&: IMAGE EVALUATION TEST TARGET (MT-3) // **% 1.0 I.I ■tt I2ii 122 2.0 14.0 u& i = IIIU4 1 1(6 < 6" ► Fhotographic Sciences Cdrporation 33 WIST MAIN STRIET WEBSTU.N.Y. MSM (716)172-4503 CIHM/ICMH Series. CIHM/ICMH Collection de microficlies. Canadian Inttltuta for Historical Microraproductiona / Inatitut Canadian da microraproductiora hiatoriquaa Tachnical and Bibliographie Notaa/Notaa tachniquaa at bibliographiquaa Tha Instituta haa attamptad to obtain tha baat original copy availabia for filming. 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Pagaa da coulaur Pagaa damagad/ Pagaa andommagAas Pagaa restored and/oi Pagas rastaurias at/ou paliiculAes Pagaa discolourad. «tained or foxet Pagas dtcolorias. tachet*es ou piquAes Pagas detached/ Pagas ditachias r~1 Pagaa damagad/ I — I Pagaa restored and/or laminated/ r~7 Pagaa discolourad. «tained or foxed/ I I Pagas detached/ rrt Showthrough/ ''•7>' Tranaparanca Quality of prir Qualit* inigala da I'imprassion Includes supplamantary matarii Comprend du material supplAmantaira I I Quality of print varies/ r~n Includes supplamantary matarial/ Only edition availabia/ Saula Mition disponibia Pagaa wholly or partially obscurad by errata slips, tissues, etc., have bean refilmed to ensure the best possible imaga/ Las pages totalamant ou partiallement obscurcias par un fauillat d'errata. une pelure, etc., ont *t* film*es i nouveau de fapon A obtanir la mailleure image possibia- a b rl n n 10X 14X 18X 22X 26X 30X 1 7 12X 16X 20X 24X f ■; 28X 32X Th* copy fllmad har* has b««n r«produc«cl thanks to ths ganarosity of: National Library of Canada L'axamplaira fiimA f ut raproduit grica i la g4n*rosltA da: BibliothAqua nationala du Canada Tha imagas appaaring hara ara tha bast quality possibia considaring tha condition and iagibility of tha original copy and in kaaping with tha filming contract apacif ications. Las imagaa suh^antas ont 4t4 raproduitas avac la plus grand soin, compta tanu da la condition at da la nattatA da l'axamplaira film*, at an conformitA avac las conditions du contrat da fiimaga. Original copies in printad paper covers are filmed beginning with the front cover and ending on the last page with a printed or illustrated impres- sion, or the back cover when appropriate. All other original copies are filmed beginning on the first page with a printed or illustrated impres- sion, and ending on the last page with a printed or illustrated impression. Lee exemplaires originaux dont la couverture en papier est imprimAe sont f ilmto en commen^ant par la premier plat at en terminant soit par la darniAre page qui comporte une empreinte d'impression ou d'iilustration, soit par la second plat, salon la cas. Tous las autres exemplaires originaux sont fiimAs en commen^ant par la pramlAre page qui comporte une empreinte d'impression ou d'iilustration at en terminant par ia darnlAre page qui comporte une telle empreinte. The last recorded frame on each microfiche shall contain tha symbol ^^ (meaning "CON- TINUED "), or the symbol ▼ (meaning "END "), whichever applies. Un dee symboles suivants apparattra sur la dernlAre image da cheque microfiche, selon le cas: le ^ymboie — ► signifie "A SUIVRE", le symbols V signifie "FIN ". IVIaps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc., peuvent Atre filmte h dee taux de reduction diff Arents. Lorsque le document est trop grand pour Atre reproduit en un seul clichA, 11 est film* A partir de i'angie sup^krieur gauche, de gauche k droita, at de haut en bas, en prenant le nombre d'imagas nteessaire. Les diagrammes suivants illustrent la mAthode. 1 2 3 32X 1 2 3 4 5 6 AR' REDUCED [THIS SY8TI THE A] KNOWI TOTHl THE ART OF READY RECKONING; OR, MENTAL AND PRACTICAL ARITHMETIC. REDUCED TO A SYSTEM, AND PUBLISHED FOR THE PUBLIC OP CANADA; BEING PARTICULARLY , , .. ADAPTED FOR MEN OF BUSINESS. AS WELL AS FOR SCHOOLS. BY JOHN BRASS. ':.'f [THIS SYSTEM WILL PROVE A VALUABLE ACQUISITION, AND FURNISH EVERY FACILITY IN CALCULATION TO THE ADULT AS WELL AS TO THE JUVENILE, ALL THOSE USEFUL AND READY METHODS OF OPERATION KNOWN ONLY TO THE FEW, AND WHICH ARE ALMOST TREATED AS A 1CY8TERY, ARE HERE INTRODUCED TO THE PUBUC IN ORDER THAT THE INFORMATION MAY BECOME GENERAL.] 1 f ■ U TORONTO: PRINTED BY LOVELL AND GIBSON, FHONT STBEET. 1851, l !>i|WMWBjaMiBa..'.Jiiii.-i.u. g f 154659- m^ ^.ill •^^ <^ I ^ f y^ Entered, according to Act of the Provincial Legislatare, in the year of Our Lord One thousand eight hundred and iifty*one, BY JOHN BRASS, In the Office of the Registrar, of the Province of Canada. •/ TO THE PUBLIC. Dear Friends, In submitting this new system of calculation to your notice, I have undertaken a task which should have fallen to the lot of a more influential person than myself; but, as none other has stepped forward to the aid of the youth of this Province, (more particularly those whose daily avocations require them to be expert and ready reckoners,) I trust this humble attempt will meet with your approbation. The liberal encouragement I have already met with/ leads me to believe that any endeavour to promote the public welfare is ever encouraged by a discern- ing and enlightened people, however humble the attempt may be. I am, dear friends, Your very obedient servant, THE AUTHOR. i 'II Toronto, March, 1851. '•I\\ mmm I i' LNTRODIICTION. As THIS WORK is undertaken with a denirc to emancipate Youth from the various difficulties imposed upon them by long established custom, 1 have ventured so far out ol' the beaten tracli, that it will be Ibund to differ very materially from every other treatise on Arithmetic, and as this I believe is the first attempt made by any individual to arrange and establish a practical system of Mental Arithmetic, adapted to the currency of the country, I take the earliest opportunity of submitting myself to public protection and patronage ; should this be awarded me, it is probable that at no distant period I may considerably add to the work. I doubt not but a glance \vill suffice to show that this work, though intended for the use of Schools, is not leas valuable to the Adult and business Man, for its operations are by no means confined; nor should any store be without it for the benefit of its clerks, as it entirely supersedes the old and tedious method of calculation, both in brevity and in sim- plicity, which enables them to calculate at a glance, with equal accuracy, that which by the old rules would require considerable time, and in many instances be attended with difficulty ; but with regard to its merits on this head I shall not say more, but trust to its general utility for its appreciation. With regard to its adaptation for Schools, I flatter myself that every Teacher will at once perceive its utility. The beauty and simplicity of the questions, and the arrangement of the lessons (unequalled by any other work,) for practice upon the black-board, are not amongst the least of its recommendations, as they will be fv. .id to simplify the art, and facilitate the progress of the learner, not only to his (the Teacher's) satisfaction, but to the delight of his Pupils and the pleasure of their Parents. I have introduced the most familiar illutrations of particular cases and examples, so as to render the subject as intelligible and attractive as possible ; to form useful exercises for the developement of the mental faculties; to excite the emulation of the young student, and create a desire to enrich his mind by the acquisition of information which will prove advantageous to him through life. The principal cause of turning my attention to this subject is the interest which a liberal and enlightened Government manifest in attempts to diffuse knowledge over that great surface of the community, which is occupied by its less affluent members, both by the \ ■ ? ;»£v^^»^naica "wimwicn *i »«i«M-i;^" .01. election of flt and proper peraona to superintend thin denirnhle object, and the appropriation of ftindi to promote it, and which have heen as happy in their results as they have been rapid in their courHe. The people that are thus favored ought not to be indifferrnt to the task of fostering the seeds of genius, which, scattered by the hand of Heaven itself, fall nn often upon the waste and steril land, as upon that which is more indebted to the labora of cultivation. ^' * ' " ' ' ''■''' " " The most unthinking, as well as the most prejudiced, must bo struck with tlie fact, that the period in which we live is extraordinary and momentous. Amongst the civilized masses of Europe, an unparalleled revolution is at work ; they have awoke from that ignorance in which they had slept for ages, and have sprung up in their new character of thinking beings, qualified to enquire and to discuss, and despising both the despotism and the bigotry that would prohibit or impede their improvement. The intellectual spirit is moving upon the ohaos of minds which ignorance and necessity have thrown into collision and confusion, and the result will be a new Creation. At no period of history has there been so great a devel- opement of the human faculties as there is in our own time ; and the cause of the present height of mental powers is well worthy the study of the philosopher. But a few centuries ago, a learned man was gazed at as a miracle, and ignorance was so common, that it passed unheeded; but in the present day learned men are so numerous, that only the most talented geniuses are at all conspicuous in society ; and to be ignorant is to be despised. That mid' night of ignorance which enveloped the human intellect has now passed away, and the bright orb of science, which at intervals sheds its feeble rays through the gloomy darkness of mental degradation, and was often extinguished by ignorance and superstition, has at length burst forth a quenchless light, and spreads its bright effulgence through nations. ' Those who have encountered the tedious process of Arithmetic, and acquired a know- ledge of the principles of the art, are best aware of the difficulties the student has to conquer. There is nothing so discouraging in Arithmetic, or that has tended so much to retard the progress of the learner, as that of fixing in the mind, by the common exercise of memory, those tables of cramp'd and unconnected sentences and subjects, with which the art is so much burdened. There is not, perhaps, in the whole range of our acquirements, any thing more difficult to be remembered; there is nothing in them that we can embody ; they, in them- selves, form no point of association that the mind can cling to ; but are, as a writer happily observes, like grains of sand that have no coherence. To remedy this inconv ' ce and promote that continuous chain of thought which is necessary to be preserved in giving effect to the most simple operations of the mind, whether -*• ftLMtAOM, that aMiatanoe ha drrived IW)m mnemonioal luuociution, or any other aid or conneetioii capable of improving the recolleotivti facultira, wore indeed an ot^ect of the greatest impor- tance. The very bases of Arithmetic are method, locality, and association ; and it is the various operations of these, that I winh to render mure simple and interesting to the student. The nnsociatinn of ideas in the natural order of the mind, wo find to bo the most pow- erftil and cfllcaeinos means of reminlHccnce, wherever one object becomes linked with another wo more CHHiiy recollect it than where it is apart or isolated. It will be proper for tliONo who are dcsirouH of attaining a thorough knowledge of Arithmetic, to study the art under a practical teacher, who will demonstrate patiently, every rule as he proceeds, and not sutfer his pupil to waste his time in useless trials and eonjecturc. It depends not altogether upon the capacity of the learner, but the clear com- nunication of his preceptor to remove the diflicullies, which, though simple, appear insupera- ble to the tyro, and otlen make him retract from his pursuit of gaining the best and most fruitful acquisitions of knowledge. It is not the number of books (in any art or science), but on their proper selection, and the ability of the master to explain them, that the rich harvest of the student's intelligence depends ; a pupil may gather more real wisdom from a single volume, when it is well digested to him than by carelessly perusing the pages of a hundred folios. When the Multiplication Table is known by the pupil, as it were at his fingers' ends, he should be taught the universal pence or money table; which is done by the three divisors, 4, 13 and 30. Any number of farthings divided by 4 bring them into pence ; any number of pence divided by 13 bring them into shillings; and any number of shillings divided by 30 bring them into pounds. These divisors are unlimited in their capacities, and much more easy and intelligible than the conunon confined pence table, hitherto published in every system of Arithmetic, and it excites my astonishment that no Author ever before suggested it. Another observation, and one of the greatest importance, which I wish seriously to impress upon the mind of the preceptor is, the necessity of his pupils proving every question of Arithmetic before they write down the facit or answer. Arithmetic is the science of truth, and contains no fallacies. By proof alone the analysis of the science is known; an operation may be worked mechanically from the force of memory, (Mrithoat its being in the least understood,) as 1 have experienced when a pupil ; but it can be proved only by com- parisons of the mind, which alone elicit the truth of the principles of the question. The pupil by my method will have something to encourage his perseverance, — ^the 'I, . I » I- ■ f i «'. Wntjr Mid utility of the queations. By the old plodding lystem, he toils upon a barren WMtei, onanimated by any cheering proepeet, not even that of the application or utility of hit labor ; nor have I, in the Mrhole coune of my experience, ever met with a pupil, who, on entering into Reduction, aAer serving an apprenticeship in the Weights and Measures by the old method, was capable of solving the most simple question in any of its rules. The great object I am striving to effect, in my new system of instruction, is to give the learner a sound practical knowledge of those branches which are more especially applicable to the affairs of life, or which can render him useAil and respectable in the line for .which ht ki destined A<>>»»WM^wMI »^0 »^k^»^ ■ ■ > »» >*> ; s '■■ •• « .# a barrra ntility of npil, who, asures by » give the pplieable for which , DEFINITION UK ARITHMETIC. A^^^^^^^^^^N^N^^I^^rf^^^^VS^^^Nrf^ W WSV^ ■' ii ARmiMmc in A BcifncA whirh rxplninn thr prnprrtirn niul hIiowh thr uttrn of niimticn. Unity, or a ('nit, ia the numbrr one. F.very othrr nunilM*r h nn (iHwuMixge of unitH. For facilitating the management ofnumhent in arithnictio, thry arc cxpnNNcd hy hignii or characters. In modem Arithmetic, all numbers are cxprrMsrd hy means of ton charactern: the nought, or cypher, or zero, U, which Iiom no value ; and the nine Hit;nilicant (iKure^ or iligitN, 1, 3, 8, 4, B, 6, T, 8, 0, which denote respectively the numhern one, two, three, four, iivc, h\x, ■even, eight, nine. The idea of these figures is supposed to have been given by the ten finders of the hands, which, no doubt, were made use of in computation before arithmetic wa.s syNtematizcd. When either of these significant figures stands by itself, or when it is followed by no other figure, it expresses merely its simple value ; but when it is followed by one figure, it •Ignifiei ten times its simple value ; when by two, one hundred times ; when by three, one thousand times; and so on by a ten-fold increase for each figure that follows it. The increased value thus denoted by a figure in consequence of its position is called its local value. Though the nought or cypher, of itself, as its name imports, stands for nothing : yet, being placed close to other figures, on their right, the combination increases their value in the same ten*fuld proportion. Suppose I want to note down in figures five hundred and three — I must put a cypher in ten's place between the 5 and 3, otherwise it would appear to be only 53 : and if I place a cypher on the right hand of 1, it instantly becomes t^n. An even number is that which can be divided into two equal parts : as 2, 4, 0, R, 1 0, 12, &c. An odd number, on the contrary, is that which cannot be halved, or which, if it can be divided by 2, always leaves a unit for the remainder, as 1 , 3, 6, 7, 0, Sic. A prime number is that, which divided by any number, between 1 and itself, would leave a remainder. A composite number is the result of two or more inferior numbers multiplied together, and the inferior numbers are called its components parts — thus 18, for instance, being a oomposite, 8 and 6 are its component parts, and on this principle all the answers in thje mul- tiplication table are composite numbers. An integer is any whole number, consisting of one unit or more of only one kind or denomination, as 3, 8, 12, 50, 100, &c. A frtution is a part of a unit and is expressed by two numbers, the one below the other, with a line between them, thus ^. A mixed number is an integer and fraction together, thus 2f . ' A common measure is a number that Will exactly divide other numbers and leave no remainder, as 4 which measures 8 and 12 exactly ; it is commonly used in reducing frac- tions to their lowest terms and in abridging terms in the Rule of Three. An aiiquot part is an even part of a number or quantity ; such a part as, when taken a certain number of times, will exactly make that number. It is always known by having 1 for the upper figure of the firaction, and is generally employed in calculating the value of oommodities. 10 DEnNITtOlf OP AMTHMETIC. I The five ruins upon which the whole of arithmetic depends are Notation or Nument- tion, Addition, Subtraction, Multiplication, and Division ; the last four of which are either simple or compound. Simple is when the given numbers arc all of the same denomination, aa all pounds; but if the operation consists of several names, as pounds, shillings, pence, &c., it is termed compound. Nutation teaches to write or express numbers by figures. Numeration is the art of reading or discovering the values of numbers already expressed by characters. Numbers arc divided into periods of six figureH, and half periods of three figures — commencing at the right hand and counting towards the left. Addition tenches the sum of numbers : it is the adding or collecting of several numbers into one amount, and the answer or number found is called their sum or total. Subtraction teaches the difference of numbers : it is the taking of a less number from a greater in order to discover the difference between them. The greater number is called the minuend, the less the subtrahend ; and the answer or number found the remainder. Multiplication teaches the product of numbers : it is the art of finding the amount of any given number when repeated a certain number of times, and is therefore a short method of performing addition. The upper line or number to be increased is called the multipli- cand. The lower line or number by which it is to be increased is called the multiplier ; and the answer or number produced by this operation is called the product. Both the multipli- cand and multiplier are sometimes called factors from their making or producing the product. Division teaches the separation of numbers : it is the art of finding how many times one number is contained in another, or dividing of any sum into any number of parts pro- posed, and is therefore a short method of performing Subtraction. The number to be divi- ded is called the dividend; the number by which we divide is called the divisor; the number which this operation produces is called the quotient or answer to the question ; and when there is anv number over at last it is termed the remainder. v.. '> ,1 .;..^-, There are two modes of Division, the one is called short, and the other long. The former is that in which the several Multiplications and Subtractions are performed men- tally, and the quotient set under the dividend. This is preferable to the latter when the divi- sor is a composite number, or any whole number below 13. In dividing by component parts, the true remainder may be found by multiplying the last remainder (if any) by the first divisor, and including the first remainder (if any) which will produce the true remainder. Reduction teaches to bring money, weights, and measures from one name or denomina- tion to other numbers of a different denomination, without altering their value, and is per- formed by Multiplication and Division. \.« In reduction there are two branches or problems : the one is termed descending, the other ascending. Reduction descending, is the reducing numbers of a higher denomination to those of a lower denomination, in which case multiply by as many of the lower as make one of the higher. Thus, to reduce £5 to shillings, multiply by 20, the number of shillings in a pound, which gives 100 shillings, the answer. Reduction ascending, is the bringing a less denomination to a greater ; in which case divide by as many of the less name as make one of the greater. For instance, to reduce 100 shillings to (>bunds, divide by 20, which gives £5, the answer. ?*■ orrnnnoir or Atmnnmo. 11 Sia^le proportion, or the Rule of Three, tenches from three piven numbers to find a fourth, called the atiswer, which, when found, shall hoye the same ratio or proportion to the third as the second has to the first Questions in the Rule of Three are of two kinds, viz : direct and inverse. Direct proportion is more requiring more, or less rfquirinp; less, for when the proportion is direct a greater third term always requires a greater answer, and a less third term a less answer ; that is, an answer less than the second or middle term. Thus, if six yards of cloth cost 12 shillings, 10 yards of the same will cost 20 shillings;— more yards requiring more money is direct proportion. Or if 10 yards of cloth cost 2») shillingH, six yards will cost 12 shillings; — less in quantity requiring less money, is direct also. Inverse proportion is more requiring less, or less requiring more : for such is the pecu- liar nature of the questions, a greater third term (that is, one that is greater than the first term) requires a less answer (that is, an answer less than the second or middle term) ; and, in like manner, a less third term requires a greater answer. Thus, if 4 men take 12 days to do a piece of work, 8 men could do it in half the time ; — more men requiring less time is inverse. Or if 8 men take 6 days to do a piece of work, four men would require double the time; — less men requiring more time is likewise inverse. In stating questions in this rule write down that number for the middle, term which is of the same denomination as the answer to the question, with two dots before and four after it; on the right, place the term vLich requires the answer; and, on the left, the remain- ing term of the same name or kind with that on the right. The next step is to reduce the right and left hand terms to one, and the same denomi- nation and the middle term to the lowest denomination mentioned in that term. Before solving the question, it must be observed that the third or last term be of the same name or description as the first. The middle term must be reduced, if necessary. The question discovered to be inverse or direct, and the terms abridged, if [mssible, which will greatly shorten the operation. ■?': If the question be direct, the method of solving it is to multiply the second and third terms together, and divide the product by the first term for the answer. But if the question be inverse, multiply the first and second terms together and divide their product by the third ; and in both cases the quotient will be the answer required in the same denomination as the second term. In those cases, where the answer requires to be brought to another name, reduction is necessary before the work is complete. To prove questions in the Rule of Three, it is only necessary to note down the answer of the former statement for a middle term; the first term for a third, and the third for a first, and proceed as before to find an answer similar to the middle term of the former statement. The terms in direct proportion are abridged by dividing the first and second, or the first and third terms, by a common measure (which, of course, should leave no remainder); and inverse proportion by dividing the third term, and either the second or first terms (but not both at once,) by some common measure ; and in both cases the quotients thus found may be used instead of the original terms. Compound proportion, or the double Rule of Three, teaches from any odd number of terms greater than three being given to find another term, called the answer, which, when found, must bear the same proportion to the one in question of the same name or kind, as the remaining terms considered, as two distinct bodies bear to each other. To state the terms, put that number in the middle, which is of the same denomination ',''\\ ■ '■ w ''■M\ M>it tf' IS DEnNinoif or AKiniMrno. or quality as the required term, with two dots before and four aOer it : on the right, place all the terms which require the answer, and on the leit, all the remaining terms, observing that like names be opposite to each other. The statement will then exhibit, on the left; hand, nil the terms of supposition to which the middle term appears to he an answer; and, on the right, all the conditional terms for which the answer of the question is required. The inverse terms may be discovered and managed thus : consider each first and third term, along with the middle term, as a separuto stuttnnent in the single Rule of Three, and apply the two definitions commencing with the words "direct proportion" and "inverse proportion" to it — which, if found to be inverse, exchange the terms by placing the third where the first was, and the first where the third was. To find whether a statement is "direct" or "inverse," if it requires more, mark with a cross the less extreme for the divisor ; if it requires less, mark the greater, which will at once decide the question. Before solving the question, observe that the terms opposite to each other be of the same name, the inverse terms exchanged, the middle term reduced, (if necessary,) and the terms abridged, if possible. In solving the question, multiply all the right hatnl terms together for a third term, and all the left hand terms together for a first ; these two thus lound along with the middle term form a statement in the single Rule of Three, direct. Thon multiply the second and third terms together and divide their product by the first, wlii^h gives the answer in the name in which the middle term was left. Practice is a short method of finding the value of any quantity of goods by the use of aliquot parts, — or, in other Avords, such a part as, when repeated a certain number of times, will exactly make that quantity or number. Tare and Tret. — The whole weight of any commodity, including the package, or what- ever else contains the goods, is called its gross weight. Tare, Tret and Clough, are certain allowances made by merchants in selling goods by weight. Tare is an allowance to the buyers for the weigl't of the package. Sec, and is either at so much for the whole, at so much per hogshead, chest, cask, &c., or at so much per hun- dred weight. '. Tret is an allowance to the vendor of 4 lbs. upon every 104 lbs. after the tare is deducted on account of dust or other waste. Clough is an allowance of 4 lbs. in every 3 cwt. after the tare and tret are deducted for the turn of the scale when the goods are retailed. Svitk is what remains after some of the allowances are deducted. Thus, after the tare is deducted from the gross, the remainder is called tare suttle ; and after the tret is deducted from the tare suttle, the remainder is called tret suttle. The Neat or Net Weight is what remains after all deductions have been made. Interest is the sum to be paid by a person for the use of money which he owes. The money due is called the principal. The sum of the principal and interest is called the amount. The rate is the money allowed for the use of one hundred pounds for any given time, but usually for a year. Compound Interest is when interest is charged, not only on the original principal, but also on the interest as it becomes due. DEFINITION or ARITIIMETir. IS In interest, five quantities are concerned : the principal, the rate, the time, the interest, and the amount ; and any three, except the principal, the interest, and the amount, being given, the rest can be '''•und. it is scarcely ..f sary to remark that per cent, means per hundred, and per annum per year. Discount is an allowance made for advancing money before it becomes due, and gene- rally consists of the interest of the sum up to the time at which it becomes due. Three days, called days of grace, are always allowed after the time a bill is nominally due before it is legally due. Commission is the sum which a merchant charges for buying or selling goods for another. Brokerage is a smaller allowance of the same nature, a per centage usually paid to brokers for negotiating bills, or transacting other money concerns. Insurance or Assurance is a contract by which one party on being paid a certain sum or premium by another on account of property that is exposed to risk engages in case of loss to pay the owner of the property the sum insured on it. Equation of Payments is a rule which teaches to find a just time for paying a debt at once, which is due at different times. Profit and Loss is that branch of arithmetic which treats of the gains or losses on mer- cantile transactions. : Exchange teaches us to find how much of the money of one country is equivalent to a given sum of the money of another. The par of exchange between the two countries signi- fies the intrinsic value of the money of the one compared with that of the other, and is estimated by the weight and quality of the coin. Fellowship is the method of determining the respective gains or losses of the partners in a mercantile company. Partnership may be of two kinds — single, and double. In single fellowship, the stocks or sums contributed by the several partners all continue in trade for the same time. In double fellowship, the stocks continue in trade for diiTerent periods. Alligation is a rule which is chiefly employed in calculations respecting the compound- ing or combining of articles of different kinds, and is of three kinds, viz : medial, alternate, and partial. Alligation Medial is when the quantities and rates of the ingredients are given to find the value of the compound. Alligation Alternate is when the rates of the ingredients are given to find what quantity of each will compose a mixture at a given rate. Alligation Partial is when the whole composition or one of its ingredients is limited to a certain quantity. Involution is the method of finding any assigned power of a given number^— or, as it is also expressed, the method of raising a number to any proposed power : for example, 2 multiplied by two, gives 4 ; the second power or square which, multiplied by two, gives 8 ; the third power or cube, and so on. Evolution, or the extraction of roots, is the method of finding a number, the continual product of which, repeated a given number of times as factor, will amount to a given number, and is the reverse of Involution. Position is a rule by which a true answer may be found to a question which cannot be solved by any of the ordinary rules of arithmetic, by adopting certain numbers to use as if they were the true ones. 1- ! !i:i *;:!( ■.* DEriNinON OP ARITHMCTIC. It is called single when one faliie number, and doable when two are requisite to find the answer. ' Progression is of two kinds, viz : arithmetical, and geometrical. Arithmetical is that in which the terms either all increase, or all decrease, by the same quantity ; and this quan- tity is called their common difference. Geometrical is that in which the successive terms all increase by a common multiplier, or all decrease by a common divisor. Either of which is called their ratio. The Purchasing of stocks is fhe buying and selling of shares in the public funds. '" ' Barter is the exchanging of one commodity for another in such a way that neither party may sustain loss. Mensuration is the art of measuring any thing that has length, breadth, or thickness. Annuities. — An annuity is a fixed sum of money payable at the ends of equal periods of time, such as years, half years, or quarters. Annuities are of two kinds : certain, and contingent. The former are those which commence at a fixed time and continue for a determinate number of years ; the latter are those whose commencement, or continuance, or both, depend on some contingent event, usually the life or death of one or more indivi- duals. Vulgar fractions. — When an operation in Division is performed, the remainder, with the divisor placed under it, forms a vulgar fraction ; and these, admitting of being added, subtracted, multiplied, and divided, have in consequence been formed into a distinct rule, called vulgar fractions. Decimal fractions. — A decimal fraction is a fraction whose denominator is 1, with as many cyphers annexed as there are figures in the numerator : the denominators therefore being 10, 100, 1000,&c., are seldom or never used in the calculation, which renders the ope- rations similar to simple addition, subtraction, multiplication, and division. Decimals are distinguished by a dot prefixed to them, called the decimal point The signs used in arithmetic are certain symbols or characters which denote what is to be performed in a shorter, better, and more significant manner than can be expressed by words at length. The character = (equal to) is the sign of equality, as 12d. = 1 shilling ; that is, twelve pence are equal to one shilling. The character + (plus or more) is the sign of addition, as 4 + 6 = 10 ; that is, four added to six are equal to ten. The character — (minus or less) is the sign of subtraction, as 8 — 5 -> 3 ; that is, eight lessened by five are equal to thjee. The character X (multiplied by) is the sign of multiplication, as 5 X 6 = 30; that is, five multiplied by six are equal to thirty. The character t- (divided by) is the sign of division, as 6 -i- 2 — 3 ; that is, six divided by two are equal to three. The character : (is) : : (so is) : (to) are the signs of proportion, as 2 : 4 : : 8 : 16 ; that is, as two are to four, so are eight to sixteen. i«^)i t. ■ -.'•*,:', >': ■S.'tti" ' ^'-fr-,.. QUESTIONS UPON THE DEFINITIONS. .:','V "»* J It is important that every Pupil as he progresses in the science of Arithmetic should first learn the rule he is about to enter upon by rote, that he may, as it were, have it at his fingers' ends, and thoroughly understand the principles he is going to work u|)on, and to keep those ever present to his memory that he has previously learnt. It is advisable for the teacher to question him upon the definitions, and for whose assistance the following ques- tions are intended : What \i Arithmetic? What is a Unit? What is every other number? How are the nunibera in Arithmetic expressed? By how many characters ore all numbers expressed? What are they? , . From what did the idea of these figures first origiiintr'? When one of these figures stands by itself, what does it express? When followed by two? By three? What is the increased value railed? What does the nought or cypher of itself import? In what proportion does it incrense the value of other figures when placed on the right? How would you note down the figures, five hundred and three? * If you place a cypher on the right hand of 1, what does it become? If two? If three? What is an even number? Give examples. What is an odd number? Give examples. What is a prime number? , What is a composite number? What Table consists entirely of composite numbers? What is an integer? Give examples. What is a fraction? How is it expressed? Give examples. What is a common measure? For what is it commonly used? What is an aliquot part? How is it always known, and for what employed? How many rules does the whole of Arithmetic depend upon? Name them. How are they divided? What is meant by simple? What by compound? What does Notation teach? What is Numeration? How are numbers divided? What does Addition teach? . ..^ What is the answer called? What does Subtraction teach? What is the greater number called? The less? The answer? What does Multiplication teach? What is it a short method of performing? What is the number to be increased called? What is the number it is to be increased by called? What is the answer called? * The Teacher can here suggest a variety of numbers as fancy may dictate. wi 1« aucsnoirs ufok thb OEnMrnoifi. I ! 'H. v.v: Why are the roultiplicand and multiplier sometimea called faoton? ,„ , What do«8 Division teach? What i« it n ahort method of performing? ' j What ia the number to be divided called? ' ' What is the number to be divided by called? ' What is the answer called? How many modes of division are there? What are they? What is the short method? How may the true remainder be found when dividing by component parts? What does Reduction teach? How many branches or problems are there in Reduction? What are they termed? What IS Reduction descending? How do you reduce numbers from a higher to a lower denomination? What is Reduction ascending? How do you bring n less denomination to a greater? What does Simple Proportion, or Rule of Three teach? Of how many kinds are questions in this rule? What are they? What is Direct Proportion? What is Inverse Proportion? When more money requires more goods, in what rule is your question? If less time requires more men, in what rule is your question? If less money requires less good^, in what rule is your question? If more time requires less men, in what rule is your question? How do you state your question in this rule? If you want money for your answer, of what kind must your second term*be? If you want weight, of what kind must your second term be? If measure, if time, what must your second term be? If your right and left hand terms are not of one denomination, what are you to do? If the middle term is not of one denomination, what are you to do? Having your terms reduced, how do you proceed to solve Direct Proportion? Having your terms reduced, how do you proceed to solve Inverse Proportion? What rule is necessary to complete the work? How can you prove questions in the Rule of Three? When is your question in Direct Proportion? When in Inverse Proportion? What terms do you abridge in Direct Proportion? What terms do you abridge in Inverse Proportion? What does Compound Proportion, or Double Rule of Three teach? How do you state the terms? What will the statement then exhibit on the left? What will it exhibit on the right? i How may the inverse terms be discovered and managed? How do you find whether a statement is direct or inverse in this rule? How do you solve questions in this rule? * Wl Ho Wl Wl Ho Wl Wl Wl Wh Wl Wl wt Wh Wh Ho Wb Wh Wh Wh Wh Wh Wh Of Wli Wh Wh Wh Wh Wh Wh Wh On Wh Are Wh Hoi Wh Nfti Wh lu'.i. What is Practice? What is Tare and Tret? What is Tare, Tret and Clough? What is Tare? What is Tret? What is Clough? What is Suttle? What is Neat or Net Weight? What is Interest? What is the money due called? What is the principal and interest called? What is the rate? y .r jilifC o Qonnom oroii tm Bvannoiii. IV) i . What ia Compound Intereat? How manjr qutntitiea are concerned in Intereat? What are thej? What does per cent, mean? And what per annum? What ia Discount? '^ > How many days are allowed after a Bill ^beoomea noiniiu41j due? What are they called? • »4i.i.i i J, ,.' i. What is Commission? , ' What is Brokerage? '»<' ' ' What is Insurance or Assurance. . , n< ' i » i r i r !• t » r i ^ What does Eqiiatlop of Payments tca^h? / ) 11^! J f. I i 1 1 j I /, What branch of ArithmctiR is Profit and Loss? What does Exchange teach? ,, .^i ii:i/y.i^V VUMil I'M- \ Y.\ 'XlC»/.AUnA What is Fellowship, and how divided? What is the diflerence between Single and Double Fellowship? What is Alligation? - — How is it divided? What is Alligation Medial? :xk\>J\' / M^V \ X^A\t:- W. - What IS Alligation Alternate? . What is Alligation Partial? hj.oii i.>i( ».• s'.-iImhII ./I What is Involution? , ■,,• , .. . What IS Evolution? What is Position, nnd of how many kinds? • -iJ-iliU. .11/ When is ii Single? WbanDouble? ...M.ii«wi...ii !<, ^f»i,^b,u.H .1/ Of how many kinds i9.PTQgres4i.Qn? i.n, •i..:.ii in,;-.'!' .7 What is A.riihmetical Progrectsion? -Itu-iM.iiJ .71 What is Geoinetrical Progression?" ' ' • ■ n 11 What is the purchasing Of Stocks? - -i •• n. m .m What is Barter? -■'^'^' -^l What is Mensuration? -■.,,1' • .1 What are Annuities?. Of how many kinds are they, what are they? What is a certain Annuity? What is a contingent Annuity? —-On what account was a distinct rule for Vulgar FraetlDns formed? * "*■ - ^ What is a Decimal Fraction? ,1:, ,. i^.j Aire th^ Denominators ever used in calculations? .1 ; t > m, 1 1 . (i; What are the operations similar to? -' i' "i....'.- > ni." How are Decimals distinguished? *• '■' ' '' ' '• •- "^'^ — - - -- - t '1 !■ l-i. ..;..! ■■<*• I. P:. <% .vf.i «i '.»! ;• '"-V.' ^ (ii.'. <■!■ : (•;. , I ! 7 M- What are the signs used in Arithmetic? r ,f. .-< <, 1)., .i; ■;.'! , Ii ..IC tit -il ! n: * . I i IS:!. .:. I .!■■ !^! Sk'* !:!. IM/l: ^. Multiplied by, . Divided by, Isi 80 is :: to : , ?tt. 1 c '11,'! )' -ri!/ 'I I '■. IP. [ r.'-n.: I !; i) .. V t- ...:• ..j; ■<' ...K .X •> .. t. .6 i't>I...o G '<■ j CI Name the characters? What ia the cbaraoter Equal to, the sign of^"] '["^^[[^ 2v..".."' « !!7t ■ Plus or More, , >jlini|s or Lessk .When questioned upon these charactera, the Pupil should represent them on the black boatd. ' .'.•; f.i. .1 '•, .!.i .U....!,'l !'-...».{ .• on4(j " .. ..:.,,!( ii'ilTiiiiic. t'L" .0'.) fy -iiiitk '-•a X .^ .OL. \\ otSlli ;?:, .ol. (jl. ( nil I ;• illi:: ;«•!«.•• f • c,i};:> n- -^ ■• •■..'lUi) '•\\- Q .■v,;;-.!q !: ... r. '■ii.t. t (■II o .^. -^s!?^^ il F .■ 'i m 1 iMI iii II *Ai'AianmwfteM. TAtuMk'i'<'%i IV. Thousands ........;....; ^-^^^ , !,• llj ^f III. Hundreds , S55 , '.^ n^ctf IL Tens 55, m M 7/ L Units 5' ef ?. I'V yii iiui'W MULTIPLICATION TABLE. Twice 1 flre2 'I... 4! 8... 6 4... 8 5... 10 6...12 7... 14 8... 16 :»j..l8 10...24 II. ..22 12...24 3 times lare3 2... 6 3... 9, 4...12 5... 15; ti...l8 7...21I 8. ..24 »...«7| 10 ..80| 1 1. ..33. 12...36 4 times 1 4 2 8 3 12 4 16 5 20 6 24| 7 281 8 32 9......36! 10 40 II 44 12 48, 5 times I are & .10 .15 .20 .25 .30 .35 .40 .45 6 times .... 6 ....12 ....18 ....24 ....30 ....36 ....42 ....48 . ...A4 10 <60jiO..<....SO II 5511 66 12 6012 72 7 limes 1 7 2 14 3 21 4 28 i 35 6 42 7 49 8. .....56 , '{!••'• ••' I0.„...70 II 77 12 84 8 times 1...... 8 2 16 3 24 4 32 5 40 6 48 7 56 8 64 9 72 10 80 II 88 12 96 9 times I are 2 3 4 5 6 7 6 9...... 10 11 12 9 18 27 86 45 54 68 72 81 90 10 times 1 are 10 2 2U 99ill 108 4...... 40 5., 6.. 7.. 8. »., 10.. 12. . 50 , 60 . 70 . 80 . 90 .100 .110 .120 ntfm«8 1 are 11 a...... 921 8.. 4.. 5. 6. 7. 8.. 9. 10. II. 12. . 83 . 44 . 55 . 66 . 77 . 88 . 99 .110 .121 .132 12t!tnes 1 are 12 2.. 3., 4.. 5., 6., 7. 8., 9. 10. II.. 12. . 24 . 36 , 48 . 60 . 72 . 84 . 96 .108 .120 .132 .144 THE FARTHINGS TABLE. 4 farthings make I penny. 2 pence. 3 do. 4 do. 5 do. 6 do. 8 ditto 12 ditto 16 ditto 20 ditto 24 ditto M' 28 farthings make 7 pence. 32 ditto 36 ditto 40 ditto 44 ditto 48 ditto 8 do. 9 do. 10 do. 11 do. 12p .ora shilling. ni 1 2 3 4 6 7: 8 » 10 12 13: 14 2 31 41 51 61 7( 8 9 10 11 £ quadra racter J .i.I-i (a-.T '.■•.i|. .If* ■>sSi 1 AUTIf1«r*TICAI. tJUOM. r a shilling. .,«n. :■■- THE PENCE TABLE. ^) 8. D. \2 pence make 1 24 ditto 2 36 ditto ;.;... 3 48 ditto 4 60 ditto 5 72 ditto 6 84 ditto 7 96 ditto 8 108 ditto 9 I2U ditto 10 P 132 ditto , 144 ft I br'ij 11 12 U v.'c 156 pence make 168 ditto 180 ditto 192 ditto 201 ditto 216 ditto 228 ditto 240 ditto 480 ditto 720 ditto 960 ditto 1200 ditto a. .... 13 .... 14 .... 15 ..,. 16 .... 17 .... 18 .... 19 £1 2 3 4 5 D. .«!/: '.un-ii/) i .pjjjj SHILLINGS TABLE. »'-l-''''«l-'i*v/li« ,bi.,s, -niifxiiv/ 20 shillings make. 30 40 m 60 70 80 90 100 110 ditto ditto ditto ditto ditto ditto ditto ditto ditto i! at I. v"/ £ 8. I 1 10 2 8 10 3 3 IQ 4 4 10 5 5 10 £ 8. 120 shillings make 6 6 10 7 7 10 8 8 10 9 9 10 10 130 ditto 140 ditto WP ditto 160 ditto 170 ditto ISO ditto 190 ditto 200 ditto ., »ff-i »ff •■(•>« h.'i; fTKc. U'j; NoiB.— 1 X as 201. SB 940d. ss 960 qr. ■(• £ s. d. and q. being the initial letters of the four Latin words lib, solidi, denarii, and quadrantes, are respectively used to denote pounds, shillings, pence, auu farthings. The cha- racter / is a corruption of the long /, ari^ng from rapidity in making it ^ denotes one farthing. ,',^;. i! » ,r.)-i f ..oiv. . vj ,.J j^ j^^ farthings, or a half a penny. ^ ,«liiJ:M!il!j.,'.-) v'uli: :'.;i't.| ^o. three fbrthinge. ■ -.hwd .1 ■•;:;•; 111',-: ;il^^■>_^ '(jj^/a .■■|.-''Mlhll-V/.! I'd', 111: .III., ■.'! i^(; ^| (t( , J ^^'V,i't■..l IK -l ^^}'U,h 'h IJ'J A. .Uhil'x.t lyy\li\L]:{ i .-.f.[i'" '!■' i .iij '.Mty\, -,: I i .J.!Mi>l .-i->iU i. ., ' a HI f. y'liiJU'l! . .li.:!. ifAi 111! (t.'ltift .• .)! i: ii. el ifiT. i ■».'■ .Villi) ■ ''I'.n. »..!.' .1 -il: H\'t> iii V^.!! Jtfgisv* ;» 'ji 'Jit;.' :^aiM ,c :i'.1;j bv'iirJ .'J.. ,«;•;«'! ' .■Jp^ !»V o,\>: J.'d> ll'l V: ■■i It.;.: - ij 5 ''1 1 1 WRQim Am m/t^-wu. \:i 'I "-I i/a'i .« .n tt r.t t-i >".! .»f ;( ^i i.) «{ b "HHW !.?.! • *» < • f I • "i>l0'v<» £1 WEIGHTS AND MEASURES. :;,;' i! •^»*. .<•»•■ »ti. TUOY WEIGHT. *24 grains^gr.) ....'.; illllke I'^ennyweight ...t.. ...... marked dwt. 20 pennjrwdghli. do. 1 ounce do. 18 ounces ;... do. 1 pound <« do. Not*.— 1 lb. na iaoi.sss240dwt«.asB57flOgr. -If? This weight was formerly used for weighiug articles of every kind ; it is now used in weighing gold, silver, jewels, and liquors, and in philosophical experiments. ««(<.. f^f vUtl. (a mull vr: f« Iwt. m 1. •«i(i b. ' o;a ■■•i.i. •:iil How many ounoet make a pound Troy? How many pvnnyweighu? How many gruint? If,, .... :>. 35840 oi. > do. T . 973,440 dr. ! .^1 ima .1 1 lb. avoirdupois «p 1^ OK. 11 dwt. IJ^gr. troy. i'^r'^'dor'?:- ■'""■ 18do. sfgr. do. y^^^ '^^^^ ^^^^-y^^'^^^V idr. do. .- Ido. 3^gr. do. '•"^"''^"'^^■^' ••"'^•^^^^ By this weight are weighed all cparae and heayy goods, such as groceries, butter, cheese, butcher's meat, bread, corn, and jqnost of the pommon necessaries of life ; likewise, all metals, except gold and silver. In long weight, 30 lbs. avoirdupois => 1 quarter; 4 quarters or 120 pounds = 1 hundred weight. A ton of stones is 21 hundred, long weight. How many hundred weight ma1H :mj--.' •:-.'lI u.a ';)•,! ■JBr" •'. ^ (V used in or. 'J ■ i7 '■\' tiMf ;r, cheese, 11 metals, ed weight. ^ weight? e of the ear. Lime*, it wm r in oommon waem aro musuBis. APOTHECARIKS WEI^T. 20 gr«lne(gr.) make I senipla in«rli#4 trr. or V) 3 icruplef do. 1 dram do. dr. or 3 8 draniK do. ] ouncti do. oi. ur | /, 12 ounce* do. 1 poond. ; r NoTB.— I IIk Hi is 01. mi Ifl dr. - t8l ter. •- S7S0 Km. !<' <> I 1.4 ,^ .1. 'r t) Apothecaries use this weight in componnding their medicines, but buy and sell their commodities by avoirdupois weight. The apothecaries IL and oz., and the lb. and oz. Troy are the same, only diflferently subdivided. Physicians writn thsir prescriptions according to the following tabic aMd characters : '■■¥ 20 gr. Troy mnke 1 Kcriipio marked ^j ,-,,- 60 gr. do do. 1 dram do. 3j — . ^iij 4H0 gr. do do. 1 ounce do. |j •« 3^<>j l-u.:^:'» . ; );). '>■ LONG MEASURE.- ''f' -'''-"'il'' o.lJ "i •jrhi:)iJ.,!<.

/ty 3 barley corns in length (b. c.) make 1 inch marked in. 12 inches , do. I foot do. ft. 3 feet do. 1 yard do. yd. 5^ yordd do. 1 pole do. pi. 40 poles do. 1 furlong da fur. ^"i x .|tvti>> '-: > >'\. »• ll ■ i!i <•• ' V'lif/ Noir— 1 £. m. « 1760 yds. — S'^80 ft. » 63,360 in. <- 190,080 b. o. A fathom is 2 yards, or 6 feet ; a hand (used in measuring horses) is 4 inches ; a span, nine inches. .«. ;;,!■.;-(: ,ioi.;; ^iii!^ i -.'.I'l - ni .«* •■!'! -!'■!.• h2V! Long measure is used to ascertain the distance from one place to another^ or anything else where length is considered, without regard to breadth. v'm' V, .:-, ^ 0^ QUESTIONS. ,1 ., How many inches make a hand, tued in meararing honaa? How manjr yardi make a mile, long meamre? 1 low many feet, how many iochei, how many barley corns? What length is a fathom? How many inches make a span? Whai is long measure iised fur? ■•'if; / "lA , .••( 'rt( iiiv •! d-./.'p '«•..-, Jt lu >.■■. • '•' i 'l'i> i /■-.'i •■iiinti « :rf -' ,;n:t\i» n .'(jfi •!!« «»()ik ■"v.;'" 'kiki «- y'- .1'-P::II i miXJMM, cm uan wummm. 11 i:i/; <\uu. -atiK, SQUABE, OR LAND MEASURE. .»«*••« t'' »* I THE MEASURB OP SURFACES. i.t^.i , ™ ., *J«8' 144 square inobM (iq. in.) main 1 aquare foot marked aq. ft. I Mil il-M 1. llfj'Jtilfil) ! «'it'nfr! 9 do. feet 30^ do. yftrda 16 do. polei 40 do. polea 10 do. chaina do. 4 dOk rooda 160 do. poles ^40 do.^ acres do. do. do. do. do. do. do. do. do. do. do. do. do. da do. do. jard.. pol*'* cliaia, rood., acre.. acre, mile. do. do. do. da do. do. do. do. sq. jrd. pi. eh. rd. ac. ac. ao. m. m'1 Kota.— 1 me. — ISO pi. — 4,840 iq. yd. -. 49,a0O iq. ft. -. 6,37'3,046 iq. in. Square measure is used to rneasure all kinds of superficies, such as land, paving, plast- ering, roofing, tiling, and every thing that has length and breadth. In measuring land, surveyors use a chain which is 4 poles or perches in length, anc* > divided into 100 equal parts, called linlu. They also compute by chains and links, hut exhi- bit the result in acres, roods, and perches. 10 square chains, or 100,000 square links, are an acre. It may be observed also that a yard of land, mentioned by old writers, is 30 acres ; and that 100 acres is a hide of land. A square is a figure which has four equal sides, each perpendicular to the ac^acent ones. A square inch is a square, each of whose sides is nn inch in length. A square yard is a square, each of whose sides is a yard in length, drc. The table of square measure is fdrftied ttotA thd t&bldof lotig measure by Multiplying each lineal dirpensibn by itself: thus a square foot is -■ \2 /( 13 — 144 square inches^ &c. QU|:9TU'N^. . ...',.. ..-S.-ft- "•- IfoY iqapy »qn«re obains and links aMthMt in an aers? What U a Muare? What is a tquare inch? ,. „ What is a iquaie yard? How is this taU*>fonBadf ' "' '''''^ i'^ " .(.; .-•!. -i--; I How naajT'polas.iSaka an Pfi^t sqaaKa riiMsare? Hoar atf n]r]sq. yar^ how m»ay tq, feaV kow maajr «i]- ioehM? , For what ti this measnre nMfl ? What is tka Isngth of the surrejrors ehatof ' How is It divided? what are those parts oalled? How do surveyors compute their woric, aad ia what do tkey skow the result? ■Kit j,r .ihtiic.'ii > mI| ,110' |.r r, ; if.oiltrii 1 >i (^vrio; C^BIC,* OR SOLID MEASURE. ! 1728 solid inches (s. in.) make ^rtiih'ii;.! i 87' I "' ill 'feet' ..«»,..>...«...'.««.»»... ... 40 .— — feet of rough tirtiber ... .«.. 50 —— feet of hewn timber 42 — . feet ... 277^ — -^ inebtis ... 2218:16 inbles ; rssin,{ ) .'i'u! rr '.ri.\t l4»*Ti' 1 solid foot, marked ^ f. I yard. do. yd. 1 ton dr load. ] ton or load. 1' ton of shipping. 1 imperral trfne, ale, beer or cdm galkni]' 1 imperial standard bushel. 1(1 (A If * A onbc is a figure >^nti a vy si' >qual squ « i>8. (Dice afRird a familiar instance of tkis figure.) A cubic Inch is a cube whose sides arc tyeh n «;('.<«•" inch; a cubic foot, a cube whose sides are each a square foot, &o. A euUe Booibar is produced by b*:ii!x; Kii'i«VU«d twioe into : .^^M; thus 27 is equal to S X 3 X 3, and 1738 to II X 13 X IS' CwkU , V Ibiek (.••••Aoni 4 broad Wl Wl ill Wl Cloth &c. TI Flemish HpwoM Row mi For whi Forwhi -n'i9 c •The said to bat nuAUb m UAn miamm. Ctbi« or 8«Ud MaMurr n UMd t^ iMMitM all bodlM tkmi lutve Ictfigtb* hiMdlli and dcpilh (Pr tbitkiMM I M llmlMr, alone Mid mo fortb. > A cubio yaril of Mrtli ii «»il«d • load t Ifti oubia fret, tbat it. a pil« of wootf, 8 Caet Ungi 4 broad, and 4 deep, make n cord of wood : but 10§ eubie feel malia a itaok. i ,'*b\.^l' ,mi ' QUISTIONB. For wh»t Is Cu^>lo or Soltd MtiMM vsiT What !•• cubic inch? Ilt br<«fl, itnd h»w many faot 4m^^ )Iuw iDtn/ cubic Tmi tn • tuoii ut wuoA,y Cipril MEASUUK. .i'.ii.hM 2^ Inches (in.) make 1 nt(K 4 nalU I quHrt»>i% ••■ 4 quarters lynrd.* 3 qiiartcra 1 «n Flemiok. 4 qiiartert 1^ inch 1 ell Stiotvh< 6 quarter* 1 oil Knglish. 6 quarters 1 ell Frenoli. " ',' < NoTi'-— I yd, ^ 4 qr. or 16 n>. ^ 3S in. Cloth MeaatAv is used in measurinf all sorts of wrought silks, Imons, woolen cloths, tapes, &o. The English ell m pftiticnlarly used in measuring linens, sailed Hollands ; and the Flemish ell, in tapestry. ,.,,.,_|,„ ,,,,., ,i,;.. .r^.„, ,.,;,;.:.. v-l.^r^ivi .■ ,<'. f .■y.vrr.nm'.^i'.' -a om t Mtrlifd ,'. ■1 na. qr. yd. *J 1 , e a. ,. ri- '■ < e. 8. e. e. -..-■r **•* e. fr. ,..,!] / i ' ^•i.f/ ,l>it .'..;, I .i"'i -'^'i-i QUESTIONS. Hpw mnj CMTtsrs iq«li« » jpnd. Cloth l^Miur^l, How aanjr saili, how mtny in^hn? For what isCleth M«uare uiedf For what it the EngUih oU particuUtrijr uadt fi;M fill,"' /i( 'I!'' ,;l'i>,Ti o'.\r> T For what tboFltqiiib ell? From what ii the iilaDdsrd length of the yv^ need b this taMe, luppoaed to b« dtrivedf In what jrsar was it -l L = 10 qr. b» ao bo, = 880 pec. « 64Q g»l ■■ 8560 qts. =» 5180 pt. ,:f; Harked. pot. gal- pec bo. St. em. ■■. •■1.' wey. L said • The tiBwdard length In this table, from which »n the others are derirert, Is »appoeed to be to bar* beM orifiiialiy fijwd io (be >Nr UOl, hf |^g^%BryJ)$t ^r^ fhM'*J*°ii^<>^^" to be the yard| whi^h Is arm. >M iOtTAra, di LAITD MBAItntB. II i» I'- li ]. ' This measure, which is a species of cubic measure, is used in measunng grain, seed, salt, and various kinds of dry articles. In many places, however, these are bought and sold by weight The old bushel contains 8 gallohs, dry measure, or 2150| cubic inches i^t should be, inside, 8 inches deep, and 18^ inches wide throughout. ' "-in ^ir» li) i 'uij> ,; 'ii V QUESTIONS. How manj quarters, bushels and pecks w a last, Dry Measure? , How many gallons, quarts and pints? For what is this measure used? ;i How many gallons docs the old bushel contain? What is its measure in cubic inches? , / How deep should it be? . .] , ; How wide should it be throughout? , ,., „, : < WINE MEASURE. Marked. 4 gills ornoggins fg.) make 1 pint. pt 1 quart «'» 1(1 .i.tl:i'! 2 pints 4 quarts t .. 10 gollons 18 gallons 1 rundlet 31^ gallons 1 barret 42 gallons ... 1 tierce. 63 gallons ^..4... > ... 1 hogshead. . 84 gallons 1 puncheon. 2 hogsheads 1 pipe or butt 2 pipes 1 tun. .»;-, ;f>qlti 1 gallon. galtr 1 anker, of brandy. . nnk. run. ,.,. ; ■ ! ■ bar. tier. ... V. hhd. pun. P. Hi i;'i !i ;;i 1^ :■■. .|!l hui; \i'\uu.\UA K0TB.--I T. s 4 hhd. : ■I if iiU't') I 999 gal. ss 1008 qt ss 9016 pt =8064 gi^.il rtul By this measure, wines, brandies, spirits, perry, cider, mead, vinegar, oil, &c., are measured ; as also milk, but by custom only. The old wine gallon, formerly in use, contained 231 cubic inches ; the new, or imperial gallon, 277.274 cubic inches, that is, 277 cubic inches and 274- thousandth parts 6f a cubic inch ; being about one-fifth, as nearly as possible, greater than the ol4 wine gallon. In the measure of foreign wines there are great varieties, -u ■ u- (!> f=';ii;)&» i./i QUESTIONS. How many hogsheads and gallons in a tun, Wine Mea- sure? , How many quarts, pints and gills? ■ ' i For what is this measure used? .::■.;< How many cubic inches did the old wine gallon con- tain? How many does the new or imperial contain? How much do they differ in sise? ALE AND BEER MEASURE* .!;»■ i .2 pints (pt.) '.make ,4 quarts ... gallons ... , 2. firkins i ... . 2 kilderkins or 36 gallons 3 kilderkins or 54 gallons... ... 2 barrels or 72 gallons 2 hogsheads or 3 barrels 2 butts §•• «•• I quart. 1 gallon. 1 firkin of beer. 1 kilderkin. 1 barrel. 1 hogshead. 1 puncheon. 1 butt • •4*a« ••■••• ••••••••••#• '«•• 1 ton. Marked, qt gal. b. fir. kil. bar. hhd. pun. bt T. KoM.'^l T. ■■4 hhd. SB 6 bar. ass M fit. w 916 ^ as SM qt m 17S8 pt i,Uv ... t * .11,,. • , 1 lO Ml ■'.{■ ■.rh;\i\. I ",. ! • > -1 i',(. ■! , seed, salt, nd sold by "—it should lUin? - .1 // laVAKE, on LAIfO MSAmTBE. 35 measured; ir imperial of a cubic 3 gallon con- lin? ... 'V « The old ale and beer gallon contains 382 cubic inches, or 10 lbs. 8 oc. and { of pure water; the new, or imperial gallon, (as before mentioned,) 277.274 cubic inches, which is about one sixtieth less than the old beer gallon, formerly used. The hogshead of ale, in London, contains 48 gallons ; the barrel, 32; the kilderkin, 16 ; and the firkin, 8. ;i' '- I '4 Ji (»;; t;'>(. ',i>. 1. ''u;-.'! QUESTIONS. How many hr^gshcada *od barrela make « ton, Beer Measure? Bow many firkimi, gnlloni, quarts and pints? How many cubic inches did the old beer gallon contain? What is the diflbmce between it and the imperial gallon? How many frailuns dues thu hogshvad uf ale, in London, oontnin? How many gallons does the barrel contain? '10 ili.lli-. 111" I! TLME. 60 thirds (th.) made 60 seconds 60 minutes 24 hours 7 dny? 4 weeks •.. 12 calender months 13 lunar months 365 days, 6 hours ICO yenrs I, . Note: — i yr. <*> 365d. = 8766 hrs. • •«••• •••••■ ••••?• ••• ••••«•••••«•••••••■•■••• ••• I second. 1 minute. 1 hour. ,. 1 day. 1 week. .. 1 month. 1 year. 1 year. 1 year. 1 century. Marked, sec , or ' m, or ' hr,: ,, 4..V ..„ y/:^,. ■., yr. yr. cen. ..aU > tu'ib . •'iUl' ^' «ri u .1/ . !. ; It M ' i' 525960 m. = 31557600 sec. The lunar month is uniformly 28 days, being the time which the moon takes in revolving round the earth. The solar year is the space of time in which the sun moves through the 12 signs of the ecliptic. This, by the observations of the best modern astronomers, contains 305 days, 5 hours, 48 minutes, 48 seconds ; the quantity assumed by the authors of the Georgian calendar is 365, 6 hours, 49 minutes. But in the civil or popular account, the year contains, as above, 365 days, 6 hours. The year is divided into twelve portions, called calendar months ; the first is January, containing 31 days; second, February, 28 days, and in leap year, 29; third, March, 31 fourth, April, 30; fifth, May, 31 ; sixth, June, 30; seventh, July, 31 ; eighth, August, 31 ninth, September, 30 ; tenth, October, 31 ; eleventh, November, 30 ; twelfth, December, 31 as indicated in the following well known, memorable lines : Thirty days hath September, ' ' April, June, and November, .'j February hath twenty- eight alone, ! And all thu rest have thirty-(ine, Except in leap-year, when's the time February's d.iys are twenty-nine. ■ ■• ' To find leap-yearj divide the year by 4; if there be no overplus, it is leap-year; but if there be 1,2, or 8, it is the 1st, 2nd or 3rd year after, respectively; QUESTIONS. How many days, hours, months and seconds in a year? How many days in a lunar month? What is a solar year? What time does it comprise? How many days does the civil year contain? How is the j'ear divided? Which months hare only 30, and which one 38 daya? How do you find lsap*yearf ¥ if liir TAIUM or AUWOrr TMOt. ir-t ti^iriv/ >" MOTION, OR ASTRONOMICAL DIVISION OP A CIRCLE. 1 second. ^.^,^^^ ^...^ /ll-wui-- iw ni-nfr, 1 minute. , ,, ,,;.;-,,, ^',;-ri>v'! 'ufi' IHegree. ]^ ,,' hh ,.(: !w.r. 1 HJgn. 1 ri;^lit angle, quadrant, or quarter of a circle' 1 circumference of a circle. h I ,arAv*h 60 third (GCT) ..made 60 second* 60 minutes 30 degrees 90 degrees 4 right angles, or 860 degrees Motion is a geographical division of any line drawn ronnd the circumference of the earth. 15 degrees of motion, or longitude, are equal to one hour, and 1 degree is equal to 4 minutes of time. This table is used in astronomical and geographical calculations. The astronomical day commences at 12 o'clock at noon. The time before noon is marked A. M., ante meridiem; and the time after noon, P. M., post meridiem. The common or civil day begins at 12 o'clock the preceding night; of course the astronomical day begins 12 hours later than the common day. It may be proper to remark, that the circumference, or a circle, is the line which contains it ; that all straight lines drawn from the centre to the circumference are equal ; that any of these lines is called a radius ; and that a line drawn through the centre, and terminated both ways by the circumference, is called a diameter. What is motion? How many degress of longitude are equal to an hour? What time is cue dogroe equal to? For what is this table used? , f, When does th« astronomical day commence? How is the timo before noon marked? QUE8TI0.NS. . ! ;. . ' How is (he time after nooa marf(ed? What do these ini(t>ils mean? When does the common or civil day commence? Wh»t is a eircHmfereace? ,;. What is a mdlus? What is a diameter? ' ' '" ' ' '' ' "f*"^ ' ■uih •rji- TABLES OF ALIQUOT PARTS. •irt! 'J- •I. >i ,;i.'. inML , : , ■ OF A POUND. a. s. 10 is the ji G 8 I 5 I 4 } 3 4 jt 2 6 I 2 ^ 1 8 i, 1 4 A 1 3 tV 1 A JO A 8 A H ^ r' H * ■'•.': ■'. ' '■'; . )'■ ! i iT a. o. 6 is the ^ « A 4 A 8} ^ 8 ^ 2i ^ 2 ^ 14 Ti» li ,*T 1 Tiff Of ,i^ Oi ^ Oi ^ a. O O 2 ■ • : .if!' il li' l»ir. ' of a circle* theearthr 4 minutes is marked ommon or ay begins h contains ; that any erminated i«nce? ihi ui •'.1 i !);ufi>'' !:- ■ J'l' ■i qibo ■'. ■ ,' M. 'i' r ,; ,(■,;>«; ^ lr.,K\ * i. IT :f ':■*'■, ., *•• * • •■ A • •• *f • •• ^ «•• ^ • •• jV • •• ih • «• Tir • •• T*» • •■ Tiir • •• Tiff ft* Tiv • tp vi« TABLCs or AuarOT FArra. 9T OP. A SHILLING. 1. D. <0 6 is the O 4 3 2 H 0. D. i a. D. 1 Of o\ 0^ is the ! ' < OF VARIOUS SUMS. ..!. / 1 8 i-M' 1 3 S. D. 2 6 ...is... \ ...of... 10 i 5 i OlO -r'a i 6 i I 7 r.\\ .-I'), ; ; . 8 ■ ■ iiii ■h! i 10 5 10 5 2 6 10 6 8 5 3 4 2 6 1 8 4 3 4 2 5 2 6 1 3 •■ • ••• ••• • ••••« ••• 8. D. S ... is... 4 8 2i 'I ,•'' li 0| 10 is the 5 4 ;: OF A TON. Cwt i 2i i 2 } 1 ')' '■!!.■• ■.f^it'.''"! '! ;; 14 7 4 16 14 8 7 4 If 1 is the OP A QUARTER. lb If 1 ■j-j' ...Ol ... * i i Vi iW 5 3 2 4 6 1 8 i. t'tt i tV i 7 ••• ••• ••• i 1 T^ i i 4 3 2 4 t*« •••••• 2 6 2 2 6 1 8 1 3 10 1 3 1 6 6 3 ' ;:;i i-r is the OF A HUNDRED. qrs. Tb ! lb 2 or 56 is the ^ 1 3^ is the lor 28 i 2 < ■ l',;] I i' is the 5^1 ■At ■■ f 15 '! i! if ff ^itr>>'' rarim^i^'^i ■^aklir' .\~,» *iM-»>J- r it I .■: t " Hi Practical Arithmetic is the art of computing by numbers : and for that purpose nine significant figures, or digits, 1, one, 2, two, 3, three, 4, four, 5, five, 6, six, 7, seven, 8, eight, 0, nine, besides the 0, or cypher, have been adopted. These are sufficient for the expression of all numbers, whether simple or compound, from unity (the root of numbers) to infinity. Notation is the writing or expression of numbers by those figures; and Numeration is the reading or discovering of their value or amount, when written or expressed. Besides their simple value, these figures have also a local one assigned to them, the value of every figure, in each successive place, towards the left, being always of ten times the amount or value which that same figure would be if it were placed ift the situation of the preceding figure towards the right. The nought, or cypher, of itself. As its name imports, stands for nothing ; but in con- nexion with other figures it increases their value by removing them to a higher place (further to the left) in the series, in the same tenfold proportion. As numbers admit of no other change than that of increase or decrease, there are but two radical principles in arithmetic, viz : Addition, and Subtractioni If numbers are added or multiplied together, the result is greater than before. But, if they are subtracted from, or divided by each other, the result is less than before. Therefore, if an increase be required, add or multiply ; and, if a decrease, subtract or divide. /2e(fuc/(on teaches to change things of one name into things of another name; as to change pounds into shillings, pence, or farthings : this is called reducing them. When I have things of a great v^lue, as pounds, which I wish- to change into things of a less value as shillings, pence, and fhrthings, I must always multiply, because I want to have more in number; and Multiplication always brings more. When I have things of a little value, which I wish to change for things of a greater value, as to change farthings for pence, shillings, or pounds, I must always divide, because I want fewer in number; and Division always brings fewer. Non. — Vox quMtion* bm th(W9 of th^ Definitions. ^ I ll lijill ■11 .» *: irpose nine ;n, 8, eight, expression 3 infinity. written or I them, the t' ten times situation of >ut in con- Lce (further re are but re. But, if Therefore, me; as to o things of I want to a greater , because I roKMATiow OP THE noimM Ain> tiuMtiMioir OP mniBEMi. W Tb« fomiatioti of the- figures is the first object to which the pupil in arithmctie must direct his attention ; and, that lieing accomplished, his next step is the rending of those figures which teaches him the progession of numbers by unity. This can be best effected by the following table: '*"12J1 * ' i' a j i i i ) '] 1 ' "::.—"::. formation of the figures. •^:J:'^^'^ ;; j; i, 2, 3, 4, 5, e, 7, s, 9, 10. Si ::.'"L::_;:.:.:i':.r!' ^ .^ .. ,i .s a .0 1 . ■- : PROGRESSION OF NUMBERS BY UNITY. ^ ,v ' - '" ■■■ I, 1.1,1, 1,1,1. 1,1, 1, • ^' •^; L j: J :'.::,: 1. 1. 1. 1. 1. 1, 1, 1. 1. --'- ~- ■■J-'XA-''\1J 1. J. 1,1,1, 1,1,1 "' \^ ' ' . ' ' ' '. ■' 3, 3, 3, 3, 3, 3, 3, 3 . J J , \ : .::.: . :":'.. 1, 1, 1. 1, i, 1, 1 - - ; „- ;"7 4, 4.4,4, 4,4,4 •..:!. : ' ■ i..; , 1,1, 1, 1, 1, 1 • ■ ■' ■ *,. , ' 5,5,5, 5,5,5 _ • " ■-■..":-■" 1.1. 1,1,1 -7 --• • ■"■ • ' • 6,6. 6,6,6 . '.'::!-. r r " ^' '•^' ^ : '';^ k: ,.^.':i .;.t;^ ;, 1, 1, I ^ ^; ; ^ ' •■• •• •■• 8,8,8 l.." ■ ^ '■■■■■ VI -: .: ^ ;•: !t 9,9 : . •U.,.M I ' .-■ .-', '.. 10 ■' •■ The learner should practice the following primary exercises which require but this single rule— namely, to add or multiply each digit in succession to, or by itself; and prove Addition or Multiplication by Subtraction or Division. tKi. AODlTIOiN AND SUBTRACTION. 'Hmii til mtiVjl. t, S. 4, 9, 6, 7, 8. 9 i'A-i .1) .i( . K..4..'l., , 1.1.1,1,1,1,1,1,1 , , i li i %' V 1 O.'.J. J i a, 3, 4. 5, 6, 7,8 .9. 10 1,1,1.1 1. I.I . 1. 1 1. 2. 3, 4 5. 6.7 .8, 9 2, 3. 4, 5, 6.7 .8, 9 2. 2, 2, a. 2,2 ,'i. 2 4, 5, C, 7.8 .9. 10. 11 ». 2, 2. 2,2 .2. 2, 2 2, 3. 4, 5.6 ,7. 8. 9 3.4,5 ,6, 7, 8, 9 3,3,3 ,3, 3. 3, 3 6,7,8 9, 10, 11, 12 3,3,3 3, 3, 3, 3 3,4,5 ,6, 7, 8, 9 4,5. 6, 7, 8, 9 4.4, 4. 4, 4. 4 8,9, 10, 11, 12. 13 4.4, 4, 4, 4. 4 4.5, 6, 7. 8, 9 8. 6. 7. 8, 9 5, 5, 5, 5, 5 10, 11. 12, 13, 14 6, 5, 5, 5, 5 5, 6, 7, 8, 9 6, 7. 8, 9 6. 12, 6, 6. 6 13, 14. 15 6, 6. 6. 6, 6 7, 8, 9 7, 8. 9 7. 7, 7 14, 15, 16 7, 7, 7, 7, 8, 8, 8, 9 9 8 16. 8, 17 8 8, 9 9 9 18 9 •|!'ru),.'>: :n 1, 9, 8, 4, 5,6,7, t, 9 f », I. I. 1, 1. 1, I. I. I )!'i .: it f .< . \r\ ,1 . ■| I'.: MULTIPLICATION AND DIVIStON. ■ /:>.• 1 ) I, 3. 3, 4. 6, 6, 7, 8. 9 i: / /()[ I / !/ ; I, 2, 3. 4, 5. 6, 7, 8, 9 2,8,4, 6, 6, 7, 8, 9 3,1,3. 8, 2, 8, 2, 2 3)4,6,8, 10, 12, 14, 16, 18 . 3, 3, 4, 5, 6, 7, 8, 9 3, 4, 5, 6, 7, 8, 9 3f 3| Of 3) 3f 3f 3 1 .' . Ill 1 1 ' r. • • '1 ' 1 ■ • •, S)9, 12, 15, 18,21,24,27 3, 4, 5, 6, 7. 8, 9 4, 5, 6, 7. 8, 9 4, 4, 4, 4, 4, 4 4 ) 16, 20, 24, 28, 32, 36 4, 5, 6, 7, 8, 9 «, 6, 7, 8, 9 5, 5, 5, 5, 5 5 ) 25, 30, 35, 40, 45 6, 6, 7, 8, 9 6, 7, 8. 9 6, 6, 6, 6 6 ) 36, 42, 48, 54 6, 7, 8, 9 7, 8, 9 7, 7. 7 7 ) 49, 56, 63 7, 8, 9 ^-.- _ - ■ 8, 9 8, 8 ■• ' ■ ' •. :•: !. «)64,7a ;• !' '■^"' ■ ■ • 1^1 . .:8, 9 1 .. "' ,1 ■ ,. i; • .■ 9 9 9)81 9 Mil .I'Cjlil) •it!!, -)?!! yd ;. :j M:/ ISKQN. >:'m{ .i'»''Jlit) MlCMTAL OAUJOLATIOir. tf ^9<^^i■^'l'i^l■■f^^■n^ '4- ,Ki'/ EXERCISES IN MENTAL CALCULATION. 'si it T w ' r t «l Exercises of this kind are of great utility to the learner ; they not only impart a prorhptness in answering on the tables, but, at the same time, prepare the mind for that peculiar abstraction which is so requisite for mental calculation. ADDITION. How many are 4 and 5? 2 fives? 2 sixes? 4 sixes? 3 sixes? 5 threes? 4 eights? 5 foars? 5 nines? 2 fours? 6 sevens? 3 fours? MM j il # SUBTRACTION. J»ke 5 from 30 5 from 36 4 from 24 9 from 40 4 from 20 6 from 24 5 from 15 8 from 17 MULTIPLICATION. ^hat are 3 times 9? 6 times 4? 4 times 6? 6 times 5? 4 times 8? 6 times 6? 5 from 10 10 from 21 4 times 9? 6 times b? M!, How many fives in 80? sixes in 36? "What is one-half of 30? One-sixth of 30? What is a fifth part of 30? < a sixth of 3U? In 30, how many times 5? , How many times 10? DIVISION. 5 in 25? 5 in 20? 6 in 30? 6 in 24? One-third of 30? One-tenth of 30? 2-fifth9 of 30? 3-fifth8 of .30? 2-8ixthsof30? 3-sixth8of36? How many times 6? How many times 15? How many fives in 30? How many fifteens in 30? If 18 be three-fiftlis, what is one-fifth? 5 in 15? 5 in 10? 6 in IM? 6 in 12? One-fifth of 30? One-fifteenth of 30? 4-fifths of 80? 4-9ixtlisof30? How many times 3? How many sixes in 30? How many threes are there in 30? How many tens are there in 30? If 24 be four-fifths, what is one-fifth? If 12 be two-fifihs, what is one fifth? If 25 be five-sixths, what is one-sixth? If 20 be four-sixths, what is one-sixth? If 15 be three-sixths, what is one-sixth? If 10 be two-sixths, what is one-sixth? "What is the halfof a fifteenth of 30? What is the third of one-tenth of thirty? What is twice the tenth of 30? What is the fifth of a sixth of thirty? iVhat is one- third of one-half of 30? » Subtract the half, third and tenth of 30 from 30, and what proportion of 30 is left? How many halves are there in five whole numbers? How many halves in six whole numbers? '^ ■ ' How many whole numbers in five halves? • ' ' - i ■ . i . How many whole numbers in six halves? How many half-pence are there in 5 pence? In 5 half- pence, how many pence? How many farthing in 5 pence? How many pence in 30 farthings? > , How many pence in 30 sixpences? ; \., ,!-'--■ 1 H III 5-fifth9 of 30? 5-sixths of 30? .Sit '- •I How many hnlf-pence in 7^ pence? In 6 halfpence, how many pence? How many farthings in 6 pence? How many shillings in 30 pence? How many pounds in 30 shilhngs? » / NfRTAL OAUHTLATKHTw 11 I « If you give 5 pence for a quart of ale, how many qunrtf will 30 pence piirchose? Hiiw many nt two |)ence? At three pence? At four penct;? How mony at six pence? At ten pence? At fifteen pence? Tf you borrofr ot 4 different timesi 5 ahiilinffs eacti time, what do you owe? If at 5 timeH, 6a. each? If at ten times, 38. tuch? If at 15 tiaies, 48. each? If you get 2 pence profit on an article, how many must you sell to get 30 pence? Uow many at 6 pence? IIow many at 10 peace? How many at 15 pence? If you sell 10 books for 30 penoe, how much is that per book? IIow much for 3 book^? ilow much for 8 books? How much for 15 books? If you spend 3 pence per day, how long will it take to spend 3 shillings? If 4 pence per day? If 6 pence per week? n^ If 9 pence per day? If 18 pence per week? If you lend 25 shillings to be repaid in 5 weeks, how much is that per week? How much in 2 weeks? In 4 weeks? In 3 weeks? In 8 weeks? . * 1. 1 ,/ I'j Kl-M )J!3xM niVJ/.'-nc rn '-• i't.il 1 " '. iKr.' .ii.lf A variety of other questions of the same nature as the be proposed to the learner before the teacher proceeds Subtraction, Multiplication, Division, and Money Tables, r'y ^. 'J'eaclier. Fiipil. TeRcher. Tldw nJanyaro 5 und 5? 10 5 from 10? ■'.HI', '♦ii-i I 5 und 5? 5 times 5? 25 fiirthings? 5 and 6? 5 times 6? 30 furtliings? 5 and 7? 5 tirnea 7? 35 farthinjjs? 6 and 8? 5 times 8? 40 farthing!)? 5 and 9? S times 9? 45 farthinsjs? 5 and 10? 5 .times 10? 50 farthings? 5 and 1 1 ? 5 times II? "5 and 12? ' 5 ;imes 12? 60 farthings? Pupil. 10 25 6^d. 11 30 nd. 12 35 8jd. 13 40 " lOd. 14 45 '^ ll^d. 15 50 I2^d 16 55 , 17-' 60 ' 15d. 5 in 25? 25 pence? 5 from 11? 5 in SO? 80 pence? 5 from 12? 5 in 35? 35 pence? 5 from 13? 5 in 40? 40 pence? 5 from 14? 5 in 45? 45 pence? 5 trom 15? 5 in 50? 50 pence? 5 from 16? 55 pence? 5 from 17? 5 in 60? 60 pence? foregoing, should (when requisite) to exercise him in the Addition, in the following manner : Pupil. Teacher. Pupil. 5 2s. Id. 25 shillings? 1 5 6 2s. 6d. 80 shillings? 1 10 7 2s. lid. 35 shillings? 1 15 8 8 ••"" ■- '■;- ■ :'■•;; „ .' • -''V 3s. 4d. 40 sbillings? 2 9 3a. 9d. 45 shillings? "2 8 10 10 43. 2d. 50 shillings? 2 10 11 4s. 7d. 55 shillings? 2 15 12 12 •• ■'■ ,-:■:/ ■ i^ii ■■^■. ... .;. 5s. 60 shillings? 3 If necessary the pupil may proceed th|ough the whole of the Multiplication Table in this manner. ■ !i-i ■' ■111 l'),i •Afi,!; It is particularly recommended that pupils should be well exercised in questions of tbis description, which will tend to call forth the latent powers of calculation, arid greatly faci- ^tate the working of the subsequent rules: . - ;j Add both simple and compound numbers together — As: 6, 8, 2 and 5 7, 4, 3 and 8 ^, 5, 9 and 7 ' '■ " 1, 6, 8 and 9 . ' ' 67 and " ""■' ' 73 and 8 n\ 826 and 5 472 and 7 9, 2, 6 and 2 : .. n\ 6, 8. 8 and 7 ■ -sM 94 and 7 '•■'. ''•-J. MnnPAL OALCtTLATIOK. at Subtract simple from compound numbers — ^as: From 76 take 4^ From 83 take 6 62 take 8 54 take 7 150 take 6 197 take 9 463 take 9 520 take 6 From 97 take 9 41 take 5 263 take 7 705 take 8 Multiply compound numbers by a simple number — as: Multiply 15 by 8 26 by 6 45 66 by 7 74 by 5 80 125 by 4 298 by 6 222 453 by 5 514 by 8 530 by by by by 4 8 9 3 53 by 9 98 by 3 406 by 7 579 by 4 1. # Divide compound numbers by a simple number— . As: 4 in 68 3 in 75 3 in 129 8 in 152 9 in 378 6 in 546 7 in 1407 9 in 1989 5 in 80 7 in 168 4 in 724 6 in 3246 6 in 96 9 in 279 5 in 875 3 in 3366 * f It is of considerable importance in Mental calculation, that before the pupil is suffered to commence the lessons, varied questions of this nature should be put to him by way of examination : S. D. 8. Add 1 8 and 5 D. 2\ together. B. 3 D. 8. 5i and 2 D. 10 together. 4 5^ and 2 10 5 6^ and 1 9i 7 0^ and 6 2i 6 1]| and 8 7 9 31 and 12 2} 10 5| and 3 4i 13 7i and 15 9* 16 7 and 9 H 8. D. a. S. D. 8. 8. D. a. Subtract 13 from 20 7 6 from 20 6 8 from 20 18 6 from 20 8 4i from 20 7 8* from 20 14 0} from 20 2 10 from 20 13 4 from 20 7 7 from 20 15 6 from 20 4 4| from 20 8. D. 8. D. 8. D. 8. D. Multiply 3 2 by 4 3 4 by 3 4 2 by 9 8 6 by 5 9 5 by 6 11 8 by 7 13 6 by 4 18 8 by 8 S Si by 8 7 6 by 6 6 8i by 8 12 4| by 12 12 sj by 2 13 5iby7 16 4iby5 19 5i by 8 8. D. 8' D. 8. D. 8. D, Divide 6 8 by 2 9 4 by 4 8 6 by 3 11 8 by 5 12 3 by 7 13 6 by 6 15 6 by 8 19 8 by 9 18 9| by 3 17 7i by 5 12 8 by 4 13 9} by 2 15 7i by 6 16 3 by 10 18 5i by 8 19 61 by 12 Cr l./ii *■ t4 inn.TinjOATioii taiu. i F .' li'il lii.'' P: i t* AN IMPROVED MULTIPLICATION TABLE or WHOLE NUMBERS, PENCE, AND SHILLIKOS. 3 3 4 6 ' 7 8 9 10 11 12 i 3 4 8 10 12 1 14 I 3 16 1 4 18 20 { 22 1 6 1 8 1 1 10 {1 1 1 3 24 2 1 4 8 6 9 J2 15 18 21 010 01S016019 1 110 24 9 1 4 27 80 88 0230 96 99 17 1 10 I 13 86 3 1 16 4 8 12 1 10 1 *.0 24 I 28 014 018030024 10 14 18 32 2 8 1 12 36 j 40 44 30 034 038 116 300 3-iO 48 4 3 8 6 10 15 1 3 20 n 1 8 1 25 { 30 35 02 10 36 2 11 1 9 1 ID 1 15 40 3 4 2 45 1 50 3 9 4 3 2 9 3 10 U 4 7 2 15 60 9 S fl 6 1 18 1 6 24 2 1 4 30 30 3 6 3 1 10 1 16 42 3 6 2 2 48 4 2 8 64 00 06 046 090 096 2 14 300360 72 6 3 13 7 14 I 3 21 1 9 1 1 28 2 4 1 8 35 42 2 11 3 6 1 19 2 2 49 4 1 2 9 50 P 4 8 2 16 08 i 70 77 053 9 10 65 3 I 3 10 3 17 84 7 4 4 8 16 I 4 24 8 1 4 32 2 8 1 12 40 48 3 4 4 2 i 8 56 4 8 3 16 64 5 4 3 4 72 1 80 6 6 8 3 18 4 88 7 4 4 8 90 8 4 16 9 18 1 6 27 2 a 1 7 36 3 1 16 45 3 9 2 9 54 4 6 2 14 63 5 3 3 3 72 6 3 12 81 1 90 99 069 76 8n 4 10 4 10 4 19 108 9 9 8 0! 10 20 1 8 1 30 2 6 1 10 40 3 4 2 U 50 4 2 2 10 60 9 3 70 6 10 3 10 80 6 8 4 90 i 100 7 6 8 4 4 lU 9 110 9 3 9 10 120 10 6 11 22 1 10 1 2 33 2 9 1 13 44 3 8 3 4 55 4 7 2 19 66 5 6 3 6 77 6 9 3 17 88 7 4 4 8 99 1 110 8 3 9 2 4 19 9 10 121 10 1 6 t 132 Olio 6 13 12 24 9 1 4 36 « S 1 16 48 4 3 8 60 S 3 72 6 3 13 84 7 4 4 96 « 4 16 106 , 120 9 10 5 8 6 132 11 6 13 144 13 7 4 * ill n i: r met TAILB. EXTENDED PENCE TABLE. 48 10 4 > 9 8 73 84 7 4 4 90 « 4 16 108 9 5 8 120 10 6 132 II 6 12 144 13 7 40 loo .... arc .... 8 4 300 10 H 240 1 SOU 1 5 400 1 13 4 mo 3 000 2 1 8 000 3 10 720 3 800 3 8 000 3 15 000 4 1000 4 3 4 1100 4 11 8 1200 5 1300 5 8 4 1400 5 10 8 1440 1500 5 1000 13 4 1080 7 1700 7 1 8 1800 7 10 1900 7 18 4 1020 8 2000 8 8 2100 8 15 3100 3200 9 8 4 3b00 11 8 340O 10 Ttne* 4 •. b. 2500 .... aro .... 10 8 4 2600 10 10 8 2040 II 2700 II 5 •2800 II 13 4 2880 12 2000 12 1 8 8000 12 10 3100 12 18 4 3120 13 3200 13 8 3300 13 15 .1300 14 3400 14 3 4 3500 14 II 8 3000 15 3700 15 8 4 3800 15 10 8 3840 10 3900 10 5 4000 10 13 4 4080 17 4100 17 1 8 4200 17 10 4300 17 18 4 4320 18 4400 18 8 4500 18 15 4500 19 4000 19 3 4 4700 19 11 8 4800 20 M rtACTtCI Am) TNI lULI or THIBB. ABBREVIATIONS IN PRACTICE, AND THE RULE OF THREE. Genual Ri;lb. — To find the value of any number of yardR, pounds, gallons, 6ic., at any price under a Hhilling pnr yard, lb. or gallon, dec. — First : Calculate (mentally) the value of the whole quantity at one prnny per yard, lb. or gallon, die, and then multiply that amount by the price of the article. When a quarter of a yard, lb. or gallon, dec, occurs in the quantity, one farthing must be ndded to what it amounts to at a penny. When half a yard, lb. or gallon, dec., one half- penny must be added. When three quarters of a yard, lb. or gallon, dec, three farthings must be added. If a farthing per yard, lb. or gallon, dec, occurs in the price of the article, one-fourth of the whole amount already found at a penny must be added, w* ?n multiplying that amount by the price, to And the sum total. When a half-penny per yard, lb. or gallon, dec, occurs, one-half must be added. When three farthings per yard, lb. or gallon, dec, occur, three- fourths must be added. What will 60 lbs. of any articlo come to at 4d. p«r lb? 60 lbs- at one penny, are fit. Multiplied by the price 4 £1 Ana. What will 84 Ibi. of flour cost at 6d. per lb? 7s. 6 £2 2 Ana. What will 120 quarts of whiskey cost at 8d. per quart? 10s. 8 £4 Ans. What will 132 lbs. of cheese cost at 9d. per lb? lis. 9 £4 19 Ans. What will 240 lbs. of sugar cost at 8^ per Ifo? £1 H £8 6 Ans. 1^ Htr* wa multiplr the £\ (whtt it oomcs to at a U.) br Sd., and add iu tha quartar ot£l, what it oomM toat |d. What will 96 yards of calico cost at 10|d. per yard? 8«. lOi £4 4 Ans. What will 84 yards of cloth cost at 7jd. per yard? 78. 74^ £2 12 6 Ans. What will 108 quarts of cider cost at 8d. per quart? 9b. 8 £3 12 Ans. What will 144 yards of Irish Linen cost at lOd per yard? 12s. 10 £6 OAns. What will 132 quires of paper cost at lO^d. per quire? lis. lOi What dosen? £6 16 6 Am. IREE. I., at any ihe value tiply that ing muBt one half- farthings ■fourth of t amount ;., occurs, ur, three* lOid per It 7id. per at 8d. per len cost at )st at lOid. nuonos a«d tu ioui or Wtwt wiU 96 IIm. of ric« oost «t 7«J. p«r lb? 8a. 7 £2 16 Ani. Wh«t will 72 Ibt. of butler co.t at 1 1 id. per lb? 6h. Hi £ 3 9 Am. What will 480 lb)< of beef cost at b^d. per lb? £2 9i £19 Am. What will 720 Ibt. of alroonda coit at 8|d. per lb? £3 •I WUat will 9ertb? £3 4 6 Ans. What will 66f lbs. i /f molasses cost at 5d 8. d. 5 6| 5 .per lb? £1 7 9}Ai», What will 1200i yards of linen cost at lO^d. per yard? X 8. d. 6 0^ m £S2 10 5^ Ans. What will 1489 volumes of books cost at 10^. per volume? £ 8. d. 6 4 1 m £63 11 10^ Ans. What will 5341 ells of cloth cost at 8id. per ell? £ t, a. 2 4 6^ »i £18 18 ?i ii4l : nil P' - ^ y QinEsnoNS. SO Il}d. per 1 9 Jd, per 7i"od. per tvi. each? [d. per tb? It lO^d. per QUESTIONS UPON THE PRECEDLNG RULE. Hdw do ynu And the value of anj number of yards, lb*, or ga'lons, when the price per yard, & or gallon is in pt-nce? When a quarter of a yard, lb or gallon occurs in the quantity, what do jou do? When a half, what do you do? When three (juarters, what do you do? If n farthing per yard, lb or gallun occurs in the price, how do you proceed? If a liuK-penny, how do you proceed? If three fai'tliiiiga, how do you pmceed? Why do you rate the whole quantity at Id. per yard, lb or gallon? Am. — Because the price of the article is in pence. What Wliui What What What What What WMiat Wliat What What What What What What What What What What What What will will will will will will will w.Il will will will will will will will will will will will will will 36 pounds of any article come to at 5d. per pound? — Answer, lis. 120 yaids of oiiy aiticle come to at 7d. per yard? — Answer, JGlJ 10s. 240 pounds of cheese come to at lOd. pi-r pouml? — Answer, £10. 720 pounds of suirar dime to at 8d. per pound? — Answer, £24. 960 pounds of any article come t.i at IM. per pound? — Answer, £44. 20 yards of libbon come to at 9d. per yard? — Answer, los. 1 cwt. of soap come to at o^d per pound? — Answer, £2 1 Is. 4d. 6<> pounds of coifi'e come to at 6^- 1, per pound? — Answer, £l 13a. lO^d. 80 pounds of honey come to at 7id. per pniiinl? — Answer, £'2 lOs- 40 perks of potatoes come to at 4|d. per peck? — Answer, los lOd. 132 pound.? of butter come to at 8^ I. per pound? — Answer, £4 lOs. 9d. 15 pounds of lamb come to at 3| I. per pound? — Answer, 4s. 8^d 130^ yards of tlunnel come (o at od. per yard? — Answer, £2 14s. 3|d. 220.J yards of lace come to at 7d per yard? — Answer, £5 Xs. 7id. 460| yards of cotton come to at 9tl. per yard? — An.swer, £17 5s. 6|d. 22i quarts of whiskey come to at 1 Id. per quart? — Answer, £1 Os. 7jd. 50 pairs of buckles come to at 7id. per pair?— Answer, £l 10s. 2^d. 30 oranges come to at 2^d. eiicli ? — Answer, 6s. lO^d. 840 yards of linen come to at Hid. per yard? — Answer, £40 5s. 1260;^ yards of cotton come to at 3id. per yard? — Answer, £18 7h. ^|d. 100 bottles of ink come to at ll^d. per bottle? — Answer, £4 138. 9d. m^ St nt 10^. id. per ell? ABBREVIATIONS IN PRACTICE, AND THE RULE OF THREE. General Rule. — To find the value of any number of yards, pounds, gallons, &c., at the rate of a shilling, or any price above a shilling, per yard, pound or gallon, &c. — First : Calculate (nnentally) the value of the whole quantity at one shilling per yard, lb. or gallon, &c., and then multiply that amount by the price of the article. When a quarter of a yard, lb. or gallon, &c., occurs in the quantity, three pence must be added to what it amounts to at a shilling'. When half a yard, lb. or gallon, &c., sixpence must be added. When three quarters of a yard, lb. or gallon, nine pence must be added. 40 PBAOnOE AHD THE MVt OF THKES. When three pence per yard, lb. or gallon, dec., ocqura in the price of the article, one-fourth of the whole amount already found at a flhilling, must be added, when multiplying that amount by the price, to find the sum total. When sixpence per yard, lb. or gallon, &.c., occurs, one-half must be added. When nine pence per yard, lb. or gallon, &c., occurs, three- fourths must be added. li: What will 140 yards of any article cost at 6b. per yard? 140 at one shilling, is £7 Multiplied by the price, 6 •£A2 Ans. What will 220 gallons of gin cost at Ss. per gallon? £11 8 £S8 Ans. What will 360 gallons of rum cost at Us. per gallon? £18 11 £198 Ans. What will 680 gross of buttons cost at Os, per gross? £34 9 £306 Ans. What will 40 yards of broadcloth cost at 128. 6d. per yard? £2 at Is. 12^ the price. £25 Ans. CV* Here we first reckon at Ii. per yard, multiply that amount by all the shillings iu the price, at the same time bringine in the 6d. per yard, by adding half what it is at the shilling. What will 160 yards of muslin cost at 6b. 6d. per yard? £8 £52 Ans. What will 80 lbs. of pepper cost at 8b. 9d. per lb? Ji £85Adi. What will 240 bushels of wheat cost at 68. 3d. per bushel? £12 £75 Ans. What will 320 pairs of shoes cost at 5s. 3d. pe^^ pair? £16 Ji £84 Ans. What will 81 ^ yards of silk cost at 7s. per yard? £ 8. d. 4 1 3 at Is. ' 7 the real price. £28 8 9 Ans. (aT Here the quarter is made up with the yards, which at the rate of a smiling per yard, is, of course, 3d. for the quarter- What will 72^ dozen stone bottles cost at 8s. per dozen? £ 8. d. 3 12 6 8 £29 OAns. What will 105| lbs. of green tea cost at 6s. per fb? £ 8. d. 5 5 9 6 £31 14 6 Ans. What will 92^ lbs. of tobacco cost at 4s. per lb? £ s. d. 4 12 3 4 £18 9 OAns. What wilU9i lbs. of snuff cost at 38. per tt>? £ B. d. 2 9 6 3 £7 8 6 Ans, PBACTtCB AND THE KULB or THKU. 41 ne-fourth ^ing that Hon, Sic, ITS, three- at 6s. 3d. 5s. 3d. pe' . per yard? rice. ^ards, which , 3d. for the cost at 8s. 1 68. per lb? 4s. per lb? 3b. per tt>? What will 90 gallons of black ink cost at 4s. Id. per gallon? £ R. 4 10 at a shilling. 4 at Id., the real price. £18 7 6An8. ^* Here 90 gallons at a Id., bein<; 7s. 6(1., that sum is added, mentally, and brought into one line, viz: £18 7s 6d. What will 52i gallons of oil cost at 7s. per gallon? £ s. d. 2 12 6 7 £18 7 6 Ana. What will 112^ lbs. of gum arable cost at 9s. per tb? £ 8. d. 5 12 3 9 £50 10 3 Ans. What will 185| yards of satin cost at 12s. per yard? £ 8. d. 9 5 7i 12 £111 7 6 Ans. What will 1 26| yards of damask cost at Ss. 6(1. per yard? £ s. d. 6 6 4i 8i £53 14 '21 Ans. What will 72 yards of flannel cost at I7^d.per yard? s. d. Call the I "id.— 17 3 6 times 12 are 72. £5 3 6 A ns. What will 87 lbs. of hops cost at 20d. per lb? 20s. 7 times 12 are 84—7 And 3 over, at 20d. is OS. to bu brought in. £7 5 Ans. 0* Here we state the price of the article in pence, viz: sod., and multiply that by as many time* 12, as there are in the yards, lbs., &o., calli;.g the product shillings; and add thereto the remainder (if any) over the twelves, to Bake the aniwer. What will 126^ yards of cambric cost at ]4di. per yard? ,, ,y„^, 8. d. * 14 6 10 times 12 are 120 10 and 6^ yards over, viz: 7s. lOJd. £7 12 10^ Ans. What will 54 dozen of herrings cost at Id^d. per dozen? 8. d. 16 3 4 times 12, and six ■ over, viz: 8s. lid. £3 13 li Ans. ■ I. I.. I. ,m ■ — . ■ ,1 .I-.- I i.ii I I y-i I - ■ -. . „ II . I - I . - What will 63 score of oranges cost at 19d. per score? «. 19 5 times 12 are 60, and 3 over, viz: 4s. 9d. £4 19 9 Ans. What will 144 pairs of silk gloves cuat at 4s. l^d. per pair? £ s. 7 4 4— l^d. £29 14 Ans. What will 126 bundles of quills cost at 9s. 2d. per bundle? £ 8. 6 6 9— 2d. £57 15 Ans. What will 84^ dozen of pencils cost at 3s. 3d. per dozen? £ 8. d. 4 4 6 3^— 3d. is i of Is. £13 14 7iAns. What will 248 lbs. of tea cost at ds. 9d. per Yb? £ 8. 12 8 5J £71 6 Ans. What will 145^ lbs. of cloves cost at 8s. 4d. per !b? £ 8. d. 8. d. 7 5 9 12 1} 8 4 Ans. 60 14 7 £2 8 7 m «l PKACncB ANU THE BULK OP THRBB. What will 63 pnirsofsilk stockings coat at 8^. 4(1. p«r piiir? X K. 3 3 8* £26 5 Ans. What will 126 "oHons of wine cost at 9s. Hd, per gallon? £ 8. 6 6 n £m 18 Anf». What will 120 bushels of wheat cost at 6s. 5^d. per busliel? £ 8. At Is. 6 10 nt 1(1. Piiie, 6 5^ price. Ans. £3S 1.5 £2 I j to l)ni>f 10 is 8. «hich l)eins the multiplier, siiy, 8 limes 8 are 64; dniible the 4. nhii h iniikrs 8, put it down fur shillings, nnil cjny C; thi n 8 times 6 are 40. iind G (i> curry, lire -40, put dotvii li atxl curry 4; then 8 times 4 are ,32 iiiul 4 are 36; milking 1366 8% Whiit yard? will 7136 yards of c 7136 U bth cost at Ans. 18s per £6422 8 What per lb? will 413266 lbs. of 413266 6 indigo Ans. cost at 12s. £247959 12 What will 4042 pair of boots cost ut 15s. per pair? 2021 15* £3031 10 Ans. ^" When the price is not even, multiplv hnlf the quan- tity by all the »hillin Here we have divided bjr IS to bring ths lbs. (wbieb «• to Buny pence) into sbilUngs. ,«, ■< ^„ , „ . ^ .-, ^ T What will 5 cwt. 1 qr. 12 lbs. of hops cost at lOd. per lb.? 12 ) 600 50s. or £2 10 10 £25 Ans. What will 9 cwt. qr. \2 lbs. of tallow cost at 6d. per lb.? 12 ) 1020 85s. or £4 5 6 £25 10 Ans. Wb What will 3 cwt. 2 qrs. lb of figs cost at 8d. per lb.? 12)392 328. 8d. or £1 12 8 £13 1 4 Ans. V^ hat will 9 cwt. 2 qrs. 16 lbs. of bees' wax cost at 5d. per lb.? 1008 the cwts. 72 the qrs. and lbs. 12 ) 1080 908. or £4 10 6 /■ .-I £22 10 Aos. .; (.' ptAcnoa AHD Tm «cl» or tbkei. EIREE. ind -what ce, should lings, and the value ]| thectku- d, the whole f pence) into And in the t lbs. in each >ps COlt at How cost at I cost at 8d. ^ns. f bees' wax What will 10 cA 1 qr. 4 lbs. of salt cost at I What will 10 cwts. 2 qrs. 12 lbs. of arrow-root 2|d. per lb. 12 ) 1152 g6fl. or £4 16 2i £12 Ans. m^ Here we multiply bv (he price, a|d., toking in the half, of X4 1 6s , for the half-p<>nny. What will 7 cwts. 2 qrs. lb. of honey cost at 4d. perlb.? 784 56 12 ) 840 cost at 2s. 6d. per lb.? 1068 ft.'fcji- 28. 6d.ofa£l is |) 1188 £148 10 Ans. IC9* Here the price is an aliquot part of X, and whan that is (he case nothing can be shiirter than to lake siioh part. What will 16 cwt». 1 qr. 20 lbs. of cupper cost at Is. 4d. per lb.? 1648 192 Is. 4d. ofa £i8-,V) ^^^^ - 708. or £3 10 4 £14 Ans. What will 8 cwts. 2 qrs. 8 lbs. of flour cost at S^d. per lb.? 864 r "^^ ewti., (omittinf the 13 lbs. on each,) and ' the qrs. and lbs. added in 96 [ The exua 12 lbs. on each cwt. 12 ) 960 80orJB4 £13 Ans. What will 15 cwts. of glue cost at lU^d. per lb. 1500 180 £122 13 4 Ans. What will 13 cwts. 3 qrs. 17 lbs. of coffee cost at Is. 8d. per lb.? 1401 156 le. 8d.ofa£i8-rV) 1557 £129 15 Ans What will 1 1 cwts. 2 qrs. 25 lbs. of gambouge cost at 3s. 4d. per lb.? 1181 132 Ss. 4d. ofa£i8^) 1313 £218 16 8 Ans. 12 ) 1680 1408. or £ 7 lOi £73 10 Ans. What will 12 cwts. 3 qrs. 12 lbs. of bacon cost at Hid. perlb.? 1296 144 12 ) 1440 * 120s. or £ 6 What will 18 cwts. 1 qr. 11 lbs. of gum arable cost at 68. 8d. per lb.? 1839 216 6s.Sd. ofa£is^)2055 £685 Ans. £70 10 Ans. At jS3 7s. 8d. per cwt., how much per lb.? S. D. Divided by 7) 67 8 Price per cwt. 9 and 4/8 over. 3 27 farthings » 6| Add i for 4/8 , 7^. per lb. NoTi.— 7s. is the price cf ) of a cwt at Id. per lb., therefore * fkrthings moat b« reckoned for tiarj 7s. con- toinsdir )rioe,lfiurthingforSi.4d.,andaid.&r4s.8d. ■f m 4* raAOnCI AND TUB lOLC OF TBBBB. IIH Whnt will 2 cwtn. 2 qi-<. 20 lb». of sugar cost ot 79*. 4(1. per cwt.? £ n, v. 300 lbs. At 1(1. = 1 5 4 £10 12 6 Ans. NoTt — 79i. 4d. is 8}(l. per lb. flf 7«. in ihc pricp of J iif II cwt. nt Id. por II). Thore- firf, .1 firtliiiilTH MIII4I bf rt'ck'Hiid fur (Mpry 7". pontiinrd in ihp piicc, 1 r,iiiliiiia \'<?■« 1 1 liitii'' iind '1* 4il. ovpr sa thi' 1 1 tiincH j|il. := Af I.; iiilcl I I'liiiliiiig tor 24. 4. 49 at 1(1. is 4 I H £1 15 H^ Ans. >Vliot will 22| lbs. < f glue cost at 84s per cwt. B. I). 1 1()| 9 17 OJ Ans. At 7^d. per lb., how much per cwt? 8. D. 9 4 nt Id. 7 and 43. 8d. at -^d. to add in. £.3 10 per cwt. An?. C^ Itule, — For pvpry ppnn}-, rpcknn 9s. 4d.; for id., 4s. 8d.; and for f 1 , 2s. 4d. This will ••ive thp price of u cwt. Thpn iho Mhole amount in hhiliings reckoned as lo maoy A. mid vit/ty id. M LQili will gift th« prist of « tpo. At 10|(1. per lb, how much per cnrt. and per ton? S. D. 9 4 at Id. 10| 7a. at |d. to add in. £5 4 per cwt. £100 6 8 per ton. Wliiit williJcwl.s. 2qr.s cost nt 86!*, 4d. per cwt.? £4 6 4 price of 1 cwt. 9^ cwt. £41 2 Ans. NoTK. — X2 3 2 to iidd in for tlie J cwt. or 2 qrs. Wlint will 12 cwts. I qr. 14 lbs. cost at 48s. per cwt.? £2 8 1 1 1 qr. 1 4 lbs => 1 8a. to add in. £29 14 Ans. At X67 13 4 per ton, how much per cwt., and per lb.? £3 7 8 per cwt. 7^ per lb. Ans. tSf n.v hiivinir tlieprippof n ton or cwt. to fin, 1 the price I f u lb., or liny iiiiiiiber if lbs. /fu/c. — 'I'liki' ilip pminils ns sliillin;:^, nnd for pvprv tpn ppiici' rcckiMi ^ I.; tliis ivill uivc tbp price of ii cwt. Tlipn i'lir pvprv 7s. ill thp piioe of ii cwt.. ri'ckMn Jd.; for 4''. 8d., ^il.; unit fur 2s. 4d., a furthin;;; ihiit will give the price uf a lb. At 46s. 8(1. per cwt., how much per lb ? There «ie 6 litnes 7s. ■= 428. and 4s. bd. over. Which 6 times fd. — 4^(1. And ^d, for 4s. 8d. n» per above rule = ^d. 5d. per lb. Ans. Whnt will 1 cwt. 2 qrs. of pepper cost at b\d, per ounce? 168 lbs. at Is. is £8 8s. 5^d. per oz. is ?s per lb. 7 £58 16 Ans. 49* The ensiest way to calculate whtit any sum per nnnc* will amount toper lb, is to reckon only 8 ounces lu the Uhf and dou ble the price of tb« ariicls. Vs i- I t aunrrioNi. t. and per I. pcrcwt.? >r 2 qrs. )st nt 4Rd. I. to ndd in. r cwt., ond Rill the price 'or ovprv ton ii«t. Tlifn ! for 4''. 8il., I the price of lb? s. bd. over. . Ans. :o8t at £^d. Whut will I cwt. I qr. 12 lbs. of niUHtard cost at 4^d. p4 £7 128. 4^d. per og. is 6s. per lb. 6 £45 12 Ans. "Wliiit will 2 cwts. 1 qr. of cloves cosr at 4|il. per ounce? 2.)2 1hii. nt Is £12 12 Uet'koii 6s. per lb. 6 Deduct I of ihc I». per lb. as 4f 1 per us. i« only 9s, 8(1. pt>r lb. 7.5 12 4 4 £71 8 Ans. Wlint will 2 cwts. 3 qrs. 7 lbs. of ginger cost nt 4J I. per o« ? 3I.> lbs. nt Is £15 15 Reckun 6a. per lb. 6 Addonethirdnrtheli.p('rlb.M4](l. ) £f)4 10 per OS. it 6*. 4d. per lb. j 5 5 £99 15 Am. Wliiit will 5 cwts. 1 qr. 15 lbs. of mnce co:«t at Sjil. pt r uz ? ()03 lbs. at Is £iO 3 8 IWiicI Jofthe In. prrlb.tsSjd. I £241 4 is only 7*. 8 J. per lb. / 10 1 £231 3 Ans. II m per nnnc* ies tu the llhf QUESTIONS. How do ynu find the vnlu« of iiny n'ticle when il consii^ts of cwts., qrs., ami pounds? How mnny diflerent methods are there of working this rule? How are tiny performed? What will 3 cwts. 1 qr. 11 lbs. of nny /irticle come to nt .5(1. ppr lb.?— Answer, £7 17 6. What will 9 cwts. 3 qrs. 4 lbs. of nny article come to nt Hd. per lb.? — Answer, £36 10 8. What will 2 cwts. 20 lbs. of nny article come to nt 4^il. pir lb.? — Aimwer. £4 6 5. Whnt will 7 cwts. 1 qr. 18 Ib.s. of nny nrliele come to nt T^il. per lb.? — Ai».* ouooinrr tails. INTEREST AND DISCOUNT TABLE FOR BUYING AND SELLING. j iff To gain so much per cwt. add to every shilling or pound prime cost. To allow so much per cwt. subtract from every shilling or pound prime cost. a. D. B. D. £ 1. D. 2ii jer cent. is 6 i n the £. ii n Is. is 5 in £1 or 2 1 8 per ct 5 ditto 1 ditto h ditto 10 ditto 4 3 4 do. n ditto 1 ditto f ditto 1 3 ditto 6 5 do. 10 ditto 2 ditto 1 ditto 1 8 ditto 8 8 do. iH ditto 2 ditto u ditto 2 1 ditto 10 8 4 do. 16 ditto 3 ditto li ditto 2 6 ditto 12 10 do. Hi ditto 3 6 ditto If ditto 2 11 ditto 14 11 8 do. SO ditto 4 ditto 2 ditto 3 4 ditto 16 13 4 do. 3H ditto 4 6 ditto n ditto 3 9 ditto 18 15 do. 96 ditto 6 ditto 2i ditto 4 2 ditto 20 16 8 do. 27^ ditto 5 6 ditto 2f ditto 4 7 ditto 22 18 4 do. 80 ditto 6 ditto 3 ditto 5 ditto 26 do. 8S| ditto 6 6 ditto 3* ditto 5 5 ditto 27 1 8 do. 86 ditto 7 ditto 3i ditto 5 10 ditto 29 3 4 do. 8H ditto 7 6 ditto H ditto • 6 8 ditto 31 5 do. 40 ditto 8 ditto 4 ditto 6 8 ditto 33 6 8 do. 4^ ditto 8 6 ditto 4i ditto 7 1 ditto 35 8 4 do. 46 ditto 9 ditto 4 ditto 7 6 ditto 37 10 do. 47i ditto 9 Q ditto 4i ditto 7 11 ditto 39 11 8 do. 60 ditto 10 ditto 5 ditto 8 4 ditto 41 13 4 do. 60 ditto ,12 ditto 5i ditto 8 9 ditto 43 15 do. 70 ditto 14 ditto 5i ditto 9 2 ditto 45 16 8 do. 80 ditto 16 ditto H ditto 9 7 ditto 47 18 4 do. 00 ditto 18 ditto 6 ditto 10 ditto 50 do. i'ii tiMPt.E nrrnnr. 4f ,i if.n\;'-4 COMPKNDIUMS IN SIMPLIC INTKKEST, FROM FIVE TO OXK AND A Ql'AUTER PKK CENT. PER ANxNUM. D. 8 per ct. 4 do. do. 8 do. 4 do. do. 8 do. 4 do. do. 8 do. 4 do. do. 8 do. 4 do. do. 8 do. 4 do. I do. 8 do. I 4 do. > do. I 8 do. ( 4 do. ) do. Ah run imterest of £l, at & i)cr cnnt. per nniium, is Is., and there bcin^ 13 months in a yrar, and 12 p'ticn in a shilling, of course the interest is Id. per month fur each £, and so in roportion for any part of a pound. Rule. — (Jalculato the int«irest for one month, by reekoninp; as many ponce as there arc pounds in the question — put down that ntnount, and multiply it by the number of months. When there are shillings as well as pounds in the question, one farthing, or quarter of a penny, for every five shillings or quarter of a pound, must bo added tu the amouiit of pence before you multiply. What is the interest of £60 for 4 months at 5 per cent? 58. 4 209. Ans. What is the interest of £156 for 10 months at 5 per cent? 13s. • 10 £6 10 Ans. What ig the interest of £96 for 8 months at 5 per cent? 8s. 8 What is the interest of £50 for 5 months at 5 per cent? 8. (1. 4 2 5 ■ £8 4 Ans. £1 10 Ans. What is the interest of £36 for 7 months at 5 per cent? 28. 7 What is the interest of i80 for 7 months at 5 per cent? 8. d. 6 8 7 £1 1 Ans. £2 6 8 Ans. What is the interest of £120 for 9 months at 5 per cent? 10s. 9 What is the interest of £1 10 for 9 months at 5 per cent? 8. d. 9 2 9 £4 10 Am. £4 2 6 Ans. What is the interest of £132 for 11 months at 5 per cent? lis. 11 What is the interest of £140 for 10 months at 5 per cent? ■. d. 11 8 10 ' £6 1 Ans. £5 16 8 Ans. ftO ■IMTLI INTBBKVr. [ i I S' What U the interest uf £l/>0 for 1 1 montbt at A per cent? *. A. V2 ft 11 £0 17 6 Ana. What in the intercHt of £.'i9 5». fur 3 munthd at 6 per cent? 1. A. 3 3^ 3 9 9j Ann. (V Hvre (it. boinK | nf • X, Hiid the intnrnt nf XI fnr a month b«inK Id., a farthing U alluwcd fur the ititureit of fit. for a mootb. What in the interest of £86 IOj. for 4 months at 5 per cent? «. d. 7 24 4 £1 8 10 Ans. What is the interest of £121 lOt). for 5 months at 5 per cent? Wliiit ix llie interest of £200 for 7| months at A [H-r ftnt? £ ». i. 1 1 8 n £7 17 1 Ans. ^r HiTP XanO %l id. p«r mnnth, Mng XI M. Sd., it ii iiiiilliplivd hy tlit> 7 nionihi), unci ^ of ihe aoiuiint tt Id. brought in mmititlly for the ^ of it month. Wliat is the interest of £720 for 5| months at 6 percent? jE3 • 5i • — 417 5 Ans. .1, What in tlie interest of £bO tor 4^ months at 5 per cent? «. d. ki^i i(< XI 10 OAns. s. d. 10 1^ 5 £2 10 7i Ans. What is the interest of £87 I5a. for 8 months at 5 per cent? s. d. 7 3J 8 £2 18 6 Ans. What is the intereut of X96 for 26 months at 5 per cent? 8i. 13 hnlf the months. 5 4 5 4 £10 8 Ans. What is the interest of £130 12s for 15 months at 5 per cent? 8. d. 10 10| 3 months. 12 6 10 9 Interest for 1 2 mths. 1 12 8^ Interest for 3 mtha. £8 3 5^ Ans. What is the interest of £480 for lOi months at 5 per eent? JlOi £21 Ans. What is the interest of X886 5s. 8d. for 1 year and 8 months at 5 per cent? yr. m. X ». d. 1 8==1». 8d., isofa jE^j )886 b 8 X73 17 liAns. 4^ Here the years are considered as shillings, and the months as pence, and such part of the principal as those ■hillings and pence are of a X are taken, which gives the answer. What is the interest of £98 7s. 6d. for 2 yearg and 6 months at 5 per cent? X 8. d. 2s. 6d. is of a £ I- ) 98 7 6 £12 5 11^ Ans. What is the interest of £324 48. 8d. for 3 years aod 4 months at 5 per cent? X s. d. 38. 4d. ia of a £ ^ ) 324 4 8 £54 g^Ans. MMnJI l. II 8 4^ half the months. £2 12 6 Ans. What is Jhe interest of £320 15s. for 7 months at 2^ per cent? £ p. I). 1 6 8| 3 J half the months. X4 13 6i Ans. Rule for 3^ per cent per annum. Cnlculate at 5 per cent und deduct ^ from that amount, — the remainder will be the answer. Or multiply the interest for 1 month at 5 per cent by § of the months, if more convenient. What is the interest of £100 for 3 months at 3^ per cent? • 8. D. For 1 month at 5 per rent = 8 4 3 Deduct ^ ) 1 5 8 4 Answer, 16 8 at 3^ per ct. What is the interest of £151 for 7 months at 3^ per cent? 12 7 7 Deduct ^ ) 4 8 1 1 9 4^ £2 18 SfAns. What is tlie interest of £248 lOs. for 12 months at 3^ per cent? X 8. D. 1 8i 8 is § of 12 months. £8 5 8 Ans. AVMiat is-the interest of £260 5s. for U years at 3^ per cent? X s. d. 1 1 Hi 12 is ^ of 18 months. Answer, £l 3 3 at 8^ per cent. Another method for 3^ per cent per annum. Calculate the principal as pence, and multiply the amount by 8, — which will give the answer. The reason for multi- plying by 8 is this — 3J^ is 8d. in the C. What is the interest of £132 at 3^ per cent per annum.'' lis. 8 X4 8 Ans. What is the interest of £240 at 3^ per cent, per annum? £1 ^ 8 £8 Ans. • What is the interest of £180 10s. at 3^ per per cent per annum? H. D. 15 Oi 8 £6 4 Ans. What is the interest of £320 5s. at 3^ per cent per annum? £ B. D. I 6 8i 8 £10 13 6 Ans. What is the interest of £560 5s. at 3^ per cent per annum? X 8. D. 2 6 8i 8 £18 13 6 Ans. 12 months 1 12 months. 1 i years at I months. r cent. er aunum. ily the amount ison t'ur multi- per cent per per cent, per Is. at 3^ per t 3 J per cent at 3^ per cent SIMPLE I.VTEREST. 53 What is the interest oit£i9 53. at 3^ per cent per annum? a. D. 4 H 8 JBI 12 10 Ans. What is the interest of £77 10s. at 3^ per cent per annum? 8. D. 6 5^ 8 £2 11 8 Ans. What is the interest of £99 15b. at 3^ per cent per annum? s. D. 8 3| 8 jes 6 6 Ans. What is the interest of £162 15s. at 3^ per cent per annum? 8. D. 13 6f 8 je5 8 6 Ans. Bulb for 1^ per cent per annum? Calculate at 5 per cent, and taVe }, or multiply the in- terest for 1 month, at 5 per cent, by ^ of the months. What is the interest of £190 5s. for 6 months at 1 J per cent? 8. d. 15 lOi 6 i)4 15 H Answer, £1 3 9^ at 1;^ per cent. What is the interest of £236 lOs. for 8 months at 1 J per cent? S. D. 19 8 i for 1 month at 5 per cent. 8 i ) 7 17 8 Ans. £1 19 5 at 1 1 per cent. Whnt is the interest of £249 ISs. for 3 years and 4 months at 1^ per cent? X A. n 1 9J 10 is the ^ of 40 months. Ans. £10 8 1 half at 1^ per cent. What is the interest of £372 13 4d. for 12 months at 1^ per cent? £ t. V. 1 11 0§ 3 is the ^ of 12 months. £4 13 2 Ans. RcLK for any rate and half rate per cent, per annum at 1}, 2}, 3^, 4), 5\, &c., &c. Multiply the principal by double the rate per cent. ; cut off the unit of the product, and call it so many pence (the figures on the left will be so many shillings) and as many farthings, except 1 must be added to the pence as there are pence in number. What is the interest of £140 at 2.J per cent per annum? £140 5 70/0 or £3 lOs. Ans. What is the interest of £260 at 3} per cent per annum? £260 7 182/0 or £9 2s. Ans. What is the interest of £395 at 4i per cent per annum? £395 9 355/5 or £17 15 6. Add ^ or Id. as per rule. Ans. What is the interest of £487 at 6i per cent per annum? £487 11 635/7 Add lid., vis, X26 15 8i. Ans. 54 QUESnOlfB. '^I!ll t QUESTIONS. What is interest? How do you calculate interest ot 5 per cent? How do you calculate interest at 2^ per cent? Why do you calculate at 5 per cent and take the linlf ? How do you calculate interest at Sff ptir cent? Why do you multiply by 8 in finding the interest at 3^ per cent? What is the value of 3^ per cent? How do you colculate interest at 1^ per cent? Why do you divide by ^ of the time at 1 \ per cent? How do you calculate interest for any rate and half rate per cent? What What What What What What What What What What What What What What What What What What What What What What What What What What What What 3 the interest of £50 for 6 months at H per cent? — Answer, £1 5s. s the interest of £280 for 4 months at 5 per cent? — Answer, £4 13 4, s the interest of £320 for 5 months at 5 per cent? — Answer, £6 13 4. 8 the interest of £850 for 9 months at 5 per cent? — Answer, £31 17 6. s the interest of £70 for 6^ months at 5 per cent? — Answer, £1 16 5^. s the interest of £96 for 7\ months at 5 per cent? — Answer, £3. s the interest of £84 for 8| months at 5 per cent? — Answer, jC3 I 3. s the interest of £234 17 6 for 1 year and 4 months at 5 per cent? — Answer, £15 13 2. s the int^est of £420 15 4 for 2 years and 6 months at 5 per cent? — Ans., £52 11 11. s the interest of £90 7 6 for 4 years at 5 per cent? — Answer, JEIS 1 6. 8 the interest of £2341 18 7 for 6 years and 8 months at 5 per ct.?— Ans., JS780 12 10^. 8 the interest of £80 for 4 months at 2/^ per cent? — Answer, 138. 4d. s the interest of £200 for 12 months at 2^ per cent? — Answer, £5. s the interest of £20 for 9 months at 2i per cent? — Answer, 7s. 6d. s the interest of £70 for 5 months at 2^ per cent? — Answer, 14s. 8|d. 3 the interest of £215 15s. for 7 months at 2^ per cent? — Answer, £3 2 11. s the interest of £84 for 5 months at 3 J per cent? — Answer, lis. 8d. is the interest of £360 for I year and 8 months at 3^ per cent? — Answer, £20. 8 the interest of £600 lOs. for 3 years and 4 months at 8^ per cent? — Ans., £66 14 5;^. 3 the interest of £205 5s. at 3J per cent?— Answer, £6 16 10. 8 the interest of £500 15s. at 3J per cent?— Answer, £16 13 10. 8 the interest of £60 for 5 months at 1^ per cent? — Answer, 6s. 3d. s the interest of £1000 for 9 months at 1;^ per cent? — Answer, £9 7 6. s the interest of £1800 for 12 months at 1^ per cent? — Answer, £22 lOs. 8 the interest of £190 at 2^ per cent per annum? — Answer, £4 158. s the interest of £365 at 3} per cent per annum? — Answer, £12 15 6. 8 the interest of £240 at 4^ per cent per annum? — Answer, £10 16s. 8 the interes*: of £968 at 5i per cent per annum? — Answer, £53 4 9i. ID 9 8' 5 1 8 Of a PER CBTTAOE TABLE. %- PER CENTAGE TABLE Op £100, FROM ONE HUNDRED DAYS TO ONE DAV, AT DIFFERENT INTERESTS. £15 13 2. £52 11 11. 80 12 lOi. 0. £66 14 5i. 2per0«nt 8i percent. S per Cent. 8^ per Cent 4 per Cent. 1 4i per Cent. 6 per Cent. 6 per Cent. -0-3 S3 1 l-t •o -o .S-0 fc *: cs « 2d. per day, and deduct ^d. every 10 days. 2 jd. per day, and add ^d. every 5 days. 2^d. per day, and add ^d. every other day. 3d. per day, and deduct ^d. every 8 days. 3id. per day, and add ^d. every 5 days. 4d. per day, and deduct ^d. every 5 days. £ 8. D. £ S. D. £> S. D. £ s. D. £ S. D. £> B. D. JC S. D. £ S. D 100 11 Oh 111 13 9 16 5A0 19 2 jl 1 lOA 3 19 qI 1 4 9Al 7 6 1 12 11 90 9 12 4^0 14 9|0 17 1 2 3 1 4 9 I 9 7i 80 8 10 11 13 2 15 4 17 6 19 10 SI 2 1 6 4 70 7 8; 9 7f0 11 6 13 5 15 3f;0 17 4 19 3 I 3 Oi ir 6 no 8 3 |0 9 10, 11 6 13 1^0 14 IO1 16 6 19 9 ^, 5 6 6 10^0 8 20 9 7 10 11^0 12 40 13 9 16 5^ ■■■> ■ ' 4 5 5 6 6 7 7 8 8 9 9 11 11 13 2 30 3 3; 4 1^0 4 11: 5 9 ;0 6 6|0 7 5 8 3 9 10^ 20 2 2A0 ifo 2 9 3 3, 3 10 4 4f0 4 11, 5 6 6 7 10 1 1 4i0 1 r. 1 11 2 2i0 2 5; 2 9 3 3J ■ 9 1 i) 1 2J0 16 1 110 14 1 a 1 lliO 2 2*0 2 H 2 llj . 8 lOfO 60 1 9 1 UfO 2 2i 027] ■ 7 9i0 lliO 12 1 4 1 61^0. 19 1 11 jO 2 3f 1 6 8 9| 10 1 If 1 Sf'o 1 6 1 7Ji0 1 111 • 5 6u 8 10 ll|0 1 10 1 3 10 1 4 1 7i • 4 50 6A;0 8 ,0 9 10< 1 ,0 1 1 14 3 4 4 6 6f 7; 9 9f|0 1 2 2i 3 4 4*0 5 6 '0 6io 8 1 10 I1 2 |0 2|0 2i0 3 3|0 4 Of a year 1 1 1 10 12 6 15 17 6 1 1 2 6 1 5 1 10 • • 1 1 5 1 10 1 15 ,2 2 5 2 10 3 .. 1 10 1 17 6 2 5 2 12 6 3 13 7 6 3 15 4 10 1 2 2 i 10 3 3 10 4 4 10 5 6 N.B. Other interests may be found hy adding any of these together. ^':i it 11 i i 1 I 66 BiifPLE nrrcRSST. COMPENDIUMS IN SIMPLE INTEREST. PROM SIX TO ONE AND A HALF PER CENT. PER ANNUM. Rule. — Multiply the principal by the number of months — cut off the unit of that product, and reckon the other figures in that line as so many shillings. The unit figure thus cut off must be considered as pence, to which add as many fifths, to complete the sum total. The interest of £l ft ' ne month being 1^. ; the interest of 16s. 8d. for the same time is Id. ; that of 12s. Od. is ^a. ; that of 8s. 4d. is ^d. ; and that of 4s. 2d. is Jd. It would be sufficiently near for business to reckon for 5, 10, and 15 shillings. :^d., Jd. and |d. i it What is the interest of £60 for 3 months at 6 per cent? 60 3 18/0 Ans. What is the interest of £80 for 4 months at S per cent? 80 4 32/0 Ans. -^ ■ - ■ ^ ' What is the interest of £100 for 6 months at 3 per cent? 100 6 60/0 Ans. ^^— i* .I.MII Ill — .1 [ l-IMI ■ — Ml-^ — What is the interest of £90 for 7 months at 6 per cent? 90 7 What is the interest of £210 for 9 months at 6 per cent? 210 9 189/0 or £9 9 Ans. What is the interest of £130 for 11 months at 6 per cent? 130 11 143/0 or .£7 3 Ans. What is the interest of £20 for 5 months at 6 63/0 Ans. What is the interest of £140 for 8 months at 6 per cent? 140 8 112/0 or ^5 12 OAns. What is the interest of £280 for 9 months at 6 per cent? 280 9 252/0 or £12 12 Ans. per cent? 20 5 10/0 Ans. What is the interest of £460 for 3 years and 4 months at 6 per cent? 460 40 months. 1840/0 or £92 Ana. What is the interest of £980 for 1 year and 8 months at 6 per cent? 980 20 months. 1960/0 or £98 Ans. What is the interest of £269 for 8 months at 6 per cent? 269 8 215/2df or XIQ 15 2^ Ans. :i..,- ; product, us cut off :al. 16 time is d. and |d. months at months at aonths at 6 I years and year and 8 I months at f Ana. smrLB ormmr. 57 What in the interest of £16 for 7 months at 6 per cent? 16 7 ll/2jfd. Ans. t^ Here the unit figure cut off, ia by tho rule constiil- ered as 2(1. and two-fifihs of a penny, which, with lis., give* the amount Us. 2i^d. "What is the interest of £78 fur 5 months at 6 per cent? 78 5 39/0 or £1 19 Ans. What is the interest of £56 for 9 months at 6 per cent? 66 9 50/4d. Ji or £2 10 4 J^ Ans. What is the interest of £105 for 1 1 months at 6 per cent? 105 11 115/5d. and^or£5 15 6 Ans. ^* Here the unit fl^re cut off is 5, which is to be reckoned as 5d. -J, and as five-fifths are equal to a penny, the pence are 6, which, with 115s. 5d., give £5 15 6, the answer. What is the interest of £68 5s. for 7 montlis at 6 per cent? 68.5 ..7 47/7.15 or £2 7 8| and ? Ans. Note.— The 7d. and I = 8^. What is the interest of £51 10s. for 3 months at 6 per cent? 51.10 3 15/4.10 or £0 15 4i and J Ans. What is the interest of S287 15s. for 2i months at 6 per cent? 287.15 2i RuLK for 4 per cent, per annum. Calculate at 6 per cent. — divide the product (afler cut- ti;.„ off the unit fij;uro,) by three, to rrduce it ^— then sub- tract that reduction from the amount at 6 per cent., and the remainder will be the answer. What is the interest of £70 for 3 months at 4 per cent? 3)21/0 7 14s. Ans. What is the interest of £60 for 4 months at 4 .pc cent? 60 1 3 ) 24/0 8 16s. What is the interest of £100 for 6 months at 4 per cent? 100 6 3 ) 60/0 20 40s. or £2 Ans. What is the interest of £50 for 7 months at 4 per cent? 50 7 3)35/0 11.8 23/4 or £1 3 4 Ans. 71/9.5 or £3 11 10 J and f Ans. What is the interest of £98 158. for 5 months at 6 per cent? 98.15 5 49/3.15 or £2 9 3| and f Ans. What is the interest of £78 for 8 months at 4 per cent? 78 8 3 ) 62/4 20/9^ 41/6|or£2 1 6| Am. I' 58 SIMPLE INTKRWr. What is the interest of £266 for 9 months at 4 per cent? 256 3)230/4 , 76/9i 153.6 J or £7 13 6 J Ans. What is the interest of £100 for 10 months at 4 per cent? 100 10 3 ) 100/0 33/4 66/8 or £3 6 8 Ans. What is the interest of £80 for 1 1 months at 4 per cent? 80 U 3 ) 88/0 29/4 58/8 or £2 18 8 Ans. What is the interest of £340 for 12 months at 4 per cent? 340 12 3 ) 408/0 136/0 272/0 or £13 12 Ans. What is the interest of £400 for 6 months at 4 per cent? 400 6 3 ) 240/0 80/0 160/0 or £8 Ans. What is the interest of £312 for 8 months at 4 per cent? 312 8 3 ) 249/6 83/2 166/4 or £8 6 4 Ans. What is the interest of £146 for 3 years and 4 months at 4 per cent? 146 40 3 ) 584/0 194/8 389/4 or £19 9 4 Ans. What is the interest of £89 10s. for 7 months at 4 per cent? 89.10 7 3) 62/6.1 J 20/10 41/8nnd^(].forthef of lOd. Ans. What is the interest of £281 fur 2 years and 6 months at 4 per cent? 281 80 3 ) 843/0 281/0 • 56/2.0 or £28 2s. Ans. Rule for 3 per cent, per annum. Multiply the principal by the number of months as at 6 per cent.— divide the amount by 2, (after cutting off the unit figure,) and the remainder will be one half of 6 per cent — the answer required. Or, when the months are even, multiply the principal by half the months, which saves the trouble of calculating at 6 per cent. What is the interest of £40 for 4 months at 3 per cent? 40 4 2 ) 16/0 8s. Ans. What is the interest of £90 lOs. for 5 months at 3 per cent? 9010 5 2)45/2.10 22/71 or £1 2 7i Ans. 8IMPLB iirrBRmr. 59 What iji the interest of £80 for 9 months at 3 per cent? 80 9 2 ) 72/0 36s. or £1 16 Ans. What is the interest of ^90 for 1 1 months at 3 per oent? 90 11 RoLB for 8^ per cent, per annum. 2 ) 99/0 49/6 or £2 9 6 Ans. What is the interest of £140 for 12 months at 3 per cent? 140 12 2 ) 168/0 84/0 or £4 48. Ans. What is the interest of £375 for 8 months at 3 per cent? 375 < 4 the hf " of eight months. 150/0 or £i lOs. Ans. What is the interest of £70 for 6 months at 3 per cent? < 70 3 the half of 6 months. 21/0 or £1 Is. Ans. t9r Here, as above, the principal is multiplied by half the months, to avoid going into 6 per cent. Calculate at 3 p«r cent-, according to the rule for that purpose, and add thereto one-fuurth of that amounL What is the interest of £80 for 8 months at 3} per cent? 80 4 the half of 8 months. Add \ ) 32/0 at 3 per cent. 8 £2 Ans. at 3J per cent. What is the interest of £58 for 10 months at 3£ per cent? 58 5 the half of 10 months. Add \ ) 29/0 at 3 per cent. 7/3 £i 16 3 Ans. at 3| percent. What is the interest of £81 for 4 months at 3 per cent? 81 2 the half of 4 months. 16/2 Ans. What is the interest of £86 for 7 months at 3 per cent? 86 3^ the half of 7 months. 30/1 or £1 10 I Ans. What is the interest of jE113 6s. 8d. for 9 months at 3j per cent? £ 8. d. 113 6 8 9 h) 102/0 at 6 per cent. Add i ) 51 at 3 per cent.^ 12 9 £3 3 9 Ans. at 3| per cent. What is the interest of £128 lis. 5jd. for 7 months at 3| per cent? £ s. d. 128 11 5h 7 at 6 per cent. J ) 90/0 2 i at 3 per cent. Add i ) 45 11 3 1 f'' t\' £2 16 3 Ans. at 3} per cent. 60 SIMPLE iMTEBBVr. Rule for 2 per cent, per annum. Multiply tho prinriptl by the lime, m at 6 per cent. — i1ivi(l« tlic amount by H, (aftor cutting ofT thp unit flf^ure,) nnri thn ri'maindc-r will be ^ of 6 per cent. — the answer required. 7 Wlint is the interest of £40 for 5 months at 2 per cent? 40 5 3 ) 20/0 68. 8<1. AnH. Whnt is the interest of £60 for 7 months at 2 per cent? 60 7 3 ) 42/0 148. Ans. What 18 the interest of £90 for 8 months at 2 per cent? 90 8 3 ) 72/0 24s. or £1 4 Ans. What is the interest of £96 for 1 1 months at 2 per cent? 96 11 . 3 ) 105/6 358r2cl. or £1 15 2 Ans. What is the interest of £32 for 4 months at 2 per cent? 82 4 3 ) 12/8 48. 2\i. and 2 remainder, Ans. What is the interest of £215 5s. for 8 months at 2 per cent? £ 8. 215 5 8 3 ) 172/2.0 . ^, , 5 and 2 remainder, or Ans. 67/4^ i *2 i7 4i Wliat i* the interest of £140 for G months at 2 per cent? . , 140 2 the third of 6 months. 28/0 or £1 8s. Ans. Whiit is tho interest of £999 10s. for 9 months lit 2 per cent? 999 10 3 the third of 9 months. 299/8.10 or £14 19 8^ Ans. r cent, per annum? you reduce it one-third? Answer — Because 4 per cent, is one-tliird less than G per cent, per annum, you calcuhite interest at 3J per cent? you add one-fourth of the amount found at .3 per cent? Answer — Ik'Ciiuse three-fourths is one-fourtli of ',i per cent, you calculate interest at the rate of 2 prr cent, per annum? you calculate interest ut tlie rate of IJ per cent per annum? you divide by 4? Answer — Because one and a half is the fourth of 6 per cent. What What What Wliat What What What What What What What What What What What What What What. What What What What What What What What What What the interest of £.50 for 9 months at 6 per cent? — Ansiver, £2 5s. the interi'st of XlOO for 12 months at 6 per cent? — Answer, £6. the interest of £2H0 for 7 months ut 6 per cent? — Answer, £9 IGs. the interest of i^20 for 4 months at 6 per cent? — Answer, 8s. the interest of J^ II 7 for 5 months at 6 pi-r cent? — Answer, £2 18s. 6d. the interest of £178 for 3 months at 6 per cent? — Answer, £2 139. 4^d. the interest of £469 for 8 months at 6 per cent? — Answer, £18 los. 2d. 'I the interest of X8o 10s. for 7 months at 6 per cent? — Answer, £2 19s. 9id. J the interest of X51 os. for .5 months at 6 per cent? — Answer, £l .5s. 7id. i the interest of £20S 15s. for 9 montiis at 6 per cent? — Answer, £9 7s. 9jd. J the interest of £57 lOs. for 3^ months at 6 per cent? — Answer, £l Os. l|d. } the interest of .£300 15s. for 11^ months at 6 per cent? — Answer, £16 I8s 3^d. J the interest of £100 for 5 months at 4 per cent? — Answer, £1 I3s. 4(1. the interest of £20 for 8 months at 4 per cent? — Answer, ,js. 4d. the interest of £17 lOs. lor 7 months at 4 per cent? — Answer, 8s. 2d. the interest of i^286 for 6 months at 3 per cent? — Answer, £4 58. 9d. J the interest of ^90 for 15 months at 3 per cent? — Answer, £3 78. 6d. the interest of £22 !0s. for 20 months at 3 per cent? — Answer, £1 29. fd. the interest of £120 13s. 4d. for 9 months at 3^ per cent? — Answer, £3 7s. lO^d. the interest of £200 for 6 months at 3| per cent? — Answer, £3 15s. the interest of £520 for 10 montlis at ','>^ per cent? — Answer, £16 5s. the interest ol £36 for 5 months at 2 per cent? — Answer, 6s. tlie interest of £140 lOs. for 6 montiis at 2 per cent? — Answer, £1 8s. Id. tlie interest of £220 15s. for 9 months at 2 per cent? — Answer, £3 6s. 2\iL tiie interest of £80 for 12 montlis at 2 per cent? — Answer, £l 12.'^. the interest of £30 for 9 months at \h per cent? — Answer, 69. 9d. the interest of £400 for 1 year and 6 months at 1^ per cent? — Answer, £9. the interest of £15 for 3 months at 1^ per cent? — Answer, Is. l^d. ■ 1 M ■} 03 COMPOUND urruuT. COMPOUND INTEREST, AT FIVE AiND SIX PER CENT PER ANNUM. V. FIVE PER CENT. Find the first year's interest for 5 per cent, as in Simple Interest, add that interest to the principal ; which sum becomes the second year's principal, and so on for any length of time. What ii« tlie coiiipound interest of £120 10s. for 2 years and 6 niontlia ut 5 per cent, per annum? £ S. N. l). 120 10 at ld.=^ 10 O^d. 12 months in a year. I year's interest, JS6 6 which added to the principal makes £126 lOs. 6d. £ t. d. R. d. Then, 126 10 6 at Id. =• 10 6^ 12 £6 6 6 the second year's interest, which added to the former princi- pal £126 lOs. 6d. makes £132 ITs., which taken as pence is = lis. 0|d. 6 months for half a year. £3 6 4^ which added to the second year's principal, gives £136 3 41 from which deduct first principal, or £120 10 0, which leaves the amount of interest, jC15 13 4^ Ans. A note became due at 3 months for £84 10s., but not being paid, it was renewed for 3 months longer, what amount of interest is to be paid upon the note when again due, 5 per cent, compound interest being allowed? £ 8. 8. d. £ g. d. 8. d. 84 10 = 7 0^ Then, 85 11 H = 7 U 3 3 £11 1^ int. for 3 mos. £1 1 4^ Ans. £2 2 6 What is the compound interest of £600, fur* borne 'li);u the piiyiT it w;i« r»'n«?Wfil lor 3 rnontl)!*, wlitit \* tl»; umoiint of iiiti;rc.«t to l>« r«>- ceivcil upon tlmt noip, coni{^uiiil iiiterent, nt 6 per oent. IxiMig allowed? i.2H0 £287 second principal. 6 3 140/0 — £7 8G/1 «=. £4 « I| to which add inttrt'Ut of fIrM principal, 7 £11 (i l;f An!*. Whut i« the compound interest of JC173 \5i. for I ypiir nnd seven monlhn nod fitteea dajrs kt () per cent, pi-r iinntun? X «. ICf *. il. 173 \'> Then, 184 3 H second principal* \2 Tj •JOM/.> -Xl()8».6d. 12H9 4 «; 92 I }> lliHjl (> 3 interest for seven month*. flftc»"n dnys, or seven nnd a half months, or jCG lb 1^ to which udd 10 8 6 the year's interest, which gives jei7 6 7i Ans. CO\BIISSION AND BROKERAGE TABLE. '■ 1 1 O TJ ... '^ «j "■ 1 — «j _-._ -— «j *i ■ii ^ 1 '„, „~ ,■3 s a a e a a p Ji ^ 6 V 1 4) a u d 6 d .^ O JJi ;. u L. U u 1 t* u u •3 *i ^ i S. K. s. ^ H» Ht £ 1 I). 1 H»< WW) t:w ij. Kit- £ 8. fH £ £ 8. I). £ S. D. £ s. I>. £ s. D. £ s. D. £ s. D. 1000 1 I 6 2 10 3 15 5 6 5 7 10 8- 15 7^17 10 900 1 I 2 6 2 5 3 7 6 4 10 5 12 ,6 15 6 9 800 ' I 2 3 4 5 i6 ,7 8 700 17 6 I 15 2 12 6 3 10 4 7 6 5 5 6 2 6 7 600 15 I 10 2 5 3 3 15 j4 10 5 5 6 500 12 6 I 5 1 17 6 2 10 3 2 6 13 15 4 7 6 6 400 10 I 1 10 2 2 10 3 13 10 4 300 7 6 15 I 2 6 1 10 I 17 6 2 5 2 12 6 3 200 5 10 15 1 1 5 I 10 jl 15 2 100 2 6 ;o 5 7 6 10 12 6 '0 15 17 6" 1 90 2 3 4 G 6 9 9 11 3 ,0 13 6 15 9 18 80 2 '0 4 6 8 10 12 14 16 70 1 9 :0 3 6 5 3 7 8 9 10 6 12 3 14 60 1 6 !o 3 4 6 6 7 6 9 10 6 12 50 1 3 2 6 3 9 5 6' 3 7 6 8 9 10 40 1 3 4 5 6 jO 7 8 30 9 1 6 2 3 3 !0 3 9 4 6 |0 5 3 6 20 6 1 1 6 2 2 6 3 ;0 3 6 4 10 3 6 9 1 1 3 1 6 1 9 9 2|0 5.V0 ^\ lOfO 1 UO 1 410 1 7 9J 8 2f0 5 7i 9J0 1 1 2iO 1 4i u 7 2^0 4-^0 3^l0 6i 8^0 lOiO 1 0^0 1 '2^ 5 6 l|0 b\ 710 9 .0 10^0 1 Oh ^ 5 1-VO 3 4i 6 |0 7iO 9 m 4 ifo ?i0 3^ 5 '0 6 7^0 H 9| 3 1 ;0 IfO 2\ 3f:o 4|0 5i0 H 7i 2 OiO UO n 2V0 3^0 3f0 H 5 1 Oi|0 1 OiO 1 lio 1|0 liO 1 2 2i DIIOOUNT, COMMIMinir, AND ■lOKCKAOI. DEMONSTUAtlONS IN DISCOUNT, INSURANCE, COMMIS- ijlON, AM) BKOKEKAGE. I In many articloH of manufacture it is customary to draw up the invoice, or bill of sale, subject to a discount of from 2 to perhaps 50 per cent. To reckon this, when the rate of discount forms an aliquot part, divide the j^ross sum by the aliquot part, subtract the amount from the (;ross sum, which will leave the net money, or the amount to bo paid ailer taking ofTthc discount. Commission and brokerRc at J, \, or J^ per cent, arc extremely useful to bankers and merchants, bcinj? allowances mado by the one to the other for keeping the accounts and trans- acting busincMH. What is the discount on i!4H6 llfl. 8d. at 6d. per £? Gd. is the «V) £486 1 1 8 Ans. £12 3 3^ What la tho discoun^oii £2347 Ss. 6d. at 2d. per jE? 2d. is the rio) £2347 8 6 Ans. JC19 11 2|andf What 18 the discount on £331 10s ntlid.per£? l^d. i8thcii3)je331 10 Ans. £2 1 5^ What is the discount on £100 at lO^d. per £? S. 1). , At Id. -=> 8 4 joi Ans. £4 7 6 What is the discount on £ 104 6s. 8d. at 7^d. per £? 8. D. At Id. = 8 8 7| and 2^d. to be added in for the 6s. 8d- Ans. £3 7 4^ What is the discount on £148 ISs. 4d. at 9ii. per £? ■. D. At Id. = 12 4 9^ and add 6d. for the 13s. 4d- Ans. £5 14 7 What is the discount of £980 7s. 6d. at 2d. on the shilling? 2d. is the ^) £980 7 6 Ans. £163 7 11 What is the discount of £180 3s. 9d. at l^d. on the shilling? l^d. is the I) £180 3 9 Ans. £22 10 5^ and ^ farthing. What is the discount of £520 10s. at fd. on the shilling? ^d. is the tV) £520 10 o' Ans. £32 10 7i What is the discount of .£97 IGs. 8d. at ^d. on the shilling? ^d. is the ^) £97 16 8 Ans. £4 1 6^ and ^. What is the discount of £2184 at ^d. on the shilling? :Jd. is the ^) £2184 Ans. £45 10 * ► MtCOVNT. MIS- 1 or ftale, rute of 5 amount er taking kere and ind trans- 4cl. at 9^d. 6d. for the J. 6d. at 2d. gd. at Hd. t farthing, tjd.onthe d. at ^d. CD ^d. on the no IK. If Iho il)«rniint In b« Ukrn n(f !< rtn tliqiiKt n«rt "f tOO, diviilM l)ii< |{ri>«« •inn liy llmt •lii|iii>( purl, •nil il will git* lh« tlivriiunt, whii'h Ik-idij; iulj|rM-iv i;ri>*« *iiin, !•••«<•• tli« not oitiiiHjr ur iuiu tu Im paid kl'tcr inking ulT th« (litciiuiii. Wliat i« thn (litcoiint uf je'200 at 30 \ft eent? XlOnt 5 [H'T ri'iit. <) times u arc 30. Ana. X'(iO at 30 |MTcent. What is the discount of £220 \Hs. 6) £384 5 38 8 6 discount. What U th<- discount o( £H'i (it. 8 Note.— Here, instead of dividing by 120, I have reduced the divisor and dividend one-tenth, as it shortens the operation and is equally correct with the former ex- ample — which might also have been reduced. Offered for sale a debenture for £230, payable 7 years hence, what amount should I give for it to pay me 10 per cent? X 17 ) 2300 £135 5 lOJ Ans. A person in want of cash, but holding provin- cial debentures to the amount of £600, payable in 3 years, is willing to allow me 20 per cent, if I will cash them, what amount must I gire for them to realize that sum? £ * 16 ) 6000 £375 Ans. What must be discounted for the ready pay- ment of £100, due 2 years hence, at 15 per cent. £ 13 ) 1000 £76 18 6 Ans. Suppose I have a legacy of £550 left me, but it is not to \)& paid for 4 years, what is its present worth if I allow 12^ per cent, discount? £ 15 ) 5500 £366 13 4 Ans. INSURANCE. Divide the given sum by the aliquot part or parts which the rate of Insurance is of £100. What is the insurance of £725 8s. lOd. at \2l per cent? £ s. d. 12i = toi)725 8 10 £90 13 7^ Ans. A man's house estimated at £580 was insured against fire, for 2^ pei cent, a year, what insur- ance did he pay annually? £ 2i = to ^ ) 580 £14 10 Ans. I possess stock to the amount of £750, the Mutual Insurance Company offer to protect me from loss by fire, for If per cent., what is the in- surance money? ^ 2 of 100 is the ifc ) 75/0 Deduct i) 15 117 6 the excess of 1|. £13 2 6Aas. OraUKAHCB— COMMItUUON. «7 give for ady pay- per cent. ift me, but its present t? [iquot part ■ance is of lOd. at 12^ was insured what insur- er £750, the o protect me hat is the in- Lcess of 1|* What is the inqprance upon a Khooner and cargo, valued at £l87o, at 7.^ per cent? £ 5 of 100 =» to i\j ) 1875 2i = i)93 15 46 17 6 £140 12 6 Ans. I send a cargo of flour, valued at £485 6.4., from Toronto to Halifax, N. S., nnd to prevent loss by casualties at sea, I insure the same at the rate of 3 per cent., what is the amount to be paid for insurance? 2 of 100 = to At ) 485 6 1 of 2 = i ) 9 4 14 17 H OJ £14 11 2 Ans. Having property of the value of £160 — it not being of a combustible nature — the various com- panies offer to insure it for \^ per cent., what would be the amount of the insurance? £ l^of 100 = to,\r) 160 £2 Ans. COMMISSION. When the Commission is one-eighth per cent, one-fortieth of the pounds will produce the shillings ; to the remainder (if any) add one-fourth of itself and consider it farthings. What is the commission on £4320 at ^ per cent? £ i -= * ) 4320 lOSs. or £5 8 commission • What is the commission on £6288 at ft per cent? S ^ = rAi ) 6288 157s. and 8 remainder. 2 or ^ of itself added. To be considered as 10 farthings. 47 17 2^ commissioo* What is the commission on £1280 at ^ per cent? £ i = 1^)1280 . , 64s. or £3 4s. commission. ^(T At } per cent. ^ of the pounds will produce the (hillings; tho remainder (if any) multiplied by 8^ will b« the t'arthini;!), to which add une, if the shillings in the given number amount to 20. What is the commission on £2068 at ^ per cent? £ ^ = ,\, ) 2068 103s. and 8 remainder. 2\ multiplier; and add 1 [as per rule. To be considered as 2 1 farthings. £5 3 5^ commission. Wlm^ is the commission on £300 at h per cent? £ i = ,\, ) 300 SOa. or£l 10 commission. 1st At ^ per cent. 1*^ of the pounds will produce the 8hillin<;s; the remainder (if any) multiplied by 5 will be furthin);s, and for every five shillings of the given sum, add three farthings. What is the commission on £7270 at | per cent? J=^i„)7270 i = n 727 363.6 1090.6 or £54 10 6 commission. C^ At } per cent., proceed as in the last rule at \ per cent., and to its result add half of the same. Another Rule for Commission at i per cent. Cut oiF the unit figure of the £, consider those not cut off as shillings. The unit figure cut off is pence, to which add as many fifths of a penny. When the question con- tains shillings as well as pounds, if 4 or 5, add one-fourth of a penny; if 8 or 10, add a half-penny; if 12 or 14, add three farthings; if 16s. 8d. and upwards, add one penny to make up the answer. What is the commission on £420 lOs. at i per cent? £ I. d. 42/0 lOs. or 2 2 Oi commissioa. 11 ti[- 68 COMMIMION — BKOKniAflE. : fl What is the commission on £974 4s. at ^ per cent? £ K A. 97/4 4s. or 4 17 5 Ans. f^ The unit fi^re cut off if) 4(1., to which add % nf % penny or three farthinKSi and one farthini; fut the 4*., which makes £4 178. 5u., the anitwer requirud. What is the commission on £1075 fis. at \ per cent? 107/5 5s. or £5 7 6;^ commission. What is the commission on £8497 at ^ per cent? 849/7 or £42 9 ^ or ^d. commission. O* The 7d. and I is equal to Sfd. or 8^d. What is the commission on £3522 10s. at 1 per cent? £ 8. D. 1 = T*B ) 3522 10 Ans. £35 4 6 commission. ff^ When the commission is 1 per cent divide the given sum by 100; when 2 per cent, by 50; when 2^ per cent, by 40; and so on. What is the commission on £324 '4s. 2d. at 2\ per cent? £ 8. o. 2\ of 100 is ,^ ) 324 4 2 £8 2 1^ commission. What is the commission on £2820 at 1 i per cent? 1 = tA;i ) 2820 i= i 28/4 14/2 £42 68. commission. i^ When the commission is 1^, 1}, or 1}, 2^, or 2} per cent, proceed as in the last rule, adding to the result the aliquot parts as above, according to the rate of the given commission, or find the commission at 1 per cent, and mul- tiply it by the given rate. What is the commission on £4240 lOg. at 1| per cent? 2 = j\r ) 4240 10 ^ 84 16 10 12 £74 4 2 commission. 1^ The commission is here found ai if at 2 per cent; and from th« reralt ^ of itself (the sum taken too much) tosobtnetsd. What i« the commission pn £1065 10 at 2} per cent? 2^ is ^V ) £1065 10 i is -i\r ) 26 12 9 2 13 3^ } £29 6 0^ f commission. What is the commission on £1000 at 4 per cent? 1000 ' 4 100)4000 ' £40 commission. t9* Multiply by the per centage, and divide by £100. What is the commission on £468 6s. 8d. at 7^ per cent? 468 6 8 \. 7i 100 ) 3512 10 ,-n, £35 2 6 commission. What is the commission at 5 per cent on 8 cwts. 3 qrs. of cochineal sold at 14s. per lb.? ', 980 lbs. 7 6 of 100 is ii\i ) 686.0 £34 6s. commission. ST Here, instead of multiplying by the price, I4s., I multiply by half the price, which prevents the necessity of dividing by 20. BROKERAGE. Rule for Brokerage at ^ per cent. Cut off the unit figure of the £; consider those not cut off as shillings. The unit figure cut off is pence, to which add as many fifths of a penny. When the question con- tains shillings as well as £, if 4 or 5, add jd.; if 8 or 10, add ^d.; if 12 or 14, add fd.; if 16s. 8d., and upwards, add Id., to make up the answer. i What is the brokerage on £670 13s. 6d. at J per cent? 67/0 138. 6d. or £3 7 Oj brokerage. What is the brokerage on £785 9b. at ^ per £ 8. d. cent? x> 8. a. 78/5 98. or \ 3 18 6i V £1 19 3^ at ^ per cent. Hod at I ptr cent, and divide oy 2. 10 at 2| QiBsion. at 4 per de by £100. 9. 8d. at 7^ ■-"f mssion. It on 8 cwta. 9 »on. a price, Ua., I he necewity of r cent. ir those not cut pence, to which 3 question con* |d.; if 8 or 10, , and upwards. s. 6d. at i per )kerage. at J per cent? ^ per cent. BROKERAOE. 69 Whati9thebrokerageon£8650 lOs. at ^ percent? i -^yhat !« the brokerage on £35683 6s. 8d. at 2«. £ a. d. 865/0 lOs. or\43 5 0^ 3 ' ~ £21 12 6^ brokerage. What is the brokerage on £3500 IGs.Sd. at ^ per cent? £ 8. d. 350/0 168. 8d. or\17 10 1 at i per cent. i) £4 7 6^ at ^ per cent. <^ Find at ^ per cent, and divide by 4. 6d. per cent? 2s. 6a. >- I) £35683 6 8 100) 4460 8 4 What is the brokerage on £1785 at 28. 6d. per cent^ 2s. 6d. = ^U) £1785 £2 3 4^ brokerage. [^^ Divide the given sum by the aliquot part or parts which the rate of broi per cent? 5 is the j^^ £8464 8 6 £44 12 1 brokerage. What is the brokerage on £922 9s. 1 Jd. at 38. 4d. per cent? £ 8. n. .38. 4.1. == ^ ) 922 9 1^ 100 ) 153 14 10^ £1 8 llfor£l93.nearIy. 23. 6d. = i 21 3 2^ 10 11 7| £31 14 9^ brokerage. What is the brokerage on £2180 at 15s. per cent? 10s., = ^^^£2180 5s. = i 10 18 5 9 £16 7 brokerage. What i8 the brokerage on £4845 at Is. 8d. per cent? Is. 8d. = £^^ £4845 100)403 15s. £4 9 brokerage. What is the brokerage on £ 1286 68. 6d. at 38. 6d. per cent? £ s. D. 2s. 6d. = ^ ) 1286 6 6 ls. = £^ 160 15 9| 64 6 3| 100)225 2 li £2 5 0^ brokerage. What is the brokerage on £1862 IO3. at 4g. per cent? 4s. = })£1862 10 100) 372 10 £3 14 6 brokerage. What is the brokerage on £737 lOs. 3d. at 6s. 8d. per cent? 6s. 8d. == ^ ) 737 16 3' 100 ) 245 16 9 £2 9 2 brokerage. 70 COMMimiON AMD BROKERAGE TABLE. COMMISSION AND BROKERAGE TABLE. s. d. For 2 or tV per cent. take T^VH of the sum. 2 6 or * per cent. take vhv of the sum. 3 4 or i per cent. take ■ehf^ of the sum. 3 9 or ■^ per cfnt. take vhu and 1 of the same. 4 or i per cent. take sh-u of the sum. 5 or i per jifut. take ihu of the sum. 6 8 or i per ceiii. take ^hj5 tf the sum. 7 6 or t per cent. take tH and i of the same. 10 or h per cent. take ^hjf of the sum. 12 6 or 1 per cent. take ihv and \ of the same. 15 or f per cent. take 77T7 and ^ of the same. 17 6 or i per cent. take isijs from the sum. £1 or 1 per cent. take Thr> from the sum. 1 5 or H per cent. take ^jj from the sum. 1 10 or H per cent. take ihv and i of the same. 1 15 or If per cent. take ■h and ^ of the same. i or 2 per cent. take ih of the sum. 2 5 or 2i per cent. take ^ and ^ of the sum. 2 10 or 2ii per cent. take iV of the sum. 2 15 or 2f per cent. take ?v and ^ of the same. 3 or 3 per cent. take ttV and ^ of the same. 3 10 or H per cent. take i\ and j^-^ of the sum 3 15 or H per cent. take it and ^ of the same. 4 or 4 per cent. take ^V and ^ of the same. 4 10 or 4i per cent. take irV and y'^ of the same. 5 or 5 per cent. take TfV of the sum. 5 10 or H per cent. take ^v and j\ of the same. 6 or 6 per cent. take tjV and ^ of the same. 7 10 or n per cent. take 1 ■5D and ^ of the same. 10 or 10 per cent. take tV of the sum. 12 10 or 12^ per cent. take i of the sum. Vi W T< H H< H H Who QUESTIONS. What is Discount? — (See definition.) How do you reckon Discount, when the rate is an aliquot part? If the Discount is an aliquot part of 100, how do you proceed? If the Discount is not an aliquot part of 100, how do you proceed? How do you find the Discount at i per cent? ■*- .ic^-t^i^ II aUESTIOMB. 71 What is the Diacount on X s. d. 320 18 6 at 4d. per £? Answer, 98 7 6 at 3d, per £? " 5200 15 OatlOd. perf? " 580 6 8 at fid. perf? " 70 10 at 2d. on the shilling? " 120 5 at |d. on the shilling? " 2184 at Id. on the shilling? " 22 10 at ^d. on the shilling? " 40 2 6 at \A. on the shilling? " 100 at 5 per cent? " 628 13 4 at 10 per cent? " 3000 at 20 per cent? " 8540 10 at 25 per cent? " 585 at 50 per cent? «< 200 at 7^ per cent? " 900 at 15 per cent? " 360 at 17^ per cent? " 972 16 8 at 35 per cent? " 255 10 at 45 per cent? " 796 at i per cent? " 5350 at J per cent? " 479 at i per cent? " 9999 10 at J per cent? " £ *. «L 6 6 H4 1 4 7 216 13 Hi 14 10 2 11 15 2 7 10 H 182 18 9 16 8i 5 62 17 4 600 2135 2 6 292 10 15 135 63 340 9 10 114 19 6 3 19 7i 26 15 1 3 Hif 12 9 n# + \; What is Commission?— (See definition.) To whom are CommiBsion and Brokerage at ^, \ and J useful? Why? How do you find the Commission at ^ per cent? How do you find the Commission at ^ per cent? How do you find the Commission at ^ per cent? How do you find the Commission at | per cent? £ B. d. 8240 at ^ per cent? Answer, 475 at ^ per cent? " 3180 at ^ per cent? '■ 380 at :J per cent? " 1450 at ^ per cent? " 1000 at ^ per cent? " 5240 at i per cent? " 630 10 at i per cent? " 2400 15 at ^ per cent? " 7960 at 1 per cent? " 80 4 2 at -^j per cent? " 150 10 at 2| per cent? " 90 7 6 at 4 per cent? " 120 13 6 at 7i per cent? " What is the Commission on £ B. d. 10 6 11 loi 3 19 6 19 2 12 6 2 10 26 4 3 3 Oh 12 Oj 79 12 2 1 4 2 9i 3 12 H 9 1 r? QUKinOMfl — KZBKOUBS. Whet is Xit-ckeriiigc? — (Sir definilion.) What is the Brokerage on h £ a. 800 i^; 980 4 2000 10 326 15 4308 12 754 boOO 675 4680 A. li at j per cent? Answer, at ^ per cent? •' at ^ per cent? " at jj' per cent? •* Rt 15*. percent? •* at 18. 8(1. per cpnt? " at 3s. 4(1. per cent? " <; at 38. 9d. per cent? " at 6s. 8d. per cent? " • £ «. d. 1 10 Oj 2 9 5 8 2 32 6 H 12 H 27 10 1 5 H i: 12 EXERCISES IN PKOFIT AND L(J>SS, rURCHASE OF PROPERTY, AKD AVERAGE CALCULATIONS. When the gain or hss per cent, is required. l?!7i.K. — Multiply the diifrrenco of the prime cost and ■elliiit; price by 100. and diviile the product by the prime cost; or, divide £100 by thf propurtional pan which the selling j^riue falls short uf the prime cost. What is \!itf gain per cent, on any article bought at 4s. 2d. per lb and sold at os? 8. d. 5 4 2 10 100 6/0 ) 100/0 Ans. 20 per cent. Or, as the selling price (in the foregoing ques- tion) exceeds the prime cost }, divide 100 hy j- and the quotient will be the rate per cent? })100 Ans. 20 per cent. When a sellir^ price in required, according to a given gain or loss per cent. Rule. — Add or subtract to or from the prime cost a gain or loss (ttccordint; to the reason of the question,) proportional to the given gain or los.s per cent At what rate must linen doth, bought at 17^d. per yard, be resold to gain 20 per cent? 20 of 100 is the ^) 17^ 3i Ans. 21 pence per yard. What is the profit on 1 cwt. of sugar bought for £2 10s. 3d. and sold at 6^d per lb? 6d. of Is. is the ^ ) 112 lbs. at 6^d. id. of 6d. is the ^'y ) 56 4 8 3 8 selling price. 2 10 3 cost price. Ans. £0 10 5 gain. i- '!l^ < •' ), KXEKCWE*— aiJBVTIONS. d. Of 2 H H What is gained per cent, on silk bought at 6s. 8d. per yard and sold at la. 6d? a. (1. 7 6 6 8 10 3 X 68. 8d. = £1 2 6 ^£100 As 92^ is to 100 185 ) 12200 I At wlint rate p»>r cwt. miut dainigfd sugar, bought at £2 \5*. per cwt., In- Mold to austuin a loss of 2 J pur cent? X ». .!. * SioflOOis A )2 1.) I -1} Ans. £12 10 or 12j percent? Note. — In c-stinmting a profit, as a ritt« per (rent., th«> theory of thu sellout, and tho practice of tradcr^i, ure at variance. Su|'|)<>.se we buy ut four und hell iit tivu, the iVrithmetiuiiin reckons this h» u gam of one on four, i>r 25 per cent; uhile the Trader, counting on the scliintr price, makes it a i^ain only of one on iivc, or '20 per cent. The two folluwiijg examples uft'urd u general rule for working the latter plan. An article which costs lojd. per lb is .sold at 17 ad. per lb, wliut is the gain per cent, estimated on the selling price? From I7^d. = 70 farthings. Take 15^d. = 61 do. Then as 70 is to 9 so is 100 9 70 ) 900 ( 13 per cent, nearly. What should the above be rated ut to obtain a profit of 7i per cent? From 100 Or, ns 185 is to 200 Take 7^ Sois 61 fiirtliings — - 200 An?. £2 13 7^ per cwt. At what rata per yard must dnmngfd cloth, bought at 13s. 4d. ptr yard, be sold to nuitain a loss of 12i per cent? ». cent., oiiQ G in the£,tal<'> -^^ of the prime cost. 3^ 9 Vn »'>'! J of the same. S 1 ^'^ of the prime cost. 6j 1 3 ^ and ^ of the same. "J I 6 ,'„ aii(H uf the same. 10 2 To"' 'l"' prime cost. 12^ 2 fi ^ of the prime cost. 15 3 ,'„ aiuH of the same. 20 4 J of the prime cost. 2.5 5 :| of tlio priuie C'>st. 30 6 \ and ^ (if the same. &U 10 ji of the prime cost. Nr)TE. — To gain a profit of 2J per cent, add ^'^ part of the prime cost to itself. — To su.stiiin a lo^s of 2.^ por cent, ileduft ^'„ of the prime cost from itself. QUESTIONS. "What is the gain per cent on goods purcha.r c*>nt. oblainfd | trAn tho purchaiut of proptrty of curtain yearly value, divide the annual rental by the number of ^eari purchasi', and tho rosult will be the per ccntage at which your tr ,iney if cxpeDded. Rui.E.~ purchasei Suppose the rental of an estate to bo f 150 per annum, and I give 12 years purchase for 'he pro- perty, what percentage do I obtain for my money? 12 ) hW Ana. £12 10 or 121 per cent. If property, which ia let ut £200 per annum, were sold for 18 yenrs purchase, what rate per cent. wuuUl it realize? £ IR )200 Ans. £11 2 2 i per cent. ♦ An estate, worth £157 Ss. per annum, was lately sold at 15 years purchase, what per centuge does it return the purchaser? £ a. 15)157 5 Ans. £10 9 8 per cent. When an estate of the annual rental of £177 68. 8d. sells for 20 years purchase, what per cent- age does it yield? £ a. d. 20 ) 177 6 8 Ans. £8 17 3 per cent. If, for property of the value of £3 1 2 ' Os . per annum, 25 years purchase be required, what per centage would it give? £ 25 ) 312 s. 10 Ans. £12 10 or 12J per cent. A person wishing to dispose of an estate, which he lets at £64 10s. per annum, oilers it fur nine years purchase, what per centage would that re- turn? £ s. d. ^ 9)64 10 • Ans. 7 3 4 or 7J per cent. ■For any deaired per ceotage ua the In order to aKertain what lum muHt be i^iven for pro- perty, in order to obtain any desired [wr rentage on the purchase, divide the annual rental by the per rentage; the quotient will be tho number of years purchase, which number of years purchase, multipli<^d by 100, gires the whole purchase money. If the annual rental of an estate be £250, what number of years purchase, and what purchase money, must be given fur it to yield 5 per cent? 50 years purchase. 100 Ans. jE5()00 purchase money. If the annual rental of an estiite be £186, what number of years purchase, and what |nirciiase money must be given for it to yield 6 per cent? £ 6) 186 31 years purchase. 100 Ana. £3100 purchase money. The annual rental of an estate being £90, what number of years purchase, and what purchase money, must be given for it tu yield 3 per cert? £ 3)90 30 years purchase. 100 Ans. £3000 purchase money. The annual rental of an estate being £324, what number of years purchase, and what pur- chase money must be given for it to yield 4J per cent? 9) £648 72 years purchase. 100 Ans. £7200 purchase money. O* Here both the rental and the per centage are doubled in order to avoid the fractions. 12 6 5 18 4 7 5 3 94 75 Whnt principal, at !> por rpnt. per annum, will What principal, at 7^ |M'r cent per annum, will produce a jcurly incuih to know the average prict; of each tti, and tin; total lunuunt? ■>. d. 2 boxes at 6 per lb. 2 7i '* 2 h] " 2 «< " 2 9? " 2 lot " 2 ll| " 2 1 0^ «' 2 1 1 " 2 1 2^ " 2 1 4 " 2 I 5 " 24 lots 12)11 3 1 1 ^ average per lb. 24 boxes £i) 12 8s. price of 1 box at Id. per lb. 1 1^ average price. 192s. = £9 123. £108 total amount. I bought 7 puncheons of brandy on the follow- ing terms, and wish to know what quantity they contain: what is the cost price per gallon, and what is the total amount of the purchase money? No. 1 contains 109 gallons. - , 2 120 " 3 95 " 4 112 " 5 122 " 6 98 " 7 116 " Gallons, 772 at Is. = £38 12 12 8. d. Total, £463 4 First cost, 3 6 per gallon. Freightage.O 6 Duty, 8 12d. cost price per gallon. 76 INDBX TO MJUITAL OALCI.XATION. THE READY RECKONER'S INDEX TO MENTAL CALCULATION, Which shows the value of the dozen, gross, and score, at so much each. . 1^ I), r. 1 1 1 1 2 U a 3 3 3 4 4 4 4 5 each is each iH each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is each is eacli is each is each is each is each is each is each is each is each is each is ?ach is each is each is each is each is each is each is < each is £ n. II. 1 1 I 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 6 6 G « 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 13 II. 3 per dozen, per (lozpii, 9 per dozen, [)vr dozen, 3 per dozen, per dozen, 9 per dozen, per dozen, 3 per dozen, C per dozen, 9 per dozen, per dozen, 3 per dozen, per dozen, 9 per dozen, per dozen, 3 per dozen, per dozen, 9 per dozen, per dozen, 3 per dozen, C per dozen, 9 per dozen, per dozen, 3 per dozen, per dozen, 9 per dozen, per dozen, 3 per dozen, per dozen, 9 per dozen, per dozen, 3 per dozen, 6 per dozen, 9 per dozen, per dozen, 3 per dozen, 6 per dozen, 9 per dozen, per dozen, 3 per dozen, G per dozon, 9 per dozen, per dozen, 3 per dozen, 6 per dozen, 9 per dozen, per dozen, £ ■. t>. £ a. n. 3 per gros.s, & per score. (} per gross, 10 per score. 9 per press, 1 3 per score. 12 per gross, 1 8 per score. IT) per gross, 2 1 per score. 18 per gross, 2 G per score. 1 1 per gross, 2 1 1 per score. 1 4 per gross, 3 4 per score. 1 7 per gro8.s, 3 9 per score. 1 10 i)er gross, 4 2 per score. 1 13 per gross, 4 7 per score. 1 1« per gro.ss, o 5 per score. 1 19 per gross, 5 5 per score. o 2 per gros.s, 5 10 per score. 2 5 per gross, 3 per score. 2 8 per gross, G 8 pep score. 2 11 per gross, 7 1 per score. 2 14 per gross, 7 6 per score. 2 17 per gross, 7 1 1 per score. 3 per gross, 8 4 per score. 3 3 per gross, 8 9 per score. 3 G per gross, 9 2 per score. 3 9 ^ per gross, 9 7 per score. 3 12 per gross, 10 per score. 3 15 per gross, 10 5 per score. 3 18 per gross, 10 10 per scoie. 4 1 per gross, 11 3 per score. 4 4 per gross, 11 8 per score. 4 7 per gross, 12 1 per score. 4 10 per gross, 12 per score. 4 13 per gross, 12 1 1 per score. 4 16 per gro«s, 13 4 per score. 4 19 j)er gross, 13 9 per score. 5 2 per gro.ss, 14 2 per score. 5 5 j)er gross, 14 7 per score. 5 8 per gross, 15 per score. 5 11 per gross, 15 5 per score. 5 14 per gross, 15 10 Der score. 5 17 per gro.ss, 16 3 per score. (> per gross, 10 8 per score. () •> per gross, 17 1 per score. 6 G per gross, 17 G per score. () per gross, 17 1 1 per score. 6 12 por gross, 18 4 per score. r. 15 per gross, 18 9 per score. 6 18 per gross, 19 2 per score. 7 1 per gross, 19 7 per score. 7 4 per gross, 1 per score. >** EASY METHODS OF RECKONING Ry the Doxen, CarofiM, Score, Sir, PAUTICULALY ADAPTKI) ' Till-: TRANSACTIONS OF THE RKTAIL MERCHANT. Rui.K FOR THR nozEM AMD oRodH. — Tlic numlier of pencr that one article is worth is the number ot'NhillinKs that a do/cii is worth. Aiul tho number of pence that n dozen is worth is the number of shillingii that a gros.s irr ofHcurcs {>cr quarter. If at 3t., ■+■ 3, and lOi. per lb. ia the Anaw«r. 4 On TiiK cuxraAav, when by the price of a lb. you have to find the value of an •t^inc., take the Hhillinf^s as farthings, and multiply by U. , EXAMPLE. I At 10*. pffr lb., what is the price of an ouncf? H«re 10s. as fartltinge, multiplied by ti, giv«s 30 farthings, or 7^d. per ounce, Answer. RiJi-E. — When the price of one article is given, to tind the value of 100 you must multi- ply the price by 5, and call the shillingH pounds ; and nhould there bo any pence in the amount, when multiplied, add the same aliquot part of a pound an the f)ence are of a shilling. EXAiu?LE. At 7«. ti(\. each, what will 100 articlps cost? Hcru 78. 3d., multiplied by .5, arc called i)36 and 3 over, for which add oa.; total, £36 5». this divi- ) Answer, dtiply the ct pence ; from this; 1 multiply gs, add 7s. )er day be hillings. ' Kpenditure wer. >., take the lings. Another method. — For every farthing take as many pence, and twice an many shll- EXAiMPLE. At 7.1J. each, what will 100 articles cost? Here 7id., or 30 farthings, as pence are 2b. 6d., and double the farthings us shillings are £3; total, £3 2 6d., Answer. Rule. — When the cost of a cwt. is given, to find the price of a lb. consider first how many shillings make up the given price, multiply them by 8, and divide the product by 7, and the result will be the price per lb. in farthings. EXAMPLE. At 688. per cwt, what is the price of a lb.? Here 688. multiplied by 3 gives 204s>, which, divided by 7, leaves 29j as farthings, or 7^d and -f . Answer. . On the contrary, when the price of a lb. is given, to find the cost of a hundred weight, consider first how many farthings there are in the given price, double the number, and call the result shillings, to which add as many four-pences as the original number of farthings, and the amount will be the answer required. EXAMPLE. At 5^d. per lb., what is the value of 1 cwt.? The 5^d., or 21 farthings, doubled as 42s., then, 21 groats, or 7s., added, gives £2 9s., Ana. Another method. — Multiply 9s. 4d., which is the price of 1 cwt. at Id. per lb., by the number of pence in the price of the article. NoTB.— Should the price include farthings, add Sa. 4d. for one farthing, 4b. 8d. for two, and 7s. for three fitrthinge EXAMPLE. At 5^d. per lb., what is the value of 1 cwt.? Here Id. per lb., or 9», 4d. multiplied bjr 5 gives £2 6 8, and add 2s. 4d. (for 112 farthings per lb.) total £2 9». per owt. I BcLE. — For finding the value of several cwts. and qrs. at any given price per lb., mul- tiply 98. 4d. (the price of 1 cwt. at Id. per lb.) by the given price, and then multiply that product by the numl)er of cwts. and qrs. „ , I ' t,j '. . ■.im uii'i^iiil:* -^ EXAMPLE. '■ -jWriKf j^/if y.^^iW.^..' '■"'■ ' At 6^. per lb., what is the value of 10 cwts. 2 qrs.? ' " Here 1 12d., or 9s. 4d , multiplied by the price, S^d., gives £2 9s., which, multiplied by the quantity, lOJ cwts., gives £25 14 6, Answer. NoTS. — If besides owts. and qr^ there should be lbs. in the question, j^e tdditioo of apjnanjr peace will be requisite. ' / . - '■'■ <-\ „■■■...'- ^ a . - J. i< , •f^i'l'.Kii' '^'' , iif s'-. Rinj!.— When the price of a lb. is given to find the value of a ton, every three farihings in the given price must be reckoned as £7 per ton. Every odd farthing over any number of three will of course give £2 6 8 more to be added. ^.^p, . •^: EXAMPLE. ' '' ' ' '-''^A ''^' ' ' ■ ■ ■*-.■.',.' f' " • If a lb. of cheese cost Sjd., what is the value of a ton? In 8jd. are 34 farthings, divided by 3 you have 1 1 and 1 over. Now, 11 multiplied by 7 --i JE77, to which add £2 6 8 for the odd farthing over. Total, £79 6 8. • ' By having the price of a lb. you may find the value of a cwt. in the following manner. Consider the pence in the price of a lb. as farthings, and for every three farthings in the price reckon 7s., and for every odd farthing 2s. 4d. These added gives the price of a cwt EXAMPLE. , At 7^d. per lb., how much per cwt.? , ' ' ^ . ,■ •.- ■ ,^w,i^ Here 7id. are 29 farthings, which divided by 3 gives 9 and 2 farthings over, then 9 multi- plied by 7 gives 638. to which add 48. 8d. for the two farthings which makes £3 7 8, the Answer. •^.'; .-: .' tMiH:,i * ri r . I" •^. m Jm^t X 'li ■." r^x^'t '• \ / "/' FINIS. ' '- , -r'.-t' .1* •'< ■•.,,v"i! ; (..* r X. ' *v ■•%.' ' y '/< ^r 112 farthing! 'ice per lb., mol- 3n multiply that multiplied by the ence will be requisite. if.s^ f 'i. Y three faithings irer any number (".^>> 1 nultiplied by 7 m 6 8. [lowing manner, farthings in the price of a cwL er, then 9 multi' ;h makes £3 7 8, , ■■ T^.:- ■■■'■ •