47. What cost 72 cords of wood at $53 per cord?

48. What cost 7 yds. of cloth at $3

49. What cost 63 gallons molasses at lon?

50. If a man travels 34 miles in one he travel in 97 hours?

51. What cost 36111 acres of land at

Ans. 8413.

per yard? Ans. $2518. 233 cents per galAns. $15218. hour, how far will Ans. 3472 $253 per acre? Ans. $916718.

52. If of of a dollar buy one bushel of corn, what will of of a bushel cost? Ans. of a dollar. 53. How many square rods of land in a garden, which is 97 rods long, and 493 rods wide ?

Ans. 4810 rods. 54. If 3 of 4 of of an acre of land cost one dollar, how much may be bought with of $18?

Ans. 197 acres.

NOTE. The following questions are to exercise the foregoing rules. 55. What are the contents of a field 767 rods in length and 18 rods in breadth ? Ans. 8A. 3R. 30p. 56. What are the contents of 10 boxes which are 73 feet long, 1 wide, and 14 feet in height?

Ans. 16917 cubic feet.
of an acre of land there were sold 20 poles

57. From
and 200 square feet. What quantity remained?

58. What cost of an acre at $1.75 per square rod?

Ans. 2R. 1p. 22 ft.

Ans. $236.92.

59. What cost of a ton at $15

per cwt. ?

Ans. $49.7318.

Ans. 9184.

60. What is the continued product of the following numbers 142, 113, 5, and 104? 61. From of a cwt. of sugar there was sold what is the value of the remainder at $0.12 per lb.?

of it;

Ans. $3.57.

62. What cost 193 barrels of flour at $73 per barrel ?

Ans. $143.

63. What cost 1383 quintals of fish at $3 per quintal?

Ans. $51237.

acres,

64. I have two parcels of land, one containing 7 and the other 911 acres. What is their value at $783 Ans. $1380.70§.

per acre?

65. From a quarter of beef weighing 1753 lbs. I gave John Snow of it; of the remainder I sold to John Cloon. What is the value of the remainder at 82 cents per lb. ? Ans. $2.0413. 66. Alexander Green bought of John Fortune a box of sugar containing 475 lbs. for $30.00. He sold † of it at 8 cents per lb., and of the remainder at 10 cents per lb. What is the value of what still remains at 12 cents per lb., and what does Green make on his bargain? Value of what remains $ 13.193. Green's bargain, 8 16.973. 67. What cost of an acre at $143 per acre?

Ans.

Ans. $2.00.

68. D. Sanborn's garden is 234 rods long and 134 rods wide, and is surrounded by a good fence 73 feet high. Now if he shall make a walk around his garden within the fence 75 feet wide, how much will remain for cultivation? Ans. 1A. 3R. 7p. 851981ft. 69. On of my field, I plant corn; on of the remainder I sow wheat; potatoes are planted on of what still remains, and I have left two small pieces, one of which is 3 rods square, and the other contains 3 square rods. How large is my field? Ans. 1A. OR. 29p.

70. Multiply of of 11 by 5 of 13 of 13. Ans. T.

Section 24.

DIVISION OF VULGAR FRACTIONS.

I. To divide a fraction by a whole number.

1. How many times will

OPERATION.

× Ans.

contain 9 ?

were to be divided equally among 9 persons. Now, if we divide of an apple into 9 equal parts, there would be 63 parts, and each person would receive; but there being, each man will receive 5 times = 3 Ans. Hence we see the propriety of the following

RULE.

Multiply the whole number by the denominator of the fraction, and write the product under the numerator.

5. John Jones owns of a share in a railroad, valued at $117; this he bequeaths to his five children. What part of a share will each receive?

Ans.. Ans. 15

Ans. z

8. James Page's estate is valued at $10,000, and he has given of it to the Seamen's Society; of the remainder he gave to his good minister; and the remainder he divided equally among his 4 sons and 3 daughters. What sum will each of his children receive?

Ans. $680.

II. To divide a whole number by a fraction.

9. How many times will 13 contain ?

OPERATION.

4×7=4= 30 Ans.

Ans. 30.

It is evident, that 13 will contain, as many times as there are sevenths

in 13, which are 7 × 1391 times. Again, if 13 contain 1 seventh 91 times, it will contain 3 sevenths as many times as 91 will contain 330 Ans. Hence the following

RULE.

Multiply the whole number by the denominator of the fraction, and divide the product by the numerator.

10. Divide 18 by 7.

11. Divide 27 by

Ans. 204.

Ans. 29.

17. I have 50 square yards of cloth, how many yards, of a yard wide, will be sufficient to line it?

Ans. 83 yards. 18. A. Poor can walk 37 miles in 60 minutes; Benjamin can walk as fast as Poor. How long will it take Benjamin to walk the same distance ?

Ans. 73 minutes.

III. To divide a mixed number by an integer.

19. Divide 173 by 6.

OPERATION.

6) 17

218
43

Ans. 248.

We divide 17 by 6, and find it is contained 2 times, which we write under the 17, and we have 5 remaining, which we multiply by 8, the denominator of the fraction; and to the product we add the numerator, 3, and the amount is 43, this we write over the product of 6, the divisor, multiplied by the denominator, 8, 48. The rationale of the above question is the same as of those in Rule I. of this section. Hence the following

RULE.

=

Divide the integers as in whole numbers, and if any thing remains, multiply it by the denominator of the fraction, and to the product add the numerator of the fraction, and write it over the product of the divisor, multiplied by the denominator.

27. Divide $173 among 7 men. 28. Divide $1067 among 8 boys.

29. What is the value of 1⁄2 of a dollar?

Ans. $224.

Ans. $1325.

Ans. $0.341.

30. Divide $1077 among 4 boys and 3 girls, and give the girls twice as much as the boys.

Ans. boy's share $103. Girl's share $2128. 31. If 8 14 will purchase of a ton of copperas, what quantity will I purchase? Ans. 1cwt. Oqr. 24lbs.

IV. To divide one fraction by another.

32. Divide by .

OPERATION.

X == 13 Ans.

Ans. 11.

To understand the rationale of this process, we find the two factors of multiplied by are, as is

4

which are and; for evident from a preceding rule. We now divide by 1, which, by case I. of this section, will be 1 × 1 = 72. Again, we wish to divide by . It is evident, that 32 will contain nine times as often, as it will a unit, and it contains a unit times, therefore it contains nine times √2 = 1 × 72 == 13 Ans. In performing this question, it will be perceived, that the numerator of the dividend has been multiplied by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor. Hence the following

RULE.

Invert the divisor and proceed as in multiplication. If, however, there be mixed numbers in the question, they must be reduced to improper fractions, and compound fractions must be reduced to simple fractions.

33. Divide by 4.

OPERATION.

J×7=18=118 Ans.

34. Divide 7 by 34.

OPERATION.

73 = 31, 33 = 4, 41 × 7=217=233 Ans.

35. Divide

by 1.

Ans. 3.