4. A man dies, leaving an estate of $71600; there are demands against the estate, amounting to $39876'74; the residue is to be divided between 7 sons; what will each one receive? 5. How much coffee, at 25 cents a pound, may be had for 100 bushels of rye, at 87 cents a bushel? Ans. 348 pounds. 6. At 12 cents a pound, what must be paid for 3 boxes of sugar, each containing 126 pounds? 7. If 650 men receive $8675 each, what will they all receive? 8. A merchant sold 275 pounds of iron, at 64 cents a pound, and took his pay in oats, at $0'50 a bushel; how n. y bushels did he receive? 9. How many yards of cloth, at $4'66 a yard, must be given for 18 barrels of flour, at $9'32 a barrel ? 10. What is the price of three pieces of cloth, the first containing 16 yards, at $375 a yard; the second, 21 yards, at $4'50 a yard; and the third, 35 yards, at $ 5'12 a yard ? 32. It is usual, when goods are sold, for the seller to deliver to the buyer, with the goods, a bill of the articles and their prices, with the amount cast up. Such bills are sometimes called bills of parcels. Mr. Abel Atlas Boston, January 6, 1827. : Bought of Benj. Burdett 121 yards figured Satin, at $250 a yard, 8 ....... sprigged Tabby,... 1'25 Received payment, 5 bags Coffee, 75 lb. each, 1 chest hyson Tea, 86 lb. Received payment, ........ BENJ. BURDett. Mr. James Paywell Bought of Simeon Thrifty 3 hogsheads new Rum, 118 gal. each, at $0.31 a gal. 1121 :::: For Simeon Thrifty, Salem, June 4, 1827. ................ cwt. $31'28 10'00 $41'25 PETER FAITHFUL. $706*521 Received payment, ASA FALLTREE. Note. M. stands for the Latin mille, which signifies 1000 and C. for the Latin word centum, which signifies 100 101'849 REDUCTION. ¶ 33. We have seen, that, in the United States, money is reckoned in dollars, cents, and mills. In England, it is reckoned in pounds, shillings, pence, and farthings, called denominations of money. Time is reckoned it. years, months, weeks, days, hours, minutes, and seconds, called denominations of time. Distance is reckoned in miles, rods, feet, and inches, called denominations of measure, &c. The relative value of these denominations is exhibited in tables, which the pupil must commit to memory. ENGLISH MONEY. The denominations are pounds, shillings,' pence, and farthings. TABLE. 4 farthings (qrs.) make 1 penny, marked d. S. 1 pound, £. * 20 shillings Note. Farthings are often written as the fraction of a penny; thus, 1 farthing is written 4 d., 2 farthings,d., 3 farthings, 4 d. How many farthings in 1 How many pence in 4 far penny? in 2 pence? things? in 8 farthings? in 6 in 12 farthings? 24 farthings? pence? shillings? ir 3 pence? in in 32 far in 36 farthings? in 48 qrs.? How many shillings in 48 qrs. ? in 96 qrs.? How many shillings in 24 in 36 d. ? 60 s.? in 6£.8 s. 86 s.? in 70 s.? in 72 d. ? in 120 d.? in 27 d.? in 30 d. ? in 51 d. ? How many pounds in 20 shillings? - in in 40 s. ? in 80 s.? in in in 128 s.? 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. ( 1. In 17£. 13 s. 6d. how many farthings? OPERATION. £. s. d. qrs 17 13 6 3 20 s. 353 s. in 17£. 13 3. 12 d. 4242 d, 2. In 16971 farthings, how many pounds? OPERATION. 17£. Ans. 17. 13s. 62d. 16971 qrs. the Ans. Farthings will be reduced to pence, if we divide them In the above example, be-by 4, because every 4 farcause 20 shillings make 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., 63 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 der.mina- To reduce low denominations tions to lower,-Multiply the to higher,-Divide the lowest highest denomination by that Jenomination 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 f 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. j 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? eas. Note. We cannot reduce guineas directly to pounds, but we may reduce the guineas to shillings, and then the shillings to pounds. 4. Reduce 3142 farthings to pounds. 6. In 38976 farthings, how many guineas? 8. Reduce 11736 pence t dollars. 10. Reduce 21£. to guin TROY WEIGHT. * By Troy weight are weighed gold, silver, jewels, and all iquors. The denominations are pounds, ounces, pennyweights, and grains. TABLE. 24 grains (grs.) make 1 pennyweight, marked pwt. 20 pennyweights 1 ounce, 12 ounces 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 mg 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 tried by fire, and is reckoned in carats, by which is the 24th of it lose the trial, it is 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 a..tet, and 18 pwts, of copper melted together |