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ing towards each other, one at the rate of 3 miles an hour, the other 2 miles; how much do they approach each other in an hour ? How much in 2 hours ? In how many hours will they meet? At what distance from each place from which they set out ?

SECTION XIII.

A. l. If you give į of an orange to one boy, and to another, how much more do you give the first, than the second ?

2. į of an orange is how many of an orange ?

3. If you give į of an orange to one boy, and I to another, how many i would you give away ? How many would you have left ?

4. į and I are how many i? 5. A man gave to one labourer of a bushel of wheat, and to another ; how many of a bushel did he give to both ? How many bushels ?

6. į and are how many ? How many times 1 ?

7. A man gave { of a barrel of flour to one man, and of a barrel to another; to which did he give the most?

8. Į is how many $?

9. A man bought į of a bushel of wheat at one time, and 3 of a bushel at another; at which time did he buy the most ?

10. } is how many $?

11. A man bought of a yard of cloth at one time, and of a yard at another; at which time did he buy the most ?

12. are how many ;? 13. A man wished to give 4 of a bushel of wheat

to one man, and } of a bushel to another ; but he could not tell how to divide it. Another man stand ing by advised him to divide the whole bushel inte six equal parts first, and then take 1 of them for one, and of them for the other. ' How many parts did he give to each ? How mapy to both ? How many had he left ?

14. į is how many < ? is how many ; ? ; and s are how many ?

15. A man paying some money to his labourers, gave each man į of a dollar, and each boy á of a dollar; how much more did he give to a man thar to a boy?

16. What is the difference between 1 and [?

17. If a man can earn of a dollar in a day, and a boy į of a dollar, how much does the man earn more than the boy ?

18. What is the difference between A and } ?

19. A boy distributing some nuts among his companions, gave } of a quart to one, and of a quart to another; how much more did he give to one, than to the other ?

Note. Change them to sixths.
20. What is the difference between į and į?

21. A man having two bushels of grain to distribute among his labourers, wished to give { of a bushel to one, and of a bushel to another, and the rest to a third; but was at a loss to tell how to divide it; at last he concluded to divide each bushel into six equal parts, or sixths, and then to distribute those parts. How many sixths did he give to each?

22. is how many ; ?

23. Å man had a horse, and a cow, and a sheep. The horse would eat of a load of hay in the win. ter, the cow ?, and the sheep á. How many i of a load would each eat? How many # would they all eat ? How many loads ?

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24. A boy having a quart of nuts, wished to divide them, so as to give one companion į, another fi

and a third of them ; but in order to make a proper division, he first divideå the whole into eight equal parts, and then he was able to divide them as he wished. How many eighths did he give to each ? How many eighths had he left for himself?

25. j is how many i ! is how many ? and and į are how manya?

26. A man gave of a barrel of flour to one wan, and of a barrel to another; to which did he give the most? How much ?

27. Which is the largest or ? How much the largest ?

28. A boy having a pound of almonds, said he intended to give { of them to his sister, and to his brother, and the rest to his mamma.

His mamma smiling said she did not think he could divide

O yes I can said he, I will first divide them into twelve equal parts, and then I can divide them well enough. Pray how many twelfths did he give to each ? 29. } is how many t'?iš how many 'a

? and I are how many tı?

30. Mr. Goodman having a pound of raisins, said ne would give Sarah }, and Mary 1, and James } of them, and he told Charles he should have the rest, if he could tell how to divide them. Well, said Charles, I would first divide the whole into twelve equal parts, and then I could take and and I of them. How many twelfths would each have ?

31. { and 1 and 1 are how many t'a ?

32. George bought a pine apple, and said he would give of it to his papa, and į to his mamma, and into his brother James, if he could divide it James took it, and cut it into twenty equal pieces

them so.

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.

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