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and then distributed them a's George had desired. How many twentieths did he give to each !

33. is how many yo? } is how many to? is how many zo ? jó is how many as ? 34. Į is how many ”

? 35. į is how many t? 36. į is how many ś? 37. į is how many is? 38. į are how many ? 39. į are how many 11? 40. į is how many ? 41. are how many i's

? 42. į are how many it? 43. are how many 21

? 44. are how many 3'5

? 45. j are how many as

? 46. are how many ? 47. io are how many ab? 48. Reduce {to sixths and į to sixths. . 49. sand fare how many ? 50. Reduce 1 and to eighths. 51. į and I are how many ; ? 52. į and į are how many ? 53. & and į are how many } ? 54. and į are how many }? 55. į and are how many ś? 56. i and are how many tó? 57. į and 1 and 1 are how many } ? 58. į and and I are how many ty? 59. and į are how many '? 60. į and į and į are how many ta? 61. i and in and are how many as ? 62. and 1 and 1 and 1 and 1 are how many is? 63. and are how many i'a ? 64. and į are how many t's

? 65. į and į are how many t'? 66. less į are how many ?

are how

67. g and , less , are how many I? 68. less are how many It? 69. less š are how many zt? 70. less are how many 35? 71. 3, and t, and }, and , less , many 72. t, and t, and , and to, and at, less }, are how many ?

73. and are how many ? 74. Á and are how many 36? 75. § and ğ are how many ?

When the denominators in two or more frae. tions 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 ä common denominator.

76. Reduce , 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 ş and to a common denominator.

78. Reduce and and to a common denominator.

79. Reduce } and to a common denominator. 80. Reduce and to a common denominator.

81. Reduce f and f and to a common denomi aator. 82. Add together and 7. 83. Add together # and If 84. Add together and is 85. Add together and fand it 86. Subtract from d. 87. Subtract from 88. Subtract & from . 89. Subtract s from

: 1. Mr. F. said he would give of a pine-apple to Fanny, and 3 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 le 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 6 bushels of wheat at one time, and 21 at anoiher; how much did he buy in the whole ?

4. A man bought 73 yards of one kind of cloth, and 67 yards of another kind: how many yards in the whole ?

5. A man bought of a barrel of flour at one time, 27 barrels at another, and 63 at another; how much did he buy in the whole ?

6. A man bought one sheep for 4ş dollars, and another for 58 dollars; how much did he give for both ?

7. There is a pole standing, so that of of it is in the mud, and of it in the water, and the rest out of the water ; how much of it is out of the water?

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*

Ans. 1.

8. A man having undertaken to do a piece of work, did į of it the first day, { of it the second day, and I 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 į 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?

Note. By dividing a line into halves, and then into fourths, it will be seen that 4 is the same as 1, a line divided into balves and then into sixths, will show that is the same as , and as 3; 4, 8, can therefore be reduced to , and to g. This is called reducing fractions to their lowest terms. It is done by dividing the greatest number that will divide it without a renainder.

1. Reduce to its lowest terms. 2. Reduce so to its lowest terms. 3. Reduce to its lowest terms. 4. Reduce to its lowest terms. 5. Reduce ji to its lowest terms. 6. Reduce to its lowest terms.

to its lowest terms. 8. Reduce je to its lowest terms. 9. Reduce to its lowest terms. 10. Reduce to its lowest terms. 11. Reduce á to its lowest terms. 12. Reduce to its lowest termis. 13. Reduce ji to its lowest terms. 14. Reduce 41 to its lowest terms.

Note. It will be seen by the above section that if both the numerator and denominator be multi plicd 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 too difficult for the pupil, he may omit intill after the pext section.

7. Reduce to

SECTION XIV.

A. 1 A boy having of an orange gave away of that, what part of the whole orange did he give

away ?

2. What is į of į?

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 į of ?

5. A boy had į of a pine apple, and cut that half into three pieces, in order to give away í of it

. What part of the whole apple did he give away?

6. What is į of į?

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 į of 1?

9. A man having į a barrel of flour, sold of That; 10w much did he sell ?

10. What is of į?

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 į 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 į of z? 15. What is į of}? 16. A man owning í of a ship, sold { of his share; what part of the ship did he sell, and what part did . be then own !

17. What is į of } ? 18. What is į of 1?

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