hi id. 69^ yards ; £1 6 6j\\. t each of his i expend ex- Ans, 60. at 13s. 6d. owes £425 ? £286 17 6. ^d. per day, !^87 16 lOi. ;i6 10, oach An*. 60. id bouglit for Ans. 8^. 6d. , but allowed a discount of J^ for cash ; how much did he receive for the linen ? Ans. £8 18 1^. 28. After the death of a gentleman, it was found in his will, that he had left to his widow £800, to his eldest son £1080 16, to each of his other three sons £500 15 6, to each of his two daughters £300 14 9, to five of his near relatives each £50 12 6, to his servants £30 17 8, and to the poor of the parish £10 19 10 ; how much did he leave in ail ? Ans. £4279 12. 29. Divide £26 3 11^ among 4 men, 6 women, and 8 children, giving each man double a woman, and each woman triple a child. Ans. A child's share 10s. 5|d — a woman's share £1 11 5i-Ta man's share £3 2 10^. 30. A merchant paid £89 6 5| for 5 pieces of cloth, each 25 yards ; at what must he sell it per yard to gain £8 17 6 on the whole ? Ans. 16s. 8id.^\. 31. If a workman gains every week 18s. 6d., and spends 10s. 4^d. ; how much does he save in a year ? Ans. £21 2 6. 32. If a man earns 3s. 9d. per day, and spends Is. 8Ad. ; how much does he lay by in a year ? Ans. £37 5 2|d. 33. A certain gentleman lays up every year £294 12 0, and spends daily £1 12 6 — I desire to know his annual in- come. Ans, £887 15. 34. A gentleman's annual income was £586 18 4 ; his household expenses in the same time amounted to £285 16 8, his rent was £65 16, taxes £14 16 10, servants' wages £56 18 6, tradesmen's accounts £42 13 9, and incidental expenses £14 10; how much did he save ? ^n*. £106 6 7. 35. Received a guinea to pay an account of 16s. 3id. what balance have I to return ? Ans. £4s. Sjd. 36. If 9^ yards cost £8 7 7^, what is that per yard ? Ans. 188. 37. In what time will a debt of £9 16 be discharged by weekly payments of 3s. 6d. ? Ans. 66 weeks. 38. A gentleman left his whole effects, amounting to £25816 10, to his son and 11 nephews ; — the son was to get i of the whole, the remainder was to bo equally divided among his cousins : how much did the son get, and what did each of his cousins receive ? Ans. £5163 6 son, £1877 11 S\ j\ each cousin. 39. A. B. andC. receive £89 19 7^, now A. and B. receive £64 6 7|, and B. and C. receive £56 10 10 ; how much does each receive ? Ans. A. £34 8 9i, B. £29 17 lOi, C. £25 12 llj. 40. A merchant paid £64 18 for 268 yords cloth, which m m i 4 ■^« 41 •« ?• BILLS OF PARCELS, OR INVOICES. getting damaged, he is content to lose £l 13 by it : at what must he sell it per yard ? Ans, 4s. 4^ ^. 41. If a gentleman's income be £37 16 9 per week, and his expenses J£25 12 6 ; how many weeks will he be in paying off a bond of £525 ? Ans, 42 |f f a- weeks. 42. A. B. C. and D. together owe F. £1242 10 2^ : A. owes him £243 16 8^, B. owes £381 Id 2|, and C. £497 11 7i how much does D. owe him ? Ans, £119 2 8. 43. How many crowns, half-crowns, and sixpences, and of each an equal number, are in £20 ? Ans, 50. 44. A maid went to market with a five-pound note, and laid out on butcher meat 14s. 8id., on cheese 8s. 5^d., on eggs 2s. 3d., on butter 3s. 4d., on tea 15s. 6d, and on sugar 5s. 2d. ; how much money ought she to have brought home ? Ans, £2 10 7. 45. Required the price of 20 horses, costing one with another £23 16 9i each ? Ans, £476 15 10. 46. If a person's income be 4s. 6d. per day, and his ex- penses £71 1 6 per annum, how much does he lay up, or overspend per annum, and how much does he spend weekly ? Ans, £11 1 laid up, £1 7 4^ weekly expense. 47. How many lbs. of cotton wool, at 2s. 3^d may be bought for £43 6 3 ; and how may it be sold per lb., to gain £11 6 on the whole ? Ans, 3781b. Sold at 2s. lO^d. 48. A merchant bought broad cloth at 22s. 6d. per ell En- glish ; how may he retail it per yard to clear 2d. on every shil- ling which it cost him ? Ans, 21s. 49. Bought 24 pieces of cloth, each containing 30 yards, for £840 17 6, and sold 400 yards of it at 24s. 3d. per yard ; how must I sell the remainder per yard to gain £84 2 6 upon the whole? ,. Ans. £1 7 6. If ir .1' II BILLS OF PARCELS, OR INVOICES. A Bill of Parcels or Invoice is an account of goods given when bought, showing their quantity and price. Quebec, July 27th, 1842. Mr. Christian Hoffman, Bought of John MacNider. 4 yards Lawn, (a> 2s. 8d £0 10 8 7 do. Shalloon, (S> Is, Id 11 1 8 do. Serge, (S> Is. 8^ 13 8 U do. Lace...... (S> la, 4d 4 8 12 do. Muslin,. (S> 58. 3d 3 3 £8 10 1 it» j^. by it : at what Ans, 4s. 4^ f . per week, and will he be in 12 mf- weeks. 142 10 2i: A. Id 2|, and C. ins, JE119 2 8. xpences, and of Ans. 50. ound note» and ise 8s. 5^d., on d, and on sugar brought home ? Ans, £2 10 7. )sting one with r. £476 15 10. day, and his ex. 58 he lay up, or I spend weekly ? iveekly expense. 2s. d^d may be i per lb., to gain Did at 2s. lO^d. 6d. per ell En. 1. on every shll. Ans. 21s. ng 30 yards, for 3d. per yard ; I £84 2 6 upon Ans. £1 7 6. CES. of goods given BILLS OF PARCELS, OR INVOICES. 42 Miss Gouinlock, Bought of Henry Wholesale. 15 Yards Cambric, (S) 8s. 3d £ 9 do. Satin, ^ 7s. 6d 24 do. Printed Calico,. .. . (S) Is. 4id 11 do. Flowered Silk, 15s I 43 do. Irish Linen,. ..... • ft!) 3s. 9d £27 10 6 Montreal, August 1st, 1842. John Greatman, Esqr. Bought of Messrs. Molson & Co. 36 Gallons Rum, (S> 14s. lOd £ , ' 18 do. Brandy,.... (a> 18s. 6d 7^ do. Malt Aqua,. . (S) 12s. Od 45 Dozens Port Wine,.. (S) 30s. 6d 24 do. Lisbon do. .. (S) 28s. 9d 10 do. Mountain do. (a> 20s. Od • £160 19 6 Mr. Timothy Trusty, Bought of G. & J.' Gouinlock. 6i Yards Superfine Black Cloth, (S) 28s. 6d. £ 12 do. do. Spanish blue, (3> 30s. 8^ do. Fine narrow do fS> 9s. 6d. 17 do. Drab Cassimere,.. .....^ 6s. 4d. 4 lb. Young Hyson Tea, "a) 4s. 9d. 25 ]bs. Refined Sugar, ^ lO^d. £37 6 Oi 27th, 1842. ;er. i ..£0 10 8 .. 11 1 .. 18 8 .. 4 8 .. 3 8 £8 19 1 Mr. James Ruthven, Bought of William Oliver. 14 Gallons Malt Aqua, fa) 10s. 6d £ 13 do. Rum, r^ 18s. 6d 12 do. Hollands, fa) 24s. 6d 9 do. Brandy, fS> 35s. 6d 15 Dozens Port Wine, fa) 42s. 6d 16 do. Sher^'V. ^ 89s. 6d £113 10 6 Vi 43 BILLS OF FABCELS, OR INVOIGES. Mr. B. Parsons, Bought of John Ruthven, 17 Reams large thick Post,.... (S) 41s. 7d.<..£ 23 do. small do. do., (3) 32s. 9d... 13 do. Superfine laid Foolscap, O 20s. 3d. . . 16 do- Coloured 4to. Post, .... © 25s. S^d. 18 do. Wove Post, (S) 24s. ll^d. '41 do. Common Cap, (3) 19s. lid.. . £150 1 11 f:: f i* "i '),■■: i § i\\ Toronto, 27th July, 1842. Mr. Henrv Williamson, Bought of J. & W. Allan. 27i Yards Superfine Black Cloth, (S) 21s. 8d. £ 171 do. Blue Cloth, ® 23s. 6d. \Sy^ do. Olive do rS) 14s. 9d. 23| do. Mixtdo.. fS 17s. lOd. 34^ do. Black Cassimerc, (S) 6s. 4^d. £94 2^ Mr. J. Anderson, Bought of W. Bates, & Co 13i lbs. Green Tea, « 9s. 17i 26$ 19J^ 27 35 (( (t (( Hyson Skin, , (S> 7s. 6^.. 3|d... <( u Souchong, (of 8s. ll^d... Pekoe, ro) 10s. 8^d... Raw Sugar, (a) S^d. . . Refined do fS ll|d... £37 12 lOf Mr. Wni. Brown, Bought of John Fisher, 56 Cwt. Raw Sugar, fd) 54s. 8d £ 29 Boxes Oranges, (a) 44s. ll^d 5 do. Lemons, (Si 53s. 4^d 150 Sugar Loaves, each 13^ lbs. (S) 10|d. per lb. 1 Tiorcc of Molasses, 52^ gals, ra) Is. &^d. per gal 1 Chest Black Tea, 87^ lbs. (S) 4s. 3Jd. per \b > > £343 4 5i BILLS OF PASCBLS, OR INVOICES. 44 Mr. George ThompscMi, Bought of David Wright. 54^ Yards Super. Brussels Carpet rs> 43. IQJd. £ 71 67| in 15^ 18 25 10 Fine Superfioe English Fine « Floorcloth, (( (( (3) ds. 9d. . . . (a) 2s. llid.'» (S) 2s. l|d... ,cd 5s. 7^d... V Crumb Cloth, (a> 8s. 9^d... Petersham (<'> 15s Superfine Pilot Cloth. . (S) 7s. 6d, . . . Fustian (S> 2s. 9d. . . . ■". !'i J675 9 Of Mr. John Simpson, ' * Bought of R. Davidson. 52 Quarters Wheat, f® 56s. 6d £> 47 " Barley, O 43s. 5d 39 " Oats (S 32s. 8d 17 « Pease, (S> 25s. 3d 19 « Beans, (3) 23s. 8d.. 117 Stones Hay, fd 9^d. , £361 4 li METHOD OF KEEPING A BOOK OF HOUSEHOLD EXPENSES. 1842. Jan. 1 2 3 4 6 7 10 11 12 15 20 21 25 Received for House expenses Paid for 3 bottles Port Wine (S) 4s. 3d •• " Bread 23. 3d Butter Is.— B«ef 5s... •• " Eggs lOid.— Milk 2s.— two Fowls 2s " Grocer's bill £2 ISs.—l doz. Porter 5s... " Postage of Letters 4s. 3d. — a Tea Pot 6s. Received for the House Paid Butcher's account " for Soap Is. 8d.— Vegetables T^d. Fish 2f •• 1 gal. Rum 78. 6d. — Mustard & Pepper Is Received for the House Paid for Potatoes 138. — Milk Is. — Postages Ss " Tea 7s. 8d.— Biscuits d^^d.— 1 Broom 2s. Cash on hand £ Rf.c'd. Paid. 210 3 5 N. B.— The next page must begin with the Cash on Hand 12 8 4 10 9 3 10^ 3 117 (5 3i 4 8 17 10 6 5i : ! 4 'i.l ■2^1, :•+ 4t BVSOCMM'i 1 . In 41200 ttdltk, tM>W mU^ ltiil«» ? ^< , 2. In 135003 yards, how many miles ? 3. In ISiftbi^SS inches, how hiaiiy miles t 4. In 533232 lines, Ww many furlongs t 5. In 2936'7'y fee'., how many leagu'^s ? SQUARE MEASURE. ^ 1. Redact 6^ ftcr^^, 2 t-oods, 14 poles, to poles. 2. Reduce 17 licre^, 2 td0d«>> 24 pdes, to is^tiare y&r^. 3. Reduce 48 toi^S, 12 pld. 12 sq. ydd. to s^. mk, 4. Reduce 26 ac. 1 ro. 3 pfe. 14 yds. "S ft. to feet. 5. Reduce 7 ac. 16 pb. 26 sq. yd. to siq. yards. 1. In 13374 poles, how many acres ? 2. In 85426 sq. yarcls, how many acres ? 3. In 1876455 sq. feet, how many acres ? 4. In 1 152293 sq. feet, how many afcres ? > . 5. In 34390 *q. yards, hC^v many acres? ■^ 1. Reduce 2. Reduce 3. Reduce 4. Reduce 5. Reduce 1. In 1648 2. In 1297 3. In 1439 4. la 658 i 5. In 1818 CLOTH MEASURE. 45 yards, 3. qrs. 1 inch, to inches. 36 yds. 1 in. to inches. 71 English ells» 4 qrs. 3 nl. to nails. 24 Flemish ells, 1 qr. 1 in. to inches^ 75 French ells, 4 qr. 2 na. to nail«. inches, how many yards ? inched, hoSv mahy yards 1 nails, how many English ells ? . r nches, how many Flemish ells? nails, how many French ells? ,^ .5! HEAPED MEASURE. '. 1. Reduce 234 chaldrons to sacks and hushels. 2. Reduce 905 chaldrons to sacks, bus, pe. aiid gals. 3. Reduce 81 chal. 8 sacks, 2 bus. 1 pie. to peCKS. 4. Reduce 27 chal. 6 sacks, 1 bus. 3 pe. 1 gal. to ^Ilons. 1. In 8424 bushels, how mahy sacks and chaldrons ? 2. In 260640 gallons, how many pe. bus. sks. and chal. ? 3. In 11769 pecks, hoW maiiy chaldrons ? 4. In 7935 gallons, how many chaldrons ? CtJBIC Ok SOLID MEASURE. f 1. Reduce 126 cubic yards to cubic inches. 2. Reduce 85 solid yaros, 17 solid feet, to solid inches. 3. Reduce 59 loads of hewn timber to solid inches. 4. Reduce 29 tons of shipping to cubic feet. ns9f^<3fm»' ■ ivf3~r'7 1. 2. 3. 4. 1. 2. 1, 2. 1. ^1 2. HH 1. 2. H 1. 1 2. ■ 1. 2. 1 ■ J* H 2. ' m 3. 4. 6. aid. 1 3. m 1. » gallons. 1 I chal. ? ; 2. 3. 4. b. ' '• 1. . ': 2. 3. iches. 4. B. 5, In 5878656 cubic m\mi bow lAA^O^ cuMc 3^4^? In 3995136 solid iaQh;^*. bpW pMmy s(!J[i<| y^rdft t In 5097600 solid inches, how many bads of hcMfn tymh^r ? In 1218 cubic feet, how many tPns of shipi^Wg t . ' COTTON YARN, MEASURE. Reduce 26 spindles, 3 hks. 4 sks. 26 thds., to tbreads. Reduce 7 sp. 12 hk?. 5 sk, 39 threads, V> inches. In 264106 threads, how many spindles ? In 4196836 inches, how mwiy spindles? FLAX YARN, MEASURE. Reduce 34 spindles, 2 hsp. 3 heers, I cut, K> threads. Reduce 81 spin. 26 Inches, to iiy;hes« In 199560 threads, how many spindles ? In 41990426 inches how many spindles ? ' MOTION. Reduce 8 signs, 16*', 26' to minytes. : . Reduce 9 signs, 21°, 17', 14" to seconds.. In 15386 minutes, how many signs ? - — lu 1048634 seconds, how many signs? TIME MEASURE. V .. • • .. Reduce 1 Julian year to hours. > ; ^ Reduce 1 leap year to minutes. Reduce 1 solar year to seconds. Reduce 181 days, 11 hours, 18 minutes, to minutes. Reduce 168 days, 16 seconds, to seconds. In 8766 hours, how many Julian years ? ' < In 527040 minutes, how many leap years ? In 31,556,928 seconds, how many solar years ? In 261318 minutes, how many days ? ' In 14,515,216 seconds, how many days ? The following questions exemplify the Srd Rule* Reduce 128 English ells to yards. Reduce 555 Flemish ells to English ells. Reduce 314 half-crowns to shillings. *^ Reduce 210 moidores to sovereigns. ^' ; ■" Hcduce 810 angels to Joannes*. / i |4 Tt! 49 EXERCISES IN t(rEI6HTS AND MEASVRI9. 6. Reduce 864 marks to ^hillings. 7. Reduce 904 lbs. troy to lbs. avoirdupois. 1. In 160 yard a, how many English ells ? 2. In 333 English ells, how many Flemish ells ? 3. In 785 shillings, how many half-crowns ? 4. In 291 sov. 12 shil. how many moidores 1 5. In 225 Joanneses, how many angels 1 a. In 11520 shillings, how many marks ? 7. In 743 Ibr avoir. 6040 gr. how many lb. troy T :l :!<« ADDITION OF Wl SIGI ITS AND MEASURES. (') C ') (•) TROY WEIGHT. APOTH. WEIGHT. AVOIR. WEIGHT. lb. oz. dwt. Sr- oz. dr. scr. gr. cwt. qr. lb. oz. 17 » 16 13 14 7 16 35 1 24 13 85 5 17 21 85 3 I 9 74 2 16 10 34 10 8 18 47 6 2 15 23 8 6 73 7 14 5 70 1 8 96 I 2^ 15 47 9 13 19 36 5 2 17 18 2 15 9 62 4 19 14 93 4 1 6 65 1 9 10 59 6 5 22 28 2 12 67 14 7 n c ) -' O ' LINEAL MBASURB. CLOTH MEASURE. SQUARE MEASURE. nils. fur. po. yds. yds. qr. na. in. ac. ro. pe. yds 74 5 27 4 73 1 3 1 38 3 34 4 16 3 31 3 4d 1 a 76 1 27 3 85 1 16 1 57 a 65 2 16 1 27 4 10 85 2 2 1 59 30 5 60 7 28 5 16 1 3 80 3 18 39 15 2 30 1 1 26 1 21 4 95 6 18 3 17 3 2 2 95 2 13 2 SUBTRACTION OF WRIGHTS AND xMEASURES. TROY WEIGHT. AVOIR. WEIGHT. LINEAL MEASURE. lb. OZ. dwt. Ri*- tons. cwt. qr. lb. po. yd. ft. in. 95 3 12 10 70 12 1 14 31 I 1 28 10 15 21 19 16 3 19 16 3 2 9 , ^ .il !■' 1 HISCET.LANEOVS EXERCISES 6 o 1 SQUARE MEASITRE. mEAS. OF CAPACITY. 1 ac. ro. per. yd. bus. pe. gal. pts. 1 70 1 24 2 64 3 3 48 3 37 5 17 3 1 5 • • da. 53 8 TIME. ho. mi. 14 31 14 52 50 se. 17 38 . . " '" _ ' » 1 MTTT TTDT m A T«Tr \M rw? -^XTx?! r*Tjrra at iiri 1 itT? A QTTD T7C« 1. 18 lb. 6. oz. 13 dwt. 8 gr. x 8 =r 148 lb. 5 oz. 6 dwt. 16 gr. 2. 74 tons 12 cwt. 1 qr. 16 lb. X 12 = 895 tons 8 cwt. 2 qr. 24 lb. 3. 53 mi. 5 fur. 17 po. 4 yd. X 32 = 1717 mi. 6 fur. 7 po. 1^ yd. 4. 48 ac. 2 ro. 31 per. 3 yd. X 45 = 2191 ac. ro. 39 per. 14 yd. 5. 63 bus. 2 pe. 1 gal. 6 pts. X 66 = 4205 bus. 1 pe. 1 gal. 4 pts. 6. 85 da. 9 ho. 25 mi. 9 sec. X 84 = 7172 da. 23 ho. 12 mi. 36 sec. DIVISION OF WEIGHTS AND MEASURES. 1. 63 cwf. 1 qr. 23 lb. 13 oz. 2. 75 ac. 3 ro. 19 per. 4\ yd. 3. 59 bus. 1 pe. 1 gal. 5 pts. 4. 841b. 9 oz. 11 dwt. 18 gr. 5. 97 mi. 3 fur. 35 po. 3 yd. = 12 cwt. 2 qr. 21 lb. 9 oz. = 8 ac. 1 ro. 28 per. 24 yd. = 2 bus. 1 pe. 1 gal. 6^| pts. = 1 lb. oz. 2 dwt. 6{\ grs. -i- 5 ~ 9 -^24 H- 84 ■f- 65 = 1 mi. 3 fur. 39 po. 5/^ yd 6. 83 da. 17 ho. 45 mi. 30 sec. -r- 73 = 1 da. 3 ho. 31 mi. 51^ sec. MISCELLANEOUS EXERCISES 1. In £51, how many shillings, groats, pence, sixpences and halfpence? Ans, 1020s. 3060 gr. 12240 p. 2040 sixp. 24480 halfp. 2. How large is an estate consisting of 10 farms, each mea- suring upon an average 148 acres, 2 ro. 25 per. 26 sq. yds ? Ans, 1486 a. 2 r. 18 p. 18 yds- 3. A piece of silk measured 42 yds. 3qrs., and there were sold of it, at different times, 10 yds. 3 qr. 3 na. — 9 yds. 1 qr. 2 na. — 12 yds. 2qr. 1 na., how much remained? Ans. 9 yds. 3 qr. 2 na. 4. How many hhds. of sugar, each 11^ cwt. will be con- tained in 141,680 lbs. ? - Ans. 110. 5. In 25 moidores, how many shillings, pence, twopences^ sixpences, crowns, half-crowns, threepences, and fkrthings ? Ans. 675s. aiOOp. 4050 twop. 1350 sixp. 13&cr. 270 halfc. 2700 threep. 32400 far. 6. How fas will a man travel in 52 days, at the rate of 35 miles, 5 furlongs^ and 36 poles per day 1 Ans. 1858 m. 2 fur. 38 po. I m ■m VX MiaCXLLANBOVS BZBBCISEI. M 'd V . '. *• 7. How many seconds are in one year, of 365 days, 5 hours, 48 minutes, and 48 seconds ? Ans. 11556928 sec. 8. What is the weight of 6| hbds. at 4 cwt. 3 qr. 11 lb. per hhd. ? * Ans, 32 cwt. 2 qr. 25i lb. 9. How many canisters, each holding 12 lb., can I fill out of 25 cwt. 2 qr. 24 lb. of tea ? Ans, 240 canisters. 10. How many inches will reach round the terrestrial globe, it being 860 degrees ; «a€h tiegree being 69^ miles ? Ans. 1585267200 inches. 11. A common of 500 acres is to be divided among 5 pro- prietors, according to the vcdue of their estates which border upon it, A. gets 59^ acres, B. 76^ acres, C. 106 a. 2 r. 16 p., D. 94 a. r. 88 p. and E. the rest, required his share ? Ans, 163 a. 1 r. 26 per. 12. If 13 silver spoons weigh 1 lb. 7 oz. 13 dwt. 6 gr. what is the weight of one ? Ans, 1 oz. 10 dwt. 6 gr. 13. In £147, how many nobles, pence, sixpences, half* crowns, and shillings ? Ans, 441 no. 35280 pen. 5880 sixp. 1176 h c. 2940 sh. 14. The distance between London and Edinburgh is 390 miles, how oflea will a coach- wheel of 15 feet circuirifcrcnoe revolve in performing the journey ? Ans, 137,280 times. 15. How many small enclosures, each 8 ac. 2 ro. and 27 per. can be made out of a common, containing 260 acres, and 10 poles ? Ans. 30 enclosures. 16. How many spoons, each 2 oz. 6 dwt. can be made out of an old silver vessel, weighing 5 lb. 2 oz. 2 dwt. ? Ans, 27. 17. In £26 how many crowns, half-crowns, and sixpences, and of each an equal number ? Ans, 66 of each. 18. In a puncheon of rum (84 gals.) how many gallons, quarts, and pints, and of eachan equal number ? Ans, 61iXf of each. 19. What is the v/eight of an English shilling, 1 lb. of silver being coined into 66 shillings 7 Ans, 3 dwt. 15^ grs. 20. What is the weight of a sterling sovereign, 1 lb. of gold being coined into 46 f^ sovereigns ? Ans, 5 dwt. 3 ffl ffrs. 21. Light runs through the space of 1000 diametere orthe earth in one minute ; how many yards is that, supposing the the diameter of the earth to be 8000 miles 7 Ans, 14,080,000,000 yards. 22. How many yards of cloth, eight qrs. broad will lino a piece of tapestry that is 24 feet long, and 8 feet broad 7 , Ans, 10| yards. 28. In 20 guineas, apd the same number of half guineas quarter guineas, crowns, h&lf crowns, and shillings; how many half peace 7 Ans, 31720 hal4>ence. QUESTIONS FOR EXAMINATION. ^^iW 24. Two men depart from the same place ; the one goes directly north 14 miles per day ; the other south, 22 miles per day ; how far are they asunder on the 24th day ? Ans, 864 miles. 25. How many farthings are tliere in 2222 pieces, each 3s. lO^d. ? Ans, 413292 farthings. 26. A gentleman's expenses are on an average £1 14 6^ per day, how many days will £630 7 8^ meet his expendi- ture ? Ans, 365 days. 27. What is the difference between 10 square miles, and 10 miles square ? Ans, 90 square miles. 28. In general, a township in Canada, is 12 miles square ; how many acres are in a township ? Ans. 92,160 acres, 29. One day, to my surprise, said a young lady, I found my pocket expenses since the 1st of January, amounted to £15 10s. ; now grandma' allows me only 7s. 9d. per week for pocket money ; pray tell me on what day of the year I made this discovery, and how many weeks after the 1st of January? Ans, Oct. 7th — 40 weeks. 30. How many lbs. of silver in 2 dozen dishes, each dish weighing 25 oz. 15 dwts., and 2 dozen plates, each 15 oz. 15 dwts. 22 grains ? Ans, 83 lbs, 1 oz. 2 dwts. a QUESTIONS FOR EXAMINATION IN THE COM. POUND RULES AND REDUCTION. What is compound Addition? How do you place the num- bers to be added? What is compound Subtraction? Do you ulacc the numbers the same as in addition? What is com- A. pound Multiplication? When the multiplier does not exceed 12 how do you multiply? When the multiplier is a compo- site number what do you multiply by? When the multiplier is not a composite number, how do you proceed? What is compound Division? Are not the varieties of compound di- vision similar to those of compound Multiplication? Yes, and they all prove each other. How do you know a compound Multiplication question from a compound Division one? Ant. When the price of one is given, to find the price of any great- er number, it is Multiphcation ; and when the price of sevc- ral is given, to find the price of one, it is Division. Are not the compound rules very useful ones? Ans, Yes, to bo well acquainted with them is essentially necessary in common life and for mercantile calculations. What is a Hill of Parcels, or Invoice? What is Reduction? How do you reduce a num- ber from a higher name to a lower? How do you reduce a number from a lower name to a higher? How do you reduce pounds to shillings, pence and fartlungs? How do you reduce i:, % '4 m [il- 53 61MPLB PROPORTION. •|,?'^.„i» ' ..3t ,■.;•»'' . I'f k * farthings to pence, shillings and pounds? Repeat Troy weight table. What articles are weighed by Troy weight? Repeat Apothecaries' weight. What is this weight used for? Re- peat Avoirdupois weight. For what purposes is it used? Repeat the general measure of capacity. What articles are measured by it? Repeat Lineal measure. What is the use of this measure? Repeat Square measure. What is the use of Square measure? Repeat Cloth measure. For what is it used? Repeat Time measure. What is measured by it? Repeat the 12 Calendar monlhs. How do you remember the number of davs in each? PART III. SIMPLE PROPORTION. Four numbers are proportional, when the first contains the second as often as the third contains the fourth ; or when the first, multiplied by any number, contain the second as oflen as the third, multiplied by the same numbers, contains the fourth. RULE FOR STATING. The three given numbers must be placed in one line. First write down the given quantity of the thing sought ; that is, of yards, if yards be sought ; of money, if money be sought, dz;c. If the number sought is to be greatelr than that written down, place the greater of the ether two towards the right hand ; but if it is to be less, place the less on the right hand of the other. RULE FOR WORKING. The two like terms are first to be reduced to the same name, and the other to the lowest name in it. Then multiply the two right hand terms together, and divide the product by the left hand term ; the quotient will be the answer of tha same name with the term first written down, ur uf the name it was reduced to. If 12 acres of land maintain 16 horses, how many horses will 27 acres maintain ? Write 16 horses first, because horses are sought ; and as 27 acres will main- tain more horses than 12 acres, write the greater, 27, towards the right of 12. ac. ac. hor. 12 : 27 :: 16 16 ■ 162 27 1 12)432 ans. 86 hories Simple vnofonrtotf. U If 24 horses be maintained on hay for a certain sum, when hay is at lOd. per stone, how many will be maintained for the same sum when the price of hay is Is. per stone ? d. 12 d. 10 hors. 24 10 (240 ans. 20 hors* After writing 24 horses, then fewer will he maintained, because the hay is dearer, therefore the less, 10d<, is written to the right of l2d. Note. — If the first term, (which is always the divisor,) and either of the other two, are measured by the same number, divide them by it, and use the Quotients instead of them. Tech- nically, this is called cancelling, and it is of the greatest im- portance to get pupils to understand it thoroughly, as it short- ens the work in many questions, in various rules. If57 yards ofcloth cost £55 4 4^; what will 152 yards come to ? yd. yd. £ a. d» 57: 152: :55 4 4i 19 8 18 8 l| Ans. 147 5 In this ^..cuiion 3 divides 57 down to 19, and £55 4 4^ to £18 8 1^; again, 19 divides or cancels 152 to 8; hence £18 8 1^ multiplied by 8 must be the Ans.-*-always draw a horizontal line through the figures you cancel. I ^1 i same name, 5 A man's yearly wages are £37 4 1 ; what are they for 78 days ? Am, £7 8 m Here 73 cancels 305 down to 5 ; hence £37 4 1 divided by 5 gives the Ans. days* da. £ s. d. 365: 73::37 4 1 S What will 100 yards cloth come to, when 48 yards cost £15 13 4 ? yd. 48 4 yd. £ 8. d. 108: :15 13 4 9 4)140 11 Ans. £35 2 Here 12 cancels 48 and 108 down to 4 and 9, therefore £15 12 4 muhlplied by 9 and divided by 4 gives the Ans^ mi .v> SIMPLB PBOPOBTIOK. i-. ;r'i.' , 1. If 4 yards of qloth cost 38.^ what will 24 y%rd» oost ?* Am^ 18s. 5. If 24 yards of cloth cost 18s., what will 4 yards cost ? Ans. 3s. 3. If I get 4 yards of cloth for 3s. how many will I get for 18^.? Ans, 24, 4. If I get 24 yards for 18s., how many will I get for 3s. An9, 4. 6. If 24 yds. cloth cost 36s., what will 141 yds. cost ? Ans. jBlO 11 6. 6. If 8 yds. cost 323., what will 51 yds. cost ? Ans. £10 4 0. 7. If 7 lb. cost 25s., what will 49 lb. cost ? Ans, M 15 0. . 8. If 17 yds. of cloth cost £4 5, what will 307 yds. como to? Ans. £76 15 0. If 100 yds. of serge cost £5 8 4, what will 37 yds cost ? Ans. £2 1. 10. If 68 yds. cloth cost £17 19 10, what will 7 yds. cost? Ans. £1 17 Oi 11. If 57 yds. of linen cost £8 11, what will 96 yds 3 qrs. cost 1 Ans. £14 16 3. 12. If 19 lb. of tea oost £4 15, what will 3 cwt. 17 lb. oost? Ans, £88 5. . 13. What must i puy for 475 gals, sherry, when 138 gals, cost £65 11 1 Ans. £225 12 14. When velvet is 18s. 6d. per yd. what will 6 nls« cost ? Ans, 6s. ll^d. 15. If 3 yds. of broad cloth cost £4 8 3, what will 24^ yds. cost ? Ans, £36 8^ 10. If 24| yds. of cloth cost £36 8i, what is the price of 3 yds ? ' 17. If I pay £36 8^ for 24^ yds. of cloth, what quantity can I purchase for £483? 18. If I pay £12 8 for 16 yds. of rich flowered silk, whnt quantity can I purchase for £111 12 ? Ans, 144 yds. 19. How much steel may be bought for £9 16 10|, when M lbs. cost 10s. 11 id. ? Ans. 2 cwt. 1 qr. 20. What is tiic price of 8 pieces of cloth, each containing tJ5 yds., at £4 19 11^ for 17 yds. ? Ans. £22 llf ||. Ul. What do a man's wages amount to in 143 days, at £28 a year? Ans, £10 19 4J ,«y. * Tho throe fullowing questions arc deduced (Vom this, nnd cverjr ex. ompio ndmits nf boinp: varied in the snmc manner. V^ nrn the terms of a question are so connected, that while one i§ in. evcMr '' the other inereases, or is diminished the other diminishes, the questii. is said to bo in direct proportion. Dut if, while the one is in. snens pKOPoKtioK. 5« 1&^. Findl the vtUtte bf 4 «wt. 9 qr. 14 'ib. of cheese, «t 65s. 4d. per cwt« iln«. £15 18 6. ^. Find th>>.■., m ^ ! ' '..1 '^ff'WP SIMPLE PROPOBTIOK* :i'f '- ' 15 days, how long will the same quantity serve 20 men at that rate ? Ana* 9 days. 42. If 186 masons can build a ibrt in 28 days, how many must be employed to finish one equally strong in 8 days ? Ans, 476 masons. 43k If 28 reapers finish a harvest in 36 days, how many reapers will do it in 9 days ? Ans, 112 reapers. 44. If 18 men mow a meadow in 4 dciys, how many will mow it in 9 days ? Ans. 8 mowers. 45. How many lbs. at 2s. 9d., are equal in value to 110 lbs., at 4s. 6d. ? Ans, 180 lbs. 46. A butcher buys a piece of linen, measuring 26 yds. at 2s. 7d. per yd., how much beef, at 10s. 8d. per stone, must he give in return 1 Ans, 6 st. 4 ^^j lbs. 47. If 9^ yards of broad cloth cost £1 2 9^ what will 33^ yds. of the same cost ? Ans, J£25 9 10. 48. If I lend a friend £100 for 12 months, how long should he lend me J&150 to requite my kindness ? Ans, 8 months. 49. A bankrupt's debts amount to £5130, and his effects ^3729 18 9 ; how much can he offer his creditors per £ ? Ans, 14s. 6^d. 50. A bankrupt owes his creditors £4678 ; how much will he pay them at lis. 6d. per £, ? Ans, £2689 17. 51. A bankrupt pays his creditors 13s. 4d. per £., paying them in all £490 ; what was his debt ? Ans, £735. 52. A garrison has provisions for 10 months, at the rate of 16 oz. to each person per day ; how much may be allowed per day, that the provisions may last for one year ? Ans, 13 oz. 6 dwt. 16 gr. 53. At 15 oz. per day for each man, a garrison's provi- sions will last 8 months ; how long will they last if each man is allowed only 12^ oz. per day ? Ans, 9 months, 18 days. 54. If a garrison of 1000 soldiers have provisions for 9 months, how many must be dismissed that the same provisions may last 15 months. Ans, 400 men. 65. How much carpeting yard-wide will cover a floor, 25 feet long and 18 feet wide ? Ans, 50 yards. 56. If it cost £26 2 6 to floor a room 30 feet by 22, what will it cost for one 24 by 18. Ans, £17 2 0. 57. How much tea at 4s. 8d. per lb. ought to be exchanged for 140 lb. at 6s. 8d. ? Ans. 200 lb. 58. If the arms of a deceitful balance be 12 inches and Hi in. respectively ; what weight on the shorter end will balance 46 lb. on the longer ? Ans, 48 lb. 59. Suppose tlic arms of a deceitful balance be to each other as 10^ to 10, and suppose a weight of 35 lb. hangs 9IMPL5 PBOPOKTION. 68 from the end of the shorter arm, what weight hung frowi the end of the longer arm will produce an equilibrium 1 An8,2^ lb. 60. If muslin i yard wide cost 3s. 6d. per yard, what should be charged for cloth of the same quality f yard wide ? Ans, 4s. 6d. 61. If a retailer has 2d. of profit on every shilling he draws, to what extent must he deal to clear £100 ? Ans. £600. 62. What is the interest of jei750 for a year at 5 per cent per annum? Ans. £87 10. 63. What is my commission on £256 18, at 2^ per cent ? Ans, £6 8 5^ f . 64. What is the brokerage of £255 at 4s. pe: ... ^t ? Ans. iOs. 2^d|. 65. If £425 gain £20 3 9, what is the rate per cent ? Ans. £4 15. 66. A traveller walks 24 miles a day, and after he has ad- vanced 42 miles, another follows him, who walks 32 miles a day, in what time will he overtake him ? Ans. 5i days. 67. If a stick 4 feet 8 inches long casts a shadow of 5 feet 10 inches, what is the height of a tower whose shadow is 125 feet 6 inches ? Ans. 100 feet 4f in. 68. A boy flying his kite with 384 yards of string, tied the end of it to a peg on level ground, and found that a knot 6 feet from the peg was 4^ feet from the ground : how high was the kite ? Ans. 288 yards. 69. A farmer borrowed 192 quarters of wheat, when tho price was £4 11, how much should he return in quantity when the price is £4 4 ? Ans. 208 quarters. 70. If 20 acres of land, worth £21 per acre, be exchanged for 35 acres of other land, what is this last valued at per acre ? Ans. £12 per acre. 71. The shadow of a cloud was observed to move 36 yards in 5 seconds ; what was the hourly motion of tho wind ? Ans. 25,920 yds., or Uj\ miles. 73. If a hare start 120 yards before a greyhound, and run 6 yards, whilst the dog runs 8^ ; how many yards must the dog run ere he catch the hare ? Ans. 408 yards. The dog gains 2^ on every 8^ ; hence, as 2^1 S^'.'. 120 : 408. 73. A. and B. depart from tiie same place, and travel along the same road ; but A. sets out 5 days j^fore B., going at the rate of 15 miles per day ; B. follows at the rate of 20 miles per day ; what distance must he travel to overtake A. ? Ans. 300 miles. jsa m ?] m •i'-'-!} 59 COMPOUND PROFORTIOir. ■f m i 74. How much cloth, 3 qrs. wide, must be given for 90 yds. of equal goodness which is 5 qrs. wide ? Ans, 150 yds. 75. A. has cloth at 4s. 6d., which he wants to barter with B. for 84 yds. at 7s. 6d. how many yards must A. give ? Ans, 140 yds. 76. If the carriage of 60 cwt. for 120 miles be £15 10, how far may I have 210 cwt. carried for the same money ? Ans, 34f miles. 77. Bartered 64 yd. linen at 2s. 8d. per yd., for 128 yds. cotton ; required the barter price of the cotton ? Ans. Is. 4d. per yd. 78. A. has tea worth 7s. 6d. ready money, but in barter will have 9s. ; B. has cloth worth 2s. 6d. ready money ; how must B. rate his cloth to be even with A ? Ans, 3s. per yd. 79. How many yds. of cloth, at 7s. 6d. ought to be recei- ved for 7 pieces, each 108 yds., at 5s. per yd. ? Ans,' 504 yds. 80. How much cloth at 7s. 6d. per yd. ought to be given in barter for 3 pieces, each 27 yds., at 5s. 3d. per yard ? Ans. 56 yds. 2 qrs. 3| na. COMPOUND PROPORTION. ; When the proportion depends upon several circumstances, it is said to be compound. One of the given numbers is of the same kind with that re- quired ; and the others, taken two and two, are like one ano- ther. RULE FOR STATING. > Write down the term which is like the number sought ; and first take two numbers of the same kind, and state them as in the simple rule ; then take other two like one another, and state them in the same manner under the former, and so on till all the numbers are stated. , . , ... 1 ■( RULE FOR WORKING. and that like the Reduce like terms to the same name ; number sought, to the lowest name in it. Multiply the terms below one another successively, which will reduce them to three ; then work as in simple proportion. If 15 pecks of wheat serve a family of 9 persons for 22 days, how long will 20.pecks of it serve a family of 6 persons? -U- COMPOUND PROPORTION. 60 that like the Days are sought, write 22 days first ; now as 20 pecks will serve longer than 15, put 20 to the right of 15; and as they will serve 6 persons longer than 9, put 9 to the right of 6. pecks, 15 : 20 : persons, 6 1 9 90 180 :22 days. *- * 1 22 K"l 360 360 m I- 9,0)396,0 ans. 44 days. For cancelling, it is better to state the question with all the terms in one line. If JC36 value of corn maintain 18 men for 9 months, when corn is at 16s. per boM, how many will be maintained 6 months for £54, when the price is 12s. ? , ^ Divisors. men 18 : a s. m. £ 12 : : 6 :: 36 c b a 3 .2 d e Dividends. £ m. s. > 54 : 9 : 16 b d c ' t /» 4 „ e men. 9 X 3 X 2= =54 ans. Here 18a cancels 36a down to 2, — 6b cancels 54b to 9, — 4 cancels cl2 and cl6 to 3 and 4,— d3 cancels d9 to 3, — e2 cancels e4 to 2 : — the divisors being all cancelled, the remain- ing dividends 9 3 2 multiplied together gives the ans. If 12 men in 15 days build a wall 30 feet long, 6 feet high, and 3 feet thick ; in what time will 60 men build a wall 300 feet long, 8 feet high, and 6 feet thick ? Ans, 80 days. Divisors. th 3 e H. 6 F. M. days M. F. 30 : 60 : 15 : : 12 : 300 b a a e b 4 4 X 10 d Dividends. H. : 8 d X 2 th. 6 c =80 ans. Here al5 cancels a60 down to 4, — b30 cancels bSOO to 10, — c6 cancels c6, — d4 cancels d8 to 2, — e3 cancels e 12 to 4 : — hence the remaining dividends 4 10 2 multiplied together gives the ans. — Carefully remember that one divisor must not cancel another divisjr, nor one dividend cancel another divi. dend, but one of the numbers must always be a divisor and ■/*i^ 1.1 m I: 'm m iu '.. 61 COMPOUND PROPORTION. 1 ' iV-i- ■;'ti. ht'i"' the Other a dividend : and always draw a line through the fYg. urcs you cancel in both divisor and dividend. 1. If 3000 copies of a book of 11 sheets require 66 reams of paper, how much paper will be required for 5000 copies of a book of 12^ sheets ? Ans* 125 reams* 2. If 8 men in 6 days make 48 roods of ditching, how many roods will 6 men make in 36 days ? Ans, 216 roods. 3. If 12 men in 4 days mow 48 acres of grass, how many must be employed to mow 192 acres in 24 days ? Ans. 8 men. 4. If a person travel 320 miles in 10 days, when the day is 12 hours long, — ^how many miles will he travel in 16 days, when the day is 16 hours long ? Ans, 640 miles. 5. If 9 persons pay £18 for 4 weeks board; what sum will discharge the board of 14 persons for 13 weeks? Am» £91. 6. If 18 men eat 16s. worth of bread in 3 days, when wheat is at 18s. per boll, what value of bread will 45 men eat in 27 fJays, when wheat is at 15s. per boll ? Ans. £15 value. 7. If 8 men can build a wall 20 feet long, 6 feet high and 4 feet thick, in 12 days ; in what time will 24 men build one 200 ft. loiig, 8 ft. high, and 6 ft. thick ? Ans. 80 days. 8. If £100 in 12 nrjonths gain £5 interest, what sum will £525 gain in 9 months ? Ans. £30 18 9. 0. If £825 gain £30 18 9 in 9 months, what will £100 gain in 12 months ? Ans. £5. 10. If £100 in 12 months gain £5 interest, what sum will gain £30 18 9 interest in 9 months? Ans, £825. 11. If £825 gain £30 18 9 interest in 9 months, what sum will gain £5 in 12 months ? Ans. £100. 12. If £100 in 12 months gain £5, in what time will £825 gain £30 18 9 ? Ans. 9 months. 13. If £825 gain £30 13 9 in 9 months, in what time will £100 gain £5 ? Ans. 12 months. 14. If 8 men accomplish 30 yards of ditching in 12 days, working 8 hours per day ; in what time will 12 men finish a ditch, supposing its whole length 60 yards, when they work only 6 hours per day ? Ans. 21^ days. 15. If 236 men eat 160 qrs. of wheat in 108 days, how many qrs. will 76 men eat in a year and 67 days ? Ans. 206j\ qrs. 16. If a chest 8 feet long, 5 feet deep, and 4^ feet wide hold 24 bolls of oats, how many bolls will a chest 16 ft. long 4 feet deep, and 5 feet wide, contain ? Ans. 42f bolls. 17. If 30 cwt. be carried 15 miles for £5 8 9, how many n^iles ought 90 cwt. to be carried for £29 ? Ans. 26 J miles. 18. If 260 sailors consume 1000 lb. of pork in 1 week, how many sailors will use 19800 lb. in 9 weeks ? Ans. 550, DISTRlBUtiVE PROPORTION. 62 19. If 12 men build a wall 60 feet long, 4 thick, and 20 in height, in 24 days, working 12 hours per day, what length of wall, 3 feet thick and 12 high, will 18 inen build in 18 days, working 8 hours per day ? Ans, 100 feet long. JO. If 336 men, in 5 days of 10 hours each, dig a trench of 5 degrees of hardness, 70 yards long, 3 wide, and 2 deep, what length of trench, of 6 degrees of hardness, 5 yds. wide, and 3 deep, may be dug by 240 men in 9 days of 12 hours each ? Ans. 36 yards. t.j m DISTRIBUTIVE PROPORTION (company or partnership.) Teaches to divide the profits and losses of merchants company, in proportion to their shares of the capital or stock. Rule. — As the whole stock is lo each particular Stock, so is the whole gain or loss to the respective shares of it. Three men A. B. and.C, make a joint stock; A's share is £64, B's £88, C's £96 ; they continue in trade until their profits are £108 ; required their shares ? £ £ £ 248: 64:: 108 88:: 108 96:: 108 A's stock £64 B's — £88 C's — £96 248 As As As 248 248 £ 27 38 41 s. d. 17 5^\ A's gain. 6 5if B's do. 16 lAi C's do. 108 proof. 1. X. Y. and Z. make a joint adventure to Jamaica ; X's share of the adventure is £230, Y's £324, and Z's £336 ; they lose £144 ; required the loss of each ^ Ans, X's £37 4 3. |^, Y's £52 8 5^ f ^, 2's £54 7 3i ^. 2. A. W. and R. buy a ship for £1750 ; of which A. paid £840, W. £485, and R. the rest. The net freight for the first voyage was £145 15 ; how much of this sum should each receive ? Ans, A. £69 19 2i |i., W. £40 7 lOi |f . R. £35 7 11. If. 3. Four merchants freight a ship to Barbadoes, value of the cargo £1260, wheteof A's flhafo is £540, B's £360, C's £240, and D's the rest ; they gain £220 ; tequired feach man's share of it ? Ans, A's £94 5 8i f , B's £62 17 1^ f , C's £41 18 1. f D's £20 1§ 0^ f . 4. A^ B. &nd C. continue in tifade for a yeai*, With tt stock of £1300 ;; at the end of which A's g&ih wad £40^ B'd £04, and C's £tt ( fequired their stocks 7 Ans, A's stock £300, B's £480, C's £420. 5. A quantity of common, consisting of 240 acres is to be m UK ■'<^^i m >^, i'^S i •^ ft} 63 DISTHIBUTIVE PROPOETION. f-r. V^vril ' i L i" ^'■*H;'1' divided amongst L. M. and N. in proportion to their estates ; L's estate is £400 a year, M's £350, and N's £200 ; what is each man's shai'e of the common ? Ans. L's 101 ac. ro. 8y^ per., M's 88 ac. 1 ro. 27Jg^ per. N's. 50 ac. 2 ro. 4^ per. 6. A. insures on a ship and cargo £95, B. £90, C, £85, D. £80, E. £75, F. £70, G. £65, H. £60, I. £55, and K. £25 ; and damages are sustained to the extent of £525 ; how much must each underwriter pay, and how much will the pro- prietor lose, the whole value of the property being £1200 ? Ans. A. must pay £41 11 3, B. £39 7 6, C. £37 3 9, D. £35, E. £32 16 3, F. £30 12 6, G. £28 8 9, H. £26 5, I. £24 1 3, K. £10 18 9, proprietor £218 15.— Loss 8s. 9d. per £. 7. A testator bequeathed to A. £260, to B. £488, to C. £622, and to D. £500, but at his death the net amount of his property was only £1243 ; how much of this sum should each legatee have received ? Ans. A's share £172 16 5^ m, B's £324 7 H i-Vr* C's £413 8 Hi _?JL, 1 8 T» D's £332 7 0* i-^i 8. A bankrupt owes to A. £126, to B. £104, to C. £98, to D. £249, to E. £84, and to F. £97 : his money and ef- fects amount to £508 ; how much can he pay per £, and what is the just dividend to each of his creditors ? Ans, 13s. 4f d. iff per £. A's dividend £84 8 lOi f-f ^, B's £69 13 llf /y^, C's £65 13 6^ f f^, D's £166 37 6 m, E's £56 5 lOf fff, & F's £65 Iffff • \). Three merchants, A. B. and C. bought a West India ship ; whereof A. paid -^j, B. j\f and C. ^g-, which amounted to £786 18 10 ; in a trading voyage, of two years, they gained £1786, after paying all expenses; how much is each man's share of the gain ? Ans. A's share £1071 12, B's £476 5 4, an^ C's £238 2 8. Note. — When the times of their continuing their stock in company are unequal, each stock must be multiplied by the time of its continuance, and use the products ; thus — A. continued his stock of £250 in trade for 3 months, B. continued his stock of £960 for 2 months, and C his of £540 for 6 months ; they gained £480 ; required their shares ? A'fl250x3=: 750 As 5910 •. 750: : 480 : JEGO 18 3^ Jy^ A's share. B's 960 X 2=1920 As 5910 ; 1920 ; :480 • 155 18 9i i^a B's do. <^'8 540x6=3240 As 5910 ; 3240- ; 480 • 263 2 11^ _^ C's do. 5910 i;480 o"o proof. DISTRIBUTIVE PROPORTION. u ir estates ; ) ; what is 27yV per. . 4^ per. [), C. £85, 55, and K. 2525 ; how nil the pro- £1200? :, £37 3 9, . £28 8 9, proprietor :488, to C. lount of his should each , D's £332 7 fii ilA ' "? TaT* to C. £98, ney and ef- )er £, and 8 10^3.0 5., , D's £166 oiUH- ^Vest India mounted to ley gained ;ach man's £238 2 8. ir stock in ied by the months, B. is of £540 hares ? UL. A's share. 1 3 B's do. i^C'B do. proof. s a vear also, they 6 1 10. A. B. and C. had a joint stock of £630 tinned only 3 months, B's 5 months, ant* C A's stock was £215, B's £310, and C% tine rest; gained £254 ; required their shares ? Ans, A's £47 8 4^ f f f, B's £113 19 fifi, Cs ^92 12 7i 11. A. and B. enter into partnership »r a year ; A. with £200, and B. with £160 ; after 4 months they admit C. with £120 ; at the end of the year their gain is £150 ; what is each man's share of it ? ^w*. A's £68 3 7i A, B's £54 10 10| VV» Cs £27 5 H TT- 12. Three farmers rent a field of grass for £42 ; A puts in 48 sheep for 4 months, B. 50 for 2 months, and C. 30 for 3 months ; what part of the rent must each farmer pay ? Ans, A. £21 2 2^ iff, B. £10 19 10^ ||f, C. £9 17 10^ V'qV- 13. A. B. and C. enter into company for a year ; A. puts in £600, but at the end of 8 months he withdraws £200 ; B,. puts in £400, and at month's end £200 more ; C. puts in. £300, and at the end of 4 months £400 more ; but at the end of 10 months he takes out £200 ; they clear £360 ; rc- , C's£l22 11 0|^\. 14. Three graziers rent a grass field at £,30 ; A. puts in 40 oxen for 4 months, B. 60 oxen for 3 months, and C. 20 oxen for 5 months ; what part of the rent ought each to pay ? Ans. A's share of rent £10 18 2 ^j, B's £12 5 5 j\' Cs £6 16 4 15. Four merchants, P. Q. R. and S. agree to trade gether for 18 months ; P. puts in £300, and at 8 months' end £400 more ; Q. puts in £600, at the end of 4 months takes out £200, and at the end of other 6 months nuts in £300 ; R. puts in £700, which continues the whole *;t^ 3 ; and S. puts in £275, and at the end of 12 months £1550 more ; they gain £1000, what is each man's share ? Ans, P's £208 17 9^ l, Q's £231 2 ^ |, R's £280, S's £280. 4 fT* to- m^ >■■' 66 PRACTICE. ! ». yards C yards fS) yards ^ yards ® yards (Si yards (S> yards (S) yards © 2s. 6d. Is. 8d. 6s. 8d. 3s. 4d. 53. 4s. , 28. lOs. Is. 6d. Id. 3d. l|d. 4d. 2d. id. id. Ans, £121 « 51 155 98 179 ft7 ^)5 198 33 21 1 11 5 8 S it H u M M «i «t u « « !• M «l 12 6 3 4 6 8 10 10 12 6 10 14 17 2 10 9 3 9 12 4 9 8 14 lOi 6 2i PRACTlCfi. 66 any num- ts. 1*: 4 ; oz. troy. wt. — i gr- — i • ^z i 1 = 1 ■ = Vo CASE 11. : When the price is less than 1 shilling, but not an even part. Rule.— Divide it into several even parts, or the less into even parts of the greater, and work for each by case first, the sum of the quotients will be the answer in the name, out of which you took your first even part. What is the price of What is the price of I 985 lb. at 2^d. 164 2 20 6i 2 ent will be 3. fy. 4. 5. ice of 6. It l^d. 7. 8. r 9. — 10. 4^ ans. 11. 12. 12 6 13. 3 4 14. 6 8 15. 10 16. 10 17. 12 18. 6 19. 10 20. L4 21. 17 22. 2 10 23. 3 24. 9 25. 12 4 20. 9 8 27. L4 lOi 1 88. 6 3i 2,0) 18,4 8i JCQ 4 8^ ans. i What is the 1. price of 5865 lb. price of 4719 lb. price of 8250 lb. price of 3081 lb. price of 1947 lb. price of 7625 lb. price of 5839 lb. price of 1370 lb. price of 8050 lb. price of 3904 lb. price of 4162 lb. price of 9251 lb. price of 2704 lb. price of 3290 lb. price of 7345 lb. price of 1938 lb. price of 6153 lb. price of 2617 lb. price of 8162 lb. price of 8074 lb. price of 4615 lb. price of 5781 lb. price of 1509 lb. price of 6240 lb, price of 5900 lb. price of 2635 lb. price of 8170 lb. price of 7462 lb. i 3587 lb. at S^d. 1793 6 597 10 149 5^ ^d. (a) li (3) l| (3) 2} (S) 2I (a) 2| (a) aj (3) 2I (3) 3| (3) 4i (3) ^ (3) 4| Cii 5 Od 54 (3) 5^ (3) 51 (3i Q\ (3> q] (a) 61 (3) 7 (3) 1\ (3) 7i (a) 7il ra) 8 r«? 8^ (3) 8i (3) 8f (a) 2,0)254,0 9 1 £127 9^ ans. Ans. £18 « 24 60 28 20 87 79 19 125 69 78 183 56 71 168 46 160 70 229 89 139 180 48 208 202 03 297 279 « u ti u u u u « (( « «i <{ l( u u it M (( (( « 4( t% U it 6 6J 11 6^ 3 1^. 17 8i 5 7^ 7 4| 1 45 19 7 15 7i 2 8 9 1 lOi 6 8 19 4i 6 5i 8 7i 4 8| 17 6i 11 H 13 2 8 23 13 li 14 6§ 16 3 6 5i 17 3^ 9 67 PRACTICfi. Um-,. P ! S 'i 29. price of 30. price of 31. price of 32. price of 33. price of 34. price of 35. price of 36. price of 37. price of 38. price of 39. price of 3607 lb. 1583 lb. 9000 lb. 4111 lb. 5555 lb. 3131 lb. 7007 lb. 2642 lb. 8380 lb. 2714 lb. 8888 lb. (a> 9i (a) dl rs) 9| (a> 10 (a) lOi (a) 10^ (a) 10| 11 Hi ra Hi (S) ll| (a) n u it a ti tt u ti « u 139 4J 62 13 2* 365 12 6 171 5 10 237 4 10| 136 19 n 313 17 H 121 1 10 392 16 3 130 435 11 2 10 Note. — When the price is any number of shillings. Rule. — Multiply the given quantity by them, and divide the product by 20, for the answer in pounds. If the price be an even number of shillings under 26, mul- tiply the quantity by half their number, doubling the first fig- ure of the product for shillings, the rest will be pounds. 1. 621 at 2s. Ans. £62 2 16. 210 at 17s. Ans. £178 10 2. 428 « 3 64 4 17. 314 "18 * 282 12 3. 777 « 4 155 8 18. 639 "19 « * 607 1 4. 882 " 5 220 10 19. 416 "20 « « 416 5. 667 « 200 2 20. 803 "21 « * 843 3 6. 527 « 7 184 9 21. 574 "22 * ' 631 8 7. 682 « 8 272 16 22. 635 " 23 * * 730 5 s. 400 « 9 180 23. 708 "24 * « 849 12 9. 614 "10 307 24. 293 "35 « 512 15 10. 816 "11 448 16 25. 314 "43 * * 675 2 11. 469 "12 281 8 26. 520 "52 * * 1352 12. 783 "13 508 19 27. 472 "64 * ♦ 1510 8 13. 855 "14 598 10 28. 795 "71 * 2822 5 14. 609 "15 456 15 29. 348 "83 ♦ « 1444 4 15. 182 "16 145 12 30. 231 "97 • * 1120 7 CASE III. When the price consists of shillings and pence, which arc not an even part of a pound ; or of shillings, pence, and far- things. Rule. — Multiply the quantity by the shillings, then take; j)arts for the inferior denominations, as in cases first and second, and add them together for the answer. ,!•> 4J 2i 6 10 lOf H 10 3 11 10 rs. divide the • 26, mul. e first fig. ids. £178 10 282 12 607 1 416 843 3 631 8 730 5 849 12 512 15 675 2 1352 1510 8 2822 5 1444 4 1120 7 which are Gf and fur* then tak(! I first anti 1 PRACTICE. 6? « What is the value of What is 1 the value of 6 i 473 gals, at 2s 5. 9|d. 2 i 1945 cwt. at 17s . 2id 2 ( 946 17 13615 3 i 236 6 1945 . f i 118 3 * 29 6| 33065 t i i 324 2 20)1330 3f 40 H £66 10 3f ans. 20)33429 8i i £1671 9 8i ans. I What is the y 1. value of 202 gal. at Is. lid. Ans. £16 2 5 2. value of 671 » 1 8^ « 58 H 3. value of 279 u 1 6 « 20 18 6 4. value of 181 it 2 9% " 25 9 OJ 5. value of 377 u 3 10^ « 73 lOi 6. value of 417 « 4 9 « 99 9 7. value of 876 »« 4 11^ « 217 3 6 8. value of 542 u 5 7 « 151 6 2 9. value of 822 u 6 8J " 235 9 ^ 10. value of 748 u 6 H « 253 4 7 11. value of 666 u 6 lOf « 229 12 n 12. value of 427 a 7 2 « 153 2 13. value of 380 ti 7 bi 141 14 2 14. value of 421 u 8 6f 180 4 n 15. value of 672 it 8 7i " 289 16 16. value of 807 ti 9 2i « 370 14 H 17. value of 172 n 9 4i 80 12 18. value of 164 ti 10 3| 84 11 3 19. value of 198 u 11 lU 118 3 H 1 20. value of 214 u 12 9 « 138 8 6 21. value of 278 u 13 8 « 189 19 4 22. value of 841 it 14 5 « 245 16 1 23. value of 374 tt 16 2J " 284 15 8i % 24. value of 669 ti 17 8 " 690 19 25. value of 800 ti 18 7i " 746 26. value of 426 It 20 9 " 440 18 9 27. value of 606 it 23 10 " 602 19 8 28. value of 712 it 24 8 " 878 2 8 29. value of 360 it 27 5 493 10 3 a. value of 236 tt 82 6 u 363 10 '4'\ "(^l' 69 PRACTICB. SI H CASE IV. WLwIi tilt price consists of pounds, with some inferior V oTiey, -ivhich is an even part of a pound. Rule.— Multiply the quantity by the pounds, and by case first, fin! the value of the inferior money : add this value and NoT^. I. — When the inferior money is not an aliquot part of a pound. Rttle. — Multiply by the pounds, and take parts for the infe- rior money ; or multiply by the number of shillings in the price, and take parts for the rest. N. B. — Sometimes the one way is easier — sometimes the other ; this depends upon the price : but it is a very good exerciee for the pupil to work the questions both ways. What is the price of 3 4 I 857 cwt. at £4 3 8^ 4 4 1 To 3428 142 16 8 14 5 8 1 15 8i £3586 18 0^ ans. 6 or thus. i 857 at £ 83 2571 6850 71131 i 428 6 i 142 10 2o; 35 H 71738 Oi £3586 18 0| It product together, i md their sum will be tY le answer. 'Vhat is the 1 price of Z •"* cwt. at £3 3 4 Ans. £1811 6 8 ' 7>ri'*,e of 49h 6 2 6 2989 ;5. -n Q 0^' '■'• 10 5 3843 16 ■h ;'5! r 0- '? ''a 7 6 8 1290 13 4 ">. *.vl; ■■'• of >r5 16 1 8 8282 18 4 0. p.i- f 5 :7 4 4 3851 8 7. prk >f 470 8 10 3995 8. price of 255 5 1 1287 15 9. price of 608 3 2 1884 16 10. price of 341 9 3 4 3125 16 8 11. price of 190 (( 1 6 8 253 6 8 12. price of 412 6 2 6 M 2523 10 PRACTICE. Find the 1. price of 478 cwt. at £3 11 8| I by case value and ' er. 6 8 I 1 15 ) 13 4 I 18 4 I 8 ) r 15 I 16 J 16 8 3 6 8 5 10 iliquot part or the infe- ngs ] in the e otb tn this r the pupil to 2. price of 866 3. price of 648 4. price of 254 5. price of 421 6. price of 611 7. price of 189 8. price of 210 9. price of 607 10. price of 514 11. price of 214 12. price of 666 13. price of 750 14. price of 342 15. price of 196 16. price of 400 17. price of 965 18. price of 508 19. price of 254 20. price of 621 u M U it u u u u u n u u u 6 2 5 20 5 3 2 17 8 1 14 5 16 10 18 14 2 1 7 4 2 11 5 8 16 6 3f H ^ n 3 6 Ans. £1713 5324 u 3 1 10 13 101 9 8" 6 8 11 19 4^ u it u u u u a a u u ({ a ii u « « 16 1 1863 1375 11 8436 3097 705 1221 6093 1497 369 4689 15 3520 6 849 6 2209 18 3532 10 3325 4 1000 13 3947 11 3027 7 4 4 5 7 3 7 11 4i 6i H U 7J- m 6 3 7 1 8 6 15 10 10 4 17 6 Note. II. — When there is a fraction in the quantity. Rule. — Find the value of the whole number by the forego ing rules, and the value of the fraction as in compound multi plication with a fraction. 1. 275f yards at 6 8 721f yards at 18 419| yards at '6 11 580^ yards at 1 5 6 194i yards at 17 8 426f yards at 1 3 9 8I2I yards at 19 4 1051 gals, at 8 2 at 7 3 at 1 4 at 6 9 at 2 11 at 3 10 at 3 9^ at 2 8 4 at 3 18 at 1 12 6 at 4 10 at 19 10 at 5 8 4 at 1 15 8 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. ins . £91 17 6 ti 649 12 m <( 124 4H «( 740 2 9 >( 171 11 9 «( 506 17 H •( 785 13 2 %i 43 65 147| gals. 163f gals. 158^ gals. 215f^ gals. 142Tflir gals. 166| gals. 809i cwt. 670t«j cwt. 416i cwt. 284yV cwt. 706Tflj cwt. 612i cwt. cwt. «< t( (( (( (( t( n ti it M 2i 53 11 10 18 53 9 10^ 9 6 31 27 31 9 10^ ^ 1955 13 9 2224 12 8 7 (I 676 1279 699 13 3317 14 651 II 6 H Of H ■I Kv ^ FSACTICE. 'V- , i" 4 ^ CASE V. When the quantity consists of several denominations. Rule. — Multiply the price by the number of integers, if it be less than 157, but if greater find their value by the former cases ; and for the other denominations of the quantity, take parts of the price of the integer ; or of one another, and add them to the value of the integral part for the answer. iVbte.— To know wlach are the integers, observe, when the price is at so much per cwt., the cwts. in the quantity are integers ; when at ao much per yard, the yards n re integers ;, when at so much per ounce, the ounces are integers^ &c. 27 yd. 1 qr. 2 na. at 15s. per yd. | 63 gal. 2qt. 1 pt. at 6s. 4d. per gal. s. d. s. d* 15 8 3 3 7 9 21 a 3 11 1 iH J&21 6 10^ ans. i 8 4 9 3 15> 7 i 26 5 4 1 2 j&26 10 2^ ans. 1. 35 yds . 2 qrs. 1 na. at 5s. 6d. per yd. £9 15 7 ^ 2. 14 « 2 » " at 16 9 u 12 2 lOi 3. 97 « 1 " 8 « at 7 8 u 37 7 4. 52 « « 2 «* at 2 H u 6 12 5H 5. 475 « 8 « 1 « at 4 9 u 113 Ui 6. 740 « 2 " 2 « at 12 6 u 462 17 9% 7. 31Q « 1 « 3 « at 15 8 u 249 8 lOi 8. 48 gal. 2 qts. 1 pt. at 3 6 per gal. 7 12 &i 9. 56 « 1 « 1 « at 4 8 H 11 19 7 ^ 10. 97 « 3 «* « at 11 8 U 67 6 11. 814 « 2 « 1 « at t 9 U 112 2ii 12. 670 « 1 « 1 " at 5 3 u 149 14 6ii 13. 408 « 3 « " at 12 6 it 255 9 4i 14. 36 qrs . 4 bus . 2 pec .at 16 4 per qr. 29 17 2^ 15. 85 " 8 «* 1 « at 13 8 it 68 7 2ii 16. 370 « 5 « 3 " at 25 6 M 472 13 3|f 17. 406 " 2 " 2 « at 88 <( 771 19 104 18. 512 " 7 " 1 " at 17 9 <« 455 4 1 i 19. 36 oz. 15 dwt. 8 gr. at 5 4 per oz. 9 16 1 A 20. 75 " 12 « 6 " at 4 8 u 17 12 lOH ■1 PRACTICE. m ons. gers, if it he former itity, take , and add r. rve, when uiantily are ! integers ;, Bi &C. d. per gal. d. 4 9 2 !i 2^ ans. 15 7 i 2 m 7 i 12 6U U4 17 91 8 lOi 12 8i 19 7 ^ 6 2ii 14 5ii 9 17 ^ 7 2ii 13 3H 19 lOi 4 1 * 16 1 A 12 lOH u it £62 13 Hj\ 21. 192 « 16 " 18 « at 6 6 22. 318 « 17 «* 12 « at 7 3 23. 460 ** 13 « 18 « at 5 10 «* 131 9 ^ 24. 64 cwt. 1 qr. 16 lb. at 7 4 per cwt. 33 12 2^ f 115 11 10 ^ 25. 18 « «♦ 14 « at 17 6* 26. 72 « 1 « 16 " at 1 8 27. 142 " 3 « « at 15 9 « 24 ** at 16 4 « 7 « at 5 10| " 21 « at 24 6 " 10^« at 19 28. 504 « 29. 189 « 30. 610 «« 31. 217 « 2 2 1 2 i( u u (t {( 15 17 Hi i 6 7^^ 112 8 3| 412 3 8 56 17 71,^ 747 15 8i ^ 206 14 3^^ Note. — When the given quantity is not of the same name with the integer whose price is given. Rule. — Reduce it to the same name ; then, find its value by the foregoing rules. 6 cwt. of sugar at 8^d. per lb. 112 672 lbs. 6 672 20) 476 8 doz prs gloves at ds 9d per pr. 12 3 9 — 12 96 pairs. — 2 5 8 £18 ans. £23 16 ans. 1. 7 cwt. sugar (3> 9|d. 2. 14 cwt. flax 12s. 3. 6^ tons tallow (S) 7 4 4. 9 cwt. beef ^74 5. 17 hhds. wine (S> 16 2 6. 20 anks. brandy O 22 7. 6 puns, rum © 16 8. 60 lb. tea ^0 7^ 9. 17 stones soap ® 9 10. 19 gallons gin fS) 5 6 11. 7 thousand quills (a) 2 9 12. 21 reams paper ® 1 3 13. 16 pounds cloves /S) 1 3 14. 27 doz. lb. candles ^ 9^ 15. 19 stones leather (a) 1 10^ 16. 8 doz. pairs gloves ® 1 6 17. 3 cwt tea 5 18. 44 yards cloth 6 10^ 19. 96 ells English rs> 14 9 per lb. " stone <( u tt u " gal. u u n tt it oz. « lb. " qt. " hund. " quire. *• oz. ♦« lb. (t tt " pair " lb. '' ell Eng. ** yd. £31 17 67 4 381 6 8 26 8 865 14 6 220 403 4 30 8 18 6 20 18 9 12 6 26 5 16 12 16 6 24 18 9 6 16 84 12 2 88 10 «"* .>'■:>. ' I pr'". i 1*1', ■' H ■ u^.'\ '3' 1 f h Ji ■ M f. 79 COMMERCIAL ALLOWANCES. 20. 37 yds. 3 qr. ^ 12 6 21. 59cwt.lqr.14lb. (B U 6 22. 18 acres 3 ro. rs> 78 23. 16 lb. 7 oz. troy ® 5 8 per ell Flem. 31 9 12 « St. 344 7 6 " ro. 292 10 ** oz. 56 7 8 COMMERCIAL ALLOWANCES; * ' OR Tare and Tret, Are certain deductions made from goods which are weighed in the chest, barrel or whatever contains them. Gross weight is the weight of both goods and packages. Tare is an allowance granted to the buyer for the weight of the barrel, &;c. containing the goods, and is deducted from the gross weij. 'it. Tret is an allowance of 4 lb. on 104 lb., or -^ on goods liable to waste, and is deducted after the tare. Cloff is an allowance of 2 lb. on 3 cwt., or y^j given to retailers for the turn of the scale, and is deducted after the tret. Note. — After subtracting* the tare from the gross weight, the remainder is called tare suttle ; and after subtracting the tret, the remainder is called tret suttle; and what remains af- ter all the deductions are made, is called net weight. Rule. — Subtract the tare from the gross weight, and from the tare suttle deduct ^ part, the remainder will be the tret suttle; and from the tret suttle deduct ,|j part, the remain- der is the net weight. Note. — In calculating commercial allowances, remainders less than 4 a lb. arc rejected, but when ^, or more they ure considered as 1 lb. What is the net weight of 6786 cwt. 2 qr., tare 18 lb. per cwt., deducting also tret and cloff? 16 i 6786 2 gross weight. 969 2 121 21 1090 2 21 tare. 26)5695 3 7 tare suttle.. 219 8 tret. i, !* 168) 5476 2 27 tret suttle. 32 2 11 cloff. ans. 5444 16 net weight. COMMERCIAL ALLOWANCES. 74 1. Find the net weight of 20 barrels figs, each 3 cwt. 3 qrs. 18 lb., tare 36 lb. per bar., also deducting tret and clofF. Ans, 68 cwt. 2 qrs. 13 lb. 2. What is the net weight of 5 casks sugar, each 13 cwt. qrs. 13 lbs., tare 12 lb. per cwt., deducting also tret and cloff? Ans, 55 cwt. 3 qrs. 24 lb. 3. What is the net weight of 4 chests of tea, each 2 cwt. 1 qr. 24 lb. per chest, deducting also tret and cloff? Ans, 8 cwt. 2 qrs. 11 lb. Note. — Tret and cloff are now generally discontinued ; but an allowance called Braft is given on some commodities to retailers to make the weight hold out. Draft is at so much per cask, per bag, &c. and is deducted before the tare. What is the net weight of 7 bags cotton wool, weighing 14 cwt. 1 qr. 11 lb. draft 1 lb per bag, tare 2^ lb. per 100 lb? cwt. qr. lb. 14 1 11 gross. 7 draft. 21 lb. per 100=|yVl 1* 1 4 1 12 tare. Ans. 13 3 20 net. 1. Find the value of 6 chests of congou, weighing 6 cwt. 1 qr. 3 lb., deducting drafl 1 lb. and tare 25 lb. per chest, at 3s. 4d. per lb. Ans, £91 3 4. 2. Find the value of 4 chests of souchong, weighing 3 cwt. 1 qr. 20 lb. ; draft 1 lb. and tare 23 lb. per chest, at 4s. 6d. per lb. Am, £,U 16 0- 3. Find the net weight and value of 5 bags cotton wool, weighing 12 cwt. 2 qr. 8 lb. ; deducting draSt 1 lb. per bag, and tare 2| lb. per 100 lb., at 2s» Id. per lb. Ana, 1368 lb. £142 10. 4. What is the net weight of 36 bags of cotton wool, each containing 2 cwt. 8 qrs. 5 lb. gross, and allowing draft at 1 lb. per bag, tare at 2| per 100 lb., and what is the value of it at Is. 9d. per lb. net ? Ana, 10951 lb. £958 4 3. 5. How many gallons net are in 14 casks oil, each weigh, ing 3 cwt. 2 qrs. gross, allowing tare at 15 lb. per cwt., and 7| lbs. to the gallon ? Ana, 633|4 gallons. 6. What is the net weight of 468 cwt. Z qrs. 16 lb. sugar, after deducting tare at 14 lb. per cwt? Ana, 410 cwt. 1 qr. 3^1b. 7. What is the net weight of 315 cwt. 2 qrs. 21 lb., tare 10 lb. per cwt. ? Ana, 270 cwt. 2 qrs. 10 lb. •It if': 5 i!5i- > ^^ ■ u 'n SIMPLE INTEREST. m •i i 8. What is the net weight of 37 bags coffee, each 4 cwt. 18 lb. after deducting tare at 13 lb. per cwt ? Ans, 136 cwt. qrs. 8 lb. SIMPLE INTEREST. Interest is the allowance given by the borrower to the lend- er for the use of his money. Principal is the money lent. Interest is the rate per cent agreed upon. Amount is the sum of principal and interest. Note. — The highest interest which the law allows is called legal interest. Usury is interest above what the law allows. I. To find the interest of any sum of money for any number of years. Rule. — Multiply the principal by the number of years and by the rate per cent., and divide the product by lOQ. What is the interest and amount of £746 15 6^ for 3| years at 6 per cent ? £ s. d. 746 15 6 4480 13 3 3i 13441 19 3240 6 9 158)82 6 20 4i £ s. d. 746 15 6^ principal, 156 16 5^ interest, 16)46 903 12 amount. 5)56 4 _ - 2)26 13 /, ^^ ' ''.^.. ',; t 110 50 .' '■, . ;"; ' ^ \ ' 1. R^uired the interest of £3748 16, for two years, at 5 pet cent. . ^ Ans, £374 17 7} SIMPLE INTESEST. 7$ 2. What is the interest of JC754 14 8|, for 1 year at 4 per cent ? Ans, £30 3 9^ ||. 3. Find the interest of £824 16 4, for 3 years at 4^ per cent. Ans, £105 3 3^ if. 4. Find tl^ interest of £1090 10 6, for 4i years at 5^ per cent. Ans, £254 18 2^ j%\.. 5. What is the interest of £450, for 5 years at 6 per cent t Ans. £135. 6. What is the interest of £132 15, for 2 years at 4| per cent? Ans. £12 12 2^ f . 7. Required the interest of £75 10, for 5 years at 5^ per cent? Ans. £20 15 3. 8. What is the interest of £400, for 2 years and 5 months (or 2y% years) at 4 per cent? Ans. £38 13 4. 9. What is the interest of £250, for 3 years, 7 months (or 3y\ years) at 6 per cent ? Ans. £53 15. 10. What is the interest of £680, for 4 years, 10 months, (i.e. 4|- yr.) at 5 per cent ? Ans, £164 6 8. 11. What is the interest of £740, for 1 year, 3 months at ^ per cent ? Ans. £41 12 6. 12. What is the interest of £320, for 2 years, 9 months at 6 per cent? Ans. £52 16. 13. Find the interest of £1000, for 5 years, 11 months, at 5| per cent. Ans, £325 8 4. 14. Find the interest of £65 15, for 3 years, 8 months at 6 per cent. ' Ans. £14 9 3^ f , 15. Find the interest of £4500, for 4 years, 2 months at 5 per cent. Ans. £937 10. 16. Find the interest of £50, for 5 months at 6 per cent. Ans. £15. 17. Find the interest of £160, for 7 months at 4^ per cent. £4 4. 18. Find the interest of £360, for 10 months, at 5^ per cent. Ans. £16 10. II. To find the interest for weeks. Rule. — Multiply the principal by the rate per cent, and by the number of weeks, and divide the product by 5200. 1. Find the interest of £852 10, for 40 weeks, at 6 per cent. Ans. £39 6 11 J^. 2. What is the interest of £653 2 7, for 36 weeks, at 5 per cent? Ans, £22 12 l||f. 3. Required the interest of £428 4 10, for 47 weeks, at 4 per cent. Ans, £15 9 7| ^. 4. Required the interest of £200 19 9, for a year and 14 weeks, at 8 per cent. Ans, £7 13 0^ ^|^. 77 SIMPLE INTEREST. 5. Required the amount of jS120, for 2 years and 18 weeks, at 3i per cent. Ans. £129 17 0^ VV. 6. Required the amount of J&106, for 1 year and 6 weeks, at 5 per cent. Ans iJUi 18 2f -jV- III. To find the interest for days. Rule. — Multiply the principal by the rate per cent, and by the number of days, and di^^ide the product by 36,500. 1. What is the interest of £743 12 4, for 142 days, at 4^ per cent ? Ans, £13 4i f f ||. 2. What is the interest of £780 14 9^, for 36 days, at 4 percent? Ans. £3 1 7 |^i|. 3. What is the interest of £780, for 257 days, at 3| per cent? Ans. £20 11 lOf f f . 4. What is the interest of £584, for 308 days, at 3f per cent? Ans. £16 12 7HHf 5. What is the interest of £850, for 308 days, at 4^ per cent ? Ans. £32 5 ej 4f 6. Find the interest of £145 13 8, from 4th of June to the 16th Oct. at 6 per cent. Ans. £3 4 2 |f ^f . 7. Find the interest of £362 15 9, from 6th May to 8th Sept. at 4 per cent. Ans. £4 19 4^ -f f. 8. Find the interest of £724 18, from 3d Jan. till August 20th at 5 per cent. Ans. £22 14 0^ VWs • 9. Find the interest of £230, from May 24th till Nov. 16th, at 3/j per cent. Ans. £3 15 9i f^|. 10. Find the interest of £154, from Jan. 7th till July 23d at ^ per cent. Ans. £3 16 10^ jY^. 11. Find the interest of £630, from Sept. 12th till Jan. 27th at 4i per cent. Ans. £10 llf ff f . 12. Find the interest of £720, from Mar. 8th till June 7th, at 6 per cent. Ans. £10 15 4| f^f IV. To find the interest when partial payments are made. Rule. — Multiply the principal and the successive balances by the number of days between the times of payments, add the products and find the interest as formerly. Borrowed March 20th, 1838, £1000, of which I j.iiid£300, Sepl- 17tli ; £150 Dec. 21st ; £220 Feb. 23d, 1839 ; and the balance July 23d ; how much^ then was due, principaJ and interest, at 4 per cent ? >. ; ) . :i; 1 18 weeks. 17 Of A- 1 6 weeks, 18 2f ,V- ;nt. and b\ 100. days, at 4^ ) AX. 5.0.2.1. > days, at 4 1 7 Llll. ^ ' 1 82S* 5, at 3f per 11 10| ^. 3, at 3f per 3, at 4^ per 2 5 6i ^. June to tlic 4 2 IHf May to 8th 19 4^ -If till August Nov. 16th, 15 H Uh ill July 23d th till Jan. lit m- 1 June 7th, 5 4| |if are made. e balances ments, add i,iiidje3oo, .839; and ncipal and SIMPLE INTEREST. 78 Mar. 20 Sept. 17 l^c. 21 Feb. 23 July 23 £ days 1000 300 181 181000 66500 35200 49500 700 150 95 550 220 64 330 330 150 332200 4 July 23d, 1839. Principal due £330 Interest due 36 8 1^ Ans. £366 8 li ^ £ s, d. 36500)1328800(36 8 1^ If Interest* 1. Required the interest on a bill of £854, due June 8th, of which £240 were paid Aug. 16th, £169 Oct. 4th, £238 Jan. 20th, and the balance Mar. 8th, at 4 per cent. Ans, £16 1 9 j'^j, 2. Required the interest on a bond of £1000, due March 16th, of which £324 were paid May 3d, £166 July 18th, £102 Dec. 2d, and the balance Jan. 6th, at 4^ per cent ? Ans, £22 12 6^ j^-^\, 3. What is the interest on a bill of £456, due May 7, of which £120 were paid June 18, £116 Sept. 27, £136 Nov. 17 ; and the balance Dec. 27, at 4^ per cent ? Ans, £8 6 10 ||ff . 4. What is the interest on a bill of £900 due Jan. 1, of which £150 were paid Feb. 28 ; £270 March 30 ; £173 June 19 ; £213 July 28 ; £57 Sept. 23 ; and the balance Nov. 17, at 3f per cent ? Ans, £13 13 2 iif . 5. Lent Jan. 20, 1838, £2000, of which I received April 7, £350 ; Sept. 28, £690 ; Dec. 18, £420 ; and the balance April 7 ; how much was then due, principal and interest, at 4^ per cent? , ilrw. £68 13 0^ aii. V. To find the interest on accounts-current. Rule. — Add and subtract the sums paid and received in tlie order of their dates. Find the number of days between the different transactions, multiply them into their respective balances ; and if the balances are sometimes due to the one party and sometimes to the other, extend the products in dif- ferent columns, then add them, and when the rates of interest are different, multiply each sum by its rate, and divide the difference of the products by 36,500 for the interest. Required the interest on the following account till Nov. 30, allowing 5 per cent, to A. B. and 4 per cent to R. S. '>', *. a 'J pi"'- I ' T» Dr. SIMPLE INTEREST. A. B's acsiount-current with R. S. Cr. Dec. 7, To balance, £103 Feb. 13, To cash, 118 Apr. 27, « " 400 Sept. 5, « «« 350 March 13, By cash, £354 June 3, « Aug. 17, «* Nov. 18, « a it 275 100 255 Dec. 7. Feb. 13. Dr. Dr. £ 103 118 days 68 Dr. 7004 6188 9612 17908 Cr. , 6118 600 2052 156 Mar. 13. Dr. Cr. 221 354 28 Apr. 28. June 3. Cr. Dr. Dr. Cr. 133 400 207 275 46 36 Aug. 17. Cr. Cr. 8 100 75 Sept. 5. Cr. Dr. 108 350 •19 Nov. 18. Dr. Cr. 242 255 74 Nov. 30. Cr. 13 12 40712 4 8920 5 162848 44630 44630 £ s, d. 36500)118218 3 4 o'i ^^»a. 1. Required the interest on the following account, at 6 per cent? Dr. Mr. Symo*s account-current with W. F. & Co. Cr. Jan. 7, To balance, £210 Mar. 7, To cash, 150 May 8, " " 240 July 21, " " 300 Sept. 18, " " 250 Dec. 24, " " 160 Ans. £17 2 7| Ml- April 14, By cash, £130 June 27, " « 215 Aug. 13, «« «« 167 Oct. 12, " " 280 Nov. 18, " « 120 i cei Dr Jul Ai Cr. ish, £354 « 276 100 255 it it |, at 5 per Fo. Cr. |h, £130 215 167 280 120 COMPOUND INTEBEST. 80 2. Require^? the interest on the following account at 4 per cent. Dr. S. M, & Go's, account-current with N. P. Cr. May 1, To balance, JB250 I June 8, By cash, £124 June 28, To cash, 140 I July 19, ** « 230 Aug. 11, « «« 340 I Oct. 20, ** ** 150 Nov. 12, « ** 221 I Dec. 12, ** « 200 Ans, £6 18 lOJ yfly 3. Required the interest on the following account till Dec. 31st, allowing 5 per cent, when the balance is due to the bank, and 6^ per cent, when due to A. B. A. B*s. account-current with the Commercial Bank. Drawn on the Bank by A. B. Paid to the Bank by A. B. Dr. Cr Feb. 24, To cash, £826 Mar, 18, By cash, £300 May 8, «* «* 131 June 28, « « 727 Aug. 16, « " 400 Sept. 6, « « 564 Sept 27, " « 348 Oct. 21, « « 322 Nov. 2, « « 408 Dec. 10, « " 68 Ans, £12 10 2| ^\. 4. On the following till Dec. 3l8t, 5 per cent, to the bank — 4 per cent, to C. D. C. D's. account-current with the Hamilton Bank. Drawn on the Bank by C. D. Paid to the Bank by C. D. Dr. March 2, To cash, £428 Mar. 29, " " 500 May 4, « " 118 Aug. 7, «• « 800 Aug. 28, " " 169 Cr. April 16, By cash, £355 June 8, « " 839 July 25, « " 466 Oct. 13, " " 422 Nov. 26, " « 166 Ans, £8 14 1| HH- COMPOUND INTEREST. Compound interest is an allowance not only for the use of the sum borrowed, but also for the use of the interest nfler it be- comes due, which is added to the principal, and the amount becomes a new principal for the next year. Rule. — Find the interest for the first year, and add it to the prinriual, then find the interest of the sum for the second year, and add it to that sum, and so on. Mi ■■•' Vi I •f: i\-- 1 ; •')^- \i\>\ll' 81 COMMISSION AND BROKERAGE. Note. — When the rate of interest is at 5 per cent, the J^ part of any sum is its interest for 1 year. What will jSlOOO amount to in 4 years, at 5 per cent per annum ? 1 ih 2V 1_ 2 j6 s. d. 1000 given principal, 50 first year's interest. 1050 second year's principal. 52 10 second year's interest. 1102 10 third year's principal. 55 2 6 third year's interest. 1157 12 6 fourth year's principal. 57 17 7^ fourth year's interest. 1215 10 1^ amount in 4 years. 1000 215 10 1^ compound interest. 1. What will J&4000 amount to in 6 years, at 5 per cent per annum ? Ans, £5360 7 7^. 2. What will £20,000 amount to in 8 years, at 5 per C^t per annum ? Ans. £29549 2 If. 3. How long slK)uld a sum be out at compound interest at 5 per ^'xnt to double itself ? ilwj. 14^ years, nearly. COMMISSION AND BROKERAGE. Commission and Brokerage are allowances of a certain rate per cent, lo bankers, agents, or brokers, for transacting the business of others. Rule I. — When the rate per cent, is £l or upwards, multi- ply the sum by the rate per cent, and divide by 100 as in interest. Rule II. — When the rate is under £1, work the question by proportion, or take parts as in Practice, — and divide by 100. According to Dr. Price's calculation, " one penny put out at our Sa* viour's birth, at 5 per cent rnmpnund interfst, would, in tho year 1791, have increancd to a greater sum than would bo contained in three hun. drcd millionfi of earths, all of solid gold ! But if put out at gimple interett it would, in the same time, hnvo amountedto no more than Ts. 5id. 1-5." That the latter is correct, any person may satisfy himself in two minutes, but the former involves a calculation of such length as few will encounter. COMMISSION AMD BROKERAGE. m it, the J^j cent per 5 per cent 360 7 7^. at 5 per 49 2 1^ nterest at IS, nearly. ;rtain rate icting the rds, multi- 100 as in lestion by |e by 100. at our Sa- [year 1791, three bun- lie intertat 5id. 1-5." iro minutes, encounter. What is the commission on £937, at 7s. 6d. (or f ) per cent? 937 ! 5 2 6 J * s. d. £ s. d. or, 100 : 937: :7 6: 3 10 3ii 234 5 117 2 6 or, je937Xf-M00=£3 10 3i i 00) 361 7 6 ans. 3 10 3Ji 1. tVhat is the commission on J5978, at 2i per cent \ Ans. £20 15 7f J . 2. What is the commission on £769 10 5, at ^ per cent / Ans. £5 13 ll.ii. 3. What is the commission on £568 14 9, at 1^ per cent? Ans. £7 2 2. ii. 4. What is the commission on £960 10, at 1 ^ per cent ? Ans. £16 12 8j. 5. What is the commission on £676 15, at 2^ per cent ? Ans. £14 8 4^. 6. What is the commission on £958 16 6, at 3^^ per cent ? Ans. £31 19 2^ f . 7. Wliat is the commission on £1242, at 2s. 6d. per cent ? Ans. £1 11 0^ 1^. 8. What is the commission on £573, at Os. 8d. per cent ? Ans. £1 18 2i a. 9. What is the brokerage on £756 19 8^, at f per cent ? Ans. £4 14 7^. 10. What is the brokerage on £1219 15 6, at 4s. per cent? Ans. £2 8 9^. 11. What is the brokerage on £675, at ;'.■ 9d, per cent? Ans. 18s. rt^d. 12. What is the brokerage on £598, at 48. 6d. per cent ? Ans. £1 6 lOf ^^. 13. How much does a broker receive .*' )r sellini? stock to the amount of ^ a million, at 28. 6d. per cent ? Ans. £625. 14. My agent writes me that he has transacted business on my account to the amount of £8560, to what con^mission is ho entitled at 2^ per cent ? Ans. £199 14 8. 15. A salesman disposes of woollen goods to the amount of £1260, muslins to £1450, and hardware to £850 ; whot is his commission at 2^ per cent ? Ans. £75 l'\. 16. My fhctor*8 sales, per the ship Silas, amount, to £917 14 11, what is his commission, at 2^ per cent ? Ans. £20 12 11^ ^y^. '.'■•If r-:MM Mt "4 % h INSUBANCE. 17. When a factor is allowed 10s. per cent, for commission, what should he charge for transacting business to the amount of £6800 ? Ans, £34. 18. Sent my employer an account of the sales of 40 hhds. sugar, the gross amount came to £2200 duty, freight, and other charges, £754 14 8 ; commission on the gross amount 2^ per cent. ; required the amount of the net proceeds. .Ans, £49 10, com. — £1395 15 4, net pro. 19. Purchased goods for my employer, to the amount of £654 14 8, and sent them according to his order; packing, cartage, and porterage £438; commission on the sum laid out 2f per cent ; required the amount of the invoice. Ans, £18 2 4| f com.— £677 8f f am. of in. m-:.- INSURANCE. Insurance is a contract by which the insurer engages to repay losses sustained by the insured, for a certain per cent- age on the sum insured. The insurer is the party who undertakes the risk. The insured is the party protected by the insurance. Premium is the sum paid to the insurer. Policy is the paper or parchment containing the contract of insurance. I. To find the premium. Rule. — Calculate as in commission and brokerage. 1. What is the premium on £1674 18, at 2s. 3d. per cent? Ans. £1 17 8 f |^. 2. What is the premium on £579 12 4, at 3s. 9d. per cent? Ans, £1 1 8^^^. 3. What is t'.^ annual expense of insuring a house and furniture to the amount of £1570, at 5s. Od. per cent ? Ans, £4 4^. 4. What is the premium of insurance on a spinning mill, valued at £3500, at "/s. 6d. per cent? Ans. £13 2 6. 5. What is the expense of insuring a ship and cargo, value £7830, at £3| per cent ? Ans. £283 16 9. 6. What is the jjremium on £35970, insured on a ship and cargo from Glasgow to Montreal, at 9| per cent ? Ans. £3372 3 9. . ' I* \v BUYING AND SELLING STOCKS. Stock is the capital of a bank, or trading company ; or it is the debt owing by government, called the public funds. Ca85 L— 'To fiod tUe vuiue of any quantity of stock. BtTlNG AND SELLING STOCK. 84 Rule. — Multiply by the rate, and divide by 100. ' 1. Required the value of £1260, three percent, consols, at 87f per cent. Ans, £1104 1 0. 2. Required the value of £860, four per cent, government stock, at 78 J per cent. . Arts, £672 19. 3. What is the price of £1640 India stock, at 230 per cent ? Ans, £3772. 4. What is the price of £3420 bank stock, at 172 per cent ? Ans. £5882 8.. Note. — Stock is bought and sold through the medium of brokers, who receive ^ per cent, for every quantity of stock which they buy or sell. Brokerage is omitted in the foregoing questions, but included in the following : — 5. Bought £3000 stock in the 3 per cent. cons, when at 63, and sold out when at 67f ; what did 1 gain ? Ans, £131 5. 6. Bought £6000 stock in the 3 per cent. red. when at 62|, and sold out when at 61^ ; how much did I lose? Ans. 82 10. Case II. — To find how much stock maybe bought for a given sum. , • Rule. — Increase the given rate by ^ ; then, as that sum is to the given purchase money, so is £100 to the quantity of stock. How much stock at 65f will £4734 purchase ? 65| : 4734 : : lOO : £7200. ans. 7. How much stock at 84| will £0178 18 purchase ? Ans. £7280. 8. How much stock may be purchased for £1638 at 68^ per cent ? Ans. £2400. 9. How much stock at 100^ will £1606 purchase ? Ans. £1600. 10. How much stock in the 3 per cent, reduced annuities may be bought for £1100, when the price is at 68f "^ Ans. £1600. Case III. — To find the rate of interest arising from money in the stocks. Rule. — As the price of any kind of stock is to £100, so is the dividend on £100 of that kind of stock to the rate of inter- est arising from money invested in it. What rate of interest arises from money vested in the 3 per cent. cons, when the prii c is at 07|^ ? 07f : 100 :: 3 : £4 8 Si per cent. 11. Whn.t rate of interest arises from money in the 4 per cent, console, when the price is 9"> ? Am. £4 4 ^ ^- i ■.:%'' I .m DISCatTNT. iiv. lir . i|, 1 12. What rate of interest arises from money vested in the 3 per cent. cons, when the price is at 57 ? Ans, £5 5 3 ^-g. 13. What rate of interest arises from money vested in In-! dia stock, when the price is at 225 ; the dividends being 10^ percent? Arts, £4: 13 4. 14. What rate of interest arises from money vested in bank stock, when the price is 218; the dividends being 10 per cent? Ans, M II 8| tW DISCOUNT. Discountf is the allowance that ought to be made for receiv- ing payment of a sum of money before it is due. The present value of a sum of money due at a future period, is such a sum as, if lent on interest for that period, at the rate proposed, would amount to the sum then due. I. True method of finding the discount. RuLE.~As the amount of JCIOO for the given rate and time, is to the interest of jSlOO for the same time, so is the given debt to the discount ; which» subtracted from the debt, leaves the present value, or. As the amount of £100 for the given rate and time is to £100, so is the debt to the present value ; which, subtracted from the whole debt leaves the discount. What discount ought to be allowed on receiving present pay- ment of a debt of £500, due 4 years hence, interest at 5 per cent? 100 4X5= 20 lao: 20::500: £83 e 8 discount. £500—83 6 8=£416 13 4 pres. vai. amt. 120 What is the present value of £250, due 9 months hence, at 5 pet cent ? m. ' ♦ 6 100 50 25 100 int. 3 15 76 5 p. c, 3,75 20 ftmt. * {r'3 15 : lOO: :250 : £240 19 f # p. V. £250 24(» 19 If preaent value. 9 ^ diseamt. 15,00 ted in the » 5 3 ,\. :ed in In*! )eing lOi £4 13 4. id in bank per cent? IT receiv- re period. It the rate and time, the given bt, leaves time is to lubtracted sent pay. at 5 per >unt. es. vffil. lence, at f if p- V. I DISCOITNT. 86 1. What ready money is equivalent to J£l50 16 4, payable 3 months hence ; allowing interest at 5 per cent ? Ans, JE14S 19 1 \\. 2. What is the discount of a bill of £70, due 6 months hence, at ^ per cent? Am, £>l 10 9| ^=VV. 3. Required the present worth of £300 15, due 8 months hence, at 5 per cent. Ans. £291 11^ if. 4. What is the discount on £56, due in 40 days, at 5 per cent? Ans, 6s. Id. ^Vt- 5. What ready money will pay a debt of £350, due 146 days hence, at 5 per cent ? Ans, £343 2 8| f f . 6. What is the present worth of £225, due 60 days hence, at 6 per cent ? Ans, £222 16 -j-f I3 . 7. Required the discount on £150, due 80 days hence, at 5 per cent ? Ans, £1 12 6 f f . 8. What is the discount on £220, due 125 days hence, at 6 per cent ? Ans, £4 8 7 yV^. 9. What is the present worth of a bill of £1000, due 285 days hence, at 5 per cent ? Ans, £962 8 6 ||H« II. — Common, or bankers' method of calculating discount. Rule. — Find the number of days the bill has to run, reckon- ing from the day it is discounted till the day it is payable, to which add 3 days of grace, then find the interest on the given sum. The answer thus found is called discount, — Subtract the discount from the sum of the bill, the difference gives the proceeds. 10. Required the discount and net proceeds upon a bill of £573 16 8, due 65 days hence, at 5 per cent ? Ans, Disc. £5 2 2^^"^. net pro. £568 14 5^ ^. 11. A bill of £400, dated Aug. 4th, at 4 months, was dis- counted on the 10th of August ; required the discount and net proceeds, at 5 per cent ? ^ri». Disc. £6 10 ^^. net pro. £393 9 7f^. 12. What is the present worth of a bill of £1000, due 285 days hence, at 5 per cent ? Ans, £960 19 2^, 13. A bill of £378, dated March 14, at 8 months, was dis- counted April 14 ; required the discount and proceeds, at 5 per cent ? Ans, Disc. £3 6 3i iff pro. £374 13 Q^ |^f . 14. What is the true, and bankers' discount, on a bill of £40, for 25 days at 6 per cent ? ' Am, True 3s. S^d.^U. bankers* 38. ^d,^, 15. What is the true, and bankers^ discount on a bill of £S00, for 360 tlays, at 6 per cent ? Ana, True £44 13 II iWf. banker'f £47 • 10||. '^i' :*^J*l ■■■< •n.-tli 1^ 3T EQUATION OF TAYMEHtS. — BARTER. w ►•» EQUATION OF PAYMENTS la the method of finding the time at which several debts, due at as many different times, may be paid at once. Rule. — Multiply each debt by the time it Jias to run before j t is due, then divide the sum of these products by the sum of the debts, the quotient will be the time required. I owe £60 in 40 days, £80 in 60, and £120 in 108 days ;' when may the whole be paid at once ? 60 X 40= 2400 80 X 60= 4800 120 X 109= 12960 days, 260 )20160(77 -573 1. R. is indebted to S. the sum of £628, which was to be paid thus ; £100 at the end of 1^ years, £266 at the end of 2^ years, £134 at the end of 3 years, and the rest at the end of 4 years,. at what time ought the whole to be discharged in one payment ? Ans. 2 ||f yrs. 2. A. bought goods from B. to the value of £750, and greed to pay £300 at 3 months^ £400 at 6 months, and the rest at 8 months, but afterwards they agree to make one pay- ment of the whole ; required the equated time for the pay- ment ? Ans, 4 If months. 3. A debt was to be discharged thus : 1 in ready money, 4- at 3 months, ^ at 4 months, f at 6 months, and the rest at 8 months : find the time for paying the whole at once. Ans. 4i months. 4. Delivered to a banker the following bills, viz : A. B's. bill for £100, due in 20 days, T. R's. bill for £264 due in 30 days, and C H's. bill for £420 due in 60 days ; at how many days should he grant me a bill for the whole ? Ans. 44 f If days. 5. A. is indebted to B. the sum of £750, which was to be paid thus : £250, at the end of 1|^ years, £100 at the end of 2 years, and £400 at the end of 4 years ; at what time ought the whole to be discharged in one payment ? Ans. 2 years 328^ days. BARTER. . . .. Barter is the method of exchanging goods without loss or gain to cither party. RtTLE. — Find the value of the goods given away; then find what quantity of the other may be purchased for that money. 1. How much tea at 6s. 6d, per lb. should be given in bar. ter for 142 yards df linen at 3s. per yd ? Ans. 65 t\ yds. baeteh. 98 :x * r 2. How many yards of cloth at 14s. per yd. should be giv- en in barter for 20 cwt. sugar at 7d per lb. ? Ans, 93^ yds. 3. Exchanged 156 yards cloth, at 16s. lOd. for 936 yds. linen ; what did the linen stand me per yd ? Ans, 2s. 9^ f . 4. How much barley, at 8s. 3d. per bushel, should be re- ceived for 100 bushels of wheat, at 10s. l^d. per bush. ? Ans, 122 j\ bush. 5. What was cloth per yard, when 66 yards of it were giv- en for 70 gross of buttons, at 8^d. per doz. Ans, 9s. ^. 6. Exchanged 86 yards broad cloth, at 19s. 6d. per yd., for Irish linen at 3s. 4d. per yd. ; how much linen should I receive ? Ans. 503 J^ yd. 7. Exchanged 159^ yards muslin, at 8s. lOd. per yd., for Holland gin at 26s. per gallon ; how much gin should I re- ceive? -^ms. 54^/^ gal. 8. Exchanged 67 cwt. tobacco, at £8 8 per cwt., and re- ceived in part, 600 lb. tea, at 7s. 4d., and for the rest I received stockings, at 2s. 8d. per pair ; how many pairs of stockings did I receive? Ans. 2571 pairs. 9. Exchanged 154 yd. cloth, at 4s. lOd., and for every 2 yd. cloth that I gave, I got in return 7 yd. muslin ; how much muslin did I get, and what did it cost me per yard ? Ans. 539 yds. at 4s. 2d. | ^. 10. E. & F. barter; E. has 60 yards superfine broad cloth, at 293. 3d. per yd., for which F. would give him 102 yd. com- mon yard wide, at 6s. 1^ per yd. and the balance in money ; how much money must E. receive ? Aiis. £^o% 10 3. 11. Exchanged 38 dozen pairs of shoes, at 7s. 8d. per pair, and got for them, equal quantities of raisins, at O^d. per lb., and figs at 5^d. per lb. ; how many lbs. of each did I receive ? Ans. 2844 1§ lb. of each. 12. A. barters silk stockings at 15s. with B. for hats, at 18s. ; but the stockings were worth only 13s. 4d. and the hats worth 16s. ; which of them was the gainer ? Ans. Neither. 13. Exchanged 97^ cwt. sugar, at 9^ per lb., for cloth, at 18s. 4id. per yard. ; how much cloth should I receive? Ans. 456 f f yds. 14. Exchanged 9 cwt. snuflJ", rt £8 15, and got for it, hemp at 9d. per lb., and flax, at Is. 4d., and got four times as much hemp as flax ; how much did I get of each ? Ans. 363 yV ^b. flax, 1453 |^ lb. hemp. 16. Exchanged 27 cwt. cheese, at 93s. per cwt., and re- ceived for it wool, at 13s. per stone, and butter, at 22s, per stone ; and got 6 stones butter as often as I got 7 stones wool ; how much did I receive of each 1 Ans. 47 |}4 St. butter, HI |f^ St. wool. sf! •1 w ^:j> s m I 4. .' m ■ : ' ■ '.yM 1. m i' •• w^M )■■■ . ^ '•'■•^ I. ; *'•*■''•« fe i ;*!■ >■ V ■1 ifiS ' "' "til 1 ^ ■ 1 \ 1 • m PROFIT AND LOSS. PROFIT AND LOSS. The difference between the buying and selling price is called Gain, when the selling price is the greater, and Loss, when it is the less. Note. — When the gain or loss on one article is given, the gain or loss on a given quantity is found by multiplying by that quantity ; and, when the gain or loss on a given quantity is given, the gain or loss on one article is fo^ind by dividing by that quantity. If the whole gain or loss, and tliat on one article, are given, the quantity is found by dividing by the gain or loss on one article. 1. Bought 428 yards cloth, at 14s. Sd., and sold it at 16s. 3d. ; what did I gain ? 2. Bought 57 Ans, £33 17 8 gain, and sold cwt. ot sugar, at £4 3 6 per cwt., it at 9^d per lb. ; what was the gain ? Ans, £21 7 6. 3. Bought 136 yards muslin, at 3s. 8d. ; how must it be sold per yd. to gain £12 on the whole ? Ans, 5s. 5d. y\ per yard. 4. Sold 257 yards linen, at 3s. 9d., and lost £9 ; what was it bought at per yard ? Ans, 4s. 5d.i |^^. 5. Sold 13 dozen pairs stockings at 3s. 7d. per pair, and gained £11 10 ; what were they bought at ? Ans, 2s. Id.^ -^^ 6. Bought cloth at 17s. 6d. ; how much of it must I sell at 19s. to gain £43 13 6 ? Ans, 582 yd. 1 qr. 1^ na. 7. By selling tobacco at 3s. 6d. per lb., which had been bought at £H 10 per cwt., I gained £130; bow much did I sell ? Ans, 25 cwt. I qr. 26 f^ lb. 8. By selling sugar at 8\d, per lb., which had been bought at £4 4 per cwt., I lost £85 ; what quantity did I sell ? Ans, 242 cwt. 3 qr. 12 lb. 9. Bought 236 feet of wood, at 3s. lOd., and sold it at 3s. 5d. per foot ; how much did I lose on it ? Ans. £4 18 4. 10. Bought 234 cwt. iron, at 4s. 8d. per stone ; at what should I sell it per lb. to lose £14 12 ? Ans, 3^. ^^. Case I. — Given the prime cost, and the profit or loss upon it ; to find the profit or loss per cent. Rule.— >^As the prime cost is to the profit or lo6s on it, so is 100 to the profit or loss per cent. . . llr Bought cloth at 3s. Sd., and sold it 4d. per yard profit ; what was the gain per cent ? Ans, 9 -^j, 12. Sold cloth worth Ws, per ylird,at Is. 6d. per yd. loss ; what was the loss per cent ? Ans, 10 p. c* 13. Bought cloth at Os. 6d. per yard, and sold it at 12s. ; what was the gain per cent ? Am, 28 y^. PROFIT AND LOSS. 90 ce is called fSf when it given, the tiplying by m quantity )y dividing liat on one ly the gain J it at 16s. ,7 8 gain. , and sold jE21 7 6. must it be per yard, what was 5d,i ^H. pair, and Is. ld.i /^ lust I sell [T, 1^ na. had been luch did I 26 f f lb. jn bought ell? qr. 12 lb. 1 it at 8s. 4 18 4. at what |d. m. 0S6 upon on it, so i profit ; . 9 Vt. nd. loss ; 10 p. c* It l!2s. ; 14. Bought tea at 5s. 6d. per lb., but getting damaged, I was obliged to sell it at 4s- 9d.; what was my loss per cent ? Ans, 13 ^j. 15. Bought 7 cwt. 3 qrs. of sugar, at 5f d. per lb., and sold it at 9d. ; what did I gain per cent, and in all ? Ans. £11 5 1 or 56 ^^ p. c. 16. How much percent is 2^d. per shilling? Ans, 20f . 17. Bought a house for £315, paid for repairs £20, and sold it £400 ; what was the gain per cent? Ans. 19 f ^. Case II. — Given the rate per cent, and prime cost, to find the selling price. Rule. — ^As 100 is to 100, with the rate per cent, added to it in oase of gain, or deducted from it in case of loss, so is the prime cost to the selling price. 18. Gained 9,^ per cent, by cloth nich I bought at 3s. 8d.;. what did I sell it at ? Ans. 4s. 19. Lost 10 per cent, by cloth, ch I bought at 15s. ^ what did I sell it at ? Ans. 13s. 6d. 20. Bought cloth at 9s. 6d. ; at what must I sell it to gain 26 j\ per cent ? Ans, 12s. 21. I bought tea at 5s. 6d., but getting damaged, am obliged to lose 13 jy per cent, by it ; what must I sell it at to lose so much? Ans. 4s. 9d. 22. Bought sugar at 5§d. per lb. ; what must 1 sell it at per lb. to gain 56 |a. per cent ? Ans. 9d. 23. Bought coflfee at 4s. per lb. ; at what must I sell it per lb. to gain 20| per cent ? Ans. 4s. 10. Case III. — Given the rate per cent, and selling price ; to find the prime cost. Rule. — As 100, with the rate per cent, added in case of gain ; or deducted in case of loss, is to 100, so is the sellings price to the prime cost ? 24. If I gain 9 ^ per cent, on cloth, which I sold at 4s. ; what was the prime cost ? Ans. 3s. 8d. 25. Lost 10 per cent, on cloth, which I sold at 13s. 6d. ; what was the prime cost ? Ans, 15s. 26. Lost 13 y\ per cent, by selling tea at 4s. 9d. ; what was the prime cost ? Ans. 5s. 6d. 27. Gained 68 ^ per cent., by selling goods at 9d. ; what was the prime cost ? • Ans. 5|d. 28. Sold a quantity of cloth at 4s. lOd. per yard, by which I cleared 20f per cent. ; what did I buy it for ? Ans. 4s. per. yard. 29. Sold cloth at 12s., on which I gained 28 -^ per cent. : what was the prime cost? Ans. 9s. 6d. per yd. i,> c>- M fi-n IMAGE EVALUATION TEST TARGET (MT-3) 1.0 1.1 w Bi |Z2 £ U& 12.0 u WMU 11.25 UU I ■ 1.8 ■■■ 11.6 // '^ Photograi^ Sciences Carporation » wnT HUM tIMIT wntm,N.Y. usio |ri*)«7S.4S0S '4^ o^ 01 MISCELLANEOUS EXERCISES. Case IV. — Given two selling prices, and the rate per cent, in proportion to one of them ; to find the rate per cent, in proportion to the other. Rule. — As the price whose rate per cent, is given is to 100, with the given rate added or deducted, so is the other given price to a fourth number, from which subtract 100 in case of gain, but which subtract from 100 in case of loss. The re- maindei^ will be the required rate. 30. By selling cloth at 5s. I gained 12 per cent. ; what did I'gain per cent, by selling it at 6s. ? Ans. 34 f p. c. 31. By selling goods at &s. I lost 14 per cent.; what will I lose by selling them at 7s. 6d. ? Ans. 19f p. c. 32. Sold goods at 15s. 6d., whereby I cleared 18 per cent., but the commodity turning scarce, I sold what remained at 16s. 4d. ; what did I clear per cent, by the latter price ? Ans. 24 f I p. c. 33. By selling tea at 5s. 3d., I gained 16 per cent. ; the same tea was afterwards sold at 4s. 6d. ; what was lost or gained per cent, by the latter price ? Ans. 4 P» c. loss. Case V. — Given the whole gain or loss, and the rate per cent. ; to find what the whole is bought and sold at. Rule. — As the rate is to 100, so is the gain to the buying price ; and the selling price is got by adding the gain or sub- tracting the loss. 34. By selling goods at 5 per cent, profit, I gained £44 16 ; what did I pay for them ? Ans. JS896, prime cost. 35. Sold 342 cwt. sugar, at 3 per cent, profit, and gained £53 14 ; what was it bought and sold at per cwt. ? Ans. £5 4 8 A, hot. per cwt. — £5 7 0| \^ sold per cwt. 36. Bought muslin at 5s. 8d., and by selling it again at 4^ per cent, profit, I gained £29 18 ; what quantity did I sell ? Ans. 2345 -^j yds. 37. Sold tea at 7s. 8d., which was at 6 per cent, profit, and gained £33 6 8 ; what quantity did I sell ? Ans. 1536 }^ lbs. MISCELLANEOUS EXERCISES. 1. Bought cloth at 15s. per yard ; how must it bo sold per yard to gain £3 8 on 80 yards ? and what will be the gain per cent ? Ans. 15s. lOd. or &f per cent. 2. By selling cloth at 17s. 6d. per yard, I cleared 8 per cent ; how much did I clear per cent, by selling the same cloth at I89. 3d ? Ans. 12 || per cent. 3. A. and B. barter ; A. has 42 cwt. 2 qr?. of sugar, at £3 MISCELLANEOUS EZEBCISES. 92 per cent, cent, in is to 100, tier given ncase of The re- It. ; what )4 f p. c. hat will I 19f p. c. per cent., naiaed at ice? I f I p. c. ent. ; the s lost or ). c. loss. rate per le buying n or sub* £44 16 ; imc cost, id gained [per cwt. [ain at 4^ I sell ? 5 ^j yds. )rofit, and 36 H lbs. ) sold per i the gain per cent, ed 8 per the same per cent, prt at jS3 15s per cwt., and 12 yards of cloth, at 9s. Id. per yd. ; B. has 333| yards of Holland at 8s. dd. per yd. ; who must pay the balance, and how miich? Ans. B. must pay £21 6 6 bal. 4. What is the interest of £10,007 for 5| years at 6 per cent ? Ans. £3452 8 3 j f . 5. My agent sends me word that he has bought goods on my account, to the value of £617 17 6, what will his com- mission come to, at 2^ per cent? Ans. £15 8 11^. 6. A certain debt is due as follows, viz : ^ at 3 months, ^ at 5 months, ^ at 7 months, and the rest at 12 months ; now if it were agreed to pay the whole at once, what would be the mean time ? Ans. 6^ months. 7. A legacy of £800 is left me by an uncle, to be paid 9 months after his disease ; but I being in want of ready money, agree with his executors to allow them 6 per cent, for prompt payment, how much will I receive ? Ans. £771 1 8 1^. 8. Delivered 450 bolls barley to, be malted, and during the process it increased in quantity at < the rate of 3 bolls on 7 ; what quantity of malt had I ? Ans. 642^ bolls malt. 9. A farmer kihi-dried 285 bolls corn, by which it inlaked 3 bolls on 40 ; how much did the dry corn measure ? Ans. 263f bolls dry. 10. A merchant's capital V7 s £1260, and he has since in- creased it at the rate of £13 on £20 ; what is it now ? Ans. £2079 present capital. 11. A gentleman has 129 oz. 15 dwts. of old silver, which he values at 4s. 3d. per oz. ; «nd he purposes to add £83 2 9| thereto, in order to purchase a very curious and valuable piece of plate, weighing 260 oz. 10 dwt. : required how much the plate was rated at per oz. ? Ans. 8s. 6d. 12. Bought hops at £5 5 per cwt. ; how must they be sold per lb. to gain 15 per cent 7 Ans. Is. 1 1. 13. Shipped for Holland 2600 pieces of linen, each 94 yds. at 3s. lO^d per yd. ; to get in return one half in gin, at £6^ per tun, the other half in tea, at £3 10 per canister ; what quantity of each should 1 receive 7 Ans. 364 tuns, 1 hhd. gin, and 6764 -^ can. tea. 14. An agent is allowed 5^ per cent for commission and risk of bad debts ; what is his income, supposing his sales to amount to £20178 17 6^, his losses to £300 17, and his doubtful debts, which are valued at 12s. 6d. per pounJ, to £600 17 6 ? Ans. £588 13 2^ ^V^r income. 15. What is the net weight of 7 chests tea, each 16 cwt. 3 qrs. 16 lb., tare 20 lb. per cwt., allowing also the usual tret and clofT? Ans. 02 cwt. 3 qrs. 10 lb. 16. An agent charges 4^ per cent for commission and risk i':!^rj *u- f^i? 93 MISCELLANEOUS EZEBCISES. h of bad debts ; his sales in a year amount to £14780, and his losses to J&230 f what is his net income ? Ans. jS398 3 0. 17. What is the interest of £256, from May 7, till Aug. 12, at 5^ per cent? Ans. £3 14 10 j^j, 18. £240 is to be paid as follows, viz : £60 in 60 days, £80 in 96 days, £40 in 250 days, and the rest in a year and 35 days : required the equated time for paying the whole ? Ans. 188f days. 19. Received 125 yards of cloth, at 5s. 6d. for 215 lb. of tea ; required tlie price of the tea ? Ans. 3s. 2^ f ^ per lb. 20. What is the interest of £150 from Jan. 7, till Aug. 23, at 6 per cent ? Ans. £5 12 5i f^, 21. If 12 men build a wall 30 feet long, 6 feet high, and 3 feet Uiick, in 15 days ; in how many days will 60 men build a wall 300 feet long, 8 feet high, and 6 feet thick? Ans. 80 days. 22. There is £1000 to be divided among 3 men, in such proportion, that if A. have £3, B. shall have £5, and C. £8 ; how much must each man have ? Ans. A. £187 10, B. £312 10, C. £500. 28. A gentleman having 50s. to pay among his labourers for a day's work, gave to every boy 6d., to every woman 8d., and to every man 16d. : the number of boys, women, and men, was the same ; required the number of each. Ans. 20 of each. 24. After the conquest of Canada from the French, a gen- tleman made a purchase of 976 acres, French measure ; how many English acres may he reckon upon, supposing 16 of the former equivalent to 19 of the latter ? Ano. 1 159 Bng. acres. 25. Wliat discount ought to be allowed on receiving pre* sent payment of a debt of £375 10, due 3 years hence ; reckoning interest at 6 per cent. Ans. £57 5 7 y^. 26. If an agent transact business to the amount of £64896 per annum, and is allowed 2| per cent., what is his income, supposing he loses by bad 4ebts £548 ? Ans. £912 3 2^ |. 27. Three gardeners, A. B. and C ^*\ving bought a^ piece of ground, find the profits of it am*.';. ? £120 per annum. Now the money which they laid down was in such proportion, that as oflen as A. paid £5, B. paid £7, and as often as B. Eaid £4 C. paid £6. Required how much each man must ave per annum of the gain. Ans. A. £26 13 4, B. £37 6 8, C. £56. 28. A. barters with B. tea worth 5s. 6d., at 6s. 8d., for rum worth 7s., at 78. lid ; who has the advantage, and how much ? Ans. A*s advantage, -^jd. per gal. 20. A woollen manufacturer sold 3 pieces broad cloth, each 27 yards, at 17s. 3d., and 5 pieces narrow ditto, each 31 MISCELLANEOUS EXERCISES. 94 and his 198 3 0. A.ug. 12) 60 days, year and rhole? I8| days. 115 lb. of \^ per lb. Aug. 23, L2 5i w\. ;h, and 3 en build a . 80 days, a, in such 3, and C. C. Je500. labourers roman 8d., >men, and of each, ch, a gen- sure ; how g Id of the Sng. acres, giving pre- .rs hence; >7 5 7 jV- of £64896 is income, 2 3 2i f ]ht a, piece ler annum, proportion, •ften as B. man must , C. £66. ^8. 3d., for [e, and how fd. per gal. cloth, each each 31 yds. at lis. 7d ; he allowed 5 per cent discount for prompt payment ; what did he receive ? Ans, £151 13 0^ f . 30. A. values cloth in barter at 6s. 3d., worth only 5s. 9d. ; how must B, value cloth worth 7s. 2d. to be even with him ? Ans. 7s. 9d ^^. per yd. 31. If 8 horses require £40 worth of hay in 6 months, when hay sells at 8d. per stone ; how much will it require to maintain 7 horses for 11 months, when hay sells at 5d. per stone? Ans. £40 2 1. 32. Exchanged 124 yards shirting at 2s. 6d per yard, for 100 yards printed cotton at Is. 4d. per yd., and the remainder in ribbons at Is. 2d. per yd. ; how many yards of ribbon should I receive ? Ans, 151 ^ yards. 33. A. B. and C. rent a grass enclosure, for which they agree to pay £80. A. put in 8 cattle for 180 days, B. 6 cat- tle for 150 days, and C. 20 cattle for 123 days, how much of the rent should each pay ? Ans. A. £24, B. £15, C. £41. 34. After seeing a flash of lightning, 24 seconds elapsed before the thunder was heard ; required the distance, sound moving at the rate of 1142 feet per second ? Ans, 5 miles 336 yards. 35. A steeple projected a shadow of 200 feet, when a staflf 4 feet high projected 6 feet of shadow ; required the height jf the steeple ? Ans, 133 ^ feet. 36. A has 96 gallons gin, worth 16s. 6d., which he wishes lo exchange with B. for wine worth £2 2 per dozen, but B. demands 45s. for his wine in barter ; how much should A. lemand fur his gin, not to be a loser, and how much wine should he get for it ? Ans, 37 4 doz. at 17s. S-i^d. 37. The capital of a mercantile house is divided into 20 shares, of which A. has 4, B. 5, C. 9, and D. 2 shares. £975 jf promts are to be divided among the partners ; how much of that sum should each receive ? Ans, A. £195, B. £243 15, C. £438 15, D. £97 10. 38. When the barometer stands at 30 inches, there are ibout 14| lb. of pressure by the atmosphere on every square inch of the human body ; now if the surface of a man's body "contain 16 square feet, how many tons weight of air has he '.0 sustain for his usual load ? Ans, 14 tons, 500 lb. 39. When I was a boy, I recollect hearing distinctly, though 42 miles distant, the report of the cannons fired in Edinburgh castle, on the 5th Nov., how long was that after Uie discharge of the gun? Ans. 3 min. 14|^f sec, 40. Bought a quantity of cloth for £412 10 ; 86 yds. get- ting damaged, were sold at 15s. per yard, whereby I lost ■'.'i •<- ' '' '; l!ti 1 •^! m QtJSSTlONS FOB EXAMINATION. J&6 7 6 ; but sold the remainder so as to gain £17 16 8 upon the whole : required the quantity bought, and at what the undamaged part was sold per yard ? Ans^ 500 yards, sold at 17s. 8d. 41. Bought goods at 6s. 3d. per qr., and sold them at £1 18 6 per cwt. ; what was gained on 27 cwt. and how much per cent ? Ans, £>IQ 4 6 or 54 per cent. 42. The sum of £20 6 is to be divided among four classes of poor people ; there are 7 in the first class, 9 in the second, 15 in the third, and 20 in the fourth ; the share of the first is double that of the second, the second triple that of the third, and the third quadruple that of the fourth ; required the share of each class. Ans. Is. l^d. share, 4th class, 4s. 6d. do. 3d class, 13s. 6d. do. 2d class, 27s. do. 1st class. 43. Sold a quantity of cloth at 3s. 3d. per yard, by which I gained £12, at the rate of 8J per cent. ; required the quantity sold, and thy prime cost ? Ans, 960 yards, bought at 3s. 44. Shipped on an adventure to Lisbon 300 barrels of salmon at £3 18 6, 450 yards linen at 2s. 7d., 1200 yards broad cloth at 16s., insurance and charges of shipping £44 8 6 ; the net proceeds, as per account of sales, was £2440 16 4 ; required the gain or loss, and how much per cent. Ans. £200 15 4 gain, £8||ff ^^ gain per cent. 45. A merchant imported 11 pipes of wine, which cost him £31 10 per pipe, and which were bottled into 52 doz. each ; bottles and other charges 2s. 4d. per dozen ; he sold one-half of it at 16s. 2d. per dozen, and the other half at 17s. per dozen ; what did he gain or lose upon the whole ? . Ans, £61 1 gain. QUESTIONS FOR EXAMINATION IN PART III. What is Simple proportion? Ans. It is the method of finding a fourth proportional number to three other given numbers, so that the third shall have the same ratio to the fourth that the first has to the second. What do you mean by ratio ? Ans. It is tl^e relation which one number bears to another with respect to mngnitudc, and can only exist be- tween quantities of the same kind, thus :~12 yards : 6 yards.* :£8 : £4 or, 4 shil. : 16 shil.: :3 yd. : 12 yd. In a Simple Proportion question, how many terms must be given ? Am, Always three to find the fourth, or answer. How do you state a question in Proportion ? After it is stated QUESTIONS FOB EXAMINATION. '^ 17 16 8 at what 17s. 8d. them at and how per cent, ong foul I, 9 in the are of the hat of the quired the ^lass, 1st class, by which quired the jght at 3s. barrels of 200 yards : shipping sales, was much per 1 per cent, h cost him loz. each ; Id one-half it 17s. per 61 1 gain. RT III. method of ther given ratio to the you mean er bears to exist be- yd. s must be Dr answer. it is stated how do you proceed in working it? What is Compoimd Proportion ? What is Distributive Proportion ? What sort of a rule is that called Practice? How are questions in Practice solved ? What are the aliquot parts of a pound ? of a shilling ? &;c. What are the aliquot parts of a cwt. ? of a qr. ? an oz. troy ? When the price of one is an even part of a penny, shilling, or pound, how do you find the price of a large number? \7hen the price consists of pence and farthings, not an even part of a shilling how do you proceed ? When the price consists of shillings, pence, and farthings, what do you then do ? &c. What is the rule on Allowances on goods commonly called ? What is the meaning of Gross weight? What is Tare ?— Tret ?—Cloff?— net weight? What is Simple Interest? What does per cent, (centum) mean? Ans. per 100. What is the meaning of per annum? Ans. Yearly. What is the principal ? — interest ? — amount ? — legal interest ? — usury ? How do you find the interest of any sum of money for any number of years ? — for months ? — for weeks ? — for days ? What is the meaning of Compound Interest ? What is Commission or Brokerage ? What is Insurance ? What is the meaning of insurer ? — insured ? — premium ? — policy ? What do you mean by the funds or stocks ? How do you find the value of any quantity of stock ? How do you find how much stock may be bought for a given sum ? How do you find the rate of interest arising from money invested in the stocks ? What is the meaning of Discount ? What is the true method of finding the present value of a sum of money due at a future period ? What is the common way, or the way bankers discount bills? Is this a true and correct method ? Ans. No ;— ^it makes the discount a little more than it ought to be. What is the meaning of Equation of Payments ? How do you find the equated or equal time ? What is the meaning of Barter ? How do you solve questions in this rule ? Is there not a rule of first rate commercial importance called Profit and Loss ? Ans. Yes : by it the merchant is enabled to calculate the gain or loss per cent., prime cost, selling price, &c., upon every transaction in business, hence this rule is peculiarly the spirit or essence of mercantile speculations, so far as the sci. once of numbers is concerned. How do vou find the profit or loss per cent., when the prime cost, and the profit or loss on it, are given ? How do you find the selling price, when the rate per cent., and prime cost are given ? How do you find the prime cost, when the rate per cent., and selling price are given ? Given two selling prices, and the rate per cent. in proportion to one of them, how do you find the rate per V 97 VULGAR FRACTIONS. cent, corresponding to the other ? Given the whole gain or loss, and the rate per cent., how do you find what the whole was bought and sold at ? ■ ( 'I ill I ■' ''^ PART IV. VULGAR FRACTIONS. 1. A Fraction is one or more parts of an integer, and is expressed by a number above, and another below a line drawn between : them thus, 4* The number below the line is called the denominator, be< cause it denominates or shows, into how many parts the in. teger is divided ; and the number above is called the numerator, because it enumerates, or shows how many of these parts the fraction contains. The numerator and denominator are called the terms of the faction. 2. There are two kinds of vulgar fractions, simple and com- pound. 8. A simple fraction consists of a numerator and denomina- tor, as -J, and is divided into two kinds, proper and improper. 4. A proper fraction is when the numerator is less than the denominator, as a^. 5. An improper fraction is when the numerator is equal to, or greater than the denominator, as |- J. 6. A compound fraction consists of two or more fractions joined together by the word of, as ^ of | of %, 7. A mixed number or fraction, consists of a whole number and a simple fraction, as 9f . 8. A complex fraction is that which has a fraction or n mixed number in either or both of its terms, as i 3 5i 2^ — or or — or — 7 lOi 9 5| When the numerator is equal to the denominator, the frac- tion is equal to the integer ; thus, f = !• And when the numerator is greater than the denominator, the fraction is greater than the integer, as f =lf. Note. — If the numerator and denominator of a fraction be either multiplied or divided by the same number, the product or quotient will be a new fraction, equal in value to the former: — thus, TV"^i=f' ^^' tV'*^ 3==3f' ^'^ of which have the same value, TV=f=if- REDUCTION OP VULGAR FRACTIONS. 98 } gain or he whole ir* and is ne drawn tatoTf be- ts the in- mmerator, parts the are called and com- lenomina- improper, s than the J equal to, fractions e number ction or a the frac- lominator, t*i action be e product le former: the same REDUCTION OF VULGAR FRACTIONS. CASE I. To reduce fractions to their least terms* . RuLE.-~«-Divide the greater term by the lessr and that divi. sor by the remainder, the next divisor by the next remainder, and so on always dividing the next divisor by the next remain- der, till nothing remains ; the last divisor is the greatest com- mon measure : by which divide the terms of the fraction for the answer. Reduce f^ to its least terms. 378)1233(3 1134 ■ ' ' ," ,*■ . ■ ' ' .' 99)378(3 ,. : : ^, 297 ., ^ ■ '' ■" '" . - ' \ 81)99(1 81 9)t¥3V=i¥t ans. 18)81)4 72 ■ '■ /■ h:\ .'■ ■ -" ^ , ' : . ; 9)18(2 18 Reduce to their least terms. 1. m ans. VW- 2. m ans. f . 3. m ans. IH- 4. Iff ans. I^f . 5. m ans. Hi, 6- iWV ans. T^. 7. T^jVff* ans. VS^j. 8. HH- ans. ?. 9. m, ans. tV«. NoT£.->To reduce fractions to less terms. Rule.— When the terms of the fraction end with 5 or 0, divide by 6 ; when with an eveij number or cipher, divide by 2 ; when there are ciphers at the end of each, cut off as many as are common to both ; and when any number will divide both numerator and denominator, without a remainder, divide them by it. Reduce to less terms. H' §• 1. n. Hi*. i* !♦*. 7. w* \ 10- H 9. H* IL W ^m- l^HH M ■;ai * i' '3 l\ i a; H \'i ■4 r. 91 I II I! c: \\\ "90 REDUCTION OF VULGAR FRACTIONS. ' CASE II. To reduce an improper fraction to a whole or mixed num- ber. Rule. — Divide the numerator by the denominator, the quo-' tient will be the whole number ; the remainder, if any, a nu- merator, and the divisor its denominator ; annex this fraction to the whole numt)er. Reduce to whole or mixed numbers. 1. ifans. 311. 2. V ^"s. 8. 3. VV a«s. 6|4. 4. »if 8 ans. 102|f. 5. «_s ans. 13. 6. »i8 ans. 19^. 7. V ans. 12. 8. VtV ans. 12JVV- ^. Wt* ans. 3^f ^. CASE III. To reduce a mixed number to an improper fraction. Rule.— Multiply the whole number by the denominator of the fraction ; to the product add the numerator, under which place the denominator. A whole number is reduced to the form of a fraction, by putting 1 for its denominator. Reduce to improper fractions. 1. 67 ans. V- 2. 4f ans. V* 3. 19 ans. y. 7. 174tV ans. ^\^K 8. 16,4 ans. VV*- 9. 3191^ ans. 8^^». 4. 6i ans. V« ^. 7 ans. f. 6. 17| ans. V- Note. — To- reduce a whole number to a fraction of a given denominator. Rule. — Multiply the whole number by the given denomina" tor for the numerator, under which place the denominator. 10. Reduce 3 to a fraction, having 5 for its denominator. Ans, y. 11. Reduce 11 to a fraction, having 9 for its denominator. Ans, Y. 12« Reduce 27 to a fraction, having 14 for its denominator. Ans, W- CASE IV. To reduce a compound fraction to a simple one. Rule. — Multiply all the numerators together for the numer- ator, and all the denominators for the denominator of the sim- ple fraction. Note. — Shorten the operation in this rule by canceling the numerators and denominatorff. Do the same when you come to multiplication, diyision, and proportion of vulgar fractions. 1. 2. 3. 4. 5. 9. 10. od num- , the quo- ly, a nu- ( fraction s. 12. IS. 12JVV' IS. 3ii|. ninator of ier which action, by 8. ^H'> s. «-»^ of a given denomina* linator. minator. Ans, y. lominatoT. Ans, V* nominator. Ans. Vi'- the numer> of the sim« iceling the I you come fractions. REDUCTION OF VULGAR FRACTIONS. loa Reduce | of H of fo ff to a simple fraction. e 2 - d a c b ■■■. - •. »•' 1 X II X i X i = 1 ans. c d b a "'%■,:-, t - e 1. 2. 3. 4. 5. ^ of I of f . ans. -^j, % of j of |. ans. yV' 1^ of I of ^y. ans. i. f ofjof 9. ans. y. t\ of f of I of 8. ans. j\. Reduce to a simple fraction. 6. ioff of7i. 7. f of6f of8. 8. iofWof7^oflO.« »|8. 9. 6f of9tVofl2. «»Y'- ans. VV- 10. foff ofyofi. 6' CASE V. To reduce fractions of different denomijiators to others of equal value that have a common one. Rule."— 'Reduce them to simple fractions, then multiply each numerator into all the denominators except its own, for the new numerators, and multiply all the denominators togeth^ er for a common denominator. Reduce |, i, | & f to a common denominator. hence the 4 new fractions are and they have the same value of the former ones ; viz. A=Hh i=T«5^» t=m. f =m» Reduce to a common denominator. Ans. y, k 1^. ?Wir» mh mh «^ mh tWt* tWt. mh & mh iH» H*» «= m- ih w» «= 1^ 3X2X3X8=144 N. 1X4X3X8= 96 N. 2X4X2X8=128 N. 5X4X2X3=120 N. 4X2X3X8=192 CD. 1. f , «s t« 2. i, 4, to h 3. -f* t» * Tftr* 4. If f.rV»fc TWIT- S' 4» ?ir» f » «e f . Q. i of ii off, to I of I 7. 3i, iof4, tofoff. 8. |of5,6f, &iof4i, Note.— -When of two fractions the one denominator can. divide the other, without a remainder, multiply the terms of that which has the less dtoomihator by the quotient. Reduce to a common denominator, 10. ^ to |. Ans. ,'S to H. I 13. ^ to y. Ans. ^ to {j. (« (( it H U U :i I 101 REDUCTION OF VULGAR FBACTIONS. I' i ■i, h 1 1 Sometinms a number of fractions may be brought to a com. mon denominator very easily, when any number of the less denominators are equal to the greatest. For example : a» 4 » 6» tV* ^h reduced to a common denominator, U^ h* i\t ^7* i*» are equal to. h h 8» tV* ^Tr» \h red. to a c. d. are ff ih ro» ih ih \h H equal to. Or, 1, CASE VI. To reduce a complex fraction to a simple one. Rule. — Reduce both the numerator and denominator to a simple fraction, then multiply the numerator of each of these fractions by the denominator of the other, for the simple frac tion. Red. 3 to a simple frac. Toi ^~ 3X4=12 — — ans* 4.1 _4ix 1=41 Red. 5^ to a simple frac. "9 V— 11X1=11 — —ans. I — 9X2=18 Reduce 2^ to a 4| simple fraction. 1. Reduce 4_ to a simple fraction. 2. Reduce 13| to a simple fraction. 19 3. Reduce ^^ to a simple fraction. ^— 7X4=28 ' — — ans. y— 19X3=57 i Ans. ^|. CASE vn. To reduce fracti}| pound ? lYoS\ cwt ? ^il4y lb. av.? jHh lb. tr.? 10. jW 11. TaViT 12. If a( 13. H m 14. jV ci 15. fl hi 16. lUi^ \r, corn ? ^ir year ? 7 mile ? :re? ile? rown ? r. guin.? ton? 17. m 02. tr ? 18. jVff quarter? 19. l\l quarter ? 20. if quarter ? 21. HH lb. tr.? 22. /^^ acre ? 23. yiy hour ? 24. U day ? NoTK. — Of two given fractions to find which has the great- er value. Rule. — Multiply each numerator into tho other's denomi- nator, and if the products be equal, so are the fractions ; otherwise the numerator of that fraction, which has the greater value, multiplied by the other's denominator, will give the ^renter product. - Whether has the greater value. 1. * oi* IH ans. f. 2. H or H ans. H. T). yy or y »I ft 1! ■'. ^^ m 105 SUBTEACTION OF VULGAR FRACTIONS. S ■J . ii 21. Add together f ho., ^^ day, and 4 week. Ans, 4 d. lOh. 36 m. 22. A person borrowed at one time J£36f , at another time £27^, at another time 17f sh. ; liow much did he borrow in all? Ans, JE64 18 8 3^. 23. B. went to market and bought 4^ cwt. -M8|lb.-{- 28}J lb. + 13| oz. of tea ; how much did he buy in all ? Ans. 544 lb. 10 oz. 9^ dr. 24. C. went to market and sold 54^ yards+16| yards+ 30} ells Eng. + 4f ells Flem. of cloth ; how many yards did he sell in all ? Ans, 112 yds. 2 qr. 2 na. SUBTRACTION OF VULGAR FRACTIONS. Rule. — Having reduced the fractions as in Addition, find the difference of the numerators; under which write the common denominator. NoTJE. — In mixed numbers, first subtract the fractions and if the numerator of the subtrahend exceeds that of the minu- end, subtract it from the common denominator, and to the remainder add the numerator of the minuend for the numer- ator of the fraction ; and carry one to the units' place of the subtrahend. From f take | ^ -h ■h ans. Ans, ^. From 63^ take 4d^j. 03 i =63H 49t»T = 49H 1. 2. f -4. Ans,%^ 3* A — i* ^^' i« 7. From ^ of f take ^ of -^jf, 8. From H ot' i tnkc J of }, 9. From 29f take 16|. 10. From 56 take 21f»-. 11. From jeiH take £^, 12. From 4 lb. tr. take 3f dwt. Ans. 6 oz. 13 dwt. Ifl^f gr. 13. From ^ tons take ^ cwt. Ans, 6 cwt. 3 qr. ICf lb. 14. From 8| acres take 3f roods. Ans, 7 a. 3 r. 25 J per. 15. Paid a debt of 7t'*|- pounds out of a purse containing 9y^ guineas ; how much remained ? Ans, 43s. 5id. |^. 10. A*8 share of a ship was ^^, of which ho sold | ; how much remained? ^ Ans, ^\, 13^f ans. 4. 7 — f of ^. Ans, ^. 6. 4| — i of I. Ans, 3yViF' 6. 4tV— § of H. Ans, 3^V«- Ans, ^h Ans, jl^, Ans, 12f|. Ans, 34|i. Ans. £S 1 ^ J. lII7LTIPLIOA3fON OF WI1GAI& FBACTI0N8. 106 % 17. A person who ha(i I3f yards of cloth, sold' 7| yards ; how much remained ? Ana, 5t. 16. What part of a ship remained after selling f of |+^ ofsj? Ans,^, 19. Sold f of l+f o^ * of a gallon of wine ; wHat part re- mained ? Arts, yy^. 20. What number h mat to which if ^ of | be added, the sum will be 1 ? Ans, f^. 21^ What number is that, to wMch if you add 7f , the sum willbefl2i? Ans, . I t'. MULTIPLICATION OF VULGAR FRACTIONS. Rule. — Multiply all the numerators together for the nu. merator of the product ; and all the denominators together for its denominator. Note.— In Multiplication and Division, reduce integers and mixed numbers to improper fractions. Mult. I by f [ Mult. 8i by 5| ^^i=*i a^- i V xy =»f « =481 ans. I. What is the product off and f ? Ans, f . 8. What is the product of | of }, and f ? Ans, y\. 3. What is the product of 5, and i<^ of V ? Ans, 5^. 4. Multiply 7}", by t^ of 4 of 10. Ans, 37f . 5. Multiply I of 7^, by f of i of 1|. Ans, l^, 6. Multiply i of f of I, by 1 I of 3i of 11. Ans, 6 J/.. 7. Muhiply 7f, 4f, O^J^, and QyV* -^ns, 2895/,. 8. Multiply 3|, | of 6|, 9tV» and 3f of ^. Ans, 02. 9. What is the value of 2o| bolls barley, at 26s. 8d. ? Ans. £27 13 4. 10. What is the value of 9fy yaaards^ at 21s. dd. per ell Eng. ? Ans, £2 18 5^. II. What is the value of | yd. cloth, at £{} per yd. ? Ans, £0 11 9^ f. 12. What is the value off acne, at £2fy per acre ? Ans, £0 19 5$ ^j, 13. What is the value of 17 fy yds., at 7-^b, per yd,? Ans, £0 7 Oi T^. 14. What is the value of 37f ells Eng. at 5f d. per yd. ? Ans. £1 1 34. 15. What is the value of f oz. silver, as £3f per lb. 7 Ans. £0 4 3f }, 16. What is the value of 60| gal. at 7s. 4tV per gal. T Ans. £22 5 10} ||. 17. What is the value of 4 cwt. 8 qr. 14 lb. at 72s. 8id. per cwt. ? Ant, £17 14 5^ |. K 'y ill \ ft I?. 1 107 DIVISION AND PfiOFOBTION OF VULGAR FBACTIONS. ''■ !■ 1 •"•>.. DIVISION OF VULGAR FRACTIONS. Rule. — Invert the divisor, and proceed as in Multiplication. Divide ^ by |. • *Xi=M=l^ans. 1. ^ ~ W. Ans, \l, 2. ^j -f- |. Ans, -if. 3. ^ -i- |. Ans. ^f . 4. 4 -7- I . ilrw. 2f . 5. i of i -^ f . Ans, r\. 6. I -r- iofi. iln«. 4. Divide 5^ by 2f VXi*if=ii=2^ans. 7. li -^ 8. Ans, ^j\. 8. 29 ^ ^. -4rw. SSf. 9. f -^ 5i. Ans, ^, 10. 76i -r 364. Ans, 2yV\. 11. iofi-f-fofi. Ans, f. 12. f of 7|^| of4.il. 6^f. 13. If 1^ yards of lawn cost 38^s., what is the price per yard ? Ams, 5s. 0^ f . 14. A farm of 17^^ acres was rented at JB14/y ; what was the rent per acre ? Ans, 16s. 3|d ^, 15. What is cloth per yard, when 7 pieces, each llf yards, cost je54f ? Ans, 13s. 4id 4. 16. A man performed a piece of work in 6|f days ; what part of the work did he perform in 1 day ? Ans, ^^ per day. 17. How many stones, each 13f inches by 7i, will lay a kitchen floor 40| feet long, and 32| broad ? Ans, 1926 ^^ stones. 18. Divide a ship of £980tV value into 21^ shares, and a prize of £1000 value into 42| shares. Ans, £45 15 9j\ and £23 9 2i f ^f . 19. Divide £160 16 8 among A., B., C, and D., so that A., B., and C. may have equal shares, and D. | of one of their shares. Ans, A. B. and C. each £44 13 6|. and D. £26 16 1^. ..- PROPORTION OF VULGAR FRACTIONS. Rule. — State the terms as in integers, and multiply and divide as directed above. 1. If f of a pound cost -^ of a shilling, what will |f of a lb. come to ? Ans, 7^d. ^. 2. If I of a yard cost 12s. 9d. how much will 2f yards come to ? Ans, £1 18 3. 3. If I of a lb. cost 5s. 6d., what will 42f lbs. of the same cost? Ans, £15 10 9. 4. If 6 J yards cost 18s., what will 9^ yards come to? Ans, £1 5 l^j\, 5. What will be the price of 7^ cwt. sugar, when j^V of a cwt. cost £3 11 8 ? Ans, £29 17 2^ f. 6. If 2j yards, which is 1^ yd. broad, will make a suit of clothes ; how many yards will it take of 1^^ yd. wide ? Ans, m yds. DEGIMAR FRACTIONS. 108 7. What will \l of a cwt. cost, at £10 4 9 per fodder of 19^ cwt. ? Ans, 9s. 4id |f . 8. If i gallon of rum cost 13s. 6^d., what will 9^ gallons cost ? Ans. £7 3 1| ^. 9. If the value of s^ of a ship be £921^, what will f come to? Ans, £1194 4 3^. 10. A friend lent me £454f for 6^ months, how long must I lend him £204} to discharge the obligation ? Ans. 13 m. 19^/y days. 11. Bought ^ of a ship, and sold ^ of my share for £300 17 6, what is the value of the ship ? ^ ' Ans, £458 9 6^ }, 12. If 2 men mow | of an acre in f of a day, how many acres will 6 men mow in 3} days ? Ans, 11^ acres. 13. If 4 men can finish 12| roods of ditching in d\ days, how many roods can 18 men do in 14y^ days ? Ans, 256^ roods. 14. If a regiment of soldiers, consisting of 975 men, use 17 J quarters of wheat in ^ of a month ; how many soldiers will 71 quarters serve 2^ months? Ans, 50 sol. 15. If 264 men, in 5| days of 11|: hours long, do a piece of work, in how many days of 9^ hours long will 30 men do the same ? Ans, 59||- days. DECIMAL FRACTIONS. 1. A Decimal Fraction has always a unit, with one or more ciphers for its denominator ; as, -f^f -f^t iVi^tt* 2. The numerator only in decimals is expressed ; the de. nominator being always 1 with as many ciphers as there are figures in the numerator. 3. Decimals are distinguished from whole numbers by a point on the left of them ; thus, *5 stands for ^, *75 for tVit* •245 for tWff* and -4356 for tWt/V- 4. A mixed number is when there are figures both on the right and left of the point ; those on the left are whole num* bcrs, and those on the right are decimals ; thus, 27*41, 345*84. 5. Ciphers on the right of decimals do not alter their value, but being placed on the left of them, with a point prefixed, de- crease the value in a tenfold proportion. 0. A Terminate or Finite decimal is one which extends only to a limited number of places, as *5, •125, &c. 7. Tnterminate dectmala are those which extend, ad infin- t/um, and ara called repeaters^ when they always repeat the same figure, as, *3333 &c. and circulq^es^ when two or more figures are continually repeated, as, *424242, *42394239, dec. « 'i l: It' I fii :!! i^ A' Nv V 109 i!UO^TI»N OF DECIMALS. Tiie notfatioQ of Decimals will /appear from this table* 6 5 4 3 2 S K H !^ ffi H g S: o en O CO o f i & g* cr o en B ce P CO f B. 2 3 4 'S 6 IS H H 'ffi S a. ex. p §• •a p o i- p From the above tabb, it appears that Decimals decrease in the same tenfold proportion towards the right hand, that whole numbers increase; towards the ieft. To express any Decimal in words. Rule.— JPut I with as many ciphers as there are figures in the Decimal for a denominator ; then ^expreM in wonds what that fraction is, which will be the value of the Decimal. Express in words 'S— -34 — •07— 'dSS— 'OQS — •066— •3587 — '0074 — •40612 — '00050 — •384051 —•007006— •0000508. :,, .. . >♦ ■ To express any Decimal fraction in figures. Rule. — Express it in the form of a vulgar fraction ; then if the numerator consists of as many places as there are ci- phers in the denominator ; set it down with a point on the left of it. But if the numerator have not a sufficient number of places, ciphers, with a point on the left of them, must be prefixed to supply the defect. Express in figures — three tenths— twenty-five hundredth parts — seventy.five hundredth parts— five hundredth parts — sixty.seven thousandth parts-— one hundred and forty-nine hundred thousandth parts — ^twenty "nine ten thousandth parts — two thousandth parts— one hundred and four thousandth parts— seventeen hundredth parts— ninety-five millionth parts — one thousand three hundred and fourteen millionth parts. ' ^' ADDITION OF DECIMALS. Rule. — Place down the numbers in such a manner that tenths may be under tenths, hundredths under hundredths, 6cc. in which order the decimal points will stand directly under one another ; and then add as in whole numbers, and put a point in the sum directly under the other points. ,i 8 table> -5 6 Cfi 9 decrease hand, that : •. .V '.' 1 -J U > figures in roras what nal. 15— •066— •007006— tion ; then icre are ci- oint on the snt number (n, must be hundredth 1th parts — I forty-nine |ndth parts thousandth [onth parts [h parts. mner that idths, 6cc. jtly under and put a STTBTR ACTION OP DECIMALS. 110 •34 •7546 •08034 •9 •653 •00719 •7405 54-517 5-86 •0748 63-4 8-00754 7^794 sum of 231-65334 sum. •6158+ -721 + -03142+ ^53 + 07431 + ^84+ ^3072 + -003185+ .618 + 3-47563 sum. 1. What is the + -943805+ '83? 2. Add together -407039. 3. Required the sum of 45-72+820-406+ -370472+ 5436-8+50-0751 + 638-714+4-000725. 4. What is the sum of 34-5146+8503-07+ -00348 + 380-874 + 7436 + 5-7056 + 73-08 + 4^53089 ? 5.Add-5408+^75+8-025+72-42+940-1368 + 56 + 7-874 + 83-6075 + -28. 6. Required the sum of eighteen hundredth parts — seven hundred and forty-five hundred thousandth parts— nine thou, sandth parts — forty-three millionth parts — five hundred and eight thousandth parts^-one hundred and thirty-two thousandth parts — one thousand and forty-four ten millionth parts — twenty-five hundredth parts — five tenths — and six hundred and five thousandth parts. SUBTRACTION OF DECIMALS. Rule. — Place the numbers as in addition ; then subtract as in whole numbers. From Take •83052610 •74308749 •08743861 From 74. 03594 Take 8. 6382 /' 65. 39774 1. What is the difference between 83*1496 and 7-36068 ? 2. What is the difiTerence between -64163 and 5^124 ? 3. What is the difference between 700*41 and 98^05769 ? 4. What is the difiTerence between 1*63370 and 9^64 ? 6. What is the difference between 6^1 and *007439 ? 6. What is the difference between seven hundred and fifty- five thousandth parts and ninety-nine thousandth parts ? 7. 83*149+ 6«6807+ 904^072+ 81 •40686 + 10M*74— 894- 5196. 8. 7*386+91'74+80726+35«03 + 2*476— 34*n8 + 63. 749361. 12 i 4 J 1 '} ^. I Ill MULTIPLICATION lUt) tlVlSlOU OF t>£CIMALS. lj?''l r 1 if- r- - > ■ !l : m Im MULTIPLICATION OF DECIMALS. Rule. — Multiply as in whole numbers, and point off in the product as many decimals as there are in both multiplicand and multiplier ; but if the product does not contain as many figures, supply the defect by ciphers on the left. Multiply 23'416 by 6-43 6-43 70248 03664 140496 150-56488 ans. 1. Multiply 617-42 by 3. Multiply •2764 by 3. Multiply 174 by 4. Multiply 62-348 by 5. Multiply •0783 by 6. Multiply •06948 by 7. Multiply •001038 by 8. Multiply •078446 by 9. Multiply •000798 by Multiply '51437 by ^0175 •0175 257185 360059 51437 3-26? 96? •149? •00172 ? •461? •0087 ? •77? 398000. 009001475 ans. Atis. 2012^7892 . *f 26^5344. "■:¥ ■ 25-926. 5. Divide 417-8125 by 37^5 (( 11-1416 6. Divide 37 '25 by 281«5 « •1323268 Hf 7. Divide •21975 by 124 (( •00177217|a 8. Divide •5 by •00725 (( 68-965517 ^V Note. I. — When the divisor is an integer with any number of ciphers annexed ; cut off the ciphers and remove the deci- mal point in the dividend as many places farther to the left as there are ciphers cut off, prefixing ciphers if necessary, then proceed as before. 1. 8463-7-i-2300 « 3. 10-4039-r 1000 2. 4738-37-r463000 , ^ 4. 94-687 -r 874000 Note II. — To divide by a unit with ciphers, remove the decimal point as many places towards the left hand as there are ciphers. 7436-5-?-100— 3817-42 -r 1000— 20472-16-MOOOO. REDUCTION OF DECIMALS. ' ^ Case I. — To reduce a vulgar fraction to a decimal. Rule. — ^Annex ciphers to the numerator as decimals, and then divide it by the denominator ; if there be not so many figures in the quotient as there were ciphers annexed, supply the defect by writing ciphers before it. Reduce ^ to a decimal. 8)7-000 *. -875 ans. 1. i»i, i»i»i»|»i»and^. 2. h h h f , h and W- 3. T^y. Ans, •0416 4. 4f « •6076949+ 5. T*T. " *037785849+ 6. iof|. « -375 Reduce 7^7 to a decimal. 400)1-0000 » j .', - . ■' ■■ •0025 ans. fractions to a decimal. 7. f off Ans, -5 6. fofi *' "^ 9. \oH -175 10. iVof^ *» '05625^ U. jh •• •00876 la- if v ** 'Oia CaIs II. — ^To reduce a decinuU to a vulgar fraction* EtTLB.— Mako the gi^en decimi^ th« numerator, and a unit, I 113 SEDUCTION OP DECIMALS. with as many ciphers annexed as there are figures in the deci- mal, the denominator of the required fraction, which redace to its lowest terms. 1. Reduce *5 to a vulgar fraction. 2. 3. •25 •75 4» 5. •125 •625 6. 7. •34 •375 ■^jj=i ans. 8. '005 9. -078 Case III. — To reduce numbers of a lower name to the deci. mil of a higher. Rule. — If the given number be simple, annex ciphers, and divide by as many of that name as make one of the higher ; but if it be compound, begin at the lowest and reduce it to the next higher name ; to this decimal prefix the next higher de- nomination, reduce this decimal to the next higher, and so on to the required decimal. Reduce 13s. 8|d. to the deci- mal of a £, 4) 1-00 12) 8-25 20)13^6875 •684375 ans. Reduce 7 oz. 5 dwt. 12 gr. to the decimal of a lb. 24)12^0 20) 5-5 ' 12) 7-275 •60625 ans. The questions in this case and the next prove each other. 1 . Reduce 9d. to the decimal of a pound. 2.-173. 6d. 3.— 12 8i 4.-7 5.. 6.— 7. — 8.— 6| 71b. 8lb. 9. — 11 oz» 17 dwt. 10. — 5 dwt. 12 gTi 11. — 7 oz. 14 dr. 23.— lOd. 24.— 198. ll|d. 25.-^14 3i 26.— 6 8 27.— la 4 28.— 11 pound. pound. pound. pound. pound. cwt. cwt. lb, oz. ewt. 12. Reduce 10 oz. 12 dr. to the decimal of a lb. av. 13.-— 3 oz. 14 dwt 8 gr. lb. 14. — 3 qrs. yard. 15. — .1 qr. 2 na. yard. 16. — 6 fur. 5 po. mile. 17. — 2 TO, 11 per. acre. 18.— 7J^. shil. 19. — 4 bus. 3 p. li g* qr. 20.— 22 m. 3 sec. , hour. 21. — 1 ro. 22 per. acre. 22.-3 d. 12 ho. year. rep. pound, pound, pound, pound, pound, pound. 32.*«J0 in. 8 pts. foot. 33.— lid. shil. 34.--10d. shil. 95.— 12s. 4|d. guiiK 36.-^ yd. 2 ft. 11 in. pole. 37.— 7 days 6 ho» year. REDUCTION OF DECIMALS. 114 29.— 17 lb. ton. 30.— 18 cwt. 13 lb. ton. 31.— 13 dwt. 16 gr. lb. 39. — 7 h. 9 min. day. 39.-^20 per. 8 yd. acre. 40. — 18 yds. 4 ft. rood. Case IV.— To find the value of a decimal. iluLE. — Multiply it by the lumber of times the integer con- tains the next lower name, and point off as many decimals from Ihe product, towards the right hand, as there are in the given decimal ; the figures in the left hand are integers of said lower name ; reduce the figures pointed off into the next lower name, and point off as before. What - is the value of What is the value of 1 A » £ •684375 lb. • 60625 troy. k s. 1 20 m oz. . 12 I" 3-087500. 7*27500 n !mI . .,' d. 12 dwt. 20 « Mk 8'250000 5*50000 ^n@ 'k ' far. 4 7o 24 ';;-i ^ - ' i I'OOOOOO 12-00000 z. 5dwt. 12gr. ans. 13s 8id ans. 1 What is »M 1. What istheval. ofie«0875 12. the yal. ( 3f '671875 lb. av. ' I^S 2. « <( £•875 13. It tt •80972 lb. troy. • ^ 3. « it £•634375 14. (t tt •75 yard. 4. (( « £•378125 15. it tt •375 yard. ' !^H 5. « (( £01875 16. (( tt •7656-^ mile. . i 0. a it £003125 17. (( it •56875 acre. 'm 7. <( it •0625 cwt. 18. «( tt •625shil. 8. (( ti •071428 cwt. 19. <{ tt •61328125 qr. ' ^^kA 9. (( « •9875 lb. troy. 20. i( tt •3675 hour. j irHy 10. (( (( •275 oz. troy. 21. i( tt •3875 acre. '" Wi 11. (( (( •004394 cwt. 22. it «( •009589 vear. i m 1 23. (( ti £•0416 28. it « •8 foot. ^ 24. <( (( £•9989583 29. u (i •916 shiUing. 25. (( <( £•714533 30. (( (( •83 shilling. ''' Wli 26. (( (( £•3 31. it (i •59027 guin. i» 27. (( (( £•6 32. tt tt 1'0S5 pole. ;,: il 1 115 CIRCULATING DECIMALS. I 3d. « « je*04603 37. « it •019863 year. 34. " « •007589 ton. 38. « u •2979 day. 35. « «' '9058 ton. 39. " » •126 acre. 36. " « •05694 lb. tr. 40. " u •015243 rood. Note. — The two following contractions arc of great prae. tical utiUty in decimal calculations ; as they appoximate suffi- ciently near the truth, and so simple that they can be per* formed mentally. I. — ^To reduce shillings, pence, and farthings to the decimal ofaje. Rule. — Take half the number of shillings for the first dc . cimal place ; and the number of farthings in the remainder, increased by 1 if it amounts to 24 or upwards, by 2 if it amounts to 48 or upwards, and by 3 if to 72 or upwards, will give the two next places. Reduce mentally to the decimal of a £. 1. 23. 6d. = '125 2.14 9 = ^737 3. 7 1^ = -357 4. 1 Hi = •ooe 5.12 1^ = •606 6. 14s. .3d. 7.16 6 8.19 1 9. 1 H 10. 3 n 11. 7id. 12. 8^ 13.1 lOi 14. 4 9^ 15. 11 4| 1. 4s. §d. 2. 7 6 3.17 9 4. 8 7| 5.18 5i II. — To find the value of a decimal of a £. mentally. Rule. — ^Double the first figure for shillings, to which add Is., when the 2d figure is 5 or more : then account the 2d and Sd figures, (when they do not amount to 50, or their ex- cess above 50, when they do,) to be farthings after having deducted 1 for every 25 in their number. 1. •82Sk,— 16s. 6d. 2. '207^ 4 If Value mentally these decimals of a £. 1. ^403 5. ^75 9. -005 3. *9b = 19 2. ^513 6. ^463 10. '034 4. •eSl = 13 7i 3. -739 7. ^578 11. -083 5. '043 = 10| 4. -841 8. ^795 12. -09 Note.— The pupil should now work by decimals, all the practical questions given under the rules of Addition, Sub. traction, Multiplication, Division, and Proportion of Vulgar Fractions. CIRCULATING DECIMALS. 1. A repeating or circulating decimal is when one or more figures are continually repeated. 2. A single repeater is when one figure continually re- peats ; as 'OBO, — '333 and are marked thus 6, 3. 63 year, day. icre. 143 rood. ;reat prae- mate sufii- ;an be per* he decimal he first dc » remainder, by 2 if it )r upwards, mal of a £, 11. 7id. L2. e| 13. 1 lOi L4. 4 9i 5. 11 4| tally. which add ouDt the 2d )r their ex- fter having nalsofa£. 9. '005 10. '034 11. -083 12. '09 Is, all the Jition, Sub. of Vulgar le or more linually re- REDUCTION OF CIBCULATIN6 DECIMALS. 116 3. A compound repeater is when two or more figures con- tinually repeat ; •4242,-617617 ; marked thus •42. — *&li, 4. A mixed repeater is that which has other figures in it besides those which are repeated ; as •28333, — 5.2321321, and marked thus ^283 — 5*232i. " • REDUCTION OF CIRCULATING DECIMALS. I. — To reduce a single or compound repeater to a vulgar fraction. Rule. — Make the given decimal the numerator, and as many 9s as there are figures in the given decimal, the de- nominator ; which reduce to its lowest terms. Reduce '3 to a vulgar fraction, f =^ ans. Reduce *27 to a vulgar fraction. H=tV ans. Reduce *063 to a vulgar fraction. 1 Ans, i 5. •36 J ins, T^. 9. •962 Ans, f^. 6 « f 6. .90 " H- 10. •14634 « y\. 2 « 1 7. •108 " 3*T- 11. •615384 « j\. 7 « i 8. •148 " ^' 12. •857142 « f. Reduce the following circulates to vulgar fractions. 1. 2. 3. 4. II. To reduce a mixed repeater to a vulgar fraction. Rule. — Subtract the finite part from the whole, the remain- der is the numerator, and for the denominator, place 9 for every repeating figure, with a cipher annexed for every finite place. Reduce •446428571 to a vul- gar fraction. 446428571 446 Reduce •3409 to a vulgar frac- tion. 3409 34 3375 9900 •-Ni ans. 446428125 999999000 \i ans. Reduce the following mixed circulates to vulgar fractions. 2 16* 1. -0083 2. •le 3. -0185 4. -83 5. -416 Ans, riir^ it *• / ** i\' u h (( A- 6. 8. •254629 •07954 •7621951 Ans, u 9. -5681 10. -03248 u u a 8¥- 117 ADDITION OB CIRCULATING DECIMALS. ADDITION OF CIRCULATING DECIMALS. . I. — When they ate single repeaters. Rule. — Extend the repeating figures one place beyond the longest finite decimal, and carry at in the right hand col- umn. II.— When they are compound repeaters. Rule. — Extend the repeating figures till they become simi- lar, and when you add the right hand column, include what would have been carried, if the repeaters had been extended farther. Add together 45-3+3-6+14 '253+ -4625. 45.3 =45.3333a 3'6 = 3-06666 14*253 =iW^5'333 •4625= -4625 63-71583 Add 30-62085+6-3028 29-00642 + 365-6 80-6208520 Q52 82 83 6-3028292 29-0064242 ,3,, 365-6666666 ^^ 431-5967712 I. add together -3813+ -42+ -.5216+ -94724. 4n5. 2-27246. 2- add -83 + 7-416 + -31855+6.25+4-38+29.G27. Ans. 43-835216. .3. add 210-3 + 194-2*1 + 85-0743 + 900-08165. Ans. 1389.700427. 4. add 8-2038+9.0468 + 7-36548 + 43-4683. - ilrw. 68-084577. 5. add 30-62085+6-3028+29-00642+365.6. Ans, 431-5967712. G. add 81-004"8164 + 3-2b5+5.07426+5-'85. Ans. 95-1427202. 7. add 39.0034+6-0526 + 82-682578+9-52i8. ' ^ Am, 136.660466971. SUBTRACTION OF CIRCULATING DECIMALS. I. — To subtract single repeaters. Rule. — Extend the repeaters one place beyond the longest flnile part, and borrow 9 at the right hand figure when nc» cessary. » II.— To subtract circulates. \LS. :. ieyond the hand col- come simi- :lude what n extended -6-3028 )65-6 052 O 83 83 48 42 s. 2-27246. 7. 49-835316. 89.700427. 58-084577. 5967712. t-1427202. 60466971. MALS. the longest when no. MULTIPLICATION OF CIRCULATIMG DECIMALS. 118 Rule. — Make the circulates similar as in Addition, and if the first figure in the subtrahend on the right of the longest finite part be greater than the one above it, add 1 to the right hand figure of the subtrahend before subtracting. From 57-25 Take 49-166 From 32-502762762762762 Take 26-042687668756875 take 37-3 take 25-375. 8-083 1. From 69-3135 2. From 69-416 3. From 931-3824 take 38-6 4. From 562-871 take 3-49683 5. From 450-8116 take 8-58 6. From 81-7175 lake 73-56i 7. From 34-851 8. From 21-453 9. From 92-3846 take 5-47325. take 13-72' take 18-674371 6-460075194005887 , Ans, 31-98016 Ans, 44-0416 Ans, 892-71573 Ans, 559-37427 Ans, 442-2227 Ans, 8-1559384 Ans, 29-37860i85 Ans, 7-726180 Ans, 73-710276093 Ans, 4-925*2947 10. From 32-78264 take 27-85735 MULTIPLICATION OF CIRCULATING DECIMALS. I. When the multiplicand is a repeater or circulate. " Rule. — When a repeater, carry at 9 on the right of each product, and add as directed for repeaters : when a circulate, to the product on the right hand figure of each line, add the carriage that would have arisen, had the circulate been ex- tended further ; and make the circles similar before you add them. Multiply 879-83 by -721 879-83 •721 87983 1759666 61688333 634-35083 Multiply 586-1635 by 827. 586-1035—635. 827- 41031449 117232712 4689308508 1. Multiply 68-416 by 32-5. 2. Multiply 6'683 by 475. 484767-2670 vln«. 2061-0416 Am, 269Q-5B8 m i>r\ ■ ii i ^ ... I" M 119 DIVISIOM OF CIRCTJLATma DECIMALS. ) r it I PI II '^. Multiply •49&38 by 12-64. itnf. e*2906d5 ; 4. Multiply 8d5«48f by -00325. -An*. 1-18781596 '' 5. Multiply •2'ti86 by 1-426. iln*. •38766074 6. Multiply -92937 by 1500. Ana. 1394-069 II. — When the multiplier is a repeater or circulate. Rule.— Reduce the multiplier to a vulgar fraction ; then multiply by the numerator and divide by the denominator. Mult. 157.525 by -46 .■ 1 4 (5)1102675 42—7 15?, . (3) 220535 90—15 73-5116 ans. Mult. 47-57185 by -9108 9 47-57185 387 9099—337 370) 9990—370 43-328956 ans. 1. Multiply 92-25 by -3 jIiw. 30-7518 2. MuH^y 8-09756 by -6 iliM. 5-39837 3. Multiply 68-285714by 6-1375 Ans. 419-1061347 4. Multiply 1725-175 by 6-4375 Ans. 11105-8788213 DIVISION OF CIRCULATING DECIMALS. I. — When the dividend only has a repeater or circulate. Rule.— Divide as in finite decimals, but annex the repeat- ing figures instead of ciphers, in order to carry on the division. J, Il.-^Whea the divisor is a repeater or circulate. Rule. — Reduce it to a vulgar fraction ; then multiply by the denominator and divide by the numerator. 7-5)39-86(5-315 375 236 225 116 75 -_.-.. 416 875 i- ■ Divide 5-37 by -78 7 66- -11 5-37 16 90- • -15 1)80-55 • • 7-0227 ans. * • k MISCBLLANEOXrs QUESTIONS. 120 1. Divide 4-19662 by 87. - > « ' Ans, -11342 2. Divide 73-416 by 6-25. Ans. 11-746 3. Divide 169-3 by -05. Ans. 3386.6 4. Divide 315-625 by 11*53 Ans, 27-866329+ 5. Divide 6129 5 by 9525 Ans. 6484*8155737+ 6. Divide 879-376 by -352 Ans. 1076-693698+ 7. Divide 577-375 by 23-85*1 Ans. 24-2067315+ 8. Divide 87.0*7317 by -576*20 Ans. 151-0909774+ MISCPLLANEOUS QUESTIONS, IN VULGAR AND DECIMAL FRACTIONS. 1. What cost 22^ cwt. sugar at £i-^ per cwt.? Ans. j&97 7^. 2. Borrowed j&|, and repaid } of a guinea; how rouch is still due? Ans. Os. l*2d. 3. Whether is £^, or jS*128125 of greater value ? Ans. equal. 4. Bought a penknife for J&-225, how many shillings did it cost me ? Ans. 4s. 6d. 5. 3oucht a hat for jS|, and sold it for £-875, whether did I gain or lose, and how much ? Ans. 2s. 6d. gained. 6. Suppose I buy i of a ship, and sell | of my share, what part have I left? An^. •^. 7. What number divided by 3^ of 7, will give 20 ? Ans. 455. 8. A ship-owner sold ^ of } of a vessel to one person, and 4 of f to another person ; what part had he remaining 7 Ans.\^i. 9. A lady*s fortune was f pf ^ of her brother's which was valued at £8000; what was the lady's fortune? Ans* £2100. 10. What is the greatest common measure of -^^ ? Ans, 4. 11. Bought 8-5 yards of cloth for £2 14 3 ; what must I give for 27-75 yards ? Ans. £21 10 U- 12. Bought I of a ship at one time, and -^ of it at another, and being now determined to buy all the ship ; required how much I have to pay for ? Ans. ■^. 18. A person left | of his estate to his eldest son, ^ of } of I to his other son, and the rest to his relations ; the eldest •on*8 share was worth £607ii^, what was the value of the es« tate ; and what did the youngest son and relations receive f Ans. £911 17 value of estate, £227 19 3 to young. est son, £75 19 9 to relations. % i^m ^.ftL I 121 MISCfiLLANEOTTS QVESTIOITS. I ! * m If I i» 14. Jane can spin a certain quantity of yarn in 12 days, and Margaret an equal quantity in 16 days ; in what time will it be spun, if both work together ? Ans, 6f days. 15. Suppose A can do a piece of work in 18 days, B. the same in 20 days, and C. in 24 days ; in what time will they perform it, all working together ? Ans, Off days. Vv 16. A person having f of a vessel, sells % of his share for £312 ; what is the whole vessel worth ? Ans, J&780. 17. What is the weight of 15f hhds. tobacco, each weigh- ing ISf cwt. ? Ans, 286 cwt. 3 qr. 8| lb. 18. What will 18f yards cloth cost, at the rate of 3^ yds, for jeif ? Ans, £9 11 6^ f 19. Sold sugar at lOfd. per lb., and gained 7^ per cent. ; what was it bought at per cwt. ? Ans, j&4 13 4. 20. Suppose M. has f of a ship, and sells to N. f of his share, and that N. sells O. ^ of his part ; what share of the ship has O., and what part has M. and N. separately lefl ? Ans, O. has ^, M. ^, and N. i. : 21. Reduce | of f of ^ of i^ of ^j to a simple fraction ? Ans, : 22. What is the difference between 100' and '001 ? Ans, 99»999. 23. What number is that from which if you take f of f, and to the remainder add ^ of -^^ the sum will be 10 ? Ans, lO^^V' 24. A. can do a piece of work in 6^ days, B. can do the same in 4^ days, and C. in 3^ days ; if you set them all at work together, in what time will they finish it ? Ans, IWW *^^y^' 2«'3. The diameter of the earth is 7970 miles and the cir. cumfercnce is 3| times the diameter : if a man of 6 feet in height wore to travel round the earth, how many yards would his head go farther than his feet ? Ans, 12^ yards. . 26. If a wall 57| yards long, 12yr> irilli ^ come 194 4 3^. squired the 12 lOH- M!§([;fiLLANfiOtrs QVESTIONS. 12^ 31. 'A gentlefmaih left an estate to his three sons( ; the eldest got f of i of it, the second got f of |, and the third £10&tf^', what Was the value of the whole e^te, and how much aid the first and second sons receive? Ails. J&8639 2 10^ |, value of estate : 1st son got £5039 10, the 2d £2591 l4 10^ |. 32. Suppose A. has ^ of a ship, and sells to B. ^ of his sharis, and B. sells ^ of his share to C. ; riequired C's shttf^, and what part A. and B. had left ? Ans, C's share f^, A. has i, and B. ^ left. 33. A bankri^pt's effects amount to f of his debts ; what is tha^ per pound ? Ans, 12s. per £• 34. Divide £78| among four men and two women, and give each of the women $ of a man*s share. Ans, A man's share £16 W, a woman's £5 12. 35. If 24S mQu, in 5^ days of 11 hours each, dig a trench of 7 degrees of hardness, 232^ yards long, 3| wide, and 2^ deep ; in how many days, of 9 hours long, will 24 men dijg a trenich of 4 degrees of hardness, 337^ yards long, 5|^ wide, and 3i^deep? Ans, 132 days. 36. A person left | of his property to A., ^^ to B., ^ to C, -^ to D., ^ to E., J^ to F., and the rest which was £800 to his executor ; what was the value of the whole property, and of each person's share ? Ans, value of property £10,000. — A's share £4000, B's £3000, C's 1260, D's £500, E's £250, F's £200. 37. Bought 18 I cwt. sugar, at £4^ per cwt., and sold it at ll^d. per lb.; what was gained or lost on it ? Ana, £19 11 l^i gained. 38. What number is that from which if you takc^ |, the rei mainder will be i ? Ans, l^. 39. What is the interest of £456| for 4f years, at 4^ per cent ? Ans, £89 16 l^, 40. Four rpen, A.B.C.D. got a present of a guinea, of which k, claims i, 3. f, C. ^, D. ^, but they find it too little, it is rcj quired therefore their shares of it in the above proportion. ' Ans, A's share 8s. 2d. /p, B's 5s. 5d. ^^ d's. " , , , 48. Id. Yr, D's 3s. 3d. t\t 4iY B. can perform a piece of work in 9 hours, C. in ^^, and D. in 6) hours;, in what time will they perform it all wotrkiiiR^tbgether ? Ans, 2\\9- hours. 43. There is a mant or pole | of its length stands in tHe grouhdy 1'2 fbet of it in the water, aiid | of its length in the air 61^ above water ; what is its whol6 leD^ith 1 An^, 216 ft. 4d« A young man received £21 0^ which was f of hi8_ elder brbihbr'fi portion ; now 3 times the elder brother^s portion 1.3 Kii Int. ^ m 123 MISCELLANEOtrS QITESTIOMS. l> 1 »t- 1 I It' f f^\ was i of the father's estate : required the value of his estate. Ans. £1890. 44. What fraction is that, to which if you add | the sum will be f ? Ans. ^4. 45. Suppose 264 men in 5f , days of 10^ hours long, can build a wall 234| yards long, 3^ broad, and 5| high ; in how many days of 0| hours long, will 25 men build another wall 337| yards long, 4^ broad, and 7^ high ? Ans, 141| days. 46. A ship worth £8000, of which £4800 are insured, is totally lost, of which i belongs to B., ^ to C, ^ to D., and the rest to E.^; what part of the insurance will each partner receive? Ans. B. £2400,0. £600, D. £480, E. £1320. ' 47. A sum put out to interest 4^ years ago, at 4^ per cent., amounts to £756^ ; what was the principal ? Ans. £628 19. 48. The rent of || of a meadow was £3 12 ; what will be the rent of f of J^ at that rate ? Ans. £1 17 l\ ^^. 49. If 27i yards of cloth, |f yard wide, cost £10 13 4 ; what will 7| yards cost when only || yard wide. Ans. £2 10 lOi |^. 50. B. C. and D. working together, can finish a piece of work in 8 days, which B. can do by himself in 24 days, and C. in 22 ; in what time could D. do it ? Ans. 26| days. 51. Three men E. F. and G. entered into company ; E. continued his share of the stock for 4 months, and claimed } of the profits, F. continued his for 9 months, G. continued his stock of £550, for 8 months, and received ^ of the gain ; required E. and F's stock ? Ans. E's £440, F's £293^. 52. Suppose a wolf could devour a sheep in an hour, a tiger in ^ hour, and a lion in ^ hour ; and that the wolf eats 10 minutes by himself, afler which the tiger arrives and eats along with him 10 minutes longer, then the lion arrives, and all three eat together ; required the time in which the sheep Mill be devoured. Ans. 21f minutes in all. 98. Two Arabians sat down to dinner ; one had 5 loaves, and the other 3 : a stranger passing by desired permission to eat with thom, to which they agreed. The party having fin- ished their loaves, the stranger laid down 8 pieces of money and departed. The proprietor of the deleaves took up 5 pie* ce«, and left 3 for the other, who obiected, and insisted on half. Upon this the affair was referred to a magistrate, who gave the foUowinff judgment : Let the owner of the 5 loaves have 7 pieces, and the owner of the 8 loaves, 1. Was this decision just 7 Ans. It was. just. •• MISCSLLAKEOUS QUESTIONS* 122 his estate. 19. £1890. I the sum Ans, ^4. s long, can ^h ; in how aother wall L41| days. I insured, is to D., and ich partner E. £1320. :^ per cent., . £628 10. irhat will be 17 Hi^jf. eiO 13 4; 10 m H. a piece of t days, and . 26f days. Kipany; E. i claimed } continued the gain ; F's £293^. an hour, a 3 wolf eats es and eats rrives, and 1 the sheep lutes in alt. d 5 loaves, rmission to having fin< I of money k up 6 pie< insistea on jtrate, who le 5 loaves Was this t was. just. , 91. A gentleman left an estate to his three sons ; the eldest got f of I of it, the second got f of |, and the third £1007/7 ; what was the value of the whole estate, and how much did the first and second sons receive? Ans, £8639 2 lOJ 4, value of estate : 1st son got £5039 10, ^e 2d £2591 14 lOi \. 32. Suppose A. has i of a ship, and sells to B. ^ of his share, and B, sells ^ of his share to C. ; required C^s share, and what part A. and B. had left ? Ans, C*s share -j^, A. has ^, and B. ^ left. 33. A bankrupt's effects amount to f of his debts ; what is that per pound ? Ans, 12s. per £. 34. Divide £78f among four men and two women, and give each of the women ^ of a man's share. Ans, A man's share £16 16, a woman's £5 12. 35. If 248 men, in 5^ days of 11 hours each, dig a trench of 7 degrees of hardness, 232^ yards long, 3f wide, and 2 J deep ; in how many days, of 9 hours long, will 24 men dig a trench of 4 degrees of hardness, 337^ yards long, 5f wide, and 3^ deep? Ans, 132 days. 36. A person left f of his property to A., j\ to B., ^ to C, ,V to I^»> ?V to E., jV to F., and the rest which was £800 to his executor ; what was the value of the whole property, and of each person's share ? Ans, value of property £10,000.— A's share £4000, B's £3000, C's 1260, D's £500, E's £250, F's £200. 37. Bought 18 I cwt. sugar, at £4]^ per cwt., arid sold it at lUd, per lb.; what was gai^d or lost on it ? ' Am, £19 11 li gained. 38. What number is that from which if you take J, the re. mainder will be i ? Ans, |f . 39. What is the interest of £456| for 4f years, at 4i per cent? Ans, £89 16 l-^, 40. Four men, A.B.C.D. got a present of a guinea, of which A. claims ^, B. i, C. ^, D. ^, but they find it too little, it is re. quired therefore their shares of it in the above proportion. Ans, A's share 8s. 2d. -ft-, B's 5s. 5d. fy^ C's 4s. Id. ^r> I^'s 3s. Sd. ^, 41. B. can perform a piece of work in 9 hours, C. in 8*, and D. in 6| hours ; in what time will they perform it all workinfftogether ? Ans, 2|4f hours. 42. There is a mast or pole } of Its length stands in the ground, 12 feet of it in the water, and f of its length in the air or above water ; what is its whole leii^h ? Ans, 216 ft. 48. A young man received £310, which was | of his elder brother's portion ; now 3 timet the elder brother's portion l2 m %' i^ii t ■S m 123 MiSCELtANEOtrS qiTESTIONS. l^ i was i of the father's estate : required the value of his estate. An9. £1890. ''■' 44. What fraction is that, to which if you add f the sum will be f ? Ana. ^f 45. Suppose 264 men in 5|, days of 10^ hours long, can build a wall 234| yards long, 3| broad, and 5| high ; in how many days of 0| hours long, will 25 men build another wall 337^ yards long, 4| broad, and 7^ high ? Ans. 141f days. 46. A ship worth £8000, of which £4800 are insured, is totally lost, of which ^ belongs to B., ^ to C, ^^ to D., and the rest to E. ; what part of the insurance will each partner receive ? Ans, 6. £2400, C. £600, D. £480, E. £1320. 47. A sum put out to interest 4^ years ago, at 4^ per cent., amounts to £756^^ ; what was the principal ? Ans, £628 19. 48. The rent of f f of a meadow was £3 12 ; what will be the rent of | of Jj at that rate ? Ans, £1 17 li VW* 49. If 27^ yards of cloth, |f yard wide, cost £10 13 4 ; what will 7| yards cost when only \^ yard wide. Ans, £2 10 lOi H. ' 50. B. C. and D. working together, can finish a piece of work in 8 days, which B. can do by himself in 24 days, and C. in 22 ; in what time could D. do it ? Ans, 26| days. 51. Three men E. F. and Q. entered into company ; E. continued his share of the stock for 4 months, and claimed } of the profits, F. continued his for 9 months, G. continued his stock of £550, for 8 months, and received ^ of the gain ; required E. and F's stock ? Ans, E's £440, F's £293^. 52. Suppose a wolf could devour a sheep in an hour, a tiger in } hour, and a lion in i hour ; and that the wolf eats 10 minutes by himself, after which the tiger arrives and eats along with him 10 minutes longer, then the lion arrives, and all three eat together ; required the time in which the sheep will be devoured. Ans, filf minutes in all. {^3. Two Arabians sat down to dinner i one had 5 loaves, and the other 3 : a stranger passing by desired permission to eat with them, to which they ngreed. The party having fin- ished their loaves, the stranger laid down 8 pieces of money and d^^rted. The proprietor of the 5 loaves took up 5 pie- ces, and left 3 for the other, who objected, and insisted on hfdf. Upon this the affair was referrea to a magistrate, who gave the foUowins judgment ; Let the owner of the 5 loaves Save 7 pieces, and the owner of the 8 loaves, 1. Was this ^kciiioD just 7 Ans, It was just. QUESTIONS FOR EXAMINATION. 124 ;; {^ij* t QUESTIONS FOR EXAMINATION, IN VULGAR AND DECIMAL FRACTIONS. All calculations in exchange may be performed by Proper - tion, and often by Practice. •'.I HOLLAND; ; AccounteFare kept in florins, or guilders, stivers and pen. Dings. There are two kinds of money in Holland, viz : hanco a^d currency : banco is more Valuable than currency, the differ- ence is called agio ;, and varies from 2 to 5 per pent. ..Exchange with Britain vi^jries- from- 34s. to , 37s;, gross ,pr Fl^mislf'per £. sterling. Usance 30 days ai\er date, and 6 days of grace. y^J »JI^ ■• ; .i sJ M %* * •.r^lf.— -^ > . ' to a vul- iater to a decimals? s? How irabt corft. ipty wh6n has a tit- r is i re. i dividend When the rr-: ij U:i,n •.. heilfiott^ uni of the h6 moii^y , which is llowed for By of any lually va- it money, 3f foreign bankers ^iHs aftdr Pfop6rl md pen. VttCO Bfid |e differ. ro8s pr 3, and 6 EXCHANGE. 126 1 stiver. 1 shilling Flemish. 1 guilder or florin. 1 rixdoUar. 1 pound Flemish. 16 pennings, or 2d. Flem. 6 stivers, or 12d. Fl. 20 stivers, or 3s. 4d. Fl. 2^ guilders, or 8s. 4d. Fl. 6 guilders, or 20s. Fl. To reduce banco into currency, and the contrary, say. As 100 : 100+agio::banco : currency. As 100 4- agio I 100 M currency I banco. 1. How many guilders current in 48.7.50 guilders banco, agio 4| ? Ans. 51,065f guilders. 2. How many guilders banco in 7864 guilders current, agio 2i ? Ans. 7690«9535 gui. banco. 3. How much sterling in 7846 guilders banco, exchange 34s. 6d. Flem. per £. sterling. Ans, £758 1 4-^f ster. 4. How many guilders in £4850 sterling, exchange 36s. 6d. ? Ans. 53,107^ guilders. 5. In £100 sterling how many stivers, exchange 36s. 6d. Flem. per £. sterling ? Ans. 21900 stivers. 6. Britain draws on Amsterdam for £464 15 sterling, how many pounds Flemish will pay the draft, exchange 35s. 4d. Flemish per £. sterling ? Ans. £821 1 2 Flem. 7. In £7968 10 Flemish, how much sterling, exchange 34s. 8d. ? iln«. £4597 4 2| j\ ster. 8. Britain remits Amsterdam 4896 guilders, 15 stivers ; how much sterling will pay the bill, exchange 35s. 4d. Ans. £461 19 If ^^ ster. .■ifO:' GERMANY. Hamburgh, like Holland, has two kinds of money. Banco and Current, the agio between which varies from 20 to 25 per cent. Bills of exchanpio are valued and paid in banco ; and exchanges are transacted by thn pound Flemish. Accounts are generally kept in marks and schillings'. Usance 30 days after date, and 12 f^ ys of grace. ^ 6 phenning = or 2d. Fl. 12 phenninj^ 6 schillings, 16 schillings, 2 marks, 3 marks, 7i mavks, or 12d. Fl. or 2s. 8d. Fl. or 5s. 4d. Fl. or 8s. Fl. or 20s. Fl. 1, How many dollars banco \n 805 90 per cent ? »i^ 1 penny Flemish. 1 schilling. 1 schilling Flem. 1 mark. 1 dollar of exchange. 1 rixdollar. 1 pound Flemish. dollars currency, agio Ans. T2()j banco* {■>}: ii'' ■'A mi i J." fat ' ■■■I'M ■m lii 127 EXCHANGE. |j i hi II 2. How much sterling in 8347 marks banco exchange 32s. 2d. per £ sterling ? Ans, JE6Q1 19 7 y^g^^. 3. How many marks banco in £9648 sterling, exchange 33s. lOd.? ilfu 122,409 marks. 4. How much sterling money in 4173 marks 8 schillings banco, exchange 32s. 2d. Flem. banco per £ sterling. Ans, £345 19 9^^. 5. In 24,680 phennings, how many rixdollars ? Am, 42rixd. 2 8 8. 0. In £684 sterling how many florins ? — l^ florin is equal to 1 rixdollar, and a rixdollar is equal to 69*485 pence ster- ling? 4»w. 4139-591 florins. FRANCE. In France, accounts are kept in francs and centimes ; and sometimes in livres, sous, and deniers. Exchange with Britain about 24 francs per £. sterling, or 29id. per french crown. Usance 30 days after date, and 10 days of grace. Par with Britain is 23 francs 23 cents per £. sterling. Old coinage. 12 deniers = 1 sou. 1 ." 20 sous =1 livre. 8 livres = 1 ecu or crowo. 25 livres, or 8 cr. = 1 Louis. New coinage. 10 centimes, = 1 decime. 10 decimes, or 100 centimes = 1 franc. 2^> francs = 1 Napoleon or Louis. 80 francs = 81 livres. 1. How much sterling in 480 livres, exchange dO)d. ster- ling per french crown ? Ans, £20 6 8. 2. How much French money in £2399 7 4 sterling* ex- change 24 francs 75 cents, per £. sterling ? Ans, 59384 francs 32^ cents. 3. In £500 sterling how many livres, exchange 24 francs per £. sterling? Ans, 1*2150 livres. 4. How many livres in £893 _8 sterling, exchange 24 li- vres 25 cents per £. sterling ? Ans, 21664 Hv. 95 cents. 5. In £1000 sterling how many francs, exchange at par ? Ans, 23230 francs. 6* How many livres in 4873 francs 56 cents ? Ans, 4934 livres 47^| cents. lange 32s. 19 7 yVV exchange D9 marks. schillings 9 9i ^V- [d. 2 8 8. In is equal >ence ster- ol florins. imes; and sterling, or ite, and 10 mts per £. m. ir Louis. O^d. ster- £20 6 8. rlipg, ez« ')2i cents. |24 francs \0 livres, 24 li. [95 cents. at par 7 to francs. ^1 cents. EXCEANG£. SPAIN. 128 -«v In Spain, accounts are kept in reals and maravedis. Mo- ney is distinguished into Vellon, or copper money, and old plate, i. e. old silver ; in the last of which exchanges are transacted by the dollar of exchange. Vellon bears to Old Plate a constant ratio of 1? to 32 : thus, 32 reals vellod— 17 reals plate. Usance 60 days after date, and 14 days of grace. 34 maravedis vellon = 1 real vellon. 34 maravedis O. P. or 64 mar. vel. = 1 re&l O. P. 8 reals O. P. or 15 reals 2 mar. vel. = 1 peso, or dol. of ex. 32 reals O. P. = 1 pistole of ex. 375 mar. O. P. 11 reals 1 mar. O. P. = 1 ducat of ex. Note.— In drawing bills of exchange on Spain, it is usual to insert the word» payable in effective^ that they may not be paid in exehequet bills, which are at a consideftible discount. 1. How much sterling in 930 reals vellon, exchange d7id. per dollar ? Ans. £9 12 11| f f . 2. In £1175 18 4 sterling, how many reals old plate ex- change 90d. ? Ans. 5t878 r. 33^ mar. d. In £867 8 6 sterling, how many reals vellon exchange 36id. per peso? Ans. 66482 re. S^Vr "^^'* 4. now much sterling in 1500 reals plate, exchange 42d. ? Ans. £32 16 3. 5. How many pounds sterling are, there in 794 pistoles, eschaoge 42 pence per peso? Ans. £556 16. PORTUGAL. In Portugal, accounts are kept in milrees and rees. Exchange with Britain 60d. to 70d. per milree. — ^par 67id. Usance 90 days after sight, and 6 days of grace. 1000 rees = 1 milree. 400 rees = 1 crusado. 4800 rees = 1 moidore. 6400 rees = 1 Joannes. 1. Reduce 2496 milrees, 120 rees, into sterling money, exchange 64d. per milree. Ans. £665 12 7^ \\ str. 2. In £421 17 6 sterling, how many milrees, exchange 67id. T Ans. 1500 milrees. 8. In 012 milrees, 300 rees, how much sterling, exchange 50d. p6r milree ? Ans. £190 1 S. 4; In £2078 16 9| sterling, ho# iMuch Portuguese mon^y, cxchanM 62f d. per milree ? Ans. 7998 m. 558^. 5. What is the intrinsic talue of a Joannes, exchange at par, or 5«. 7di. ? Ans. 368. iter. w It J V, :p ■m ■ " .43 M 129 EXCHANGE. '§j 6. What is the intrinsic value of a moidore, exchange at par, or 5s. 7^d. ? - Ans. 27s..ster. '" ITALY. Money is here distinguished into lire and pezza or exchange money, or into moneta buona and moneta lungUf the former is more valuable than the latter in the ratio of 24 to 23. Ac- counts are kept in the latter and exchange transacted by the former. Par 49.455 pence. 5. 12 denari = 1 soldo. | 20 soldi = 1 lira. Venice exchanges by the ducat banco of 61 lire. Genoa exchanges by the pezza of 5§ lire. ' • ' -^ "*"' '• ' * Leghorn exchanges by the piastre of G lire. .- L^ ,'vv ' Florence exchanges by the ducat of 7^ lire. The ducat, pezza, piastre, &c. are each divided into 20 soldi, and those into 12 denari, in the same manner as the lira money. Usance 3 months afler date, and no days of grace. At Rome, accounts are kept in scudi or crowns, jiulis or paoli. Exchange with Britain by the scudo for a variable number of pence ; par 84.59 pence. Usance 2 days after ac ceptance, and no days of grace. At Naples, accounts are kept in ducats, carlins, and grains. Exchange with Britain by the ducato di regno for a variable number of pence ; par 44 pence. Usance 3 months after date, and 3 days of grace. 10 grani = 1 carlino. 10 carlini = 1 ducato. 12 carlmi = 1 scudo. 1. How much change 52d. ? 2. How many cat? 3. In 47.868 change 51|d.? 4. In £10,821 61|d.? 6. How many 51d.7 6. How many 62d.? 7. How much 3i. 4d. ? (llifr Sterling in 7860 ducats banco of Venice, ex- Ans. £1703 ster. ducats in £2014 10, exchange 51d. per du- Ans. 9480 ducats, pezze of Grenoa ; how much sterling, ex. Ans. £10,321 10 9 ster. 10 9 sterling, how many pezze, exchange Ans. 47,868 pezze. lire of Leghorn in £665 2 6, exchange Ans. 18,780 lires. lire of Florence in £132 10 6, exchanffc Ans. 8847 lires, 10 aoldi. sterling in 1102 ducats of Naples, exotiauge Ans. £188 13 4 ster. SXCHANCe. 130 :change at 27s. ster. r exchange the former D 23. Ac- cted by the . lira. led into 20 inner as the no days of tfvns, jiuUs or r a variable ays after ac- , and grains. V a variable lonths after |f Venice, ex- £1703 ster. Isid. per du- |g480 ducats, sterling, ex- |1 10 Q ster. te, exchange [7,868 pezze. 16, exchange |l8,780 lires. 6, exchanffe ies, 10 aoldi. |es, exi^iiziug^ 13 4 ster. 8. Reduce £548 14 6 staling into ducats, exchange 4s. per ducat ? Ans, 2743f ducats. DENMARK AND NORWAY. In Denmark and Norway accounts are kept in rix-doUars, marcs, and skillings. Exchange with Britain from 4 to 5 rix-dollars per £. — ^par 48. 9*67. Usance 60 days after sight, and 10 days of grace. 16 skillings = 1 marc. I 4 marcs = 1 ort. 6 marcs = 1 rix-dollar. | 11 marks = 1 ducat. 1. In £6780 sterling, how many rix-dollars exchange 4^ ? Ans, 30,510 rix-dollars. 2. In 8964 rix-dollars, 2 marcs, 8 skillings, how oiuch ster- ling, exchange 4f ? Ans, £1854 14 1^ ^| . 3. Reduce £480 sterling into rix-dollars currency, ex- change 3s. 6d. per rix-dollar. Ans, 2742^ rix-dollars. 4. How much sterling money in 1000 marcs, exchange at 4s. 2d. per rix-dollar ? Ans, 34 14 S^ ^. ' PRUSSIA. ' '■ In Prussia and Poland accounts are kept in Polish rix-dol- lars and groschen. 12 pfenings = 1 grosche. " ,; 24 groschen = 1 , rix-dollar. 30 groschen = 1 florin. In Dantzick 18 pfenir-gs = 1 groschc. Exchange with Britain at so many rix-dollars per £. ster. 1. How much Prussian money in £576 sterling, exchange 6i rix-dollars ? Ans, 3600 rix-dollars. 2. In 2925 rix-dollHrs Prussian ; how much sterling mo- ney, exchange 6^ rix-dollars ? Ans, £450 ster. RUSSIA. In Russia accounts aro kept in rubles and copecs. Ex- change with Britain by the ruble. Usance 3 months after date, and 10 days of grace. 100 copecs = 1 ruble. 1. What is the value of 1636 rubles drawn on London, exchange 4s. 5^d. ? Ans, £364 13 10. 2. Reduce £703 sterling into rubles, exchange Ss, 4d. per ruble. Ans, 4578 tubles. I I- 1^ i **■' ll' 7 ik "•■(ii ■■L 131 EXCHANGE. r SWEDEN. In Sweden exchanges are computed in rix-dollars, skillings, and fennmgs, by giving a variable number of rix-dollars for £1 sterling. The intrinsic value of the rix-dollar is 57'82d. sterling, and the par of exchange 4 rix-dollars, 7 skillings per JE. sterling. ' -.t;v 12 fennings = 1 skilling. 48 skillings = 1 rix-dollar. 1. Reduce 4963 rix-dollars, 12 skillings Swedish money to sterling, exchange at 4 rix-dollars, 24 skillings per £, ster- ling, t* Ans. £1102 18 10^ f. 2. In £1102 18 10^ f sterling, how much Swedish mo- ney, exchange at 4^ rix-dollars per £. sterling ? Ans, 4963 rix-dlls. 12 skill. *^ WEST INDIES. Accounts are kept in all the English West India Islands in pounds, shillings, and pence, currency. The currency fluc- tuates in value in all the islands except Jamaica, where the ratio of currency to sterling is as 7 to 5 ; that is, £7 Jamaica currency, are equal to £5 sterling: £140 currency are equal to £100 sterling. The Spanish dollar is the principal coin circulating in the West Indies, and it seems to be the stand, ard by which the value of all other monies is regulated. When the currency is as £140 to £100 sterling, it passes for 6s. 8d., and other coins in proportion. In Jamaica, bills on London have been sometimes at a premium of 20 per cent, above the legal exchange, and they are seldom under 10. Dollars occasionally bear a premium of 3 or 4 per cent. 1. In £960 10, Jamaica currency, how much sterling, exchange £140, per £100 sterling? Ans. £686 1 5|. 2. Reduce £686 1 b\ sterling to Jamaica currency, ex- change £140 currency per £100 ster. Ans, £960 10 cur. 3. Reduce £778 16 4 currency to sterling, exchange at £166 currency per £100 sterling. Ans, £469 3 4. 4. Reduce £469 3 4 sterling to currency, exchange at £166 currency per £100 sterling. Ans, £778 16 4. UNITED STATES OF AMERICA. ^^ In the United States, accounts are kept in dollars, dimes, and cents, and in some parts in pounds, shillings, and pence currency. Exchanges are computed in dollars and cents ; the par be- EXCHANGE. 132 ing 4 dollars 44 cents, per pound sterling, or 4s. 6d. ster. per dollar. ^'* The exchange with London is either at par, or at so much per cent, above or below par, according to the balance of trade. The gold coins of the United States are eagles, half eagles, and quarter eagles, the eagle being of the value of 10 dollars. The silver coins are dollars, half dollars, quarter dollars, dimes or tenths of dollars, and half dimes: — a cent is the only copper coin. ^ ^ . ?*• : ■ ^* 10 cents = 1 dime. 10 dimes, or 100 cents = 1 dollar (=4s. 6d. ster.) 10 dollars = 1 eagle. The current value of the dollar varies considerably in dif- ferent States. In the New England States, Virginia, Ken- tucky, and Tennessee, the dollar is worth Os. currency ; or J64 currency equal to £3 Sterling. In Pennsylvania, New Jersey, Delaware and Maryland, the dollar is worth 7s. 6d. currency ; or JE5 currency ; equal to £2 sterling. In New York and North Carolina, the dollar is worth 8s. currency ; or £16 currency equal to JE9 sterling. In South Carolina and Georgia the dollar is worth 4s. 8d. currency ; or j£28 currency equal to J£27 sterling. 1. Reduce 891 dollars 90 cents to sterling money, the ex- change being at par, or 4s. 6d. sterling per dollar. Ans, £200 13 6i f . 2. Reduce £200 13 6^ | sterling, to American states money, at par. Ans. 691 dol. 90 cents. 3. Reduce 2141 dollars, 25 cents to sterUng, exchange at 2 per cent above par, or at a premium of 2 per cent. As 100 : 102: :Q4d : 55-08 pence. As 100 cents : 55-08: 1214125 cents : £491 8 4^y ans. 4. Reduce £491 8 4^ sterling to United States money, at 2 per cent above par. . _, ♦ as above — 56*08 pence; 100 cents: : 117940*05 pence! £491 8 4^^ ans. 5. Reduce £1823 dollars, 25 cents, to sterling, exchange at 2 per cent under par, or at a discount of 2 per cent. 102 :ioo::54: VjtY* ih X VjtV X » 8 ya 5 =£402 3 9 ans. 6. Reduce £40273 9 sterling, to American United States money, exchange at 2 per cent under par. Ans» 1823 dols. 25 cents. 7. How much sterling in £1200 10 Virginian currency, exchange at £133 6 8 currency, per £100 sterling? Ans. £900 7 0. I MA m n m .M^ % n 133 EXCHANaE. 8. Reduce £900 7 6 sterling to Virginian currency, ex* change at jSl33^ currency per £ ster. Ans, J£l200 10. See Appendix No. 3. ,' ^ !> > I- BRITISH NORTH AMERICA. In the British possessions of North America, accounts are kept in pounds, shillings, and pence, Halifax currency. The ratio of currency to sterling is ^^ , that is £90 sterling arc equal to £100 currency. Bills on London generally sell at a premium. 1. In £800 Halifax currency, how much sterling, exchange at par ? Ans, £720 ster. 2. Reduce £720 sterling to Halifax currency, exchange at par. Ana. £800 Hal. cur. 3. Reduce £500 Canadian currency to sterling, exchange at 2 per cent above par, or at a premium of 2 per cent. 100 : 102: :v, 8 gallons at 7s. 7d., and with 3 gal- lons of water ; what is the value of the mixture per gallon ? s, d, 9 gal. at 5s. 4d. = 48 8 « at6 8 = 53 4 8^ « at7 7 = 60 8 3 water s. d. 28 )162 0(5 H 4 ans. 1. A erocer mixes 8 lb. sugar, at 7d. per lb. with 5 lb. at dd. per lb. and 7 lb. at Is. per lb. ; what is the price of the mixture per lb.? Ans. 9d. per lb. 2. A {ipirit-inerchant mixes 19 gallons of cognac brandy at 22s. per gaUon» and 17 gallons of wine brandy at 17s. 6d. with 10 gallons of another sort at 16s. lOd. ; what is a gal- lon of the composition worth ? Ana, 19s. 7|d ^\, 8. A maltster mixes 70 bushels of malt at IDs. per bushelf 100 bushelf at 98. 6d., 60 bushels at 9s. 2d., and 87 bushels ALLIGATION ALTERNATE. 136i ish, which mall pay. arts lead, ut on ac- use, their I cash are merchan- id weight, are used being de- I best sort ish reckon taining the I is divided les, to find divide the feed with 8 mih 3 gal- ►er gallon ? ans. th 5 lb. at rice of the 9d. per lb. I brandy at It 178. 6d. sit is a gal' 8. 7|d ^\. r bushelf 87 bushelS' at 8s. 9d. per bushel ; what is the mixture rate of a bushel ? Ans, 9s. 5id ^. 4. Eight lbs. of tea at 5s. 7^d. were mixed with 12 lbs. at 8s* 3d., and with 16 lbs. at 9s.; required the value of a lb. of the mixture ? Ans. 8s. per lb. 5. A compounder of spirits mixes 18 gallons at 3s. 6d., with 12 gallons at 5s. 7d., and 16 gallons at 4s. 4d.; at what must he sell the compound that his gain may be 10 per cent ? Ans, 4s. 91 per gal. ALLIGATION ALTERNATE. Given the rates of the mixture and simples, to find the quantity of each simple. Rule. — Write the rates of the simples under each other, with the mixture rate on their left hand. Connect, or link the rates of the simples, so that one less than the mixture-rale shall be always linked with one that is greater. Write the difference betwixt the mixture-rate and that of each of the simples opposite to that rate with which it is linked. These ^fferences, or their sum, if more than one, will be the quan- tities at the rates opposite to which they stand. How much sugar, at 4d. 6d. and 9d. per lb. must be mixed together, that the composition may be worth 8d. per lb. ? 8 ( 4—, 1 lb. at 4 = <6i 1 lb. at ,6 = (9i-'4+2=6 1b. at9 = a 4 6 54 )64(8d. proof. 64 1. How much tea at 6s. and 4s. 6d. per lb. must be mixed tegether to form a composition worth 5s. 6d. per lb. ? Ans, 1 lb. at 6s. and ^ lb. at 4s. 6d. or any quan- tities in the same proportion. 2. How much wine at 4s., 5s., 6s., and 8s., must be mixed together, that the composition may be worth 7s. ?' Ans, 6 gal. at 8s., 1 gal. of the rest. Note I.— When the composition is limited to a certain '. quantity, say. As the sum of the quantities, found as above, is to the given quantity, so is each, of the quantities found to the required quantity of each. 3; How much brandy, at 4s., 5s., and 6s,, per gallon, must be mixed together to form, a composition of 24 gallons, worth Ss. 6d. 7 Ant, 16 at 6s., 4 at tlie rest^ '.> '■Mi. » f/ m m m ^1 •i* ;i ^1 •M ^tf 1 137 ALLIGATION ALTERNATE. 4. How much snuff, at 4s., 6s., and 9s. per lb. must be mixed together to form a composition of 40 lb., worth 7a. per lb. ? Ans. 20 at 98., 10 at the rest. Note II. — When one of the simples is limited, say, as the quantity of that simple found by the n.ethod of linking is to the limited quantity, so are the other quantities found to the re- quired quantity of each. 5. How much wine, at 4s. 6d. and 7s. per gallon, must be mixed with 6 gallons, at 5s. per gallon, that the mixture may be worth 5s. 6d. per gallon ? Ans, 6 at 5s. and 6s., 18 at the rest. 6. How much brandy, at 5s., 5s. 6d., and 6s. per gallon, must be mixed with 3 gallons, at 4s. per gallon, that the com- pound may be worth 5s. 4d. per gallon ? Ans, 3 at 4s., 6 at 6s., 12 at 5s., and 24 at 5s. 6d. Remark, — As in these last two questions there are two simples greater than the mixture price, and two less, they may be linked different ways, and consequently give two different sets of answers : thus, d. 60- 8 the different sets of answers arising from these different re- sults are, however, equally correct or true answers. The an- swers already given arise from the first method of linking — those arising from the second, are — 3 at 4s., 6 at 6s., | at 5s. and 1^ at 5s. 6d. INVOLUTION. Involution is the method of finding the powers of numbers. The number to be involved is itself the first power ; or it is called the root of that power it is required to be raised to. If it be multiplied once into itself, the product is its square or se- cond power. If twice into itself, the product is its cube or third power, &c. Second and third powers of the nine digits. Ist power, or root, 2d power, or square, 8d power, or cube, 1. Raise 23 to the biquadratic, or 4th power. Ant, 279841. 1 2 3 4 6 6 7 8 1 4 9 16 25 36 49 64 81 1 8 27 64 125 216 343 512 729 the bet be s. per e rest. as the I :o the the re- fiust be re may 10 rest. gallon, le com- 58. 6d. are two ley may ]ifferent jrent re- The an- linking — ., I at 59. numbers. • ; or it is ed to. If lare or se- i cube or 8 9 64 81 312 729 f. 279841. EVOLUTION. 138 2. Raise 31 to the sursolid, or 5th power. Ans. 28629161. 3. The lineal side of a square table was 38 inches ; how many square inches did it contain ? Ans, 1444. 4. The lineal side of a cubic block of marble measures 5 feet ; how many solid feet does it contain ? Ans, 125. 5. How many f inch cubes can I get out of a 9 inch cube ? ,^ iln*. 3375. ' '• EVOLUTION. • ■». . i ' .-'-}•■ Evolution is the method of finding the roots of numbers. The square root is that of which the given number is the square. The cube root is that of which the given number is the cube. TO EXTRACT THE SQUARE ROOT. Rule. — Divide the number into periods of 2 figures, begin- ning at the place of units. Find the greatest square contained in the left hand period, and place its root in the quotient, and subtract the square itself from that period, and to the remainder annex the second period for a dividend. Double the figure in the quotient or root for a divisor ; by which divide the dividend, omitting the right hand figure, and place the result both in the root and on the right of the divi- sor ; also, by it multiply the divisor thus completed, and sub- tract the oroduct from the dividend, and to the remainder annex the next period for a new dividend. To the completed divisor add the figure last put in the root, the sum is a new divisor, with which proceed as before. * , Required the square root of 1903140625 ? 19,03,14,06,25(43625 root. 16 83) 303 3 249 i>;^:- 866) 6 'i 5414 5196 • >'»', •> 144 le number is riven nuiQ- 1. What are the two mean proportionals between 5 and 320 ? Ans 20 and 80. i. e. 5 : 20! :80 : 320. 2. What are the two mean proportionals between 64 and 512.? * Ans, 128 and 25G. 3. What are the two mean proportionals between 7 and 15379? Ana, 91 and 1183. II. To find the side of a cube equal in solidity to any given solid, extract the cube root of its solid content. 1. The solidity of a sphere is 11390.625; required the li. neal side of a cube of equal solidity. Ans, 22*5. 2. A stone of the form of a cube contains 21952 solid feet; required the area of one of its sides ? Ans. 28 X 28=784 feet. 3. Required the side of a cube equal in solidity to a globe, containing 15625 cubic inches ? Ans, 25 inches. III. Having the dimensions of a solid body given, to find the dimensions of a similar one, any number of times greater or less. Rule. — Multiply or divide the cube of each of the given di- mensions, by the number of times that the required solid is to be greater or less than the given one ; then the cube root o( each product or quotient will be the dimensions of the solid rnq- »d. L ^ water cistern is 5 feet long, 4 broad, and 3 deep ; re- quired the dimensions of another cistern that will contain 5*832 times as much ? Ans, 9 feet long, 7*2 broad, and 5*4 decn. 2. If the length of a ship's keel 1^ 44 feet, the midship beam 15, and the depth of the hold 9 ; requii'ed the dimensions of another ship of the same form* that will carry 3 times the burden ? Ans. length of keel 63*45+, midship beam 21*63+, depth 12*97 + . Note. — Similar solids are to each other as the cubes of their sides and diameters, i 3. If a ball of 4 inches diameter weigh 9^ lb.; required the weight of a similar one whose diameter is 7 inches f Ans, 50*9 lb. 4. If a cube of silver, whoso side is 3 inches, be worth J£8 17 6 ; required the side of a cube of the same silver, whoso value would bo 3 times as much ? Ans, 4*326+. 5. A mound jf earth is 660 feet long, 120 feet broad, and 208 deep ; required the side of a cubic one equal to it ? Ans, 264*446+ feet. AS -A •111 if I ;ht 145 POSITION. r<* ^i "■i f^ It! , •s| ; ii I':, 6. If a globe of 8 inches diameter weigh 18 lbs. ; what will be the diameter of another weighing 162 lb. ? Ans. 16*64 -t- inches. 7. The length of a stone is 8 feet, its breadth 6 feet, and its thickness 4 feet ; what are the dimensions of another 10 times as large, and al^o the side of a cube equal to both ? Ans. 17-235 feet long, 12'926 broad, 8'617 thick. — 12*83 feet side of cube. ^. If a ship of 300 tons be 75 feet long in the keel ; re quired the burden of a similar ship whose keel is 100 feet long^ Ans. 711*i tons. 9. There are 3 chests, the first contains 10*000 solid in- ches, the second 16,656, and the third 20,000 ; required the side of a cubical chest that will contain as much as all the three ? Ans. 36 inches. POSITION. This Rule is called Position, or Supposition, because with the help of supposed numbers, and by reasoning from them ac- cording to the nature of the question, we find the true ones. This rule is divided into two parts, — Single and Double ; in the former, one supposition is used, and two in the latter, SINGLE POSITION. Rule. — Suppose any number at pleasure, and work with it as if it were the true one, then if the result be either too little or too much, say, as the result of the position is to the posi- tion ; so is the given number to the number required. What number is that to which if we add the half, the third, and fourth of itself, the sum will be 125 ? Suppose it to be 24 i 12 i S i 6 90 125 proof. 1. A man being asked his age, said. If to my age you add i i and } thereof, the number will be 68 : what was his age ? Ant, 86 years. As 50 2 :24:a25 12 5 1^ i 60 ans. 80 20 15 POSITION. 146 2. A jockey being asked the value of his horse, said, that if from his value you take ^ and ^ thereof, the remainder will be £15 : required at what he valued his horse ? Ans, £36. 3. A gentleman bought a coach, two horses, and harness, for £150, the horses cost 5 times as much as the harness, and the coach as much as both horses and harness ; how much did he pay for each ? Ans, harness £12 10, horses £62 10, and coach £75. 4. Divide £1085, among 4 persons, A. B. C. and D. in such a manner that B. may have twice as much as A., C. three times as much as A., and D. five times as much as A. Ans, A. £98,:^. B. £197tV» C. £295|f and D. Md2^. 5. Three persons A. B. and C. discoursing about their ages, find that A. is as old again as B., B. three times as old as C. and the sum of their ages is 210 years ; required each person's age ? Ans, A. 126, B. 63, and C. 21. 6. Required a number to which i + i of itself being added, and } of the sum subtracted, the remainder shall be 76 ? Ans, 60. 7. A person after spending J and \ of his money had £72 left, what had he at first ? Ans, £240. 8. A. B. and C. purchased a house for £800, of which A. was to pay double of B., and B. 3 times as much as C. what should each pay ? Ans. A. £480, B. £240, C. £80. 9. The number of fruit>trees in a garden was 252 ; there were ^ more bearing apples than pears ; the number of those bearing plums was f of those "bearing pears, and the number of those bearing cherries ^ of those bearing plums ; how ma* ny were there of each ? Ans, 80 apple, 60 pear, 48 plum, 64 cherry. 10. A young gentleman was lefl a fortune, — ^ of which he spent in gambling, } among his companions, ^ on a house and furniture, ^ on a stud of horses ; he then finds that he has only £4240 remaining, what was his fortune 1 .,. ., Ans, £10176. ,.: iL r '\ DOUBLE POSITION. Rule- — Make two positions, and proceed with each ac- cording to the nature of the question ; Tmd how much the re- suits are diflferent from the given number ; then multiply each of these difTerences or errors* by the other's position, and if the errors be both too much or too Httle» divide the difference of the products by the difference of the errors ; but if the one error be too much and the other too Uttlo, divide the sum oC n3 • :' m i 1. .,' M fe,^ i'il?-a / 147 POSITION. 1 V ' ;f:: )i 'i the products by the sum of the errors, aiid the quotient will be the answer. ,.^ ... A. B. and C. playing a game at cards for 1296 crowns, disagreed about ihe game, and the money being upon the ta- ble, each seized as much as he could ; B. got 60 more than A., and C. got ^ of both their sums ; required how much each got? Suppose A. got 200 Suppose A. got 600 B. got 260 B. got 660 ,• , . / '- C. got 92 C. got 252 i ^ 552 too little by 744. 1512 too great by 216. Errors. — 744 X 600 =446400 + 216 X 200 = 43200 960 )489600(510 A. 510 V B. 570 > answers. C. 216 i 1296 proof. 1, What number is that, which being multiplied by 7, and lessened by 30, if the remainder be divided by 5, the quotient will be the same as the required number 1 Arts. 15. 2. Three men, A. B. and C. have £36 to be divided among them, so that B's share shall be £4 more than f of A's., and C's. £5 more than f of B's.; required their shares? V * Ans. A. ll^J^, B. IIW, C. 13/^. 3. If to my age there added be, , - One-half, one-third and three-times three. Six score and ten the sum will be ; What is my age, pray shew it me ? Ans. 66. 4. A gentleman has two horses, Diamond and Swift, and a saddle worth £50, which, when set on the back of Diamond, makes his value double that of Swift ; but when set on the back of Swift, makes his value triple that of Diamond ; re- quired the value of each horse ? Ans. Diamond £30, Swift £40. 5. A miser having about him a certain number of crowns, said, if ^ + i + i + -iV °^ ^^** ^^ '^^^ ^®'® added to 10 the sum would be 45, how many crowns had he? Ans, 72. 6. A farmer being asked how many sheep he had, an* swered, that he had them in five fields, in the fir»t he had \ of his flo next year to give him 2 sovereigns, on the same day the third year 4 sovereigns, and so on, always doubling his payment for 20 years : required how much the 1000 acres would cost him, not counting interest ? Ans, 1,048,575 sovereigns. 5. A servant agreed with a master to serve him 11 years, without any other reward than the produce of a wheat grain for the first year, that product to be sown the second year, and so on from year to year till the end of the 11th year ; re- quired the sum of the whole produce, allowing the increase to be in a tenfold proportion ? Ans. 111111111110 grains of wheat, or 2260561^ bushels, at 5s. per bushel=£56514 7^, reward. Note. — 7680 grains of wheat fill a pint. MULTIPLICATION OF DUODECIMALS. This rule is chiefly used by artificers in taking the dimen- sions and computing the contents of their work. Feet multiplied by feet give feet. Feet multiplied by inches give inches. Feet multiplied by seconds or parts give parts. Inches multiplied by inches give parts. fi'i ! h- : '^M it-'-Jf i m ■I J. '. *li4 m ;.>* ,•>:^^ m m 153 MULTIPLICATION OF DUODECIMALS. I , i-^i., 1*: Inches multiplied by parts give thirds. Parts multiplied by parts give fourths. •' " 12 fourths make 1 third. 12 thirds make 1 part, or second. 12 parts make 1 inch. 12 inches make 1 foot. Rule. — Place feet under feet, inches under inches, (fee. ; ' then multiply the lowest denomination of the multiplicand by the highest of the .multiplier, setting dovirn the products ac- cording to the above table ; proceed with the less denomina- tions of the multiplier in the same manner. Multiply 11 feet, 5 inches by 7 ieet, 6 inches. ... . ft. in. 11 5 7 6 Multiply 7 feet 6 inches 4 parts by 5 feet 7 inches 8 parts, ft. in. p. ;,-, 7 6 4 .. --■ 5 7 8 79 11 5 8 6 ,, 85 7 6 ans. 37 7 8 4 4 8 4 2 8 42 5 4 6 San. 1. Mult. 7 2. « 6 Ans, M (( (( 3. 4. 5. 6. 7. « 8. 9. 10. 12 11 17 6 26 « 108 « 20 « 175 11. « 78 12. « 63 13. « 91 ft. 4 in. by 4 ft. 2 in. ft. 7 in. by 9 ft. 3 in. ft. 5 in. by 4 ft. 9 in. ' ft. 10 in. by 12 ft. 10 in. ft. 9 in. by 13 ft. 6 in. ft. 4 in. 7 pts. by 6 ft. 7 in. 3 p,« ft. 3 in. 4 p. by 10 ft. 6 in. 7 p." ft. 7 in. by 5 ft. 7 in. 8 p. ft. 8 in. 4 p. by 8 ft. 7 in. ft. 6 in. 3 p. by 16 ft. ft. 11 in. 4 p. by 7 ft. 8 in. 3 p. ft. 4 in. 8 p. by 8 ft. 9 in. 6 p. ft. 4 in. 9 p. by 9 ft. 7 in. 9 p. To find the area of a board. i< « it u u u « (( « u ft. in. p. /// //// 30 6 8 60 10 9 ; .- 58 11 9 151 10 4 •y ■ 239 7 6 42 1 9 2 9 277 2 3 11 4 612 3 5 8 177 7 6 4 2808 4 606 10 7 8 557 3 7 4 881 7 9 9 Case I.— ' Rule. — Multiply the length by the mean breadth. 1. What is the area of a board 10 feet 3 inches long, and 1 foot 6 inches broad ? Ans, 15 feet 4 inches 6 parts. 2. Find the content of a board 15 feet 1 inch long, and 17 inches broad. Ans, 21 feet 4 inches 5 parts. 3. Required the content of a deal 57 feet 8 inches long, and 2 feet 7 inches 3 parts broad 1 Ans, 150 ft. 2 in. 1 pt. MVLTIPLICAtlON OF DUODECIBiALS. 154 4. How many superficial fe^ in a buara 18 feet 2 inches by 2 feet 11 inches ? Ans, 38 fem 11 inches 10 parts. 5. Required the content of a board 2# feet 4 inches long, 2 feet 6 inches broad at one enu. waA I foot 10 inches at the other. Jmt. 44 feet inches 8 parts. 6. What is the area of a bo««i 30 feet 8 inches long, and its mean breadth 3 feet 4 inches ' Ans. 102 ft. 2 in. 8 pts. 7. Required the superficial content of a fir deal 18 feet 10 inches long, and 1 foot 4 inches 3 parts broad ? Ans. 25 ft. 6 in. OJ^ pts. Case II. — To find the solid content of squared timber. Rule. — Multiply tne mean breadth by the mean thickness, and the product by the length, gives the solid content. 1. How many solid feet in a log of wood 26 feet 8 inches long, 3 feet 2 inches broad, and 2 feet 1 inch deep 1 Ans, 175 ft. 11 in. 1 pt. 4'". 2. How many cubic feet in a stone IB f, , 9 in. long, 2 ft. 11 in. broad, and 1 ft. 9 in. deep ! Ans. 70 fl. 2 in. 2 pts. 3'''. 3. Required the content of a fir log, the length 27 ft., the mean breadth 1 ft. 10 in. and the mean thickness 1 ^ ft. Ans. 81ft. lOin. 6pv:. 4. Required the solid content of a stone 3 ft. 11 in. thic'., 7 ft. 9 in. broad, and 13 ft. 8 in. long. Ans. 414 ft. 1 fn. 1 pt. 5. Find the content of a log of timber, its length being 25^ feet, and its mean breadth and thickness each 20 in. Ans. 70f feet. 6. Required the solid content of a log of mahogany 7 feet 8^ in. broad, 9 ft. 5^ in. thick, and 58 ft. 6 in. long. Ans. 4247 ft. 4 in. 1^ pts. 7. How many solid feet in a block of marble 4 ft. 8 in. long, 8 ft. 11 in. thick, and 2 ft. 3 in. broad? Ans. 41 ft. 1 in. 6 pts. 8. Required the solid content of a beech log 19 ft. 4^ in. long, 2 ft. 3^ in. broad, and 9f in. thiol;: . Ans, 3' ft. 4 in. 0^ pts. Case III. — To find the solid content of round timber. Common Rule. — Take ^ of the m'lan girt and multiply it by itself, and the product by the length for the solid content. Note. — This rule gives the content too small by 3 feet on 11, yet it is universally used in practice, and was originally introduced to compensate the purchaser of round timber for the waste occasioned by squaring it. The true Ruki though never used, is — Take one fifth of the girt and multiply it by itself, and the product by twice the lenth for the true content, o ' >1 1 i- m m 'a" " lii ^i 155 EXERCISES IN ASTIFICERS* MEASURING. 1. Find the content of a piece of round timber, its length be- ing 10 feet, and its mean girt 60 inches. Ans, 15f feet. 2. How many solid feet are in a tree, its length being 25 feet, and its mean girt 6 feet ? Ans, 56^ feet. 3. Required the content of a tree 24 feet long, and its girts at the ends 14 and 2 feet. - Ans. 96 feet. 4. How many solid feet in a tree 26 ft. 8 in. long, and its mean girt 6 feet ? Ans. 59 ft. in. 9 pts. 5. Required the content of a tree 48 ft. long, and its girts at the ends 60 and 18 inches. Ans. 31*6875 feet. M EXERCISES IN ARTIFICERS' MEASURING. Note. — 36 square yards are termed a rood of building, and 100 square feet are called a square of flooring. The standard thickness for brick-walls is 3 half bricks, and for stone walls 2 feet. 1. Find the expense of ceiling a room at 6d. per yard, the length being 20 ft. 9 in., and breadth 15 ft. 4 in. Ans, 17s. 8^d. 2. What will be the expense of painting the outside of 5 windows, each 6 feet 3 in. by 3 ft. 8 in. at 7d. per yard, to be paid for as work and quarter ? Ans. 9s. 3^d. 3. Find the expense of glazing a window, at Is. 6d. per foot, its day-light measure being 5 ft. 11 in. by 3 f\. 5 in. Ans. 30s. 3|d. 4. A log of wood, 14 ft. 10 in. long, was sawed into 7 deals, each 2 fl. 11 in. broad ; how many square feet did they con- tain ? Ans. 302 ft. 10 in. 2 pts. 5. What is the solid content of a box, 7 ft. 9 in. 3 pts. long, 2 ft, 3 in. 6 pts. broad, and 1 ft. 11 in. 11 pts. thick ? Ans. 35 ft. 5 in. 10|ff ^ pts. 6. A window measures 7 ft. 8 in. 6 pts. by 4 ft. Of in. ; how many square feet does it contain ? Ans, 37 ft. in. 6^ pts. 7. What is the expense of a common brick floor, measur- ing 35 feet 5 in. by 34 ft. 11 in. at 2s. 2d. per square yard? Ans. £14 17 8^. 8. What is a marble slab worth, whose length is 5 ft. 7 in., and breadth 1 ft. 10 in., at 6s. per foot? Ans, £3 1 5. 9. A round pillar is to be painted, whose height is 18 ft. 4 iri., and the girt 10 ft. 6 in. ; how many square yards are in it? Ans, 21 yds. 3 feet 6 in. 10. What is the difference of the areas of the floors of two rooms, the one 42 ft. 8 in. by 30 ft. 2 in., the other 28 ft. 5 in. by 19 ft. 7 in, ? Ans, 730 ft. 7 in. 6 pts. 11. The canal which joins the Forth and Clyde is 27 miles long, 36 feet broad, and mean depth 7 feet ; required the num- ber of cubical yards of excavation. Ans, 1,330,560 c. yds. 2lj in laid bfoc yan who R sel, lengg »th be- 4 feet, ing 25 )\ feet. its girts »6 feet, and its . 9 pts. its girts 75 iieet. G. ing, and cks, and ard, the .7s. 8^d. ide of 5 ird, to be 9s. S^d. 6d. per 5 in. )0s. 3|d. o 7 deals, hey con- in. 2 pts. pts. long* 9| in. ; in. 6| pts. ', measur- are yard 1 4 17 8i. J ft. 7 in., £3 1 6. is 18 ft. 4 rds are in feet 6 in. )r8 of two er 28 ft. 6 in. 5 pts. 8 27 miles d the num- 60 c. yds. TONNAGE OF SHiFiS. 156^ 12. How many bricks will build a wall 60 feet long, 8 feet high, and two bricks thick, at the rate of 140 bricks per stand, ard square yard ?* Ans. 9955f . ~ 13. How many square yards of standard brick- work are in a wall, 40 ft. 6 in. long, 22 ft. 9 in. high, and 2]^ bricks thick ; and what is the expense of the materials and workmanship, at 8s. 6d. per square yard ? Ans. 170f yds.— £72 10 3^. 14. What length of a stone wall, which is 4 feet high, will make a rood ? Ans. 81 feet. 15. What will be the expense of lining a water cistern 2 ft. 10 in. long, 2 ft 6 in. deep, and 2 ft. broad, with sheet lead, 10 lb. to the square foot, at J£l 18 9 per cwt. ? Ans, £5 3 2i Jf . 16. How many square yards of standard brjck-work in a wall 75 feet long, 15 ft. 9 in. high, and three bricks thick ? Ans. 262 yd. 4 ft. 6 in. 17. What is the value of 5 Oak planks, at Is. 9d. per foot, each 17 ft. 6 in. long, and whose breadths are, two of them each 1 ft. 1 in. 6 pts. in the middle ; the third 1 foot 6 in. in the middle ; the fourth 11 in. 3 pts. ; and the fifth 1 ft. 2 in. 3 pts.? Ans. £8 19 11. 18. Find the expense of digging a cellar, the length of which is 40 ft. 4 in , breadth 25 ft. 7 in., and depth 9 ft. 9 in., at 6d. per solid yard. Ans. £9 6 3^ 19. A piece of ground, measuring 25 ft. 3 in. by 6 ft. 7 in. is to be paved with stones, each measuring 1 ft. 5 in. by 8 in.; how many stones will it requirp, and what will be the expense at Is. 3d. per square foot? I'^Oy^y stones. £12 9 4}. 20. How much plastering on a partition 7 ft. 8 in. long, and 10 ft. 3 in. high, deducting a door 6 ft. 3 in. by 2 ft. 10 in. ; and what will it cost at 5d. per square yard ? Ans. 6 yd. 6 ft. 10^ in.— Cost 2s. 9d.^ V*? • * Note. — To reduce a brick-wall of any thickness to stan- dard thickness, muhiply by the number of half bricks in the thickness, and divide by 3, , 21. One has paved a rectangular court yard, 42 feet 9 inches in breadth, and 68 feet 6 inches in length ; and in it he has laid a foot way the length of the court yard, and 5 feet 6 inches broad ; the foot way is laid with purbeck stone, at 3s. 6d. per yard, and the rest with pebbles at 38. per yard ; what will the whole come to? Ans. £49 17 OJ. TO FIND THE TONNAGE OF SHIPS. RuLi?. — ^*ultiply the length of the keel, taken within the vcs. sel, or ns much as the ship treads upon the ground, by the length of the midship beam, taken also within, from plank to m M ■"il III *• r i W m ■4'IS'' °^' a IE I. I , m i i 157 PEBMUTATION. • .1 :"i SI plank and that product by half the breadth, taken as the depth ; then divide the last product by 94, and the quotient will give the tonnage. 1. If the length of a ship's keel be 80 feet, and the midship beam 30 ; required the tonnage. Ans, 382 ||. 2. If the length of a ship's keel be 87 feet 6 inches, and the midship beam 2& feet 8 inches ; required the tonnage. Ans. 382|^f . 3. What is the tonnage of a ship whose keel is 160 feet, and midship beam 30 ? Ans, 765|i^. PERMUTATION Is a name given to the number of changes of order or position,, of which two or more things are susceptible. Rule. — Multiply all the terms of the natural series of num^ bers, from one up to the given number of things, continually together, for the number of permutations sequired. 1. How many changes can be rung on a chime of 8 bells ? 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8=40320 ans. 2. How many permutations can be made of the 9 digits ? Ans. 362880. 3. How many permutations can be made of the letters in the yAord authorised! Ans. 3628800; 4. How many changes can be rung on 12 bells, and how long would it take to ring them at 10 per minute, counting the year 365 days, 6 hours ? Ans, changes, 479001600 ; — time 91 1- years*. MISCELLANEOUS QUESTIONS. 1. A gentleman has a garden in the form of a parallelo** gram, whose dimensions are 64 fathoms by 36, he intends to have a square one of the same area ; required the side of the square. ^ Ans, 48 fathoms. 2. 90 noay be so divided, that the first part increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, shall all be equal ; required these parts. Ans, 18,22,10,40. 8. I have received advice from my factor, that he has dis. burscd on my a count the sum of 4000 guilders, 15 stivers ; I demand what sum I must remit for that in English money, exchange 33s. 4d. flemish per £, sterling, and also what his commission comes to at 2 per cent. Ans, £400 1 6— com. £9j^v» 4. There are two towera on a plain, the one 240 feet hish, and the other 180 ; a ladder placed in the line of distance be. t ween them, 215 feet from the bottom, of the lowest, will touch Ion ho^ ceili 8qu( i depth ; irill give midship 382 tf . and the 382fH- reet, and 765H- position,' I of num- ntinually 8 bells ? 1320 ans. digits? 362880. ers in the 3628800i and how counting I t- years*. parallelo*- intends to tide of the fathoms. Ased by 2, 2, and the [;se parts. 1,22,10,40. le has dis« stivers ; 1 sh money, what his ) feet high, istance be- will touch MtSCfiLLANEOUS EXERCISES. 158 the top of both towers : required the length of the ladder, and the distance between the lowers. Ans. 280.4+ feet, length of ladder, 360 feet distance. 5. If a ship of 72 tons burden be 45 feet long in the keel, 17*3 in breadth, 8'7 in depth ; required the dimensions of a similar ship that will carry 5 times as much. Ans. length 76'94-l-, breadth 29-.'>8+, depth 14-87 4-. 0. A court yard is 50 feet long, and 40 feet 6 inches broad; what will the paving of it cost, at 8s. 7^6. per square yard ? Ans, £40 15 7^. 7. If a house have 3 tier of windows, 4 in a tier ; and if the height of the first tier be 6 feet 3 inches, of the second 5 feet 4 inclies, and of the thira 4 feet 9 inches, and the breadth of each 3 feet 6 inches ; what will the glazing come to, at 1 5d. per foot? Ans. JE14 5 10. 8. A gentleman on his travels, received at Paris 12250 francs for a bill of exchange, the value of which in England was JE500 ; what was the course of exchange between England and France ? Ans. 24 francs 50 cents. 9. A square plantation, where the trees are 12 feet distant, contains 108900 trees : what is the length of the side, and how many acres does it contain ? Ans. 1316 yards, 357ff| acres. 10. There are tv.o circular ponds in a gentleman's pleasure ground ; the diameter of the smaller is 100 feet, and the greater is three times as large ; what is its diameter ? iliw. 173-2 -f feet. 11. There are two columns in the ruins of Persepolis left standing upright ; the one is 64 feet above the plain ; and the other 50 ; in a straight line between these two, stands an an* cient small statue, the head of which is 97 feet from the sum- mit of the higher, and 86 feet from the top of the lower, the distance of the base of which column from the centre of the statue's base is 76 feet ; required the distance between the tops of the columns. Ant, 157+ feet. 12. What will the digging of the foundation of a house 68 feet long, 33 feet broad, and 5 feet deep, come to at Is. 3d. per solid yard ? Ans. 415{^ yd., £25 19 5^. 13. (low many yards of painting in a room 45 feet 6 inches long, 24 feet 10 inches broad, and 13 feet 4 inches high, and how much will it cost, reckoning the white-washing of the ceiling at l^d. per square yard, and the rest at lO^d. per square yard 7 Ans. ceiling 125 yd. 4 (i. ll=16s. S\ VV* ^^^^^ ^^^ yd. 3 ft. 6f in.=£9 2 4-|f or cost io all £9 1% Ok i|. "ml M M m ' •■ I* It,, . ' m ^ { Hj * . >i '1 'M .<■ A' 150 KISCBLLANEOVS EXERCISES. - 4.4. K ti I iH " s hes diameter, weigh 13^ lb., what will be .!.e '^•araeti L .>i j. bull that weighs 62^ lb.? -4n«. 10 inches. 15, ' a slup*s keel be 125 feet long, the midship beam 25, iiiii Vre depth of the hold 15; required the dimensions of another Hini of th-^ ?,vwe form, that will carry but half the quantity. Ans. length of keel 99*2+ ft., midship beam i9-84+feet, depth of hold 11-9+feet. 6 'me being asl n his age, said, if f of the time I have !"v '? _. irJiltinlied by c , and f of the product be divided by 4, I ^. jOn Jibe ; what was his age ? Ans. 56. i*? \ y-j:i,. -m^ spnt an order to his grocer for 1 cwt. sugir ■ ' ' ' 3r L», the grocer has none at that price, ihougJi pleiiiy Td.^ 9d., and lid., per lb.; how many lbs. at each of these j- ces must he mix together to execute the or- der? Ans. 16 lbs. at 7d., 16 lbs. at 8d., and 80 lbs. at lid. 18. A gentleman bought a house, with a garden, and a good horse in the stable, for J£500 ; now he paid 4 times the price of the horse for the garden, and 5 times the price of the gar- den for the house : what did the house, the garden, and the liorse, severally cost him ? AnSi the house £400, the garden J&80, the horse £20. 19. Fow many days can a company of 12 persons sit in a ditlerent position round a table at dinner, and what would be tlie whole expense, supposing each dinner cost 32s. 6d. ? Ans. 479001600 days, £776377600 expense. 20. An Indian, named Sessa, having invented the game of chess, shewed it to his king, who being highly pleased with it, hid him ask what he would have for the reward of his ingenu- ily ; Sessa, with great modesty, asked, that for the first little square of the chess board he might have one grain of wheat given him ; for the second two, and so on, doubling continu- ally according to the number of squares on the board, which %*icre 64 ; the king, who intended him a noble reward, was displeased that he asked, what he thought, such a trifle ; but Sessa declaring ho would be contented with it, it was ordered to be given him ; the king was astonished when he found that tliis would raise so vast a quantity, that the whole world could not produce it ; required the number of grains, and what they would amount to at 10s. Sfd. per bushel. Ans. 18446744073709551615- grains, at 10s. d|d. per bushel, come to £19351404648857 11 10|. Note. — 7680 grains of wheat fill a pint. will be inches. jam 25, another ,ntity. I 9 + feet. 3 I have led by 4, Ins. 56. r 1 cwt. It price, y lbs. at 3 the or- . at lid. id a good the price the gar- , and the rse £20. B sit in a would be a? expense. game of d with it, ingenu- irst little of wheat continu- d, which ard, was ifle ; but ordered und that rid could ^hat they QUESTIONS FOR EXAMINATION. QUESTIONS FOR EXAMINATION. 160' What is meant by exchange ? What do you mean by the par of exchange ? What do you mean by the course of ex- change ? Is the course of exchange not always the same as the par of exchange? What is the meaning of agio? — of usance ? What do you mean by days of grace ? How does Britain exchange with Holland? — with Hamburgh? — with France ? — with Spain ? — with Portugal ? — with Denmark and Norway ? — ^with Prussia and Poland ? — with Russia ? — with Sweden ? — with the United States of America ? — with Canada ? Are Usance and days of grace different in all these countries ? What is the meaning of Alligation ? What is the meaning of Involution ? What is the meaning of Evo- lution ? What do you mean by the square root ? What do you mean by the cube root ? Why is the rule of Position so called ? What is Arithmetical Progression ? Mention an increasing series in Arithmetical Progression. A decreasing series. What is Geometrical Progression ? Name an in- creasing series in Geometrical Progression — a decreasing series. What is the use of Multiplicatipn of Duodecimals t How is the Tonnage of ships found ? What is meant by Permutation ? . '■. I i III 't'" # -■'i/ii .w m M 11 lOi. t - . ■ > f_ APPENDIX. No. I. BOOK-KEEPING BY SINGLE ENTEY. In Book-keeping by Single Entry, only two books are ne- cessary ; — ^the Day-Booh and the Ledger. In the Day-book are recorded, promiscuously as ^hj-y hap- pen, what goods are sold on trust, and what money or goods are received. In the Ledger are inserted the several accounto belonging to each person, which lay dispersed in the Da}- -book, and are arranged in their proper order of Dr. and Cr. : the left hand side of every folio being appointed for the Dr. and the riglit for the Cr. An Index is prefixed to the Ledger, coutaining he names of the persons whose accounts are in it. • DntECTIONS FOR THE LBAENER. * Copy into iIk: Day-book one month's accounts, and calculate them by their proper rules. Then begin with the first account of the Day-book, and post it into the Ledger, leaving a space below it to contain more accounts ; if Dr., write on the Dr. «ide To GoodSf or Cash : if Cr., write on the Cr. side By GoodSf itr Cash ; next enter the name in the Index under the first letter of the surname ; and lastly write the figure deno- ting the folio of the Ledger, where it is placed opposite to the account in the Day-book. Do the same with ?11 the first month's accounts, and then copy the second month's into the Day-book, and calculate and post them in the same manner : and proceed thus until the whole be finished. Note. — Before posting an account, look into the Index, to see if the name be there ; if it is, post the account in the space below it : and should any soace be filled up, you must open A new account, and transfer the balance of the former one to il. 3 are ne- hey hap- or goods )eIoiiging :, and are left hand the riglit. outaining 1 calculate St account [g a space »n the Dr. . side By under the ure deno- >site to the the first s into the manner : I Index, to I the space must open it one to il. DAY-BOOK. (to Hamilton, Jan. 1, 1840. WiUiam Johnson^ Dr, 29 bushels wheat, (S) 12s. 6d. 72i do. malt, " 10 2 41 do. barley, ..••••..«•" 5 1 67 do. oats, " 4 162 // Robert Jenkinsoui Dr, 1074yds. brown cloth, ••.»^...'® 4s. 6^d. u Joseph WakefieUf Dr. 4^ lb. green tea, •• ® 10s. Od. 9|lb.bohea, " 9 10 6 oz. nutmegs, " 6^ 10^ oz. black pepper,... " 2^ 19ilb.soap " 10 15 Jonathan Wintertont Dr, &\ gallons brandy, (S> 26s. Ul do. red port " 18 13 do. Malaga " 20 17| do. Lisbon, " 19 7 do. Mountain, " 21 24 Henry GoodfelloWf Dr, 6 gallons Rum, • •••••^ 18s. 10| do. Qin '' 20 £, 78 242 16 15 8 57 19 d. 4i. 7 H 6 m ,''■«! ^1 ■•;# '4i Ifi t; I 163 DAY-BOOK. Hamilton, Jan. 26, 1840. Andrew Tomlinson, Dr, . 11 pairs black Silk Stockings,..^ 18s. Od. 9 do. white do. do. .."24 19 do. Worsted do. ,," 4 17 do. Cotton do. ,," 5 6 // Jolm Westerleyt Esq., Dr. ' 27 pairs Harrateen Hangings, (3) 96s. lOd. 19 do. Cotton do. " 59 4 28 Joshua Housekeeperf Dr, 27 bush., 3 pecks pea^e, • • ro) 9s. per bush. 4 do. 2^ do. tares,..." 14 do. _—__>- Feb. 1. — — — Humphrey Armstrongt Dr, 7 thousand quills,. ,.,(S> 2s, 9d. per hund. 21 reams paper, " 1 3 per quire. _ — 8 — Thomas BarrowmaUf Dr, 17 stones sbap, f® lOd. per lb. 15 _^ — _ — Mrs, Arabella Farmer, Dr, 19^ yards Flanders Lace,. • »*fa) 12s. lOd. 30 do. Ribbon, " 1 U 4 Fans, " 5 6 Sarcenet Hoods, " 8 11 21 The Hon, Lord George Mountain, Dr. 17 hhds. Wine,. 'S £54 1 6 (2.) £, s. d. 29 6 187 10 15 14 6 35 9 17 18 6 19 910 9 5i 6 (2.) 9» d. 29 6 87 10 15 14 a 35 17 6 9 18 )19 DAY-BOOK. (3.) Hamilton, Feb. 21, 1840. Lady Lustring, Br, 6 pairs Lamb Gloves, (S> 2s. S^d. 8 pairs Kid Gloves "2 6 24i yds. Muslin, " 6 10 __ 24 Miss Louisa Darlington, Dr, 17f yards red Silk, (S> 10s. 2d. 20 yards brocaded Satin, ••.." 19 6 14^ yards flowered Silk, " 6 9 8 yards black Silk, " 4 2 20^ yards Silk damask, " 16 10 Mar. 4. — Joseph Wilmotj Dr. 8 stones Bacon, (3) lOd. per lb. ., 15 _ < Sir Henry Greatman, Dr. 4 table sets China, ^ 54s. 9d. 2^ dozen Plates, " 55 14 Coffee Cups,.. . . • ,(S) 10s. 6d per doz. 7 large Dishes,. . • (3> 14s. lOd. n __«__^______ Gregory Emerson, Dr. 28 English Readers ^ 2s. S^d. 16 Euclid's Elements "7 6 23 — Gregory Emerson, Dr. 32 bushels Wheat, (S) 12s. 6d. 164 £. s. d. 4 9 19 H 51 18 9 13 23 1217 9 20 i if Mi I i 165 DAY-BOOK. (4.) — . Hamilton, Mar. 30, 1840. James Newcastle, Dr, 17 doz. Penknives, (S) I5s. 29 Fire-shovels, " 3 7d. 1 6 Candlesticks, " 6 l^d. Apr. 4 Alexander Penrith, Dr. 96^ yards Nankeen, (S) 2s. 4d. 33^ yards super, blue cloth,.. •" 38 27^ yards super, drab do " 34 24 yards super, red do " 63 10 Cr, Thomas Barrouman, By Cash in full, '. 16 Miss Louisa Darlington, Dr, 83^ yards figured Silk, (a) 8s. 20 Miss Arabella Farmer, Dr. 120 yards Ribbon, (S) 7^d. 36 yards Camlet, " Is. 9 36 yards Crape, " 1 8 60 yards Bombazine, " 4 40 yards grey stuff, " 1 9 _ 25 . WiUiam Ogle, Dr. 28^ yards sup. blue cloth, , ..(S 36s. 15| yards sup. blue grey, '' 34 28^ yards sup. raven grey, " 34 £. s. d. 22 16 11 197 9 16 13 6 25 8 128 10 6 (4.) I. \s.\d. 22 1611 197 9 18 13 6 26 8 12810 6 (50 DAY-BOOK. 166 Hamilton, 27 April, 1840. Sir Henry Greatman^ Dr, A Silver Cup, wt. 47 oz., 16 dwt., gr. > (a) 7s. 6cl. per oz ^ A Silver Punch Bowl, wt. 16 oz. 17 dwt. 12 gr. (ri) 6s. lOfd 3 doz Spoons, wt. 30 oz. 18 dwt. gr. (a> 7s. 2d 8 Candlesticks, wt. 51 oz. 4 dwt. 6 gr. (a) 7s. 5d 10 Plates, wt. 67 oz. 13 dwt. gr. (w Os. 7d. 29 Cr, The Hon. Lord George Mountain, By a Bill on Messrs Douglas, & Co. // Lady Lustring, Dr, 20 yards Calamanco, • . . .^ Is. 5d. 25 yards Persian, " 3 6 21 yards Lawn. " 7 6 22 yards Cambric "18 May 1. George Trader, Dr, 894 yards Check, (S Is. Od. 183 yards Check, " 1 2 434 yards Check,. " 1 1 253 yards Check, " 1 1^ Cr, William Johnson, ByCash, £78 By abatement, 16 // Nicholas Cheesemonger, Dr, 8 cwi, 2 qr. 17 lb. Cheshire Cheese, > ; (S> 84s. per cwt., ....^ 1 cwt. 3 qr. 141b. Gloucester do. ® 74s. 8a 4 cwt. qr. 16 lb. Suffolk do. "65 4 6 cwt. 2 qr. 20 lb. Yorkshire do. " 56 5 £. 76 250 s. d. 41 33 93 78 54 9 16 H 11 lliii'i M i:i ■m •I I m m ■M 167 DAY-BOOK. (6.) Hamilton, 6 May, 1840. Moses Greenwellt Dr. 31 yards Worsted White Shag,. ,(a) Is. 9d. 30 yards Worsted Blue Shag,.. . ." 1 10 30i yards Worsted Blue Shag,.. ." 1 11 31 yards Worsted Scarlet Shag,.." 2 8 16 yards Worsted Blue Hair Shag," 5 9 12 Miss Louisa Darlington, Dr. 24 yards Ducape, (S) 7s. 6d. . 1 11 yards Brocade, " 9 8 10^ yards Lustring, " 5 3 4| yards Persian, " 1 9' 19 Joseph Wakefield^ Dr. 4 lb. Green Tea, (3> 10s. Od. 121b. Bohea, " 10 Olb.Pepper " 2 9 8i lb. Coffee, " 2 9 7 lb. Raisins, ... .• " 1 6 i.3- ?»-•«« 27 Cr, Robert Jenkinsonj By cash ih full...... June 6. Joshua Housekeeper, Dr. 6 qrs. Oats, (S) 4s, Od. per bush.; // // 18 bush. Pease, 12 bush. Beians, 19 bush. T«ires, " 7 qrs. Malt, " Vb ib. Hops, I* ..••<•• 9 7 14 10 1 6 2 do. do. do. do. 6 pdr lb. £. 5. d. rs!i 17 4i 17 9 10 17 Hi 242 15 4i 65 (6.) e. J. I d. 17 2 4i 17 9 4 10 17 IH 242 15 4i , 651 7 (7.) DAY-BOOK. 168 Hamilton, 11 June, 1840. Erasmus Gordmit J)r, 14 cwt. Flax,.,. (3> 12s. per stone, // Cr, Humphrey Armstrongj By Cash in fi-ill, , 19 William. Johnson, Dr. ,6 I'iAsts Barley,. . . . . ..^ 5s. Id. per bush. 25 ^'Andrew Harrison, Dr. 27 Cuklf Skins (^ 7s. Od. 75 Sheep Skins, " 3 6 30 Sheep Skins, " 3 9 15 Buck Skins, "21 17 Russia Hides,. "20 9 120 Lamb Skins, " 2 4 July 7 je. s. 6 John Montague, Dr. 19 gallons Gin, (^ 6s. 6d. per qt. 20 ankers Brandy, " 25s. per gal. 12 Thomas Merchant, Dr. I cwt. 2 qr. 18 lb. pepper, O 3s. 4d. per lb. cwt. 3 qr. 14 lb. cloves,." 16s. " 30 cwt. 1 qr. 7 lb. raisins,." 140s. per cwt. 4 cwt. 2 qr. 19 lb. soap,. .." 93s. 4d. " 14 6 Joshua Housekeeper, Dr» 27 dozen lb. Candles,. . . . .^ lOd. per lb. 67 d. 35 17 122 76 6 274 14 343 13 10 0i p. ,"i' .■..(III 1^: ■^4 169 DAY-BOOK. (8.) Hamilton, July 14, 1840. Cr, Sir Henry Greatmarif " By 14 lasts Wheat,. . . .^ lis. 9d. per bush. 20 " ...." 12 6 " 20 The Hon. Lord George Mountairit Dr. 6 puncheons rum,. ,,,(S) 17s. 9d. per gal " «___ Miss Louisa DarlingtoHf Dr. ' I Of yards Satin, (S 9s. 6d. 15 yards Brocade, "10 8 II Scarfs, "10 14 yards Genoa Velvet, "17 4 10 yards Lustring, " 5 2 __ 26 Cr. Henry GoodfelloWf . . , . . By Cash in full, . " . George Candlestick, Dr. 6^ tons tallow,. • (3> 7s. 4d. per st. Aug. 1 — . Josdph Wilmotf Dr. 30 St. 12 lb. Bacon,. • • .® 10s. 8d. per st. 18 firkins butter, "54 6 per fir. William Ogle, Dr. 4d| yards Broad Cloth, ^ 35s. 100| yards common yd. w " 8 72 yards fine narrow,. • " 11 24 yards sup. blue, ••«••." 38 je. s. d. 1658 447 6 6 33 19 6 H 6 381 6 51 17 u 202 3 (8.) sAd. 558 447 6 33 19 6 oi 6 381 6 61 17 7 i 2021 2 3 DAY-BOOK. \^ ^^^""" ' ' ■■■■-■■■■IB ■^■^^■^M I ■ III .. -mm^^^^ ■(III Hamilton, Aug. 4, 1840. Thomas Merchant, Br, 10 cwt. 3 qr. 18 lb. sugar,. . •(S> 79s. 6d. 1 cwt. 1 qr. 17i lb. tea,./© £39 12 15 cwt. qr. 17^ lb. raisins,. .® 93 4 8 cwt. qr. 14 lb. hops,. . . ."113 9 10 '• Sir Henry Greatman, Dr. 10 oz. 14 dwt. 8 gr. Gold-plate, > ^ £5 14 9 per oz \ // Cr, Jonathan Winlerton, By Cash in full, 14 James Newcastle, Dr, 5 doz. fine steel Snuffers, (S> 8s. 6d per pr. 2^ doz. London Razors,.." 2 4 each. 6f doz. Kentish Hammers," 19 per doz. 20 Cr, John Westerley, Esq, By Cash inpart^. • 24 — . Joshua Housekeeper, Dr, 20 blue Quilts, r3> 10s. ll|d. Chintz do "24 9 15 pairs blankets, " 17 8^ — J3ep. 6 Cr, Mrs, Arabella Farmer, By Cash in full, • 170 je. 6 215 19 11 61 9 8i 57 9 35 8 100 85 Ui 44 17 5i m m ■■ •(• ij I m m ■4 ' I. i'' >-..i>. 171 DAY-BOOK. < a I:, >■ -t: r 1^- (10.) i ifl Hamilton, Sep. 6, 1840. Joshua Housekeeper, Dr. 161 bushels Oats, « .i® 4s. 417 bushels Barley,. ......" 5 10 Sir Henry Greatman, Br, 82^ hhds. beer, (54 gal.) (a) Is. 6cl. per gal. 19 gallons Gin "6 6 per qt. 12 Cr, John Westerly, Esq, By Cash in full, 16 !_ Nicholas Cheesemonger, Dr, 2 cwt. 1 qr. 7 lb. Cheshire, (S) 84s. per cwt * 3 cwt qr. 19 lb. Gloucester, (3) 74s. 8d. per cwt ^ cwt. 1 qr. 16 lb. Stilton, rd) 149s. 4d. pe^' cwt 7 cwt. qr. 14 lb. Suffolk, Od 65s. 4d. per cwt . 17 ■ Miss LouUa Darlington, Dr. 69| yards diaper, ("> 4s. — . _ 20 Joseph Wakefield, Dr. 60 lb. Tea,. , . .^// . ,*»,,((>> 7id. per oz, —_——_^_— ______ " __«-«———————— Cr, Joseph Wihnot, By Cash in full,. . * < r / • ( 27 James Newcastle, Dr. 5 qrs. Oats, ^'^ 4s. per bush. 7 qra. Bran " 1 lOd. " 9 bush. Beans, " 7 0" 19 bush. Tares, "14 ¥ 16 bush. Peas, " 9 ^ • > i i » £. 140 d. 9 154 87 15 1 10 92 13 30 56 11 19 1 10 Hi 37 (10.) . U* M* 9 )4 15 87 10 (n.) DAY-BOOK. 172 Hamilton, Oct. 2, 1840. The Hon, Lord George Mountain, Dr, 25 oz. 10 clwt. 10 gr. silver-plate, ^^ 7s. 9d. " "66 " "64 85 oz. 14 dwt. 15 gr. 29 oz, 16 dwt. 15 gr. Alexander Penrith, Dr. 18f yds. Scarlet, -:? 30s. 6d. 200 yds. Shalloon, 12 doz. twist Buttons,. . . . ." 1 2i // 1 6 s. 47 lOi 5. It. ' ii '1 Cr. George Trader, By Cash in part,i 41 38 10 8^ ■Vli ■•SI // 92 11 1 13 19 30 5610 Lady Lustring, Dr. 6^ yds. Diicape, ^' 6a. 4d. 53| yds. Brocade " 8 10 7U yds. Persian, " 1 2i 21f yds. Lustring, '. ." 5 3 8 George Trader, Dr. 19 stones L(3ather, (^ 2s. 6d, per lb. Cr. Joshua Housekeeper, By Cash in part,. . . . r, ft 35 «3 182 12 10 T4 37 2 10 Thomas Merchant, Dr, 45 cwt. 1 (p*. 10 lb. sugar, rJ' 848. per cwt. 12 Sir Henry Grealman, Dr. 184f gal. mountain Wine,. ,(n) 18s. 6 190 6 165 18 9 * p f ^7S DAY-BOOK. -,- — Hamilton, Oct. 16, 1840. ^ — Cr, Joseph Wakefield, By Cash in part, // Andrew Tomlinson, Dr, 15 pairs Cotton Hose, fS 3s. 7d. 12 pairs Worsted do ..." 3 10 18 pairs Strawberry, " 4 16 pairs Silk Gloves,.........." 5 11^ 74 pairs Norwich Hose,,,. **-..." 2 6 11 pairs Silk do "16 6 18 Cr, John Montague, By Cash in full, '/ Cr, Thomas Merchant, By 19 cwt. 3 qr. hops,. . . .^ 105ai. lOd. By 10 cwt. 1 qr. hops,....." 99 , 20 Miss Louisa Darlington, Dr, 17 ells Flem. 1 qr. Flanders Lace,®17s.6id. 30 Cr, George Candlestick, By 131 yds. 1 qi. na. Irish Linen, > (a) 4s. 8id. I By 87 yds. 1 na. Mualin^ »^,j(ii) Ss. 7id, Nov. 1 Cr. William Ogle, By 37 qrs. 7 bush. Oats, ® 32s. ^ ^ II ____________________ Cr, Ladjf JUtstring^ I By Cash in full,., ,,....,.,.>. (12.) £, s. 40 d, 31 6 274 13 14 155 15 3 6 68 60 4 IS H 3 78 15 0i (12.) 40 sAd* 31 274 lapr 14 155 15 411i 68 60 33 I 78' 12 16 01 DAY-BOOK. (13.) Hamilton, Nov. 1, 1840. Cr, Miss Louisa Darlington, By Cash in part,* 7 Joshua Housekeeper, Br, 28 cwt. 2 qr. 17 lb. sugar,. . . .ro) 79s. 4^. // , Cr. Joseph Wholesale, Esq. By 420 yds. broad cloth,, ...... .® 30s. . 10 Cr, Moses Greenwell, By Cash in full, — . 12 The Hon. Lord George Mountain, Dr. 112 lb. Coffee, (a) 5s. 4d. 52 St. Sugar " 7 6 __ 16 Cr. Erasmus Gordon, By 7 gross Buckles,, .f® Is. 2^d. per pair. _- 18 George Jaminson, Dr. 4 boxes Raisins, wt. 448 \h... ,(n) Os. 8d. 6 boxes Raisins, wt. 827 lb. ... " 1 3 1 box Prun(3s, wt. 604 lb " 2 4 8 bags Pepper, wt. 1774 lb. . . ." 3 2 . — 20 Cr. Andrew Tomlinson, Js By 181 yds. Cloth, (S) lOs. OJd. e4 — The Hon. Lord George MountaiWy Dr. » 137 gallons Rum (^ 173. 6d. 157 gallons Rum " 18 174 3 6 6 100 113 030 s. 14 17 2 49 60 d. n I) 4i 417 97 261 18 19 17 5 « \m >4 Il ITS DAY-BOOK. ' (14.) Hamilton, Nov. 26, 1840. Cr, James Newcastle, By Cash in full,... . 27 Sir Henry Greatman, Dr. 871 oz. Plate, 'S 5s. 4d. 95 5 d, 4 232 Dec. 6 Cr. Alexander Penrith, ByCashinfull,... Daniel Roberts, Dr. ' 171 yards Shalloon, (^ 2s. 7d. 173 yards Shalloon, " 2 11 175 yards Yorkshire Cloth, " 9 6 177 yards Fine Narrow, " 7 10 Cr. Joshua Housekeeper, By Cash in full,. . • . // Amhrose Patterson, Dr. 12 p 20 p 18 p 10 p 10 p . Ribbon, meas. 179 yd "^ 6^d. . Ribbon, meas. 979 yd " 7^. . Ribbon, meas. 917 yd " 7|. . Ribbon, meas. 821 yd " 9^^ . Ribbon, meas. 171 yd,. . ..." 9^. 238 12 lOf 199 201 15 Cr, iVilliam Jo'i- ^on, By Cash in lujl,.. , '#♦■•• // -» '*»■ Cr, Nicholas Cheesemonger, .By Cash in part,. .... #«».•••••*•••»••. 103 122 9i Q3i 9 40 Cr. 32 5 4 3812 19915 4 201 4 i 1 103 8' 0^ 122 (15.) DAY-BOOK. ir& Hamilton, 16 Dec. 1840. Cr, Andrew Harrison, By Cash in full, 20 Cr» George Jaminson, By Cash in pa2*t,. . .c»,. // Sir Henry Greatman, Dr. 746 yards Linen, (o) 3s. 4d. 873 yards Muslin, " 6 8 27 6 Cr, The Hon, Lord George Mountain^ By Cash in full, // William Hardware, Dr, 350 Razors (S) Is. 3fd. 420 Penknives, " 9^. 950 pairs Scissors, " 2^. 230 pairs Scissors, " 4| // CV, Joseph Wakefield, By Cash in full,. . . 28 I CV. Gregory Emerson, By Caih in full,,, , 40 01 29 Cr, Miss Louisa Darlington, ByCashinfull......... 76 80 d. 6 45 9 2i^ 29 4 2 10 m m ll i /.' x'. it: .i$''' 4n "5 k" r h 177 DAY-BOOK. (16.) Hamilton^ 29 Dec, 1840. Cr, George Jaminson, By Cash in full,.«< 30 Cr. Ambrose Patterson, By Cash in full,. • • . 6 337 103 s. 19 9 5 '^:^ l-V ••• T K' j.'...' . • «\ « s Htt rl^wM L^>■•.■>■ .s 2 5 6 m Mountain Lord George. . Montague John Merchant Thomas 3 6 6 B Newcastle James 4 Darlington Louisa 3 O Ogle William t Emerson Gregory 4 5 F Farmer Arabella. ...... 2 P Penrith Alexander Patterson Ambrose 4 7 O Goodfellow Henry Greatman Sir Henry... . Greenwell Moses Gordon Erasmus 1 4 5 5 n Roberts Daniel. •....■■■ 7 I* H Housekeeper Joshua. . . . Harrison Andrew Hardware William I Johnson William Jenkitison Robert Jaminson George 2 6 7 1 1 6 Tomlinson Andrew Trader George W Wakefield Joseph Winterton Jonathan . . . . Wei;terly John, Esq Wilmot Joseph Wholesale Joseph, Esq... 1 5 1 I 2 3 6 4 m ','51 '\. il i i f' 'tli >: •■sTv .1 1 ' r! I 179 LEDGER. 1840. Jan. June Jan. 7an. May Sep. Jan. Jan. Jan. Oct. Dec. 19 '() Dr. To Goods,. To Goods,. WILLIAM Dr. To Goods,. ROBERT Dr. To G )ods,, To Goads,. To Goods,. JOSEPH Dr. 5! To Goods,. JONATHAN .'4 6 n Dr. To Goods, HENRY Dr. To Goods,. . To Goods,. . To Balance,. ANDREW (1.) 1 7 1 6 10 78 122 200 s. 16 16 242 15i H 2 12 8 2| 3^ 10 I7|lli 30i 0,0 49 21 57 d 19 6 29 m 97 3 13 19 6 7 in 171 Oi 78 16 d. 122 0, 200 16 242il5i 4i 8 2. H 10 nliH 30i 0,0 491 21 57 1 9 19 7! 6 2 I2 29 U6 3i 6 13 7 19111 971 171 Oil (10 LEDGER. 180 1840. May Dec. 4 12 27 16 27 10 26 20 > JOHNSON, Bv Sundries. ». Cr. 5 14 6 12 15 9 8 13 78 122 16 d. By Cash, 200 242 40 9 16 15 May JENKINSON, By Cash,. ........./... Cr. 44 Oct. WAKEFIELD, By Cash, Doc. Bv Cash 2| \ 1 49 57 19 97 97 1 7 17 2J Aug. WINTERTON, By Cash, Cr. 9 < July • GOODFELLOW, Bv Cash Cr. 6 Nov. TOMLINSCN, By Groods »• »» 9f t Cr. 0| -»•■.! . "< 17 n I m -•til «5'^^. IMAGE EVALUATION TEST TARGET (MT-3) 4p {./ % ^ 1.0 V^ Ui m m i2.2 ~ 13.6 ^BB HI III u •* u in II : 1^ yfi >j Photographic uCi6nG6S Corporation ^ n WHT MAIN ITINT \WMITII,N.V. UIM (7I*)I79-4S09 4!^ 4^ Ii • i Itl LEDGER. 1840. Jan. 26 Jan. 28 June 6 July 14 Aug. 24 Sep. 6 Nov. 7 4^ . Feb. Fob. 8 Feb. April De. To Goods,, # HUMPHREY De. To Goods,. THOMAS 15 20 De. MRS. ARABELLA To Goods,. To Goods,, (2.) De. JOHN To Goods, ■ V " " ■ ■ ' De. JOSHUA To Goods To Goods, To Goods, To Goods, To Goods, To Goods, 2 6 7 9 10 13 187 d. 10 187 10 15 65 13 35 140 113 14 10 7 9 14 6 7 111 H 383 16 m 35 17 6 9 18 19 25 9 8 54 44 17 H (2.) 1 iS. U. 187 10 187 1 10 1514 65 6 7 13 10 35 7 Hi 9 14 H 140 113 383 leioi 35 17 6 918 19 25 9 8 5i 44 17| 5i (2.) LEDGER. 18i 1840. Aug. Sep. Oct. Dec. June April Sep. 20 12 WESTERLY, Esq. Cr. By Cash By Cash, HOUSEKEEPER, Cr. By Cash, By Cash, 11 10 9 10 11 14 ARMSTRONa, Ck. By Cash, BARROWMAN, Cb. By Cash FARMER, ? Cb. By Cash, • 100 87 187 s, 1 10 10 182 201 12 4 10 0* 383 16 lOi 35 17 6 18 9 44 44 17 17 »i H i 183 LEDGER. t- h w <<., 'M'. 1840. Feb. July Oct. Nov. Feb. April Oct. Feb. April May July Sep. Oct. 21 29 5 34 16 12 20 17 20 1 I March Aug. Dr. LADY Dr. i^h To Goods,. To Goods,, JOSEPH (3.) Dr. the HON. lord 21 ToGoods,. 20 ToGoods, 2 ToGoods, 12 ToGoods 24 ToGoods, 2 8 11 13 je. 919 447 47 49 261 1724 s. 5 6 3 7 6 d. 6 4 6 To Goods, To Goods, To Goods, Dr. miss LOUISA ToGoods, ToGoods, ToGoods, , ToGoods, , ToGoods, , ToGoods, 3 5 11 8 4 6 8 10 12 8 8 9 33 35 78 19 9 7 15 51 13 17 33 13 15 145 18 6 9 6 19 2 4 51 56 4 9 4 3 13 17 10 i 11* If (3.) d. 6 4 91 5 a\ 6 \n\ 3 19 7 31 31 6 24 6 2i 919 H 33 9 4 35 78 7 15 9i 51 18 » 13 6 17 9 4 33 6 H 13 19 16 21 3 145 1 94 413 5117 4 74 56101114 (3.) LEDGER. 184 1840. April Dec. Nov. Nov. Dec. Sep. 29 27 GEO. MOUNTMN, Cr. By a bill on Mess. Douglas & Co. By Cash, 5 15 LUSTRING, By Cash, Cr. 1 29 20 DARLINGTON, Cr. By Cash, By Cash, £. 250 1474 s. 6 d. 24 1424 6 24 12 WILMOT, By Cash, Cr. 10 78 15 94 78 15 94 100 45 1 04 145 1 94 56 56 10 10 114 114 1! 1 ^. »i '.■•' H ■< .ff 185 LEDGER. 'I la '•i 1840. March April Aug. Sep. Oct. Nov. Dec. March March Aug. Sep. April Oct. 15 27 10 10 12 27 20 15 23 80 14 27 Dr. To Goods,, To Goods,, GREGORY Dr. ALEXANDER To Groods,, To Goods,, (4.) Dr. sir henry To Goods, To Goods,. To Groods,.- To Goods,.. To Goods, To Goods To Goods, To Balance, Dr. JAMES To Goods,* To Goods, To Goods 3 5 9 10 11 14 15 £. 23 76 61 154 165 232 415 528 1658 3 3 s. 12 1 9 15 18 5 6 10 d, 1 4* 8* 9 4 3 6| 4 9 10 4 11 9 20 29 4 4 2 2 22 35 37 95 16 8 11 3 2 197 41 238 5 7 12 3 8| 101 De( (4.) s. d. 23 76 61 12 1 9 5415 65 132 H5 )28 18 5 6 10 358 7 41 8* 9 4 8 61 9 4 2 20 29 22 35 37 16 8 11 3 2 95 5 4 197 41 5 2 2881121101 81 (4.) LEDGER. 186 1840. July Dec. Nov. Dec. 14 28 GREATMAN, Cr. By Goods, 8 EMERSON, By Cash, Cr. 26 6 NEWCASTLE, Cr. By Cash, PENRITH, By Cash,.....'... Cr. 1658 d. 15 1658 14 14 29 29 95 5 95 5 238 12 23812 105 m y 'I ,1 ■i '* 1^ n 1 ':•« 11 1 ;' it I "■*■'• m ■•-51 'rli 187 LEDGER. 1840. April Aug. May Oct. May Sep. May June 25 1 1 8 Dr. To Goods,.'. To Goods,. . WILLIAM Dr. To Goods,. To Goods,, GEORGE 4 16 Ds. To Goods,, To Goods,. NICHOLAS 6 11 Dr. To Goods,. MOSES Dr. To Goods,, ERASMUS (5.) 4 8 128 202 330 10 2 12 d. 6 3 9 5 11 5 10 6 93 33 126 2 3^ 31 54 92 147 11 11 5 6 17 H 67 <■>, »."• \y: 67 128 202 330 10 2 d, 6 3 12 93 33 126 5 3i H 54 92 11 11 5 147 2 6 17 H 67 67 « * (5.) LEDGER. 1840. Nov. Oct. OGLE, Cr. By Goods,. . By Balance,. TRADER, Cr. Dec. Nov. By Cash,.. By Balance, 12 Nov. 10 CHEESEMONGER, Cr. By Cash,. . , By Balance, GREEN WELL, Cr. By Cash, , 15 GORDON, Cr. By Goods,. . By Balance,. 18a 12 11 14 13 13 60 270 330 12 12 d. 9 9 38 87 126 10 17 ii 3A 40 107 147 2 6 6 17 ^ 60 6 li 67, 18 6 41 !l li i 189 LEDGER. mi; Ifr' (6.) 1840. Dr. ANDREW June 25 To Goods,. Dr. JOHN July 7 To Goods,... Dr. THOMAS July 12 To Goods, Aug. 4 To Goods, Oct. 10 ToGoods,. Dr. GEORGE July 26 ToGoods,,. Dr. JOSEPH To Balance, Dr. GEORGE - ,. Nov. 18 ToGoods,... I.I S1t««*'-* 4 ' t^i 76 d. 6 274 14 7 9 11 343 215 190 749 7 19 8 16 7 11 6 381 381 63 w 6 6 8 8 13 417 19 417 19 (6.) s. re 6 7414 343 215 19b 749 7 19 8 7 11 6 16 381 3»l 6 6 63 3ii 8 8 41' 19 41*51191 5 (6.) Ll!r0GE[it.^ 190 HHI 184(k Dec. Oct. Oct. Oct. 16 • By Cash)* • • ••■•'• • •-• • •-•■• *-«•• •' 18 HARRISON, Or. MONTAGUE, By Cash , Cr. 18 MERCHANT, Cr. By Goods,. . By Balance,. 80 Nov* Dec. CANDLESTICK, Cr. By Goods,. . By Balance,. WHOLESALE, Esq. Cr. By Goods,* 20 20 JAMINSON, ? Cr. By Cash,, By Cash,. .;'I;;-' 15 70 12 12 274 si\ d» & 14 12 155 594 749 4 11 16 IH Oi 13 68 313 15 16 381 630 6 4i 8 80 337 417 19 19 5 5 :i % lit ■ 'H m "^ ''■'■'I I ' i( i 191 LEDGER. 1840. Dec. Dec. :-J'- Dec. S . Dr. . ^ To Goods,. DANIEL 8 27 Dr. To Goods,, AMBROSE Dr. To Goods,. WILLIAM Dr. BALANCE, To William Ogle, To George Trader, To Nicholas Cheesemonger,. To Erasmus Gordon, To Thomas Merchant, To Greorge Candlestick, To Daniel Roberts, To William Hardware, To Present net Capital,, (7.) 14 14 15 JB. 190 8, 15 d. 4 6 7 103 9 6J 54 10 270 87 107 6 594 313 199 54 1632 437 17 2 6 11 2 15 16 9 H 6 Oi 4i 4 10 U 51 6| (7.) L9915 4 103 9 GJ 54 010 270 87 107 6 594 813 199 54 17 2 6 11 2 9 6 Oi 4i 151 4 10 1632 16 U II 437 5 (7.) LED6BR. 19a 1840. Dec. 30 ROBERTS, By Balance,. •!•.• PATTERSON, By Cash, Cb. Ce. HARDWARE, Cr. By Balance,* . . . r • • « i ^''- . r BALANCE, ; Ce. By Andrew Tomlinson, By Sir Henry Greatman, By Joseph Wholesale, Esq By Present net Capital, i - ■i. ' t •' !♦ « 16 1 4 6 £. 109 15 d. 4 103 9 6i 54 10 36 528 630 437 19 10 5 lU 6$ 1632 16 H • '■ * il • M 7 , ■H ■U'.J :':(« '%M i>-'iu''i-i.i.'ii4 ver. Note. — This rule is very easy when the number of ar- tides does not exceed 300 or 400, and the price any number of pence, not exceeding 3 shillings. If the price be more than 1 shilling and less than 2, palculate for the number of pence above 12, to which add as many shillings as there are articles. If the price be more than 2s. and less than 3s., calculate for the number of pence above 2s. to which add twice as many shillings as there are articles, &c. What is the price of 76 lb. of beef, at 4d. per lb. 76a. = 6s. 4d. the value at Id. per lb. 4 3 = 10 w £1 6 4ans. -' -•- 1 », £ 8,d. d. £ 8, d. = £3 3 38 yds. (S> 3 Aru» 9 6 139 yards (S> 6 Ans, 8 9 6 = 40 54 " 4 18 146 // " 7 // 4 6 2 =: 6 12 66 " 6 1 7 1 152 II " 8 n 6 1 4 = 1 17 6 79 " 7 2 6 1 173 It " 10 II 7 4 2 = 44 86 '' 8 2 17 4 184 II " 11 II 8 8 8 = 15 7 94 " 9 3 10 6 190 II " 12 II 9 10 = 3 10 D 102 " 10 4 6 210 II // 14 It 12 6 9 = 7 10 I 124 " 11 6 18 8 228 II " 16 II 18 18 9 = 30 1 186 " 4 3 6 262 II " 18 II 19 18 9 = 12 19 1 lae " ft 5 2 12.6 800 II " 28 II 97 10 I :!i! y r2 % •1 i'^ : I'- ll!! ■i 195 MENTAL ARITHMETIC. II. To find the value of any number of articles, when the price is an even part of a penny, shilling, or pound. Rule. — ^Divide the number of articles by the part which the price is of a penny, shilling, or pound ; and the quotient will be the answer in pence, shillings, or pounds respectively. je s. d. s, d. £ s, d. 58 {S> i = " 1 2 156 (a> I 4 = 10 8 56 " h — // 2 4 156 " 1 8 = 13 58 " Id. — II 4 8 156 " 2 = 15 12 56 " 2 — II 9 4 156 " 2 6 — 19 10 56 " 3 =. II 14 156 " 3 4 ^ 26 m " 4 — // 18 8 156 " 4 ^ 31 4 56 " 6 - 1 8 156 " 5 = 39 56 " l3.0 = 2 16 156 " 6 8 =: 52 66 '' 1 3 = 3 10 156 " 10 =: 78 III. To find the value of any number of articles when the price is an even number of shillings. Rule. — Multiply the given number by half the price — dou- ble the first figure in the product for shillings, and the rest will be pounds. s, £ 8, d, 699 yds. ^ 12 Ans, 419 8 734 " " 14 " 513 16 878 " " 16 " 702 8 987 " " 18 " 888 6 1032 " " 22 " 1185 4 8, £ s, d, 103 yds. r,d 2 An8, 10 6 224 " " 4 " 44 16 386 " " 6 " 100 10 422 " " 8 " 168 16 574 " " 10 " 287 IV. To find the value of a dozen articles, having the price of 1 given. Rule. — For every penny in the price reckon one shilling. Note I. — For any number of dozens, multiply the price of ofie dozen by the number of dozens. Note 2. — If the rate per dozen be given, to find the value of one article ; for every shilling in the price per dozen, reckon a penny for the value of one article. For the value of several articles, multiply the price of one by the number. Note 3. — The value of any number of articles, not cx- Deeding 200, may be very expeditiously calculated by the as. aistance of this rule. Thus : suppose the vnlue of 153 ar- ticlos be required at lOd. each ; we have 12 dozen and 9 ar- ticles at lOs. per dozen. when the irt which 3 quotient pectively. « MENTAL ARITHMETIC. 12 doz. (S) 10s. £6 9 art. " lOd. 7 6 1 IOC 1 £6 7 6 ans. r. d, 8 15 12 19 10 £ 10 13 26 31 39 52 78 4 IS when the )rice — dou- ind the rest jS 8. d, f.419 8 513 16 702 8 888 6 1183 4 ig the price }ne shilling. 1 the price of id the value per dozen, lor the value le number. bIcs, not ex. Id by the as- P of 163 ar- tn and 9 ar- d. uOZ. lbs. (S> 3i u u « 4i u « 5f u " 6i n « 7 u « 7i it it n d. s. 3 6 4 3 5 9 6 3 7 7 6 11 d. 2 doz. yds. fS) 8 = 3 4 5 6 7 8 a it (4 (( tt it « « 10 «* 13 « 14 " 15 « 16 « 18 £ 1 2 3 4 5 7 8, d, 10 10 12 10 10 12 4 V. To find the value of 20 articles, or a score. Rule. — For every shilling in the price reckon one pound. Note 1. — If there be 6d. in the price, add 10s. — if 4d. add 6s. 8d. — if 3d. add 5s. ; and so on according to the aliquot parts of a shilling. For any number of scores, multiply the price of 1 score by the number of scores. Note 2. — If the rate per score be given, to find the value of one article ; for every pound in the price per score, reck> on a shilling for the value of one article. score (a) (( « 2 3 u <( u a, d. £ ©30 — 3 * 4 6 — 4 "54 — 5 "63 — 6 " 12 — 12 « 15 — 30 « 11 — 33 8. d. 10 6 8 5 VI. To find the value of 100 articles. Rule. — For every shilling in the price reckon £5, and for every farthing in the pence, or pence and farthings, reckon as. Id. 8, d, 100 yds. (n) & Q 100 « « 6 « 100 100 " 100 « 100 " •* 4 « 7 «* 8 "06 £ s, d 2J 30 22 10 3.J 40 47 10 8. d, £ 8, d, 100 yds. '^ 10 2i - 51 10 100 " "113 - 56 6 100 " " 2 3|. 11 11 3 100 " « 12 li . 60 10 5 200 « " 13 7^ . 186 5 800 ** " 14 6 . 317 10 8, d* £ 8.d. f,,-i 4 score 7 6 each 30 - j 5 « « 14 « 70 !]| 1 « « 17 4 « 17 6 8 .'A *■ if 6 « " 16 " 06 ■■ 1 « "23 « 2 5 3 « « 2 6 « 7 10 I " " 18 " 18 fi I 197 MENTAL AEITHMETtC. II VII. To find the value of 1 cwt., or 112 articles. Rule. — Multiply 9s. 4d. by the number of pence in the price for the answer. Note. — If there be farthings in the price ; for \ add 2s. 4d.; for i add 4s. 8d.; and for f add 73. For any number of cwts., multiply the price of 1 cwt. by the number of cwts. d, £ 112 lbs. fa) 4 = 1 112 "5 = 2 112 « 7 = 3 112 « 7i = 3 112 « 8| = 4 112 « 9i = 4 s. d. 17 4 6 8 5 4 10 1 8 8 8 d. £ 112 lb. fS) lOi =4 112 «* " Hi = 2 cwt. (a) 6 per lb. 3 « « 4i " 4 « « 5| « 10 14 8 5 « « 8 « 18 13 4 5 5 6 s, d, 18 5 12 6 VIII. To find the value of 120, 240, 480, or 960 articles. Rule. — For 120 reckon a pound for every 2d. in the price ; for Id. reckon ten shillings ; for a ^d. five shillings ; and for a ^ reckon 2s. 6d. For 240 reckon a pound for every penny in the price ; for a |d. reckon ten shillings ; and for a | five shillings. For 480 reckon a pound for every |d. in the price, and for ■\ ten shillings. For 960 reckon a pound for every farthing in the price. s. d. 120 Ca) 7 each = 120 " 9^ 120 " 111 240" 1 4 240 « 2 3^ 240 " 4 9| u u u £ s. d. 3 10 4 15 5 17 6 16 27 10 67 15 480 (a) 480 « 480 " 960 « 960 " 980 " .-». d. £ 1 3 each = 30 1 n 2 3| u it 9 1 7i 2 n u a.d. 39 55 10 6 36 77 135 • IX. To find the interest of any sum of money for a year, at 5 per cent. Rule. — ^Divide the given sum by 20 for the answer in pounds. Note 1. — For any number of years, multiply the interest of one year by the number of years. Note 2. — ^If at the rate of 6 per cent, find the interest by the rule as above, to which add \ of ibiolf; if at 5^ per cent, add ^. If the rate of interest be at 4 per cent, deduct 4 of itself; ifat4| deduct^. ^ ^ PfiOfiRAL M0Nfii« 199 m the i 2s. 4d.; imber of cwts. s, d, 18 5 12 6 10 14 8 18 13 4 £ 4 5 5 6 articles. Jd. in the shillings ; price ; for pe, and for e price. £ 30 39 55 36 77 136 10 e for a year, answer in the interest interest by {^ per cent, deduct ^ of £l4.5 (o) 5 per cent, for 1 year = J67 482 « 5 u u u u u (( 734 836 982 1500 2000 2540 3483 « 5 4690 « 5 5 5 5 5 (I -+«> ^l-jwliiit^oH* 0*QiocDt«aD3oa»Of-iooi-ioeo^<^io«t«aoaoabOFHO a i 8 . Hn Hn Hn ^ie* <-in -is% 'if* 'if* '^ -ie* '^ ^^ O'^OiHfHNcicoco^'^iiiOiotocot^t-aDaDOsoooi-^i-^o d 1-4 l-l 1-4 1-4 ••Tjl^Tf»^^TjlTt*^'^*"-^'*'*^'»t'^<^<^Tt<'**«H'« ^>i>«|«i>e*«»H«» *|«o«|i*«iM»H«* «|ii>n|ii>M(«>H'« *)•<» Mfuj nl«» H«» •(•• Q^sOl-HOOf-<(Ne»^^Tt«to«^•QOX)a^Ol-HOOl-H(^lco<^•<« IH l-l i-H l-l . . Hn HeiHMHnHNHNHNHNHeiHNHNHN 0'«Oi-ii-ic«(Ncoso'^Tji»oio«oot'i'aDaooi050©i-i^© 1-4 f-4 rH 1-4 Q ticocQcooooococoeocQcoeocoeococQeococQcocceoe'sco^ . . H«» ^><»«|u»Nl«>H'o *|us«|u»e^«i»H'o .*|'«s«l"»«l'oH'o *|ic ^s|u» «!•« H"* ^l-jnH 1-4 l-l • • Hn O'^ O l-l ^ip% ^ifn ^ie% 'ie* wip* He* hn Hm Hn Hn p^ i-i«(NeOTO^rfiOiO<0«t-»^aDaD©©©©p-ii-i© i-t 1-4 -H iM • .ii|i«n|>«ei|u)Hx* *|>cM)ioe*«»H«> «♦!«» «i|«i» eil«» H-i .H«» «l«o m)"* H"> ^^owHwl"* ■«ODQDOSO»-i©©rH(N«^^ir:©l^QDa0050i-l©©^« r-l pH »H i-I d • • HN tS © l-l HN HN HN HN HN Hn -|n Hn Hn Hm Hn i-4«wco«^T}4ioijra©t^oDaooi©©©i-*^© 1— 1 1-4 »H iH 1 1 ,^ i^ ,^ _ri _ri .7 1 .III ri ..< ■ 1 i.i 1 1 Ht M^ r^i O-tt O 1-4 je^xsH"! *<«»«|uje^'<»H'« •!«» «|u» m|"o H-^ ^ixs n|»> eH« Hy» tl"* r*« 5J* H"* (Mc»5^^»o©t-aDaD©o^©oi-4(Neg^'^»ocDr* OOOOwwwwwwWW^^^^^^»^^^^i^^'^^^ . . Hw hnHM'*«HnHnh«-*'HnHnHnhn 0'^OiH.-i©ic5cocc^^»o»o«o-ot'r*aDQD©©©©f-«»HO P^ ^^ ^^ •"^ d«©©©©©©©©©o©o©©oo©o©oo©e^ << il 201 FEDERAL MONEY. iX PRACTICAL QUESTIONS IN FEDERAL MONEY. 1. What cost 35 lb. chees^t at 8 cents per lb. ? Ans, $2 80 cents. 2. What is the value of 29 pairs of shoes, at 1 dollar 51 cents per pair t Ans $43 79 cents. 3. What cost 131 yards Irish linen, at 38 cents per yard ? Ans, $49 78 cents. 4. What cost 140 reams paper, at 2 dollars 35 cents per ream ? Ans. $329. 5. What cost 94 bushels of oats, at 33 cents per bushel ? Ans, $31 2 cents. 6. What is the value of 75 yards satin at 3 dollars 75 cts. per yard ? Ans, $281 25 cents. 7. What cost 367 acres of land, at 14 dollars 67 cents per acre ? Ans, $5383 89 cents; . 8. What will 857 bis. pork come to, at 18 dollars and 93 cents per bl. 1 Ans, 16223$ 1 cent. 9. Bought 25 lbs. of coffee for 5 dollars, what is that per lb. ? Ans. 20 cents. 10. If 131 yards of Irish linen cost 49 dol. 78 cents, what is that per yard ? Ans, 38 cents. 11. If a cwt. of sugar cost 8 dollars 96 cents, how much is that per lb. ? Ans, 8 cents. 12. If a reckoning of 25 dollars 50 cents be paid equally by 15 persons, what do they pay a piece ? Ans. 1$ 70cts. 13. If a man's wages are 237 dollars 25 cents a yeur, how much is that per day ? Ans. 65 cents. 14. The salary of the President of the United States, is $25,000 a year, what is that per day ? Ans, 68$ 49if ^ cts. 15. What is the interest of 73$ 65 cents for a year at 6 per cent ? Ans, 4$ 41^^ cents. 16. Required the interest of 85$ 45 cents for a year at 7 |)er cent ? Ans, 5$ 9833^^ cents. 17. What is the interest of 789$ for 2 years at 6 per cent? Ans. 94$ 68 cents. 18. What is the interest of 37$ 50 cents, for 4 years at 6 per cent, per annum ? Ans. 9$. 19. If an agent sell goods to the amount of 5000 dollars, M'hat will his commission come to at 65 cents per cent ? Ans. 32$ 50 cents. 20. What is the insurance of an East-India ship and cargo, valued at 123425 dollars, at 15^ per cent? Ans, 19130$ 87^ cents. Calculations of all kinds in federal money being so simple and easy, and particularly well adapted to mental arithmetic : ' t f fi&ERAL MONEY. lONEY. 80 cents. [ dollar 51 > 79 cents, ►er yard ? 78 centa. cents per ins. $329. bushel? 1 2 cents, ars 75 cts. 25 cents. 7 cents per ) 89 cents; ars and 9^ 3$ 1 cent, is that per r. 20 cents, cents, what \ 38 cents. )W much is IS. 8 cents. »aid equally 1$ 70cts. 1 year, how 9. 65 cents, d States, is I 49f ^ cts. a year at 6 4hjSj cents, a year at 7 9S-^\ cents. 6 percent? $ 68 cents. L years at 6 Ans. 9$. 000 dollars, r cent ? $ 50 cents. p and cargo, J 87 i cents. )g so simple arithmetic : 202 J22 iu* ** J/®°*^ P®'' ^^- = 7 dollars, inn ; *' 16 cents per lb. = 16 dollars. >. inn y. • ** ^^ ^®°*« P®'^ y^'= 25 dollars. 100 yds. at 38 cents per yd. = 38 dollars. fhnf ^r® *^® """"^^ ^^ *'°""«^ *o * ^^^ ""'"ber of dollars !o t &r ""'" "'''*' ^" '^^^ P'^""'~^^ '° * *»»^ number,-.20 to&t of'L*"'*^^''' of reducing thecurrency of one State in- to that of any other State \ also sterling, Halifax currency mto the currency of any State, and the coWary, carefX ?n ^pect the following table of rules. 0^ ^ caretuiiy m. ■'3 t '■*: t.'i'i.fi''' »CjI I •«• !ii : !«• t .,& .divide the product by 16. • Mult the given sum by 15, and divide the product by 14. From the given sum deduct fV* Deduct -^-g from the given sum. Deduct i\f from the given sum. 1 To the ster. mo- ney add ||iy. Add ^ to the given sum. ■■7 : - ■ - p 1^* I 205 FEDERAL MONEY. Exercises on the preceding table» to reduce the different currencies of the several States into each other, at par. 1. Reduce J&84 10 8 New-Hampshire, &c. currency, into New-Jersey cuirency. Ans» £105 13 4. 2. Reduce £120 8 9 Connecticut currency, into New-York currency. Ans, £160 11. 3. Reduce £120 10 Massachusetts currency, into South' Carolina and Georgia currency. Ans, £93 14 5^. 4. Reduce £410 18 11 Rhode-Island currency, into Cana-^ da and Nova-Scotia currency. Ans^ £342 9 1^. 5. Reduce £524 8 4 Virginia, &c. curre cy into Sterling money. Ans, £393 6 3. 6» Reduce £125 10 4 New- York, &c. currency, into South- Carolina currency. Ans. £73 4 4J, 7. Reduce £214 9 2 New-Jersey, &c. currency, into New- Hampshire, Massachusetts, &c. currency. Ans. £171 114.. 8. Reduce £100 New-Jersey, &c. currency, into New- York and North-Carolina currency. Ans. £106 13 4.. 9. Reduce £100 Dielaware and Maryland currency, into Sterling money. Ans^ ,£60, 10. Reduce £116 10 New-York currency, into Cbnxiecti- cut currency. Ans, £87 T 6» 11. Reduce £112 7 3 South-Carolina and Georgia curren- cy, into Connecticut, &c. currency. ' Ans. £144 9 3^. 12. Reduce £100 Canada and Nova-Scotia currency, into Connecticut currency. Ans. £120. 13. Reduce £116 14 9 sterling mpney, into Connecticut currency. , Ans, £155 13.^ 14. Reduce £104 10 Canada and Nova-Scotia currency,^ into New- York currency. Ans. £167 4:. 15. Reduce £100 Halifax currency, into New-Jersey, &c. cvrrencjr. il«». 4B150, 1' f -5. 1 1 .. .. 1 " \ f i " ''' 1 sa '., ■■- ■ ^p^s \ .'•*•. / ^>^ t - ■^,yi~t-'- - -«■• ■ II! ii 1: FORMS OF Si£C£IPTS. 206 iiflferent p. cy, into b 13 4. 5W-York ;160 11. j South' 3 14 5^. ito Cana' 42 9 l^. ) Sterling J393 6 3. ito Soutb- £73 4 4^. into New- 171 11 4. into New- 5106 13 4. ency, into Ans^ .£60. Gon^^ecti- . ie87 T 6. ffia curren- |l44 9 34. rrency, into Ans. iei20. Connecticut ,. jei55 13. a currency,^ ns. £167 4,; Jersey, &c. Aus. ^150,. » A Table showing the interest of any sum of money, from £1 to £1000, for any number of months, at 6 per cent. SUM. 1 month. 2 months. 3 months. 6 months. 1 year. £ s. D. £ s. D. £ s. D. £ s. D. £ s. D. £1 1 ^ H 7 1 2i 2 H H 7 1 2i 2 41 3 H 7 lot 1 H 3 7 4 n 9J 1 H 2 4f 4 9^ 5 6 1 6 3 6 0' C 7 2i 1 n 3 7 7 2i 7 H ^ 2 1 4 2i 8 4| 8 H 7 2 4t 4 H 9 7 9 lOf 9i 2 8i 5 4| 10 9i 10 1 2 3 6 12 20 2 4 6 12 14 30 3 6 9 a 18 1 16 40 4 8 12 1 4 2 8 50 5 10 15 1 10 3 60 6 12 18 1 16 3 12 70 7 14 1 1 2 2 4 4 80 8 16 1 4 2 8 4 16 90 9 18 1 7 2 14 5 8 100 10 1 1 10 3 6 200 1 2 3 6 12 300 1 10 3 4 10 9 18 400 2 4 6 b 12 24 500 2 10 5 7 10 15 30 1000 5 10 15 30 60 APPENDIX NO. IV. FORMS OF RECEIPTS, BILLS, &c. A Receipt is a written acknowledgment of having received a sum of money. In general, on settling an account, nothing more is neces> sary than writing below it, 1840, Feb. 1. Settled the above, or By Cash in full. 1840, Mar. 10. By Cash in part, or Received in part. 1840, April 17. By promissory note, at 1 month, '''^ ^ in full, or in part. 7 -' ^ By accei>tance at 3 moaths, do.^ (with Bignature.) s2 "'1 1^1 907 BILLS. W w M :i it* H :■ Graltt 12th March, 1840. — Received from John Black, Esq. twenty pounds ten shillings, in part payment of his account. JB20 10. Robert Wilson. Dundas, 4th Dec, 1839. — Received from Mr. James Stew* art, thirty-four pounds eight shillings, in full of his account to this date. William Douglas. Toronto, 14th Jan., 1840, — Received of James Greatman, Esq., seventy-five pounds, in part of a bill of one hundred pounds. £75. Adam Somerville. Hamilton, Received, 17th April, 1839, of Mr. Robert Wal- ton, one hundred pounds, for self and company. £100. James Alderman. Received from Mr. Henry Mortimer, Junior, fifty pounds, which I promise to repay on demand. Gait, 1st Jan., 1840. David Morgan. Quebec, 15th Sep., 1838. — Received from Mr. George TurnbuU, six pounds, for half-a-year's interest of two hundred pounds, lent on bond to the trustees of Albion Chapel, due the Ist inst. £6. Timothy Careful. Toronto, 4th June, 1840. — Received from Mr. James Scot- land, twenty-two pounds ten shillings, being half a year's rent of the house and garden, rented by him from me, due at Whit- sunday last. X22 10. Alex. Laird. Montreal, 10th April, 1889. — Received of Messrs Jameson and Christie, assigneeo of the effects of Thomas Mercer, a bankrupt, thirty pounds; being my proportion of the said bankrupt's effects, and is after the rate of ten shillings per pound, for my debt of sixty pounds, proved under the said com- mission. David Linendrapir. £30. BILLS. 1. A Bill is a document providing for the payment of a cer- tain sum of money, at a specified time. 2. A Promissory Note is a bill expretied in the form of a promise from one person to pay to another. 3. A Drqft it a bill expressed in the form of an order, sign* ed by one person* and aiddreased to another ; requiring the latter to pay the epeeified siun to the former) or to some third Deraoo. BILLS. 206 ck, Esq. ;count. ION. les Stew, ccount to LAS. rreatman, hundred ILLE. bert Wal- IMAN. [ty pounds, iRGAN. Ir. George wo hundred tpel, due the lEEFUL. James Scot- L year's rent lue at Whit. liAlRD. }srs Jameson IS Mercer, a o{ the said shillings per the said com- BNDBAFKR* I mentofacer- the form of a m order, sign- requiring the to some tbird 4. The person who signs the draft is called the Drawer ; the person to whom it is addressed is called the Drawee; and the person to whom the payment is to be made is called the Payee, 5. The Drawee binds himself to pay the bill by writing his name within it ; afler which he is called the Accepter* 6. The bill is said to be drawn by the Drawer ; dravm upon the Drawee or Accepter : and dravm in favour of the Payee. 7. A person who transfers his right of receiving payment of a bill to another, or who becomes security for its payment, writes his name on the back of it : he is then said to endorse the bill, and he is called the Endorser, ^ 8. When the Endorser, besides writing his own name, spe- cifies the person to whom he transfers his right, the bill is said to be specially endorsed : when he writes his own name only, the endorsement is called blank or general, 9. The term of a bill is the space of time at the end of which it is to be paid. 10. The term of a bill is sometimes a specified time after datCf that is, after drawing ; sometimes it is a specified time after sighty that is, afler acceptance. 11. Bills to be paid in the same country in which they are drawn, are called inland bills : and bills to be paid in a differ* ent country from that in which they are drawn, are called/or- eign bills. 12. The Drawer of a foreign hill generally makes out sever- al copies of it, which together are called a set of Exchange^ and remits them by different ships or posts, to guard against loss or miscarriage. In this case, acceptance and payment of each of the sets are required only on condition that the oth- ers have not been accepted or paid ; and a clause to this ef- fect is always inserted in such bills : therefore, when one bill of the set is accepted, the duplicates are of no further use. 13. When a bill is not paid for at the proper time, the hol- der of it puts it into the hands of a Notary, who demands pay- ment from the Drawee ; in default of which, he signs a docu- ment called a Protest which facilitates the recovery of the amount of the bill. In certain cases, a bill may be protested for non-acceptance. 14. A bill which a person has to receive the amount, is called, to that person, a Bill Receivable ; and one of which a person has to pay the amount) is called to him a Bill Payable, 309 INLAND BILLS. PROMISSORY NOTES. ^ £450 18. Dundas, 9th April, 1840. Six months after date, we promise to pay to James Cun- ningham, or order, the sum of four hundred and fifty pounds, eighteen shillings, Halifax currency, value received. John Wilson, 4* Go, £310 2 6. Kingston, 10th Nov., 1839. Four months after date, I promise to pay to Messrs Robertson, & Co.» at the Commercial Bank here, the sum of three hundred and ten pounds two shillings and sixpence, Hal- ifax currency, value received. James Thomson, jeiOO. , Gait, March 16, 1840. Three months after date, we jointly and severally prom- ise to pay to James Clerk, merchant, Montreal, at the Gore Bank, Hamilton, the sum of one hundred pounds, Halifax cur- rency, value received. John Blair, ^ Charles Scott, £200. Toronto, 15th Jan., 1840. 1 promise to pay to Mr. Isaac Trotter, two hundred pounds, in manner following, viz. — fifty pounds three months ai\er date, fifty pounds at six months, and the remaining hun- dred pounds, at twelve months, for value received. Peter Justice, I INLAND BILLS. X150r Hamilton, Jan. 3, 1840. Three months after date, pay to my order, one hundi'ed and fifty pounds, Halifax currency, for value received. To Mr. Wm. Neshit, } John Johnstone, . Merchant, Brantford. y accepted, William Nesbit, £57 16. Montreal. 6th March, 1840. Sixty days after date, pay to Mr. George Renton, or or* der, fifty-seven pounds, sixteen shilling/s, for value received.. To Adam Kerr, Esq, ^ Robert Smith, Kingston. ) accepted. Adam Kerr, payable at Commercial Bank, nere. L840. es Cun- pounds, 5- Co. 1839. , Messrs tie sum of ace, Hal- lomson. , 1840. illy prom- the Gore alifax cur- 3lair, s Scott, ., 1840. hundred ree months lining hun- Justice. . FOREIGN BILLS OF EXCHANGE. FOREIGN BILLS OF EXCHANGE. 210 1250 guil. London, 3d Oct. 1839. At usance and half usance, pay this our first of exchange, second and third not paid, to E. Van Braam, or order, twelve hundred and fifty guilders, value received, and place the same to our account, as per advice from To E. Bushnell, Amsterdam. RoBj DaviSf Sf Jone^. E, Bushnell. 8700 livres at 29d. Paris, 21st May, 1839. At forty days after date, pay to John Bosanquet, or order, eight thousand seven hundred livres, exchange 29d. per ecu, value received, as per advice, from To James Goldsworthy, Esq. London. i Philip Le Rouxy James Goldsworthy. £450 ster. New- York, 1st Jan., 1840. Sixty-five days after sight, pay this my first of exchange, (second and third not paid,) to the order of John Thompson, James Brown, & Co., four hundred and fifty pounds sterling, value received, as advised by Jonathan Wallace. Mess. Smithson, <^ Sons, > ' seen Feb. 24, 1840. Liverpool. J Smithson, ^ Sons% |3, 1840. 10 hundred kd. jhnstoM. NesbU. Ih, 1840. iton, or Of' I received.. Smith. payable ftt .here. ti »•■ 211 EXPLANATION OF COMMESCIAL TERMS. APPENDIX, NO. V. A SHORT EXPLANATION m COMMERCIAL TERMS OR EXPRESSIONS. Accommodation, when applied to Bills or Notes, are those tor which no value has been given ; that is, when the Drawee only lends his name ; and that the Drawer engages to provide him with the means of payment when the bill falls due. Account current, means the account sent from one corres- pondent to another, of all their mercantile transactions, and is usually a copy from the merchant's or trader's ledger, by means of which, once a year a balance is made, and any er- rors rectified. Account sales, is a term used for an accmint rendered of any parcel of goods sold. Adventure, when a merchant exports goods to, or from a foreign market on his own account and risk, it is called an in- dividual speculation, or adventure to, or from that place. Advice, mercantile intelligence ; to advise a bill is to des- cribe the amount, date, term, to whom payable, &c., and re- quest the person on whom drawn to accept it. Affidavit, signifies an oath in writings sworn before some person who is authorised to take the same. Agent, a person duly empowered to transact business for another. Arbitration, the determination of a cause 6y persons mutu- ally chosen by the parties. Assignee, a person deputed by another to manage the af- fairs of a bankrupt. Average, a contribution made for losses at sea, which falls upon the proprietors or insurers in a just proportion. Balance of Trade, the difference between the commercial exports and imports of one country with respect to another. Bank Bill, a bill drawn on and accepted by a banking house or banker. Bankrupt, a trader whom misfortune or extravagance has rendered unable to pay his debts. Bill of Entry, a list of the particulars of goods entered at the Ci'stom-house. Bill of Lading, a printed agreement between the shipper of goods and the captain of a ship, binding the latter to deliver them " in good order and well conditioned," on payment of a fiXPLANAflON OF COMHfiRCIAL TERMS. 212 >NS. are ttios© e Drawee to provide lue. ne corres- 9ns, and is ledger, by nd any er- endered of k, or from a •ailed an in- place. ill is to des- zCi and re- )efore some business for jrsons mutu- nage the af- i, which falls tion. commercial [o another, a banking ivagance has Ids entered at the shipper of Iter to deliver Ipayment of a certain freight. It is usual to make out three bills, one for the shipper, the second to be held by the captain, and the third to be sent to the person to whom the goods are con> signed, by which he can claim them on their arrival. Bill of Sale, is a solemn contract, under seal, whereby a person conveys the right and interest which he has in goods and chattels. Bill of Store, is a license granted by the Custom-house to merchants, to carry such stores and provisions as are neces- sary for a voyage, free of duty. Blank Credit, the permission which one house gives to another to draw on it to a certain extent, at any time, for their own accommodation. Broker, an agent employed by merchants in buying and selling ; who, for a trifling charge, finds the merchant buyers in one case, and sellers in the other. There are several kinds of Brokers, such as Ship Brokers, Insurance Brokers, Ex. change Brokers, Stock Brokers, &;c. Bonded Goods, are certain articles which, on being landed, are warehoused upon bond being given by the owner for the payment of duties, &;c. Bottomry, is a contract in the nature of a mortgage of a ship, when the owner of it borrows money, to enable him to carry on a voyage, and pledges the keel or bottom of the ship, as a security for the re-payment ; 'and it is understood, that if the vessel be lost, the lender loses his money. Bounty, is a premium paid by Government to the exporters of certain British commodities, for foreign parts, &c. it is also called Drawback, Capital or Stock, the effects of a house in money or wares, by means of which it carries on trade, and supports its credit. Charter Party, the engagement between the owner of a ship and the merchant, who engages the whole ship to go from one port to another with goods, for a certain sum. Circulating Medium^ cash, bank-notes, or other paper money payable on demand. Circular Letter, the printed notice of the establishment or dissolution of a house, or alteration in the firm, <&;c. see Firm. Cocket, a Custom-house warrant given ou the entry of goods for exportation, to signify they have paid the duty. Commission of Bankruptcy, an order under the great seal, directing five or more Commissioners to iu([airc into the af- fairs of a bankrupt. Composition, part of a debt talv(3n in lieu uf the whole. Compromise, to adjust a dispute by mutuul concessions. 213 EXPLANATION OF COMMERCIAL TERMS. Consignment^ goods sent by one house to another to sell for their account, allowing them so much per cent, for their trouble. Contraband TradCt that which is prohibited by law. Convoy^ ships of war sailing with other ships in order to protect them. Counter-Ordevj an order sent to revoke a former one, eHher for the sale or purchase of any commodity. Creditf in general, the confidence which one house reposes in another ; more particularly the reverse of Debit, Currency^ the money in circulation, as distinguished from bank paper, &c. Currenty a term used to express the present time. Hence, the price.current of any merchandise is the known or ordinary price at the time it is published. Custom-house, where entries are made on goods exported or imported, and the duties imposed by law paid. Dishonour, an expression made use of when bills of ex- change, &c. are refused acceptance or payment. Dividend, a share of any. capital, debt, or profit ; also the interest in the stocks. Dubious-paper, means Bills drawn on houses of little credit. Due Protection, regular acceptance or payment of a draft or bill. Duty, the tax imposed by government upon the import or export of goods. Effects, monies, goods, or moveables, in the hands of one person belonging to another. Embargo, an arrest on ships or merchandise by public au- thority. Emporium, a principal place for the importation and sale of merchandise. Excise, is an inland charge or imposition on various com- modities. ' ' ^^ Finances, a term generally applied to the public revenues. Firm, the mercantile appellation of a house engaged in commerce. First-rate paper, bills drawn or accepted by a good house, such as has always paid its bills regularly. Flat, an article of merchandise is said to be flat when there are few buyers. Freight, the sum paid for transporting merchandise by sea, &c. Chiarantee, a person who undertakes that certain stipula- tions shall be fulfilled. Honour, to honour a draft is to accept it on presentation. .1 HMS. Qother to sell for cent, for their 1 by law. hips in order to armer one, eHher : ] »ne house reposes \ ' Debit, I istinguished from | nt time. Hence, nown or ordinary goods exported or i. when bills of ex* tent. r profit ; also the ses of little credit. rmeni of a draft or >on the import or ;he hands of one disc by public au- rtation and sale of 1 on various com- 3 public revenues, louse engaged in by a good house, t)e flat when there Irchandisc by sea, |at certain stipula- [>n presentation. EXPLANATION OF COMMEBCIAL TERMS. 214 Impostf a certain tax or duty levied on merchandise im- ported. Insolvent, a tradesman who has not a capital adequate to the payment of his debts is said to be insolvent. Instalments, payments of a debt in certain proportions and at stipulated times. Land/waiter, an officer belonging to the Custom-house, whose duty it is to take an account of the goods imported. Letter of Advice, a letter giving notice of any transaction. Letter of Attorney, or power of Attorney, a writing which empowers one person therein named to act for another. Letter of Credit, a letter by which one person can receive money on the credit of another. , Letter of License, is a written permission granted to a per- son under embarrassment, allowing him to conduct his affairs for a certain time without molestation. Letters of Marque, a power granted by the Lords of the Admiralty to ships fitted out by individuals to act against the common enemy. License, a privilege from government for carrying on a trade or business, on which a certain duty is laid. Manifest, a list of a ship's cargo, which paper must be signed by the master of the vessel, before any of the goods can. be landed. Maturity, in bills, is when they become due. Maximum, the highest price of any article, as fixed by some law or regulation. Nonclaim, is where a creditor neglects to make his claim within a proper time, in which case he cannot enforce his de- mand. Notary Public, is a person legally empowered to attest deeds and other writings; also to note and protest bills, drafts, or notes, when refused or returned. Order, a direction from one house to another to effect cer- tain purchases, &;c. upon limited or unlimited conditions. Pierage, money paid for the support of an established pier. Prime Entry^ the first or original entry made at the Cus- tom-house on goods imported or exported. . Price Current, a list of the articles in the market, with the present prices annexed to each, and is generally furnished every month. Procuration, the power of using the signature of a house on letters and bills. Quarantine, the time a ship suspected of infection is re- I h 215 - EXPLANATION OF COMMERCIAL TERMS. stricted from intercourse with the shore ; also certain duties imposed on ships. Remittancei a sum of money sent either in bills of exchange, or otherwise, from one house to another. Renewal of a hill, is the cancelling a bill or promissory note due, and accepting another at a given date in lieu thereof. Solidity, the character which a house bjars as to property. TidewaiterSf officers employed to see the loading and un- loading of ships, in order to prevent contraband trade. Tonnage, the measurement of a ship, by which she pays the tonnage duty ; or it is her actual capacity for stowage, and is in that case commonly called her burden. Turmage, an impost of so much per tun on liquors imported or exported. Umpire, when two arbitrators cannot agree in settling a dispute, a third person is named, who is called an umpire ; and whose decision is binding. Value, to valuer in a mercantile sense, is to draw a bill ; the words " value received," or " value in account," are al- ways mentioned in every bill of exchange. Underwriters, persons who insure ships, cargoes, or other risks, which is performed by writing their names under a policy of Insurance. Wharfage, money paid for the use of a wharf. THE END. RMS. SO certain duties Mils of exchange, lI or promissory ren date in lieu 9 as to property, loading and un> ind trade, lich she pays the [• stowage, and is liquors imported jree in settling a jailed an umpire ; s to draw a bill ; account," are al- iargoes, or other ' names under a fiarf. 'M'