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and then distributed them as George had desired. How many twentieths did he give to each ?

33. # is how many ? } is how many zo? is how many zd? I's is how many zt?

34. 4 is how many t'o ? 35. 1 is how many it? 36. is how many $ 37. 1 is how many 15? 38. are how many 39. are how many zt? 40. is how many l'o? 41. are how many to 42. are how many is 43. 4 are how many 21 44. & are how many 3 45. are how many s6 46. ğ are how many 36 47. are how many at? 48. Reduce { to sixths and f to sixths. 49. f and are how many ? 50. Reduce 1 and 1 to eighths. 51. f and I are how many $? 52. 1 and į are how many ? 53. and are how many ? 54. 1 and ž are how many ? 55. { and į are how many $? 56. j. and are how many t'? 57. 1 and 1 and 1 are how many ? 58. and and are how many It? 59. and į are how many ? 60. and 1 and 1 are how many 11? 61. and 3 and 4 are how many at? 62. 1 and 1 and fand 1 and 1 are how many ? 63. 1 and are how many tų? 64. and į are how many is? 65. and ž are how many t's 66. less

are how many t?

69. &

67. f and , less , are how many ty?
68. & less gare how many I's?

less g are how many 24? 70. & less , are how many ? 71. ), and, and t, and , less , are how man, 72. 4, and }, and , and it, and at, less ;, are now many ty?

73. and are how many ł?
74. and are how many 36?
75. and ğ are how many 61?

When the denominators in two or more fractions are the same, the fractions are said to have a common denominator. Thus and have a common denominator. We have seen that, when two or more fractions have a common denominator, they may be added and subtracted as well as whole numbers. We add or subtract the numerators, and write their sum or difference over the common denominator. The first part of the process in the above examples was to reduce them to a common denominator.

76. Reduces and to a common denominator. Note. They may be reduced to twelfths.

If it cannot be immediately seen what number must be the common denominator, it may be found by multiplying all the denominators together; for that will always produce a number divisible by all - the denominators.

77. Reduce and to a common denominator.

78. Reduce and t and to a common denominator.

79. Reduce and to a common denominator. 30. Reduce and } to a common denominatok

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81. Reduce 4 and 3 and 4 to a common denominator.

82. Add together and .
83. Add together and
84. Add together f and 18.
85. Add together and fand 7
86. Subtract from 1.
87. Subtract is from .
88. Subtract 4 from
89. Subtract from

B. 1. Mr. F. said he would give 4 of a pine-apple to Fanny, and to George, and the rest to the one that could tell how to divide it, and how much there would be left. But neither of them could tell; so he kept it himself. Could you have told if you had been there? How would you divide it? How much would be left ?

2. A man sold 14 bushels of wheat to one man, 4 bushels to another; how many bushels did he sell to both ?

3. A man bought 64 bushels of wheat at one time, and 24 at another; how much did he buy in the whole ?

4. A man bought 7 yards of one kind of cloth, and 63 yards of another kind; how many yards in the whole ?

5. A man bought of a barrel of beer at one time, 24 barrels at another, and 6 at another; how much did he buy in the whole ?

6. A man bought one sheep for 44 dollars, and another for 50 dollars ; how much did he give for both ? 7. There is a pole standing, so that f of it is in the mud, and if of it in the water, and the rest out of the water ; how much of it is out of the water?

8. A man, having undertaken to do a piece of work, did of it the first day, of it the second day, and of it the third day; how much of it did he do in three days ?

9. A man, having a piece of work to do, hired two men and a boy to do it. The first man could do of the work in a day, and the other of it, and the boy of it; how much of it would they all do in a day?

C. It will be seen, by looking on plate III. that is the same as 1, and that & is the same as 1, and that is the same as f; &, &, can therefore be reduced to t, and 4 to g. This is called reducing fractions to their lowest terms.

1. Reduce to its lowest terms. * Ans. A
2. Reduce by to its lowest terms.
3. Reduce to its lowest terms.
4. Redu

to its lowest terms. 5. Reduce it to its lowest terms. 6. Reduce is to its lowest terms. 7. Reduce to its lowest terms. 8. Reduce is to its lowest terms. 9. Reduce to its lowest terms. 10. Reduced to its lowest terms. 11. Reduce şi to its lowest terms. 12. Reduce š to its lowest terms. 13. Reduce a to its lowest terms. 14. Reduce & to its lowest terms.

Note. It will be seen by the above section, that, if both the numerator and denominator be multiplied by the same number, the value of the fraction will not be altered; or, if they can both be divided by the same number without a remainder, the fraction will not be altered.

* If this article should be found ton difficult for the pupil, he may omit it till after the next section.

SECTION XIV.

A. 1. A Boy, having 3 of an orange, gave away of that; what part of the whole orange did he give away ?

2. What is of 1?

3. If you cut an apple into three pieces, and then cut each of those pieces into two pieces, how many pieces will the whole apple be cut into ? What part of the whole apple will one of the pieces be?

4. What is 1 of } ?

5. A boy had of a pine-apple, and cut that half into three pieces, in order to give away of it. What part of the whole apple did he give away?

6. What is 1 of 1?

7. If an orange be cut into 4 parts, and then each of the parts be cut in two, how many pieces will the whole be cut into ?

8. What is 4 of ?

9. A man, having 1 a barrel of flour, sold I of that; how much did he sell?

10. What is I of ?

11. If an orange be cut into 4 equal parts, and each of those parts be cut into 3 equal parts, how many parts will the whole orange be cut into ?

12. What is of ?

13. A boy, having of a quart of chestnuts, gave away £ of what he had. What part of the whole quart did he give away?

14. What is 1 of 1? 15. What is į of ?? 16. A man, owning of a ship, sold of his share ; what part of the ship did he sell, and what part did he then own ?

17. What is šof ??
18. What is $ of 1.

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