LESSON III. REMARK. The following lines represent a yardstick, marked off or divided into halves, fourths, and eighths of a yard.. leighth. 1 eighth. 1eighth. 1 eighth. 1 eighth. 1 eighth. 1 eighth. 1 eighth 1. One half equals how many fourths? Ans. Two. 2. One fourth equals how many eighths? 3. One half equals how many eighths? 4. If you cut an apple into halves, and then cut each half into two equal pieces, into how many pieces will the apple be cut? What part of the whole apple is one of these small pieces? 5. One half of an apple is equal to how many times one fourth of an apple? 6. How many fourths of an orange are equal to one half of an orange? REMARK. The following lines represent a yardstick divided into thirds and sixths of a yard. One third. One third. One third. One sixth. One sixth. One sixth. One sixth. One sixth. One sixth, 7 One third equals how many sixths? 8. If you cut a cake into thirds, and then cut each third into two equal parts, into how many equal parts I will the cake be cut? Each of the small picces will be what part of the whole cake? 9. One third of a cake is how many times one sixth of the same cake? 10. If you cut a pie into halves, and then cut each half into three equal parts, what part of the pie will one of these small pieces be? 11. One half of any thing is how many sixths of the same thing? 12. How many sixths of an apple are equal to one third of an apple? 13. How many sixths of an apple are equal to one half of an apple? 14. If one half of an apple is cut into four equal pieces, what part of the whole apple will one of these small pieces be? 15. How many eighths of an apple make one half of an apple? 16. If one fourth of an apple is cut into two equal parts, what part of the whole apple will one of these small pieces be? 17. How many eighths of a pear make one fourth of a pear? 18. What is meant by one eighth of any thing? 19. If a barrel of flour be worth 8 dollars, and if it be divided equally among 8 men, what will one man's share be worth; that is, what is one eighth of a barrel worth? What are two eighths, or one fourth, of it worth? What are three eighths of it worth? What are four eighths, or one half, of it worth? 20. If 8 dollars will buy a box of tea, what part of a box will 1 dollar buy? What part will 2 dollars buy? 3 dollars? 4 dollars? 5 dollars? 6 dollars? 7 dollars? 21. What part of eight is one? Ans. One is one eighth of eight. 22. Two is what part of eight? Ans. Two eighths, or one fourth of eight. 23. Three is what part of eight? Ans. Three eighths of eight. 24. Four is what part of eight? Ans. Four eighths, or one half of eight. 28. Nine are how many times eight? Ans. Once eight and one eighth of eight. 29. Ten are how many times eight? Ans. Once eight and two eighths of eight, or once eight and one fourth of eight. NOTE. The second answer to Example 29 is the best, if the pupil is able to make the reduction. The teacher should ex ercise his own judgment in all such questions. 30. Eleven are how many times eight? 31. Twelve are how many times eight? 32. Thirteen are how many times eight? 33. Fourteen are how many times eight? 34. Fifteen are how many times eight? LESSON IV. 1. IF cranberries cost 7 cents a quart, what part of a quart may be bought for 1 cent? What part for 2 cents? For 3 cents? 4 cents? 5 cents? 6 cents? 2. If wood is worth 7 dollars a cord, how many cords may be bought for 8 dollars? For 9 dollars? 10 dollars? 12 dollars? 14 dollars? 3. What is meant by one seventh, two sevenths, three sevenths, etc., of any thing? 4. How many sevenths make a whole one? 5. If corn is worth 7 shillings a bushel, what is one seventh of a bushel worth? What are two sevenths worth? Three sevenths? Five sevenths? 6. If blueberries cost 7 cents a quart, what will one seventh of a quart cost? Four sevenths? Six sevenths? 7. One is what part of seven? Ans. One is one seventh of seven. 8. Two is what part of seven ? Ans. Two se venths of seven. 9. Three is what part of seven? 10. Nine are how many times seven? Ans. Once seven and two sevenths of seven. 15. When rye is worth 9 shillings a bushel, what is one ninth of a bushel worth? What are two ninths of a bushel worth? What are three ninths, or one third of a bushel worth? Four ninths? Five ninths? Six ninths, or two thirds? Seven ninths? Eight ninths? 16. When coal costs 7 dollars a ton, what part of a ton can I buy for 1 dollar? What part for 2 dollars? For 3 dollars? For 4 dollars? For 5 dollars? 6 dollars? For 7 dollars? How much can I buy for For 10 dollars? 8 dollars? For For 11 dollars? For 17. One is what part of nine? 18. What is meant by one ninth, two ninths, three ninths, etc.? 19. How many ninths make a whole one? LESSON V. 1. IF a laborer earns 3 shillings in a half day, how much will he earn in a whole day? 2. Three is one half of what number? Solution. If 3 is one half of some number, then two halves, or the whole of the number, must be twice 3, which are 6; therefore 3 is one half of 6? 3. Five is one half of what number? Why? 4. If a boy picks 2 quarts of chestnuts in 1 hour, how many quarts will he pick in 3 hours? 5. Two is one third of what number? Solution. If 2 is one third of some number, then three thirds, or the whole of the number, must be three times 2, which are 6; therefore, 2 is one third of 6. 6. Four is one third of what number? Why? 7. Seven is one third of what number? 8. If one fourth of a dollar will pay for 6 oranges, how many oranges may be bought for a whole dollar? 9. Six is one fourth of what number? 10. Nine is one fourth of what number? 11. Three is one fifth of what number? 12. Five is one seventh of what number? 13. Four is one eighth of what number? 14. If three fourths of a pound of raisins cost 15 cents, what will a pound cost? Solution. If three fourths cost 15 cents, one fourth will cost one third of 15 cents, which is 5 cents; and four fourths will cost 4 times 5 cents, which are 20 cents. 15. Charlie's mother said to him, "I have just bought 5 eighths of a watermelon for 15 cents; and if you will tell me what the whole melon is worth, I will give you money enough to buy one." Had you been Charlie, what would you have answered? 16. Fifteen is 3 fourths of what number? 17. Fifteen is 5 eighths of what number? 18. Twelve is 3 fifths of what number? |