4q. 17£. Ans. 17. 138. 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 1 17., with the several repenny, we multiply the pence mainders, 13 s. 6 d. 3 qrs. con(4242) 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. 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. to farthings. 5. In 29 guineas, at 28 s. each, how many farthings? 7. Reduce $163, at 6 s. each, to pence? 9. In 15 guineas, how many pounds? 4. Reduce 31472 farthings to pounds. 6. In 38976 farthings, how many guineas? 8. Reduce 11736 pence to dollars. eas. 10. Reduce 21£. to guin Note. We cannot reduce guineas directly to pounds, but we may reduce the guineas to shillings, and then the shil lings to pounds. TROY WEIGHT. By Troy weight are weighed gold,* silver, jewels, and all liquors. The denominations are pounds, ounces, pennyweights, and grains. TABLE. 24 grains (grs.) make 1 pennyweight, marked pwt. 20 pennyweights 12 ounces 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 ing 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 nothing 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 to be 12 ounces fine. The standard for silver coin is 11 oz. 2 pwts. of fine silver and 18 pwts. of copper, melted together. APOTHECARIES' WEIGHT. Apothecaries' weight* is used by apothecaries and physi cians, in compounding medicines. The denominations are pounds, ounces, drams, scruples, and grains. TABLE. 20 grains, (grs.) make 1 scruple, marked 9. 3 scruples 12 ounces 17. In 9 lb. 83.13. 29.1 19 grs., how many grains. 1 dram, 1 ounce, 1 pound, 3. 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 : pois. 1 lb. Troy G 192 oz. avoirdupois, and 175 lb. 5760 grains, and 1 lb. avoirdupois Troy-144 lb. avoirdu 7000 grains Troy. 124 cents a pound, may be bought for $82'625? 19. What will 5 cwt. 3 qrs. 20. How much sugar, at 17lb. of sugar come to, at 12 cents a pound. 21. A merchant would put 109 cwt. 0 qrs. 12 lb. of raisins into boxes, containing 26 lb. each; how many boxes will it require? 22. In 470 boxes of raisins, containing 26 lb. each, how many cwt.? 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. 4 nails, (na.) or 9 inches, make 1 quarter, 4 quarters, or 36 inches, marked qr. yd. 1 yard, 1 ell Flemish, 1 ell English, 1 ell French, 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, rds, feet, inches, and barley-corns. 31. How many barley-corns 32. In 4755801600 barleywill reach round the globe, it corns, how many degrees? being 360 degrees? Note. To multiply by 2, is Note. The barley-corns beo take the multiplicand 2 ing divided by 2, and that times; to multiply by 1, is to quotient by 12, we have .take the multiplicand 1 time; 132105600 feet, which are to to multiply by, is to take the be reduced to rods. We canmultiplicand half a time, that not easily divide by 16 on is, the half of it. Therefore, account of the fraction ; but to reduce 360 degrees to stat-16 feet: 33 half feet, in 1 ute miles, we multiply first by rod; and 132105600 feet = the whole number, 69, and to 264211200 half feet, which, the product add half the multi- divided by 33, gives 8006400 plicand. Thus : rods. 360 691 3240 2160 Hence, when the divisor is encumbered with a fraction, or, &c., we may reduce the divisor to halves, or fourths, 180 half of the multiplicand. &c., and reduce the dividend to the same; then the quo25020 statute miles in 360 de-tient will be the true answer. grees. 33. How many inches from 34. In 30539520 inches, Boston to the city of Wash-how many miles? ington, it being 482 miles? 35. How many times will a 36. If a wheel, 16 feet 6 wheel, 16 feet and 6 inches inches in circumference, turn in circumference, turn round round 12800 times in going in the distance from Boston to from Boston to Providence, Providence, it being 40 miles ?what is the distance? |