4. When either term of the fraction is a mixed number, reduce to the form of a simple fraction.

5. If the numerator of the dividend is divisible by the numerator of the divisor, and the denominator by the denominator, divide without inverting.

23. Divide of 33 by 3 of 7. 48. Divide 1913 by 159.

24. Divide 97 by 81.

25. Divide of 7 by 6.

49. Divide 5 by 2 of 1

50. Divide 5205 by of 90.

51. At of a dollar a pound, how much butter can be

bought for

52. At

of a dollar?

of a dollar a yard, how much cloth can be bought or of a dollar?

53. If a bushel of potatoes cost of a dollar, how many bushels can be bought for of a dollar?

54. If of a ton of hay will feed 1 horse one week, how many horses will of a ton feed, the same time?

55. If of a bushel of apples cost of a dollar, what will 1 bushel cost?

56. What will a barrel of flour cost, if of a barrel cost of a dollar?

57. If of a bushel of apples cost of a dollar, what will 1 bushel cost?

58. How much molasses at of a dollar a gallon, can be bought for 1 dollars?

59. A man sold of a mill, which was of his share : what part of the mill did he own?

60. What number multiplied by 4, will give a product of 15?

61. What number multiplied by 5, will give a product of 146?

62. The dividend is 520, and the quotient 36% what is the divisor?

63. What number is that, which if multiplied by of of 15, will produce & !

64. If 7lb. of sugar cost of a dollar, what will 1 pound cost?

65. If 10 lb. of nails cost of a dollar, what is the price per pound?

66. If of a yard of cloth cost $3, what will 1 yard cost? 67. A family consumes 1653 pounds of butter in 8 weeks: how much do they consume in 1 week?

68. At $9 a barrel, how much flour can be bought for $138?

69. If a man divides $35 equally among 8 beggars, how much does he give them apiece?

70. If 8 pounds of tea cost $75, what is the price per pound?

71. If of a ton of hay sells for $103, what is the price of 1 ton?

72. If of an acre of ground produces 84% bushels of potatoes, how many bushels will 1 acre produce?

73. What quantity of cloth may be purchased for $5, at the rate of $6 a yard?

74. How long would a person be in traveling 125 miles, if he traveled 31 miles per day?

75. How many bottles, each holding 1 gallons, can be filled from a barrel of wine, containing 31 gallons?

76. How long will it take 11 men to do a piece of work, that 1 man can do in 158 days?

77. If of a barrel of flour costs 6 dollars, what is the price per barrel ?

78. Eighty-one is of how many times 8?

79. Five-eighths of 48 is of how many times 9?

80. How many times can a vessel, containing

be filled from of a barrel of 31 gallons?

of a gallon

81. If 5 lb. of tea cost $43, what is the price of 1 pound? of a ship is worth $2540, what is the whole.

82. If of

vessel worth?

83. If of how long will 9

of a barrel of flour will last a family 1 week, barrels last them?

COMPLEX FRACTIONS.

175. A COMPLEX FRACTION is only another form of expression for the division of fractions: thus, is the same as divided

by; and may be written, ÷ 3 = 13.

176. To reduce a complex fraction to a simple fraction.

Rule.-Reduce both terms of the fraction to simple frac tions: then divide as in division of fractions.

175. What is a complex fraction?-176. How do you reduce a complex to a simple fraction?

Applications in Fractions.

1. What will 51 cords of wood cost, at of of of $50 a cord?

2. A farmer sold of a ton of hay for $63: what would be the price of a ton at the same rate?

3. A person walks 77 miles in 10 hours: at what rate is that per hour?

4. From the product of and 11, take, and multiply the remainder by 203.

5. How much greater is of the sum of,, 4, and 1, than the sum of,, and ?

6. If of a ton of hay is worth $71, what is 23 tons worth?

7. If of a dollar will pay for of a yard of cloth, how many yards can be bought for $11?

8. What is the value of 3 cords of wood, at $43 a cord? 9. At of a dollar a peck, how many bushels of apples can be bought for $63?

10. What is the difference between of a league and of a mile?

11. What is the sum of 4% miles, of a furlong, and of 14 yards?

12. At $1 per day, how many days' labor can be obtained for $363?

13. Bought 5 yards of cloth at $4 a yard, and paid for it in wheat at $1 a bushel: how many bushels were required? 14. What number must be taken from 273, and the re mainder multiplied by 143, that the product shall be 100? 15. Three persons, A, B, and C, purchase a piece of prop erty for $6300; A pays of it, B, and C the remainder: what is the value of each one's share?