ling 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 low many hours will they meet? At what distance from each place from which they set out ? SECTION XIIL A. 1. L you give 4 of an orange to one boy, and t to another, how much more do you give the first than the second ? 2. of an orange is how many toi au orange? 3. If you give 3 of an orange to one boy, and to another, how many would you give away How many + would you have left? 4. $ and are how many ?? 5. A man gave to one labourers of a bushel of whrat, and to another; how many of a bushe. did he give to both ? How many bushels ? 6. j and fare how many t? How many times 1 ? 7. A man gave of a barrel of flour to one man, and f of a barrel to another; to which did he give the most? 8. is how many ? 9. A man bought of a bushel of wheat at one time, and į of a bushel at another; at which time did he buy the most? 10. is how many ? 11. Å man boughts 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 $? 1 to one man, and $ of a bushel to another; but he could not tell how to divide it. Another man, standa ing 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. j is how many 1! is how many ? $ and $ are how many ? 15. A man, paying some money to his labourers, gave each man of of a dollar, and each boy t of a dollar; how much more did he give to a man than to a boy? 16. What is the difference between $ and ? 17. If a man can earn of a dollar in a day, and a boy of a dollar, how much does the man earn more than the boys 18. What is the difference between and £? 19. A boy, distributing some nuts among his companions, gave g 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 then to sixthe. 21. A man, having two bushels of grain to distribute among his labourers, wished to give of a bushel to one, and 4 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. A man had a horse, and a cow, and a sheep. The horse would eat of a load of hay in the winter, the cow }, and the sheep 3. How many of load would each eat? How many & would they al eat? How many loads? 24. A boy, having a quart of nuts, wished to diride them so as to give one companion d, annther t, and a third $ of them; but, in order to make a proper division, he first divided the whole into cight equal parts, and then he was able to divide them as he wished. How many eighths did be give to each ? How many eighths bad he left for himself? 25. 4 is how many f? { is how many f? f and and are how many ? 26. A man gave of a barrel of flour to one man, and g of a barrel to another; to which did be give the most? How much ? 27. Which is the largest, or $? How much the largest ? 28. A poy, naving 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 I can, said he; I will first divide them into twelve equal parts, and then I 'an divide them well enough. Pray how many twelfths did he give to each? 29. is how many ? is how many ? and are how many ? 30. Mr. Goodman, having a pound of raisins, said he would give Sarah , and Mary }, 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 of them. How many twelfths would each have? 31. 1 and 1 and are how many yz? 32. George bought a pine-apple, and said he would give of it to his papa, and to his mamma, and it to his brother James f he could divicie it. James took it, and eut it in twenty equal pieces them so. and then distributed them as George Lad deats many twentieths did he give to each i 34. is how many to? 35. is how many t? 36. is how many ? 37. } is how many is? 38. are how many f? 39. are how many z1? 40. Ž is how many to? 41. are how many ts? 42. Å are how many t's 43. $ are how many ? 44. are how many 45. are how many s6 46. ] are how many $6? 47. iy are how many at? 48. Reduce I to sixths and ļ to sixthu 49. f and fare how many ? 50. Reduce 4 and 1 to eighths. 51. f and are how many ? 52. 1 and 1 are how many ? 53. q and are how many ? 54. and are how many ? 55. j and I are how many f? 56. 1 and are how many it? 57. and į and } are how many ? 58. 1, and and to are how many it? 59. and į are how many ? 60. į and į and t are how many 12? 61. fand and 4 are how many sto? 62. 3 and 1 and 1 and 4 and I are how many ? 63. and are how many ?? 64. und į are how many it? 65. j and are how many 86. i less are how many ? 67. 4 and , less , are how many th? 68. & less iš are how many is? 69. less s are how many zk! 70. less are how many as? 71. 1, and #, and t, and is less ý, are how man. ? 72. 4, and , and %, and I'd, and ab, less ), ar adw many ? 73. and are how many ? 74. & and are how maiiy g'o 75., and are how many o'z When the denominatus no two or more fractions are the same, the fractions are said to have a common denominator. Thus and if have a common denominator. We have seen that, when two or more fractions have a common denominator, they may be added and subtracted as weil 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 denoininator. 76. Reduce and to a common denomina or. Nore. 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 f and if to a common denominator. 78. Reduce s and and if to a common denom inator. 79. Reduce f and to a common denominator. 30. Reduce 4 and to a common denominator |