and then the ounces by 12, because 12 ounces make 1 pound. How do you reduce tuns to pounds? A. First multiply by 20, because each tun will make 20 hundred weight, and then multiply by 4, because each hundred contains 4 quarters, and lastly, by 28, because each quarter contains 28 pounds. How do you reduce guineas to pounds? A. Multiply the guineas by 28, and the product will be shillings, and then divide the shillings by 20, and the quotient will be pounds. How do you reduce pounds to moidores? A. Multiply the pounds by 20, and the product will be shillings, and then divide the shillings by 36, and the quotient will be moidores. Suppose a barrel of wine is to be racked off, in pint bottles, quart bottles, and 2 quart bottles, and an equal number of each is required; how would you proceed to tell the number of bottles required to hold the wine? A. Add, in one sum, the number of pints that would fill the bottles once, for the divisor, and then reduce the barrel to pints for a dividend, and the quotient would show how often the bottles could be filled. COMPOUND ADDITION, Is collecting together two or more numbers of different denominations in one sum. RULE.-Place the numbers, so that those of the same denomination may stand directly under each other. Then add the right hand denomination the same as a sum in simple addition, and divide the amount by as many as it takes of that-denomination to make a unit in the next higher denomination; set down the remainder under the denomination added, and carry the quotient to the next higher denomination; and so proceed with all the denominations until you come to the left hand denomination, and there set down the whole amount the same as in simple addition." NOTE. The principles in compound quantities do not essentially differ from those of abstract numbers, that is, simple, refined, pure, not broken numbers. In the one case, we carry by 10; in the other, by the number of units which it takes to equal a unit in the denomination; so that the student will find the work easy, if he has acquired a knowledge of the tables, and will only keep in mind the rule given for the operation of the work. Yet it is to be regretted, that the wisdom of our legislature, has never reduced compound quantities to the decimal system, which would greatly simplify the operations of work in arithmetick. The French have reduced all compound quantities to the decimal scale, except the division of time, which does not appear to be capable of change. A wise policy may dictate never to adopt hastily a new system; but after the utility of a system has become obvious, neither national pride nor narrow prejudices should prevent its adoption; no matter by what individual or individuals the system may have been simplified, or by what nation adopted, the benefits are the same. EXAMPLES. STERLING MONEY. 1. In £41 13s. 6d. 2qrs., £48 11s. 4d. 3qrs., £96 16s. 10d. 3qrs.; how many pounds, shillings, pence, and farthings, when added together? £ S. d. qrs. 10 £187 1 10 DEM.-We first add the denomination of farthings, and find it amounts to 8, which we divide by 4, because 4 farthings are equal to one penny, and we find that the quotient is 2, and the remainder a cipher; so we. set down the cipher and carry 2 to the pence, the next higher denomination, because the 8 farthings are equal to 2 pence; by adding the pence, we find the amount 22, which we divide by 12, because it takes 12 pence to make a shilling, and the quotient is 1, and the remainder 10; we set down 10 under the column of pence, and carry the quotient, which is 1 shilling, to the shillings; and in adding the shillings, we find they amount to 41, which we divide by 20, because it takes 20 shillings to make 1 pound, we find the quotient 2, and the remainder 1, which we set down under shillings, and carry the quotient, which is pounds, to the pounds; and in adding the left hand denomination, we carry the same as in simple work, and set down the whole amount in adding the left hand column. In all other sums in compound addition we observe the same rules; always carrying by that number which is equal to a unit in the next higher. Proof, the same as in simple work, only carry as in the first adding. 5. What is the amount of £47 16s. 11d. 3qrs., £105 14s. 11d. 2qrs., £89 18s. 4d. 1qr., and £844 13s. 10d. Oqrs., when added? Ans. £1088 4s. 1d. 2qrs. 6. What is the amount of one hundred and five pounds, fourteen shillings, sixpence, one farthing; eighty-four pounds, ten shillings, four pence, three farthings; and five hundred pounds, fifteen shillings, ten pence, three farthings, when added together? Ans. £691 0s. 9d. 3qrs. 7. What is the amount of 2s. 6d., 4s. 8d., 9s. 3d., 4s. 9d.? Ans. £1 1s. 2d. 8. A man bought a wagon for £18 16s. 8d., a plough for £2 10s., a span of horses for £55 10s. 6d. ; what must he pay for the whole ? Ans. £76 17s. 2d. 9. Three men found a prize, and having divided it equally among them, each man received £18 4s. 1d.; what was the amount of the prize? Ans. £54 12s. 3d. 5. Bought a set of silver spoons weighing 1lb. 1oz. 9pwts. 17grs., a silver cup weighing 5oz. 10pwts. 14grs., and a silver tankard weighing 1lb. 11oz. 7grs.; what was the weight of the whole? Áns. 3lb. 6oz. Opwts. 14grs. cause 28 pounds make a quarter; and from quarters to hundreds by 4, because 4 quarters make a hundred; and from hundreds to tuns by 20, because 20 hundred make a tun. 4. Bought 4 fat oxen, weighing as follows, viz., 12cwt. 3qrs. 16lb., 13cwt. 2qrs. 12lb. 13oz., 15cwt. 1qr. 21lb. 11oz., 16cwt. 1qr. 24lb. 8oz.; what was the weight of the whole in tuns ? Ans. 2T. 18cwt. 1qr. 19lb. APOTHECARIES' WEIGHT. 7. Bought 4 pieces of cloth, the first 96yds. 3qrs. 2n.; the second 84yds. 3qrs. 3n.; the third 75yds. 1gr. 2n.; the fourth 96yds. Iqr. in.; how much did the four pieces contain? 1. LONG MEASURE. Ans. 353 yards. 2. Deg. m. fur. rd. ft. in. b.c. 3. Deg. m. fur. rd. yds. ft. in. b. c. 84 65 6 35 4 2 95 55 7 14 5 1 37 1 2 0 0 2 6 2 11 1 3 2 79 65 7 13 11 10 1 34 65 6 35 14 11 2 NOTE.-When halves or fractions occur with the remainder after the division, they must be carried back in the inferiour denominations according to the value; and if by carrying back it increases the inferiour denominations so as to equal a unit, or exceed a unit, at the left, a unit must then be added to the superiour, and the excess set down in its proper place; for fractions must never be placed in a sum, when there are denominations at the right. LAND, OR SQUARE MEASURE. 1. Pol. ft. in. 19 180 135 25 250 120 Rood. 13 90 85 Ans. 1 18 250 16 DEM. In adding the inches, we find they amount to 340 inches, which contain 144 twice, and 52 remain, which we retain, and carry the 2 to the feet; we find the feet amount to 523, which we divide by 2724, which we find contained once, and 249 remain, and as we cannot set down a fraction in the superior denominations, we reduce the of a foot to inches, which produce 108 inches, and the 52 inches added which was our remainder in inches, we have 160 inches, which are equal to 1 foot and 16 inches; we then set down the 16in. under inches, and add the foot to 249 feet, which gives 250 feet, which we place under feet, and carry 1 to the poles, and by adding we nnd the poles amount to 58, which divided by 40, the number of poles in a rood, gives 1 rood and 18 poles. in. A. rds. pol. ft. A. rds. pol. ft. 87 2 39 150 185 3 36 27 19 1 7 9 |