penny? in 3 pence? pence? in 8 pence? in 9 pence? in 12 pence? things? in 1 shilling? in 2 How many farthings in 1 How many pence in 4 far in 2 pence? things? in 8 farthings? in 6 in in 32 far in 48 qrs. ? How many shillings in 48 qrs.? 96 qrs.? in How many shillings in 24 in 12 farthings? 24 farthings? in 36 farthings? lings? in 3 s. ? in pence? in 36 d. ? in in 48 d. ? It has already been remarked, that the changing of one kind, or denomination, into another kind, or denomination, without altering their value, is called Reduction. ( 27.) Thus, when we change shillings into pounds, or pounds into shillings, we are said to reduce them. From the foregoing examples, it is evident, that, when we reduce a denomination of greater value into a denomination of less value, the reduction is performed by multiplication; and it is then call. ed Reduction Descending. But when we reduce a denomination of less value into one of greater value, the reduction is performed by division; it is then called Reduction Ascending. Thus, to reduce pounds to shillings, it is plain, we must multiply by 20. And again, to reduce shillings to pounds, we must divide by 20. It follows, therefore, that reduction descending and ascending reciprocally prove each other. Ans. 17£. 13s. 63d. Farthings will be reduced 16971 qrs. the Ans. to pence, if we divide them In the above example, be- by 4, because every 4 farcause 20 shillings make 1 things make 1 penny. Therepound, therefore we multiply fore, 16971 farthings divided 17. by 20, increasing the by 4, the quotient is 4242 product by the addition of the pence, and a remainder of 3, given shillings, (13,) which, which is farthings, of the it is evident, must always be same name as the dividend. done in like cases; then, be- We then divide the pence cause 12 pence make 1 shil- (4242) by 12, reducing them ling, we multiply the shillings to shillings; and the shillings (353) by 12, adding in the (353) by 20, reducing them given pence, (6.) Lastly, to pounds. The last quotient, because 4 farthings make 117., with the several repenny, we multiply the pence mainders, 13 s. 6 d. 3 qrs. con74242) by 4, adding in the stitute the answer. given farthings, (3.) We Note. In dividing 353 s. by then find, that in 17£. 13 s. 20, we cut off the cipher, &c., 6 d., are contained 16971 as taught ¶ 22. farthings. T 34. The process in the foregoing examples, if carefully examined, will be found to be as follows, viz. To reduce high denomina-| To reduce low denominations tions to lower,-Multiply the to higher,-Divide the lowest highest denomination by that denomination given by that number which it takes of the number which it takes of the next less to make 1 of this same to make 1 of the next higher, (increasing the pro- higher. Proceed in the same duct by the number given, manner with each succeeding if any, of that less denomina-denomination, until you have tion.) Proceed in the same brought it to the denomination manner with each succeeding required. denomination, until you have brought it to the denomination required. EXAMPLES FOR PRACTICE. 3. Reduce 32£. 15 s. 8 d. Note. 4. Reduce 314~2 farthings to pounds. 6. In 38976 farthings, how many guineas? 8. Reduce 11736 pence tc dollars. eas. 10. Reduce 21£. to guin We cannot reduce guineas directly to pounds, but we may reduce the guineas to shillings, and then the shillings to pounds. TROY WEIGHT. * By Troy weight are weighed gold, silver, jewels, and all iquors. The denominations are pounds, ounces, pennyweights, and grains. 24 grains (grs.) make 1 pennyweight, marked pwt. 20 pennyweights 12 ounces TABLE. 1 ounce, 1 pound, oz. lb. 11. Bought a silver tank-] 12. Paid $44'28 for a silard, weighing 3 lb. 5 oz., pay-ver tankard, at the rate of ang at the rate of $1'08 an $1'08 an ounce; what did it ounce; what did it cost? weigh? 13. Reduce 210 lb. 8 oz. 14. In 50572 pwt. how 12 pwt. to pennyweights. many pounds? 15. In 7 lb. 11 oz. 3pwt. 16. Reduce 45681 grains 9 grs. of silver, how many to pounds. grains? The fineness of gold is tried by fire, and is reckoned in carats, by which is understood the 24th part of any quantity; if it lose noning in the trial, it is said to be 24 carats fine; if it lose 2 carats, it is then 22 carats fine, which is the standard for gold. Silver which abides the fire without loss is said te re 12 ounces fine. The standard for silver coin is 11 oz. 2 pwts. of fine si.ver, and 18 pwts, of copper melted together APOTHECARIES' WEIGHT. Apothecaries' weight* is used by apothecaries and physicians, in compounding medicines. The denominations are pounds, ounces, drams, scruples, and grains. TABLE. 20 grains, (grs.) make 1 scruple, marked э. 3 scruples 12 ounces 17. In 9tb. 83. 13. 29.1 19 grs., how many grains. 18. Reduce 55799 grs. to [pounds. AVOIRDUPOIS WEIGHT.† By avoirdupois weight are weighed all things of a coarse and drossy nature, as tea, sugar, bread, flour, tallow, hay, leather, medicines, (in buying and selling,) and all kinds of metals, except gold and silver. The denominations are tons, hundreds, quarters, pounds, ounces, and drams. Note 1. In this kind of weight, the words gross and net are used. Gross is the weight of the goods, together with the box, bale, bag, cask, &c., which contains them. Net weight is the weight of the goods only, after deducting the weight of the box, bale, bag, or cask, &c., and all other allowances. Note 2. A hundred weight, it will be perceived, is 112 lb. Merchants at the present time, in our principal sea-ports, buy and sell by the 100 pounds. *The pound and ounce apothecaries' weight, and the pound and ounce Troy, are the same, only differently divided, and subdivided. 175 oz. Troy Dois. 1 lb. Troy 192 oz. avoirdupois, and 175 lb. Troy: 144b. avoirdu5760 grains, and 1 lb. avoirdupois 7000 grains Troy. G 20. How much sugar, at 19. What will 5 cwt. 3 qrs.] 17 lb. of sugar come to, at 12 cents a pound, may be 12 cents a pound. bought for $82'625 ? 21. A merchant would put 22. In 470 boxes of raisins, 109 cwt. O qrs. 12lb. of containing 26 lb. each, how raisins into boxes, containing many cwt.? 26 lb. each; how many boxes will it require? 23. In 12 tons, 15 cwt. 24. In 7323500 drams, how 1 qr. 19 lb. 6 oz. 12 dr. how many tons? many drams? 25. In 28 lb. avoirdupois, how many pounds Troy? 26. In 34lb. 0 oz. 6 pwt. 16 grs. Troy, how many pounds avoirdupois? CLOTH MEASURE. Cloth measure is used in selling cloths and other goods, sold by the yard, or ell. The denominations are ells, yards, quarters, and nails. TABLE. 1 nails, (na.) or 9 inches, make 1 quarter, marked 4 quarters, or 36 inches, 3 quarters, 5 quarters, qr. 6 quarters, 1 ell French, LONG MEASURE. Long measure is used in measuring distances, or other things, where length is considered without regard to breadth. The denominations are degrees, leagues, miles, furlongs, rods, yards, feet, inches, and barley-corns. |