51. Gave $81.75 for 20 cords of wood; required the price of 70 cords at the same rate. Ans. $286.12. 52. John Smith gave Thomas Ayer $19.75 for 2 dozen of hats; what then should Smith give for 1972 dozen?

Ans. $193.3812.

53. If 3cwt. of potash cost $47.25, what must be paid for 11 cwt. Ans. $179.81. 54. If 47 casks of lime cost $50, what is the value of 5 casks? Ans. $5.3143. 55. Peter Quimby bought of Silas Noyes 19 tons of hay, for which he paid $ 300; what then was the cost of 132 tons? Ans. $209.7733′ 56. If a staff 4 feet long cast a shadow 6 feet, what is the height of that steeple whose shadow is 180 feet?

Ans. 120 feet. 57. If 8 men eat a barrel of flour in 20 days, how long would it last 12 men? Ans. 13 days.

58. If 23 men build 272 rods of wall, which is 53 feet high, in 5 days, by laboring 10 hours each day, required the number of days it will take 46 men to perform the same labor by working 8 hours each day? Ans. 3 days.

59. Henry Smith can reap a field in 10 days, by laboring 8 hours a day. His wife, Sarah, the same field in 9 days, by laboring 12 hours day. How long would it take both to reap the field, provided they labored 8 hours a day?

Ans. 534 days. 60. If 15 tons 7cwt. 2qr. 181b. of cotton cost $2067.48, what cost 1lb.? what lcwt.? what cost 1 ton? what 78 tons? Ans. $10483.20. 61. If it cost $93 to carry 17cwt. 3qr. 74lb. of sugar 87 miles, how far may it be carried for $73.87?

Ans. 650158 miles. 62. Bought a bale of cloth for $963; I dispose of it for of the cost, and by so doing I lose $2 on a yard; required the number of yards in the bale?

Ans. 18

yd.

63. Bought a horse and chaise for $250, and I paid for the harness of what I paid for the horse. The chaise cost the value of the horse. What was the price of each?

Ans. 30

Ans. Horse, $ 13019; chaise, $11913; harness, $83713 64. At of a dollar a peck, how many bushels can be ob tained for $17§ ? bushels. 65. If it require 23 bushels of wheat to sow I acre, how many acres will 174 bushels sow? Ans. 7 acres.

66. If 174 bushels of wheat sow 7 acres, how many bushels will require to sow 1 acre?

Ans. 23 bushels. 67. John Jones sold his horse for $176.18. He received in part pay 473 bushels of rye at $1.37 per bushel; and for the remainder he received wheat at $23 per bushel. Required the quantity of wheat. Ans. 453 bushels.

68. Sold apples at of a dollar a bushel. What did I receive for 8 bushels? Ans. $1.174. 9. Sold 183 bushels of rye for $21.47. What was received for bushel? what for 74 bushels? Ans. $9.19. 70. Gave 17£. 8s. 11d. for 9 tons of coal. What cost Ans. 36£. 16s. 5111d. made of 756 yards of yards?

1 ton? what cost 194 tons?

71. How many garments can be cloth, if each garment requires 73

72. If 184 cords of wood cost what cost 1718 cords?

Ans. 100 garments. $90.00, what cost 1 cord? Ans. $830.502.

miles in 36 hours, how far will Ans. 392363m. how far will he Ans. 166 miles.

73. If a man travel 147 he travel in 1 hour? how far in 974 hours? 74. If a man travel 500 miles in 973 hours, travel in 32 hours?

75. If a horse eat 193 bushels of oats in 87 many will 7 horses eat in 60 days?

days, how

Ans. 93 bushels.

MISCELLANEOUS QUESTIONS.

1. How far will a man walk in 17 hours, provided he goes at the rate of 47 miles an hour?

Ans. 82m. 4fur. 8rd. 1ft. 4in. 2. How much land is there in a field which is 297 rods square? Ans. 5A. IR. 32p. 141ft. 10915ĝin. 3. How much wood in a pile which is 17 feet long, 7 feet high, and 43 feet wide? Ans. 4cd. 66197ft. 4. What is the value of 197 barrels of flour, at $63 a barrel? Ans. $134.159. 5. What is the value of 37611 acres of land, at $75 per Ans. $28387.064.

acre? 6. What cost 1719 quintals of fish, at $4.75 per quintal ? Ans. $81.55,65. pounds of coffee, at 12 cents per Ans. $212.9912.

7. What cost 1670 pound?

8. What cost 28 tons of Lackawana coal, at $112 a ton? Ans. $333.273.

hogsheads of molasses, at $ 17.62§ a hhd.; Ans. $655.20

what was the whole cost?

9. Bought 37

10. What cost

of a cord of wood, at $5.75 a cord?
Ans. $5.03.

11. What are the contents of a field which is 139 rods long, and 384 rods wide? Ans. 33A. 3R. 15}p.

12. Bought 15 loads of wood, each containing 113 feet, cord measure. I divide it equally between 9 persons; what does each receive? Ans. 194ft. 13. If the transportation of 183 tons of iron cost $48.15, what is it per ton? Ans. $ 2.624. 14. If a hhd. of wine cost $987, what is the price of one gallon? Ans. $1.561.

15. If 5 bushels of wheat cost $83, what will a bushel be worth? Ans. $1.64. 16. What will 11 hogsheads and 171 gallons of wine cost, at 193 cents a gallon? Ans. $140.323. 12 pints, are suffi

17. How many bottles, each containing cient for bottling a hhd. of cider ?

Ans. 288.

18. I have a shed which is 18 feet long, 105 feet wide, and 711 feet high; how many cords of wood will it contain ? Ans. 11cd. 12482ft.

19. What will 67 pounds of tea cost, at

652 cents per lb. ?

Ans. $4.523. contain, that is 82 Ans. 146 ft. to cover a side

20. How many cubic feet does a box feet long, 57 feet wide, and 3 feet high? 21. How many feet of boards will it take of a house which is 46 feet long and 171⁄2 feet high ?

Ans. 812ft.

22. Required the number of square feet on the surface of 7 boxes, each of which is 54 feet long, 25 feet high, and 31⁄2 feet wide; required also the number of cubic feet they would Occupy. Ans. 5274ft.; 286 cubic feet. 23. A certain room is 12 feet long, 111 feet wide, and 71 feet high; how much will it cost to plaster it, at 23 cents per square foot? Ans. $13.487.

24. A man has a garden that is 144 rods long, and 104 rods wide; he wishes to have a ditch dug around it, that shall be 3 feet wide and 4 feet deep; what will be the expense, if he gives 2 cents per cubic foot? Ans. $223.761. 25. How many bushels of grain wil' a box contain which is

14 feet long, 511 feet deep, and 4 2150 cubic inches in a bushel ?

feet wide, there being
Ans. 29433bu.
by how much, a box

26. Which will contain the most, and that is 10 feet long, 8 feet wide, and 6 feet deep, or a cubical one, whose each side measures 8 feet?

Ans. The last contains 32 cubic feet the most. 27. Divide $1112§ equally among 129 men. Ans. $83. 28. Bought 68 barrels of flour, at $711 per barrel; what was the amount of the whole ? Ans. $5381. 29. What cost 8 acres of land, at $423 per acre?

Ans. $369.20.

30. How shall four 3's be arranged, that their value shall be nothing?

31. I have a room 20 feet long, 15 feet wide, and 8 feet high. This room contains 4 windows, each of which is 5 feet in height and 3 feet in width. There are two doors 7 feet high and 3 feet wide. The mop-boards are of a foot wide. A mason has agreed to plaster this room at 64 cents per square yard; a painter is to lay on the paper at 9 cents per square yard; the paper which I wish to have laid on is 23 feet wide, for which I pay 5 cents per yard. What is the amount of my bill for plastering, for papering, and for paper?

Ans. For plastering, $5.1128; for papering, $4.37; for paper, $2.80.

SECTION XXII.

DECIMAL FRACTIONS.

A DECIMAL FRACTION is a fraction whose denominator is a unit with as many ciphers annexed as there are places in the numerator. Thus, 1%, 75%, 10%, &c.

The denominator being in all cases formed in this obvious manner, there is no necessity of expressing it, and therefore it is not written; but a point is placed before the first figure of the numerator, to indicate that the figure or figures on the right of the point denote a decimal, and not a whole number. Thus, for we write .5, for, .15, &c. This point is called the separatrix.

Ciphers annexed to the right hand of decimals do not increase their value; for .4, and .40, and .400 are decimals having

the same value, each being equal to or ; but when ciphers are placed on the left hand of a decimal, they decrease the value in a tenfold proportion. Thus, .4 is, or four tenths; but .04 is, or four hundredths; and .004 is Too, or four thousandths. The figure next the separatrix is reckoned so many tenths; the next at the right, so many hundredths; the third is so many thousandths; and so on, as may be seen by the following

From this table it is evident, that in decimals, as well as in whole numbers, each figure takes its value by its distance from the place of units.

NOTE. If there be one figure in the decimal, it is so many tenths; if there be two figures, they express so many hundredths; if there be three figures, they are so many thousandths, &c.

NUMERATION OF DECIMAL FRACTIONS.

Let the pupil write the following numbers.

1. Three hundred twenty-five, and seven tenths.
2. Four hundred sixty-five, and fourteen hundredths.
3. Ninety-three, and seven hundredths.

4. Twenty-four, and nine millionths.

5. Two hundred twenty-one, and nine hundred thousandths. 6. Forty-nine thousand, and forty-nine thousandths.

7. Seventy-nine million two thousand, and one hundred five thousandths.

8. Sixty-nine thousand fifteen, and fifteen hundred thou sandths.

9. Eighty thousand, and eighty-three ten thousandths.