241. To divide one complex fraction by another.

Reduce the complex fractions to simple ones, then proceed as in division of simple fractions. (Arts. 229, 239.)

62. Divide by

9X4

Or, since the given dividend= and the divisor=

the answer. (Art. 231.)

2X9

1X4

3X7

9X4 3×79×4×3×7 21

But, (Art. 232,)

2X9X1X4

or 101 Ans

2X9X1X4

2

242. Ex. 1. A merchant bought 153 yards of domestic flannel of one customer, 194 of another, 12 of another, and 41% of another: how many yards did he buy of all?

2. A grocer sold 164 lbs. of sugar to one customer, 112 to another, and 33 to another: how many pounds did he sell?

3. A clerk spent 263 dollars for a coat, 93 dollars for pants, 63 dollars for a vest, 5 dollars for a hat, and 64 dollars for a pair of boots: how much did his suit cost him?

4. A man having bought a bill of goods amounting to 85 dollars, handed the clerk a bank note of 100 dollars: how much change ought he to receive back?

5. A lady went a shopping with 135 dollars in her purse she paid 17 dollars for silk, 35 dollars for trimmings, 37 dollars for a shawl, and 143 dollars for a muff: how much money had she left?

6. A man having 1563 dollars, spent 365 dollars, and lost 562 dollars: how much had he left?

head?

7. What will 563 sleep cost, at 24 dollars per 8. What cost 748 barrels of flour, at 73 dollars per barrel? 9. What cost 3784 yards of cloth, at 4 dollars per yard? 10. What cost 1121 lbs. of tea, at 5 shillings per pound? 11. What cost 430 gallons of oil, at 14 dollar per gallon? 12. What cost 4 of an acre of land, at 150 dollars per acre? 13. A man worth 25000 dollars, lost of it by fire: what was the amount of his loss?

14. A garrison had 856485 pounds of flour; after being blockaded 60 days, it was found that of it were consumed: how

many pounds of flour were left ?

acres produce, at 31

15. At 17 dollars per ton, what cost 1034 tons of hay? 16. How many bushels of corn will 115 bushels per acre?

17. What cost 675 tons of iron, at 45 dollars per ton? 18. If a ship sails 140 miles per day, how far will she sail in 49 days?

19. If a Railroad car should run 41 miles per hour, how far would it go in 12 days, running 10 hours per day?

20. A young man having a patrimony of 12234 dollars, spent of it in dissipation: how much had he left?

21. At 2 of a dollar per yard, how many yards of satinet can be bought for 124 dollars?

22. How many pounds of tea, at 3 of a dollar a pound can you buy for 131 dollars?

23. How many gallons of molasses, at of a dollar per gallon can you buy for 235 dollars?

24. At 8 pence a pound, how many pounds of sugar can you buy for 163 pence?

25. At 54 pence a yard, how many yards of lace can be bought for 279 pence?

26. A dairy-man has 229 pounds of butter which he wishes to pack in boxes containing 8 pounds each: how many boxes will it require?

27. A farmer wishes to put 384 bushels of apples into barrels, each containing 2 bushels: how many barrels will it require? 28. If 4 yards of cloth make a suit of clothes, how many suits will 141 yards make?

29. One rod contains 5 yards: how many rods are there in 210 yards?

30. A merchant paid 2045 dollars for 57 yards of cloth: how much was that per yard?

31. A grocer sold 50 barrels of flour for 311 dollars: what did he get per barrel?

32. A merchant wishes to lay out 657 dollars for wheat, which is worth 1 of a dollar a bushel: how much can he buy?

33. At 183 cents a dozen, how many dozen of eggs can you buy for 87 cents?

34. A grocer sold 15 pounds of coffee for 93 cents: how much was that a pound?

35. A shopkeeper sold 16 yards of satin for 163 shillings: how much was that per yard?

36. Bought 19 sacks of wool for 250 dollars: what was that per sack?

37. Paid 575 dollars for 9673 yards of cloth: what was the cost per yard?

38. Paid 15654 dollars for iron, valued at 374 dollars per ton: how many tons were bought?

39. Paid 13155 dollars for the transportation of 1286 barrels of pork: what was that per barrel ?

40. Bought 375 pounds of indigo for 652 dollars: what was the cost per pound?

41. Paid 1679 dollars for 475 kegs of lard: how much was that per keg?

42. If an army consumes 5637 pounds of meat per day, how long will 150000 pounds supply it?

43. The cost of making 25 miles of Railroad was 856235 dollars: what was the cost per mile?

SECTION VIII.

COMPOUND NUMBERS.

ART. 243. Numbers which express things of the same kind or denomination, are called Simple Numbers. Thus, 3 oranges, 7 books, 12 chairs, &c., are simple numbers.

Numbers which express things of different kinds or denominations, as the divisions of money, weight, and measure, are called COMPOUND NUMBERS. Thus, 15 shillings 6 pence; 10 bushels 3 pecks, &c., are compound numbers.

OBS. The origin of Compound Numbers is ascribed to the wants and necessities of the earlier ages of the world. Their divisions and subdivisions are generally irregular, and seem to have been suggested by the caprice, or the limited business transactions of the rude ages of antiquity. It is much to be regretted, both on account of simplicity and their adaptation to scientific purposes, that their different denominations were not graduated according to the law of increase in the decimal notation.

Note.-Compound Numbers, by some authors, are called Denominate

Numbers.

FEDERAL MONEY.

244. Federal Money is the currency of the United States. The denominations are, Eagles, Dollars, Dimes, Cents, and Mills.

OBS. 1. Federal money was established by Congress, Aug. 8, 1786. It is based upon the principles of the decimal notation. The law of increase or radix, is the same as that of simple numbers, and it is confessedly one of the most simple and comprehensive systems of currency in the civilized world. Previous to its adoption, English or sterling money was the principal currency of the country.

QUEST.-243. What are simple numbers? What are compound numbers? 244. What is Federal money? Recite the table. Obs. When and by whom was it established?

2. The names of the coins or denominations less than a dollar, are significant of their value. The term dime, is derived fro:n the French disme, which signifies ten; the terms cent and mill, are from the Latin centum and mille, the former of which signifies a hundred, and the latter a thousand. Thus, 10 dimes, 100 cents, or 1000 mills, make 1 dollar.

3. The sign ($), which is prefixed to Federal money, is called the Dollar mark. It is said to be a contraction of "U. S.," the initials of United Sales, which were originally prefixed to sums of money expressed in the Federal currency. At length the two letters were moulded or merged into a single character by dropping the curve of the U. and writing the S over it. Thus, the sum of seventy-five dollars, which was originally written "U. S. 75 dollars,” is now written $75.

245. The national coins of the United States are of three kinds, viz: gold, silver, and copper.

1. The golds coin are the eagle, the double eagle, half eagle, quarter eagle, and gold dol'ar.*

The eagle contains 258 grains of standard gold; the half eagle and quarter eagle like proportions.†

2. The silver coins are the dollar, half dollar, quarter dollar, the d me, half dime, and three-cent-piece.

The dollar contains 4124 grains of standard silver; the others, like proportions.†

3. The copper coins are the cent, and half cent.

The cent contains 168 grains of pure copper; the half cent, a like proportion. Mills are not coined.

OBS. The fineness of gold used for coin, jewelry, and other purposes, also the gold of commerce, is estimated by the number of parts of gold which it contains Pure gold is commonly supposed to be divided into 24 equal parts, called cara's. Hence, if it contains 10 parts of alloy, or some bater metal, it is said to be 14 carats fine; if 5 parts of alloy, 19 carats fine; and when absolutely pure, it is 24 carats fine.

246. The present standard for both gold and silver coin cf the United States, by Act of Congress, 1837, is 900 parts of pure

QUEST.-245. Of how many kinds are the coins of the United States? What are they? What are the gold coins? The silver coins? The copper? Obs. How is the fineness of gold estimated? Into how many carits is pure gold supposed to be divided? When it contains 10 parts of alloy, how fine is it said to be? 5 parts of alloy? 246. What is the present standard for the gold and silver coin of the United States? What is the alloy of gold coin? What of silver coin?

Added by Act of Congress, 1849.

+ According to Act of Congross, 1837.