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 ? 915752 SECTION XIII. How many Ą. 1. If you give { of an orange to one boy, and to another, how much more do you give the first, than the second ? 2. of an orange is how many į of an orange ? 3. If you give of an orange to one boy, and to another, how many would you give away ! would you have left ? 4. and are how many ? 5. A man gave to one labourer { of a bushe. of wheat, and to another ; how many , of a bushel did he give to both ? How many bushels ? 6. 1 / 을 and are how many i ? 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. 11 is how many : ? 9. A man bought į of a bushel of wheat at one time, and of a bushel at another; at which time did he buy the most ? 10. į 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. f are how many ; ? to one man, and į of a bushel to another ; but he could not tell how to divide it. Another man standing by advised him to divide the whole bushel into six equal parts first, and then take of them for one, and of them for the other. How many parts did he give to each ? How many to both ? How many had he left ? 14. Į is how many ? } is how many ;? } and į are how many ă? 15. A man paying some money to his labourers, gave each man } of a dollar, and each boy ở of a dollar; how much more did he give to a man than to a boy? 16. What is the difference between į and į? 17. If a man can earn ã 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 4 and 1 ? 19. A boy distributing some nuts among his companions, gave } of a quart to one, and 1 / 2 to another; how much more did he give to one, than to the other ? Note. Change them to sixths. 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 ś? 23. Å man had a horse, and a cow, and a sheep. The horse would eat į of a load of hay in the winter, the cow }, and the sheep & How many å of a load would each eat? How many } would they all eat ! How many loads ? of a quart 24. A boy, having a quart of nuts, wished to divide them, so as to give one companion į, another 4, and a third of thèm ; but in order to make a proper division, he first divided 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. 1 is how many ; ? ; is how many ; ? ; and and į are how many š? 26. A man gave of a barrel of flour to one man, 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 mainma smiling said she did not think he could divide them so. 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. į is how many i ? } is how many iz ? } and are how many 'ı? 30. Mr. Goodman having a pound of raisins, said he would give Sarah ḥ, 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 į and and of them. How many twelfths would each have ? 31. 1 and 1 and į are how many i's ? 32. George bought a pine apple, and said he would give of it to his papa, and to his mamma, and to his brother James, if he could divide it. James took it, and cut it into twenty equal pieces, ! and then distributed them as George had desired. How many twentieths. did he give to each ? 33. į is how many o'y? } is how many zo ? 용 is how many to ? jó is how many zo 34. is how many ? ?? 44. are how many 3'5 ? 45. are how many 36 ? 46. § are how many so 47. , are how many ? 48. Reduce { to sixths and į to sixths. 49. i and are how many ? 50. Reduce and to eighths. 51. į and are how many ; ? 52. į and į are how many ? 53. and I are how many : ? 54. and are how many ? 55. 1 and 1 are how many f? 56. į and į are how many to ? 57. į and ; and † are how many ? 58. 1 and 1 and i't are how many to ! 59. g and į are how many ? 60. į and į and } are how many ta? 61. 1 and is and are how many at ? 62. and 1 and and and ia are how many ız? 63. į and are how many "? 64. and į are how many i's 65. and are how many i's 66. less ; are how many š? 67. f and less are how many is? L ? 70. less are how many 35 71. 1 and , and }, and pa, less s are how many how many o 72. . and , and , and to, and a'r, less are ? 73. 4 and jare how many a's ? 74, and are how many 56 75. ^ and are how many o'z ? 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. Reduce s and into 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 s 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. |