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1. How many farthings are there in 2 pence? In 3? In 4? In 6? In 8? In 10? In 12? In 20?

2. How many pence are there in 2 shillings? In 3? In 5? In 7?

3. How many shillings are there in 2 pounds? In 3? In 6?

4. If 1 pair of gloves is worth 8 pence, how many pence are 2 pair worth? 3 pair? 4 pair? 5 pair? 6 pair? 10 pair?

5. When a bushel of wheat costs 10 shillings, what will 2 bushels cost? What will 4? What will 6? What will 9? What will 12?

6. If 1 cart cost 1 pound, how many shillings How many 3? How many 4? How many 5? 9? How many 12?

will buy 2! How many

7. How many farthings will buy 2 inkstands, if they cost a penny apiece? How many will buy 3? How many will buy 4?

Note. The characters used for English money are £. for Libra, the Latin for pounds; s. for Solidi, the Latin for shillings; d. for Denarü, the Latin for pence; and grs. for Quadrantes, the Latin for farthings.

A pound sterling is equal to $4,444 cents, Fed. Money

An English guinea,

An English shilling

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4,75 cents,
23 cents, 66

81, Federal Money, is equal to 4 s. 6 d. sterling.

Q. How is 1 farthing sometimes written?

How are 2 farthings sometimes written?
How are 3 farthings sometimes written?

Exercises for the Slate.

66

A.

d.

A.

d.

A. I d

42. How many shillings in 3 pounds? In 4200 pounds? 4. 84060 shillings.

43. How many pence in 3 shillings In 2600 shillings / A. 31238 pence

44. How many farthings in 4 pence? In 2700 pence? 4. 10816 farthings.

45. How many pence in 8 farthings? In 6200 farthings? 4. 1552 pence.

PRACTICAL APPLICATION OF REDUCTION, Involving the Rule, with Miscellaneous Examples.

1. At 20 cents a quart, what will 2 gallons of rum cost! What will 4 gallons? What will 5 gallons?

2. At $60 a hogshead, what will 2 pipes of wine come to? What will 4? What will 6?

3. How many minutes in 2 hours? In 4? In 6?

4. How many weeks in 14 days? In 21? In 49?

Q. What are such questions as these in ?

A. Reduction.

Q. What, then, is the changing numbers from one denomination us another called?

A. Reduction.

Q. In 2 bushels of corn, how many pecks

Q. Are 8 pecks of corn as much as 2 bushels?

Q. Is the value altered, then?

Q. Do you multiply or divide, to find how many furlongs there are in 2 miles?

Q. When, then, the reduction is performed by multiplication, what is it called?

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in 8

A. Reduction Descending.

Q. Do you multiply or divide to find how many gallons there are quarts

Q. When, then, the reduction is performed by division, what is :1 called ?.

A. Reduction Ascending.

Q. From the preceding remarks, how many kinds of reduction do there appear to be? and what are they?

A. Two-Reduction Ascending and Descend ing.

RULE.

Q. What do you multiply 2 furlongs by, to bring them into rods Q. As a general rule, then, what do you multiply furlongs by? A. By what makes a furlong.

Q. What do you multiply days, bushels, &c. by 1

A. Bushels by what makes a bushel, days by what makes a day, &c.

Q. What do you divide by to bring 8 gills into pints?

Q. As a general rule, then, what must you divide gills, minutes, quarters, &c. by?

A. Gills by gills, minutes by minutes, quarters by quarters, &c.

Q. Why do you divide thus ?

A. Because 4 gills are equal to 1 pint, 60 minutes to 1 hour, &c

Q. What do you multiply pounds (money) by ↑

A. Shillings.

Q. What do you multiply shillings by?

A. Pence.

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Q. What do you multiply by, to bring 25 pounds into farthings? A. By 20, 12, and 4.

Q. How do you bring 40 cwt. into tons? I cwt. into drams 1 1 ton into drams? Drams into tons? Drams into cwt.? 1 lb. into grains? Grains into pounds? Ells Flemish into nails? Nails into ells Flemish ? Quarters into ells English? Ells English into quarters! 5 bushels into pints? 200 pints into bushels? 360 degrees into inches1 Feet into furlongs 7 5 weeks into seconds? Seconds into weeks 1 Years into seconds? Seconds into years? How do you tell what I tun of wine will cost, at 6 cents a gill?

Exercises for the Slate.

46. At 6 cents a pound, what will 2 qrs. 8 lbs. of sugar cost? OPERATION.

qrs. lbs.

2 8

28

56 lbs.
8 lbs.

64 lbs.

6 cts.

$3,84 Ans.

Q. Why do you multiply the 2 qrs. by 28 lbs.?

A. Because, since it takes 28 pounds to make 1 qr., there will of course be 28 times as many pounds as quarters; that is, 28 times the quarters.

Q. What do you do with the 8 lbs.?
A. 1 add it to 56 lbs., making 64 lbs.
Q. Why do you multiply the 64 lbs. by
6 cents?

A. Because every pound of sugar così 6 cents; that is, 6 times the pounds.

Proof of the foregoing Example.

47. How many quarters of sugar can you buy for 334 centa,

at 6 cents a pound?

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Q. Why do you ☎vide 384 cents by @ cents?

A. Because, sines there are 6 times as many cents as pounds, as often as 6 is contained in 384, so many pounds there will be."

Why do you divide 64 pounds by 28 pounds? A. Because every 28 pounds make I quarter.

Q. What, then, appears to be the method of proof?

A. Reverse the operation; that is, make the divisors in the operation the multipliers in the proof, and the multipliers the divisors.

In examples like the following, where more than one operation in a simple rule is employed in their solution, their entire work is inserted in the Key, by means of signe, indicating the exact process of each, with all their intermediate results, to the final one, or answer. Besides, when the question is at all intri date, the reason for every step in the required operation is fully shown

More Exercises for the Slate.

48. At 5 cents a gill, what will 8 pints of rum cost? A. $1,60. 49. How many gills in 20 pints? In 40 pints? A. 240 gills. 50. How many pints in 80 gills? In 120? A. 50 pints.

51. A merchant sold 5 hhds. of brandy, at 3 dollars a gallon, how much did it amount to? A. $945.

52. How many hogsheads in 126 gallons? In 945? 4. 17 53. At 6 cents a quart, what will I hhd. of molasses come to? 4. $15,12.

54. How many quarts are there in 3 hhds.? In 100? A.

25956.

55. How many hogsheads are there in 756 qts.? In 252 qts. 1 A. 4.

56. Sold 1 tun of wine, at 5 cents a gill; what did I get for it? 4. $403,20.

57. How many gills in 10 tuns? A. 80640.

58. At 8 cents a pound, what will 3 cwt. 2 qrs. of raisins cost 4. $31,36.

59. How many pounds in .5 cwt. 1 qr.? A. 1708.

60. At 8 pence a peck, how many pence will 3 bushels of sal st? A. 96.

W. How many pence are there in 20 shillings? A. 240.

62. How many pence in 5 £.? In 10? A. 3600.
63. How many pounds in 480 d.? In 1440 d.? A. 8.
64. How many farthings in 4 £.? A. 3840.

65. At 6 pence per lb., what will two qrs. of rice cost? A. 336 pence.

66. How many qrs. of rice, at 6 pence per lb., may be bought for 336 pence? A. 2 qrs.

67. At 6 cents a gill, what will 1 tun of wine cost? a. $483,84.

68. How many tuns of wine, at 6 cents a gill, may be bought for $483,84. A. 1 tun.

69. At 9 pence per quart, what will 16 gals. 2 qts. of molasses come to in pence? A. 594 pence.

70. How many gallons of molasses, at 9 pence per quart, may be bought for 594 pence? A. 16 gals. 2 qts.

71. What is the value of a silver cup, weighing 10 oz. 5 pwts 18 grs., at 5 mills per grain? A. $24,69.

72. At 5 mills per grain, what will be the weight of a silver cup that $24,69 will purchase? A. 10 oz. 5 pwts. 18 grs.

73. At 12 cents a pound, what cost 5 cwt. 2 qrs. 18 lbs. of sugar? A. $76,08 cts.

74. How many hundred weight of sugar, at 12 cents per lb., may be bought for $76,08? A. 5 cwt. 2 qrs. 18 lbs.

75. At 9 pence an hour, what will 2 yrs. 6 mo. 3 weeks, 6 da 12 h. labor come to in pence? A. 187380.

76. How many years' work, at 9 pence per hour, may be obtained for 187380 pence? A. 2 yrs. 6 mo. 3 weeks, 6 da.

12 h.

77. At 20 cents a nail, what is the price of 4 yds. of cloth? A. $12,80.

78. At 320 cents a yard, what will 64 nails of cloth cost? A. $12,80.

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79. At 1£. 2 s. 64 d. per yard, what will 20 yds. of broadcloth cost in farthings? A. 21640.

80. At 6 cents a pint, what will 20 bu. 0 pks. 3 qts. 1 pt. of dax-seed cost? A. $77,22.

p.

81. How many shillings, at 2 farthings a gill, will 5 T. 1 I hhd. 2 gals. 2 qts. 1 pt. 3 gills, cost? A. 1935 s. 7 d. 2 qrs. 82. At 2 shillings a quarter, how many dollars will 8 yds. 1 qr. of broadcloth cost? A. 11.

83. At 2 pence a gill, he inany dollars will buy 50 gala 2 qts. 1 pt. 2 gills of ale? A. $45,055.

84. In 3600 dollars, how many farthings? A. 1036800. 85. In 1036800 farthings, how many dollars? A. 3600. 86. In 25 guineas, of 28 s, each, how many pence? A. 8400 87. In 8400 pence, how inany guineas? A. 25.

88. In 15 lbs, how many ounces, drams, scruples, and graina 180 ounces, 1440 drams, 4320 scruples, E6400 grains.

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