24. A boy having a quart of nuts, wished to divide them, so as to give one companion, another , and a third of them; 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. is how many? is how many? are how many? and and 26. A man gave of a barrel of flour to one man, of a barrel to another; to which did he give the most? How much? and 27. Which is the largest, or §? How much the largest ?. 28. A boy having a pound of almonds, said he intended giving 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 them So. O yes I can, said he, I will first divide them into twelve equal parts, and then 1 can 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. many twelfths would each have ? 31. and † and are how many? How 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. 8 and then distributed them as George had desired. How many twentieths did he give to each? 33. is how many is how many? is how many? is how many? 34. is how many? ? 35. is how many 42. 43. 44. are how many 35 ? 45. are how many? 46. are how many? 47. are how many? 48. Reduce to sixths and to sixths. 49. and are how many? 50. Reduce and to eiguhs. 51. and are how many? 52. and are how many? 53. and are how many? 54. and are how many? 55. and are how many? 56. and are how many? 57. and and are how many ? 58. and and are how many? 59. and are how many? 60. and and are how many? 61. and and are how many? and and and are how many? 62. and 63. and are how many? 64. and are how many? 65. and are how many? 66. less are how many? are how many? 71., and, and, and, less, are how many 72., and, and , and, and, less, are how many? ? 73. and 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; for that will always produce a number divisible by all the denominators. 77. Reduce and to a common denominator. 78. Reduce and to a common denom inator. and 79. Reduce and to a common denominator. 80. Reduce and to a common denominator. B. 1. Mr. F. said he would give of a pine ap to George, and the rest to the how to divide it, and how much But neither of them could tell; Could you have told if you How would you divide it? How ple to Fanny, and 2. A man sold 1 bushels of wheat to one man, 42 bushels to another; how many bushels did he sell to both? 3. A man bought 64 bushels of wheat at one time, and 2 at another; how much did he buy in the whole ? 4. A man bought 7 yards of one kind of cloth, and 63 yards of another kind; how many yards in the whole? 5. A man bought of a barrel of flour at one time, 2 barrels at another, and 6 at another; how much did he buy in the whole? 6. A man bought one sheep for 4 dollars, and another for 5 dollars; how much did both? he give for 7. There is a pole standing, so that 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? 8. A man having undertaken to do a piece of work, did of it the first day, of it the second day, and 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 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; a line divided into halves and then into sixths, will show that is the same as, and as ; 4,, can therefore be reduced to , and to. This is called reducing fractions to their lowest terms. It is done by dividing the greatest number that will divide it without a remainder. 1. Reduce to its lowest terms.* to its lowest terms. 2. Reduce 3. Reduce to its lowest terms. Ans. . 13. Reduce to its lowest terms. 14. Reduce to its lowest terms. Note. It will be seen by the above section that if both the numerator and denominator be multiplied 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 omi it till after the next section. |