When a smaller denomination is to be reduced to a greater, divide the smaller denomination by that number which is required of the smaller, to make a unit of the next greater: the quotient will be of the greater denomination, and the remainder will be of the same denomination with the dividend. Perform a like operation on this quotient, and on each succeeding quotient.

1. Reduce £351 13s. Od. 1 qr. to its value in farthings. 2. How many pounds, &c. are there in 6169 pence? 3. In 59 lb. 13dwt. 5gr. Troy, how many grains? 4. Change 20571005 drams to its value in tons, &c. 5. In 231 33 03 09 5gr. how many grains? 6. How many English ells are there in 352 nails? 7. Reduce 7 bushels and 6 quarts to pints. 8. How many hhds. are there in 9576 pints of wine? 9. How many pints in 1 bl. 1 fir. 1 pt. of beer? 10. How many miles, &c. are there in 26431 rods? 11. In 3 square miles, how many square rods? 12. In 1259712 cubic inches, how many cubic yards? 13. Reduce 1 solar year, 7 d. and 10h. to seconds.

ADDITION OF COMPOUND NUMBERS.

The operation of adding compound numbers, differs from that of adding simple numbers, only, with respect to the irregular system of units, which determines the principles of carrying from one denomination to another.

RULE. Write the numbers so that each denomination shall stand in a separate column. Add the numbers of the lowest denomination together, and divide their sum by that number which is required of this denomination to make a unit of the next higher: write the remainder under the column added, and carry the quotient to the next column. Thus proceed through all the denominations.

14. What is the sum of £9 8s. 4 d., £250 8s. 5d. 3qr., £9 7s. 4 d., £20 16s. 4 d., and 3s. 6d. 2qr.?

15. Add together 10 oz. 14 dwt. 16gr., 5lb. 9oz. 6 dwt 22 gr., 4lb. 1 oz. 18 dwt. 9 gr., and 11 dwt., Troy 16. Add together 15 T. 19cwt. 3qr. 2 lb. 7 oz., 25 Ť 13cwt. 2qr. 20lb. 15 oz., and 3qr. 26 lb.

17. How much is 18 yd. 3qr. 3na., 15yd. 2qr. 3na., 25 yd. 1qr. 2na., and 57yd. 3qr. 2 na. of cloth?

18. Add together 25 bu. 3pk. 7 qt., 100 bu. 2 pk. 4qt., 215 bu. 2pk. 2qt. 1 pt., and 57 bu. 3 pk. of corn.

19. Add together 4p. 125 gal. 3qt., 75 gal. 2qt. 1 pt.,. 35 p. 92 gal., and 39 gal. 3qt. I pt. of wine.

20. How many acres are 13A. 3R. 38 r., 87 A. 2 R. 33 r., 28 A. 2 R., 41 A. 2R. 28 r., and 36r.?

21. How much hewn timber is 9T. 19 ft. 1725 ir 150T. 39 ft. 1695 in., and 500 T. 31 ft. 915 in.?

SUBTRACTION OF COMPOUND NUMBERS.

RULE. Write the several denominations of the smaller quantity under the same denominations of the greater quantity: then, begin with the lowest denomination, and perform subtraction on each denomination separately. Whenever a number expressing a denomination in the upper line is smaller than the number under it, increase the upper number by as many as make a unit of the next higher denomination, and consider the number of the next higher denomination in the upper line, to be 1 less than it stands.

22. Subtract 1lb. 10 oz. 16 dwt. from 3lb., Troy. 23. From 6 T. 3 cwt. take 7 cwt. 2qr. 15 lb., Avoir. 24. From 273 take 73 63 29 5gr., Apoth. wt. 25. Subtract 3 qr. 3na. from 5yd. 2qr. 1 na. of cloth 26. Subtract 8 bu. 1 pk. 6 qt. 1 pt. from 50 bu. of corn. 27. From 3hhd. 25 gal. take 41 gal. 2qt. of wine. 28. From 6 bl. 1 kil. take 1 fir. 6 gal. 3qt. of beer. 29. Subtract 3yd. 10 in. from 5 yd. 2 ft. 2 in., Long mea. 30. Subtract 57 A. 2R. 31 r. from 1 m., Square mea. 31. Subtract 2Y. 90d. 4h. 55 m. from 4 Y., Time.

MULTIPLICATION OF COMPOUND NUMBERS

RULE. Begin with the lowest denomination, and multiply each denomination separately; divide each product by the number which is required of its own denomination

to make a unit of the next higher; write the remainder under the denomination multiplied, and carry the quotient to the product of the next higher denomination.

32. Multiply £215 19s. 6d. by 72 or its factors. 33 Multiply 2lb. 5 oz. 7 dwt. 10gr., Troy, by 56. 34 What is 16 times 18 cwt. 3 qr. 15lb., 14 oz.? 35. What is 81 times 36 bu. 3 pk. 6 qt. 1 pt., Dry mea. 36. Multiply 4p. 105 gal. 3qt. of wine by 60. 37. Multiply 2m. 7 fur. 35r., Long mea., by 63. 38. Multiply 4m. 320 A. 1 R. 9 r., Square mea., by 15. 39. Multiply 2Y. 250d. 14h. 30 m., Time, by 96.

DIVISION OF COMPOUND NUMBERS.

RULE. Divide each denomination separately, beginning with the highest. Whenever a remainder occurs, reduce it to the next lower denomination, add it to the number expressed in the lower denomination, and divide their sum.

40. Divide £251 15 s. 7 d. 2qr. into 46 equal parts. 41. Divide 15 lb. 3oz. 7 dwt. 5gr., Troy, by 13. 42. Divide 12 T. 27 lb. 15 oz., Avoirdupois, by 5. 43. Divide 136 E. e. 3qr. 3 na. of cloth by 31. 44. Divide 1621 bu. 2 pk. of corn into 50 equal parts 45. Divide 1 pipe of wine equally among 9 owners. 46. Divide a Leap year into 100 equal parts.

FEDERAL MONEY.

The denominations of Federal Money are, the eagle, the dollar, the dime, the cent, and the mill. 10 mills make 1 cent, 10 cents 1 dime, 10 dimes 1 dollar, and 10 dollars 1 eagle. Dollars, $, and Cents, cts. are the only denominations commonly mentioned in business- eagles being counted as tens of dollars, dimes being counted as tens of cents, and mills not being denoted.

100 cents

$11 cent...=

Too of $1

The cents in any number of dollars are expressed by the same figures which express the dollars, with two

ciphers annexed; $15=1500 cents. The dollars in any number of cents are distinguished by cutting off two figures from the right for cents; 325 cts. = $3.25.

Operations on numbers expressing Federal money, are performed as on simple numbers; care must however be taken, in addition and subtraction, to place dollars under dollars, and cents under cents; these denominations being separated by a point.

47. What is the sum of $34.21, $7064.04, 36 cts., $10004.85, $96, $900.10, $14, $1.99, and $76529 ? 48. Subtract $4926 from $12262.37.

49. Subtract $297.18 from $100000.

50. Suppose $295.48 to be a multiplicand, and 25 the multiplier; what is the product?

In multiplication, only one of the factors can be Federal money, and the product will be of the same denomination as this factor. If, therefore, there be cents in either factor, two figures must be pointed off for cents, from the right of the product.

51. What is the product of 96 cts. multiplied by 43? 52. What is the value of 1304 pounds of coffee at 9 cents per pound?

53. How many times $7 are there in $29.46?

In division, when both the dividend and divisor are Federal money, they must both be of the same denomination. If therefore, one of the numbers contain cents, and the other dollars only, the latter number must have two ciphers annexed to it.

54. How many barrels of flour, at $4.36 per barrel, can be purchased for $4370?

55. Divide $4279.50 into 746 equal parts.

56. If 407 pounds of Hyson tea cost $395, what is the cost of 1 pound?

57. How many times are 95 cts. contained m $56 ? 58. A merchant sold 1248 yards of cloth, at such price as to gain 1 cent on every nail. How much did he gain? 59. What is the gain on a hogshead of molasses, sold at an advance of 3 cents per gallon?

60. A jeweller sold a silver pitcher 3lb. 8oz. 16 dwt., et 7 cents a pennyweight. What did it amount to?

61. What is the freight of 60480 pounds of cotton from Charleston to Liverpool, at $4 per ton?

MISCELLANEOUS EXAMPLES

62. How many bottles, holding 1 pint and 2 gills each, are required for bottling 4 barrels of cider?

63. How much will 46 bushels of oats cost, at 4 pence 2 farthings for every two quarts?

64. A brewer sold 96 hogsheads of beer for £388 16s. What was the price of 1 pint at the same rate? 65. A certain tippler spent 12 cents a day for ardent spirit, during 39 successive weeks, and then died, the victim of his folly. What did the spirit all cost?

66. Bought five loads of wood; the first containing I cord 32 cubic feet, the second 1 cord 64 cubic feet, the third 112 cubic feet, the fourth 1 cord 28 cubic feet, and the fifth 1 cord 20 cubic feet. How many cords were there in the whole ?

67. Bought goods to the amount of £25 13s. 10d. 2qr.; and afterwards sold goods to the same man, amounting to £30 10s. 4 d. 2qr. What is the balance of money favor?

in

my

68. A farmer sold five lots of land, at $9 an acre; the first lot containing 30 A. 2 R. 20 r., the second 41 A. 3R 8r., the third 14 A. 1 R. 10r., the fourth 25 A. 36 r., and the fifth 54 A. 6 r. What did the whole amount to?

69. How many cubic inches in a brick 8 inches long, 4 inches wide, and 2 inches thick?

70. How many cubic inches in the cube of 2 inches? in the cube of 3 inches?. . . . . in the cube of 4

inches?. . . . . in the cube of 5 inches?

71. If the cube of 4 inches be taken from the cube of 1 foot, how many cubic inches will remain ?

72 If the cube of 4 inches be taken from the cube' of 2 feet, how many cubic inches will remain?

73. A young man, on commencing business, was worth £643 10s.; the first year he cleared £54 11s. 7 d. 2 qr.; the second year, £87 Os. 10d. 1qr.; but the third year he lost £1967 s. 11 d. 3qr. How much was he then worth'