and of a barrel to another; to which did he give the most? How much? 27. Which is the larger, or? How much the larger? 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. Oh, 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? is how many? is how many? 29. are how many? and 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 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, and then distributed them as George had desired. How many twen tieths did he give to each? ཝ 33. is how many? is how many? f is how many? is how many? 34. is how many? 35. is how many? 36. is how many? 37. is how many? 38.are how many? are how many? 39. 40. is how many? 41. are how many? and are how many? and and and are how many? are how many? 64. and are how many? are how many? 66. less are how many? 67. and, less, are how many? 68. less are how many? 69. less are how many ? 70 less are how many? 71, and 2, and 1, and 2, less §, are how many? 72.4, and, and , and, and, less , are how many? 73. and are how many? 74. and are how many? 75. 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 denomina tor. 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 denomi nators. 77. Reduce and to a common denominator. 78. Reduce and 2 and to a common denominator. 79. Reduce and to a common denominator. B. 1. Mr. F. said he would give of a pine-apple to Fanny, and to George, and the rest to the one that could tell how to divide it, and how much there would be left. But neither of them could tell; so he kept it himself. Could you have told, if you had been there? How would vou divide it? How much would be left? 2. A man sold 14 bushels of wheat to one man, 43 bushels to another; how many bushels did he sell to both? 3. A man bought 64 bushels of wheat at one time, and 24 at another; how much did he buy in the whole? 4. A man bought 73 yards of one kind of cloth, and 6 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 63 at another; how much I did he buy in the whole? 6. A man bought one sheep for 43 dollars, and another for 5 dollars; how much did he give for both? 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 is the same as ; a line divided into halves and then into sixths, will show that is the same as, and as;,, can therefore be reduced to, and to. This is called reducing fractions to their lowest terms. It is done by dividing by the greatest num ber that will divide it without a remainder. C. 1. Reduce & to its lowest terms.* 2. Reduce to its lowest terms. 3. Reduce to its lowest terms. Ans. 2. If this article should be found too difficult for the pupil, he may ɔmit it till after the next section. 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. SECTION XIV. A. 1. A BOY having of an orange gave away of that, what part of the whole orange did he give away? 2. What is of ? 3. If you cut an apple into three pieces, and then cut each of those pieces into two pieces, how many pieces will the whole apple be cut into? What part of the whole apple will one of the pieces be? 4. What is of } ? 5. A boy had of a pine apple, and cut that half into three pieces, in order to give away of it. What part of the whole apple did he give away? 6. What is of } ? 7. If an orange be cut into 4 parts, and then each of the parts be cut in two, how many pieces will the whole be cut into? 8. What is of ? |