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Ans. 3 is 2 times the half of 3; but 1 half of 3 is 3 halves, or 1 and 1 half,* therefore 3 is 2 times 1 and 1 half.

3. If 3 fifths of a yard of cloth cost 4 dollars, what will 1 fifth of a yard cost? 4. 5 is 3 times what number??

3 5. If 3 sevenths of a barrel of pork cost 2 dollars, what will 1 seventh of a barrel cost ? V3

6. 2 is 3 times what number ?

7. If 4 thirds of a bunch of shingles cost 5 dollars, what does 1 third of a bunch cost ? 1'44

, 8. 7 is 4 times what number? 9. 2 is 4 times what number?

10. A man bought 4 ninths of a barrel of flour for three dollars; what would be the price of 1 ninth of a barrel at the same rate ?

11. 5 is 4 times what number ?

12. A man bought 5 eighths of a hundred weight of sugar for 6 dollars; what would 1 eighth of a hundred weight cost at the same rate ?

13. 7 is 5 times what number ? 14. 3 is 5 times what number? 15. 8 is 5 times what number? 16. 9 is 4 times what number? 17. 11 is 6 times what number? 18. 13 is 7 times what number? 19. 14 is 8 times what number? 20. 17 is 5 times what number ? 21. 18 is 3 times what number ? 22. 17 is 9 times what number ? 23. 15 is 10 times what number ? 24. 20 is 9 times what number ? 25. 22 is 10 times what number ? 26. 24 is 7 times what number? 27. If 2 thirds of a barrel of beef cost 3 dollars,

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what will 1 third of a barrel cost? What will the whole barrel cost?

28. *If 5 is 2 thirds of some number, what is 1 third of the same nunber? 2 and 1 half is 1 third of what number ? Then 5 is two thirds of what number?

29. If 3 fourths of a barrel of flour cost 5 dollars, what will I fourth of a barrel cost? What will the whole barrel cost ?

30. If 8 is 3 fourths of some number, what is 1 fourth of the same number? 2 and 2 thirds is 1 fourth of what number? Then 8is 3 fourths of what number?

31. A man bought 2 sevenths of a barrel of oil for 5 dollars, how much will 1 seventh cost at the same rate ? How much would a barrel cost ?

32. If9 is 2 sevenths of some number, what is 1 seventh of the same number? 4 and 1 half is 1 seventh of what number? Then 9 is 2 sevenths of what number?

33. Bought 5 eighths of a chaldron of coal for 7 dollars, what is the price of 1 eighth at the same rate ? What is the price of the whole chaldron !

34. If 12 is 5 eighths of some number, what is 1 eighth of the same number ? 2 and 2 fifths is 1 eighth of what number? Then 12 is 5 eighths of what number?

35. If å man can do 7 ninths of a piece of work in 4 days, how long would it take him to do 1 ninth of it ? How long would it take him to do the whole ?

36. If 3 is 7 ninths of some number, what is 1 ninth of the same number? 3 sevenths is 1 ninth of what number? Then 3 is 7 ninths of what number?

37. If 3 fifths of a chaldron of coal cost 8 dollars, what is the whole chaldron worth ?

38. 7 is 3 fifths of what number?

39. A man bought 6 sevenths of a cask of raisins for 5 dollars; what was the whole cask worth ? 40. 8 is 6 sevenths of what number ?

* See section VI, article B, examples 8 and following.

41. A man had 4 sixths of a week's board for 3 dollars; how much is that for a whole week ?

42. 3 is 5 sixths of what number?
43. 9 is 5 eighths of what number?
44. 10 is 7 thirds of what number ?
45. 11 is 6 fifths of what number ?
46. 12 is 7 fifths of what number ?
47. 15 is 2 sevenths of what number?
48. 17 is 3 tenths of what number?

49. A man bought 5 eighths of a cask of wine for 19 dollars, what would the whole cask cost?

50. 19 is 3 eighths of what number? 51. 21 is 4 fifths of what number?

52. Bought 5 ninths of a ton of logwood for 23 dollars; what would a ton cost at that rate ?

53. 23 is 7 ninths of what number? 54. 21 is 3 tenths of what number? 55. 29 is 4 sevenths of what number? 56. 31 is 5 eighths of what number? 57. 33 is 6 sevenths of what number ? 58. 38 is 4 ninths of what number?

59. A man bought 1 barrel and 1 seventh of a barrel of wine for 41 dollars; what was that a bar

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NOTE. 1 barrel and 1 seventh of a barrel is the same as 8 sevenths of abarrel. If 8 sevenths of a barrel cost 41 dollars, what does a barrel cost?

60. 35 is 8 sevenths of what number ?

61. A man bought 1 ton and 4 fifths of a ton (that is, 9 fifths of a ton) of fustic for 43 dollars, what was that a ton ?

62. 52 is 9 fifths of what number?

63. Bought 1 ton and 2 sevenths of a ton of log wood for 48 dollars, what was that a ton?

64. 67 is 9 sevenths of what number? 65. 53 is 7 tenths of what number? 66. 58 is 9 eighths of what number?

67. 61 is 10 ninths of what number?

68. Bought 2 barrels and 1 fifth of a barrel of gin (that is, 11 fifths of a barrel) for 65 dollars; what was that a barrel ?

69. 65 is 9 fifths of what number?
70. 71 is 8 elevenths of what number?

C. l. A boy gave away 2 apples and 1 half, which was 1 fourth of all he had; low inany had he ?

2. A man gave away 3 dollars, which was 2 fifths of all the money he had; how much had he ?

3. A man sold a cow for fifteen dollars, which was 4 fifths of what she cost him ; how much did he lose by the bargain ?

4. A man sold a piece of cloth for 37 dollars, which was 9 eighths of what it cost him; how much did he gain by the bargain ?

5. There is a pole 3 fifths under water, and 7 feet out of the water; how long is the pole ? :

6. A man sold a piece of cloth for 47 dollars, by which bargain he lost 2 ninths of what the cloth cost him; how much did it cost him, and how much did he lose ?

VE? Miscellaneous Examples. 1. If a staff 5 feet long cast a shadow 4 feet at 12 o'clock, what is the length of a pole that casts a shadow 67 feet at the same time?

2. If 53 gallons of water, in 1 hour, run into a cistern containing 97 gallons, and 44 gallons run out in an hour, in what time will it be filled ?

3. A man bought a cask of wine containing 75 gallons; 2 sevenths of it leaked out, and he sold the remainder for 1 dollar a gallon; how much did he sell it for?

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4. A cask of wine cost 67 dollars; what is 5 eighths of it worth?

5. A man bought 9 oranges for 6 cents and 2 sevenths apiece, and sold them for 67 cents; what did he gain by the bargain ? /

6. A man bought 10 yards of broadcloth for 70 dollars; how must he sell it

' per yard in order to gain 14 dollars ? casie.

7. If when the days are 12 hours long, a man perform a journey in 3 days, how many hours is he in performing it?

8. If a man perform a journey in 36 hours, how many days would he be in performing it when the days are nine hours lóng ?

9. If when the days are 11 hours long, a man can perform a journey in 5 days, in how many hours will he perform it? In how many days when the days are 9 hours long?

10. What number added to 2 fifths of 33, will make the number 17!

11. How many yards of cloth, that is 1 quarter of a yard wide, will line 10 yards, that is 3 quarters wide ?

12. 8 yards of cloth that is 1 quarter wide are equal to how many yards that is 4 quarters wide ??

13. How many yards of cloth, that is 3 quarters wide, are equal to 7 yards that is 5 quarters wide ?

14. How many yards of cloth, that is 6 quarters wide, are equal to 37 that is 4 quarters wide ?

15. If a piece of cloth, 5 quarters wide, be worth 37 dollars, what is a piece of the same length, 3 quarters wide, worth?

16. If.cloth 4 quarters wide is worth 8 dollars a yard, what is 1 yard of the same kind of cloth, that is 5 quarters wide, worth?

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