Solution. One third equals, and is, ofis; and therefore she gave pie to each ? NOTE. Multiplying the denominator by 2 makes twice as many parts in the unit, and therefore each part is only one half as great; hence, multiplying the denominator by any number, divides the fraction by the same number. 34. Three fifths of a barrel of flour were divided equally among 4 poor families; what part of a barrel did each receive? 35. If of a bushel of chestnuts are divided equally among 5 boys, what part of a bushel does each receive? 1 eighth of § ? 36. What is 1 sixth of ? 37. What is 1 ninth of ? 1 twelfth of 7? 38. Mary having a nice large pineapple, gave of it to Sarah, to Fanny, to Laura, and kept the rest herself; what part of the pineapple did she give away? What part did she keep? 39. What is 40. What is 41. What is 42. What is 23 +A+A? 17? H-A? fi+A? LESSON II. of a whole 1. ONE half is equal to how many sixths?3 Solution. Since & make a whole one, one will be of §, which is ; therefore, etc. 2. One third of an apple is equal to how many sixths of an apple? 2 3. James gave of a pear to William, to George, and kept the rest himself; how much did he give away? How much did he keep? NOTE. Change the fractions to sirths. Before fractions that have different denominators can be added together, or before one can be subtracted from another, it is necessary to change them to other fractions that have like denominators. 4. what?1-8=what? = 5. A man gave of a dollar to one of his workmen, and of a dollar to another; how many fourths of a dollar did he give to both? How many dollars? 6. 1+2 are how many 4? How many times 1?5 NOTE. Read the first question in Ex. 6 as follows. One half and three fourths are how many fourths? Read all similar examples in like manner. 7. A man gave of a barrel of apples to one of his neighbors, and of a barrel to another; did he give more to one than to the other? 8. and are how many? How many times 1 ? 9. Henry gave of an orange to his brother John, to his sister Marion, and kept the rest himself. With this division the selfish John was dissatisfied, saying that Henry had given more to Marion than to him. No, John, said Marion, Henry has given just as much to you as to me. Now which was right, What part of the orange did Henry John or Marion? is how many †? ++} how many? How many times 1? 12. Samuel worked of a day for Mr. Adams, and of a day for Mr. Daniels. Mr. Adams paid Samuel 50 cents. Now, at the same rate, what should Mr. Daniels pay him? How much, at that rate, will Samuel earn in a day? What part of a dollar? 13. are how many? 14. A boy wished to give of a pear to his sister, and to his brother; and in order to do this most conveniently, he first cut the pear into 6 equal pieces; how many pieces did he give to each? How many pieces had he remaining? 15. Samuel gave of a dollar to one poor boy, and of a dollar to another; what part of a dollar did he give away? How much more to one boy than to the other? 16. What is 1 ? ? } - 1 ? 17. James had a box of strawberries, and said he would give of them to Addie, to Willie, and the rest to Georgie, if he could tell how to divide them. Georgie won; how did he divide them? 18. Harriet having 3 quarts of cherries, said she would give of a quart to Mary, of a quart to Martha, and the rest to any one of the company who would most quickly tell how to divide them. Would you have won had you been there, and how would you divide them? 19. are how many? 3 are how many? 20. how many ? 3 = what? 21. A man having 2 bushels of wheat to give to 3 of his workmen, wished to give of a bushel to the first, of a bushel to the second, and the rest to the third; how much should he give to the third? 22. 3 are how many +'? are how many? 23. A farmer had a horse, a cow, and a sheep. The horse would eat of a ton of hay in a month, the cow, and the sheep; how much would they all eat? How much more would the horse eat than the sheep? How much less would the sheep eat than the cow? 24. are how many? are how many? 25. A man gave of a ton of coal to B. and 3 of a ton to C; to which did he give the most? How much? How much to both? 26. A little girl having a pound of figs, gave of them to one schoolmate, to another, and kept the rest; what part of the pound did she give away? What part did she keep? 27. are how many? are how many 3 ? 28. A spendthrift having received a fortune, squandered of it the first month, and of it the next month, after receiving it; what part of it had he then remaining? 1. REDUCE to its lowest terms. Ans. }. 3. Reduce & to its lowest terms. 4. Reduce 5. Reduce to its lowest terms. to its lowest terms. 6. Reduce to its lowest terms. 7. Reduce to its lowest terms. 8. Reduce to its lowest terms. 9. Reduce to its lowest terms 10. Reduce to its lowest terms. to its lowest terms. 14. Reduce 15. Reduce 1 16. Reduce to its lowest terms. to its lowest terms. to its lowest terms. to its lowest terms. to its lowest terms. 17. Reduce 19. Reduce to twelfths. to fifths. 22. Reduce to fourths. and to equivalent fractions having a common denominator. 23. Reduce 24. Reduce least common denominator. and so that they shall have the 25. Reduce and 3. 26. Reduce and §. 27. Reduce and . and 1. 28. Reduce, 3, and 4, so that they shall have the least common denominator. 29. Reduce, 15, and 24. 30. Reduce, §, and 4. 31. Add together and . 32. Add together and . 2 and 3. and J. 39. A and B engage to do a piece of work. A can do of it in a day, and B can do 4 of it; what part of the work can they together do in a day? What part of it would remain for the next day? What part of the next day would it take them to finish the work? 40. A, B, and C engage to do a piece of work. A can do of it in a day, B can do of it, and C can do of it; what part of the work can they all do in a day? What part would remain for the next day? What part of the second day would it take them to finish the work? 41. is what part of ? what part of 33? 3% LESSON IV. 1. A BOY having of an apple, gave away of that; what part of the whole apple did he give away? 2. What is of?is how many ? ? 3. A boy having of a melon, gave away of that; what part of the whole melon did he give away What part did he keep? 4. What is of ? of? 5. James having of a day for play, spent of that time with his cousin Alfred; what part of the whole day was he with Alfred ? 6. What is of }? } of {? 7. A man having of a cord of wood, gave away of that; what part of a cord did he give away?· What part did he keep? 8. What is of 1 ? 2 of 1 ? Ans. ofis; and of is 3 times, or . |