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 how many hours will they meet? At what distance from each place from which they set out ? SECTION XIII. A. l. 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 of an orange? 3. If you give { of an orange to one boy, and to another, how many t would you give away? How many would you have left ? 4. 4 and 1 are how many ?? 5. A man gave to one labourer 4 of a bushel of wheat, and to another; how many of a bushel did he give to both ? How many bushels ? 6. f and fare 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. I is how many ? 9. A man bought of a bushel of wheat at one time, and 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 6 of a yard at another; at which time did he buy the most? 12. are how many t? to one man, and of a bushel to another; but he could not tell how to divide it. Another man, standing by, advised him to divide the vhole bushel into six equal parts first, and then take ţ of them for one, and f 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 ?? is how many 1? and are how many ? 15. A man, paying some money to his labourers, gave each man of a dollar, and each boy 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 à boy of a dollar, how much does the man earn more than the boy? 18. What is the difference between and ??. 19. A boy, distributing some nuts among his companions, gave of a quart to one, and 4 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 1 and 1?: 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. , man had a horse, and a cow, and a sheep. The horse would eat of a load of hay in the winter, the cow 4, and the sheep 4. How many & of a load would each eat? How many & would they all eat? How many loads ? 114 and 24. A boy, having a quart of nuts, vide them so as to give one companic t, and a third of them; but, in orde proper division, he first divided th: eight equal parts, and then he was them as he wished. How many eigntis uiu mu give to each ? How many eighths had he left for himself? 25. is how many $? is how many f? 4 and and } are how many $? 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, for ? How much the largest ? 28. A boy, having a pound of almonds, said he intended to give of them to his sister, and I to his brother, and the rest to his mamma. His mamma, 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 be give to each? 29. } is how many th? is how many ? and 1 are how many tiz? 30. Mr. Goodman, having a pound of raisins, said he would give Sarah $, and Mary 4, 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 4, and t, and of them. How many twelfths would each have ? 31. and { and 4 are how many rz? 32. George bought a pine-apple, and said he would give 1 of it to his papa, and to his mamma, and 3 to his brother James, if he could divide it. James took it, and cut it into twenty equal pieces, to then distributed them as George had desired. Aow many twentieths did he give to each ? 33. 1 is how many ? * is how many ? is how many zt? It is how many at? 34. 4 is how many to? 35. is how many 4? 36. is how many ? is how many is? f are how many f? are how many ? 40. is how many ? 41. are how many it? 42. are how many is? are how many 4? and ž are how many ś and are how many it? 3 and j and I are how many to? 59. and i are how many ? 60. and 1 and 4 are how many ? 61. & and and 1 are how many ? and 1 and 1 and 4 and I are how many ? 1 and are how many ? and į are how many it? 65. and are how many ? 66. less are how many ? 67. f and 4, less A, are how many ty? less s are how many t?. 69. & less are how many ? less are how many ts? 71. 1, and t, and t, and , less g, are how many 72. , and }, and s, and to, and zbo, less }, are how many to ? 73. and fare how many it? 74. & and are how many as? 75. and ğ are how many ? 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 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 ; forthat will always produce a number divisible by all the denominators. 77. Reduce and to a common denominator. 78. Reduce and and to a common denominator. 79. Reduce and to a common denominator. 80. Reduce i and to a common denominator. |