19. 4 ninths of 36 is 8 tenths of how many times 20. 3 fourths of 40 is 5 sevenths of how many times 8? 7? 21. 6 ninths of 45 is 3 fifths of how many times > 22. 5 sixths of 48 is 10 sevenths of how many times 3? 23. 4 sevenths of 63 is 6 fifths of how many times 8? 24. 5 ninths of 72 is 4 sevenths of how many times 9? B. 1. 4 fifths of 15 is 6 tenths of how many thirds of 21? 2. 4 thirds of 18 is 8 ninths of how many sevenths of 35? 3. 6 sevenths of 21 is 2 thirds of how many thirds of 24? 4. 5 fourths of 24 is 10 sevenths of how many fifths of 40. 5. 5 eighths of 32 is 2 fifths of how many fifths of 35? 6. 4 sevenths of 63 is 6 eighths of how many ninths of 45? 7. 3 sevenths of 56 is 4 ninths of how many fourths of 28? 8. 3 eighths of 64 is 6 tenths of how many sixths of 30? 9. 2 eighths of 72 is 3 tenths of how many fifths of 40? C. 1. Two times eleven are how many ! 6. Two times sixteen are how many? 7. Two times seventeen are how many? 8. Two times eighteen are how many? 9. Two times nineteen are how many? 10. Two times twenty are how many? 11. Three times eleven are how many? 12. Three times twelve are how many? 13. Three times thirteen are how many? 14. Three times fourteen are how many? 15. Three times fifteen are how many? 16. Three times sixteen are how many? 17. Three times seventeen are how many? 18. Three times eighteen are how many? 19. Three times nineteen are how many? 20. Three times twenty are how many? 21. Four times eleven are how many? 22. Four times twelve are how many? 23. Four times thirteen are how many? 24. Four times fourteen are how many? 25. Four times fifteen are how many? 26. Four times sixteen are how many? 27. Four times seventeen are how many? 28. Four times eighteen are how many? 29. Four times nineteen are how many? 30. Four times twenty are how many? 31. Five times eleven are how many? 32. Five times twelve are how many? 33. Five times thirteen are how many? 34. Five times fourteen are how many? 35. Five times fifteen are how many? 36. Five times sixteen are how many? 37. Five times seventeen are how many 38. Five times eighteen are how many? 39. Five times nineteen are how many? 40. Five times twenty are how many? 41. Six times eleven are how many? 42. Six times twelve are how many? 43. Six times thirteen are how many? 44. Six times fourteen are how many? 45. Six times fifteen are how many? 46. Six times sixteen are how many? 47. Six times seventeen are how many? 48. Six times eighteen are how many? 49. Six times nineteen are how many? 50. Six times twenty are how many? 51. Seven times eleven are how many? 52. Seven times twelve are how many? 53. Seven times thirteen are how many ? 54. Seven times fourteen are how many ? 55. Seven times fifteen are how many? 56. Seven times sixteen are how many? 57. Seven times seventeen are how many? 58. Seven times eighteen are how many? 59. Seven times nineteen are how many? 60. Seven times twenty are how many? 61. Eight times eleven are how many? 62. Eight times twelve are how many? 63. Eight times thirteen are how many? 64. Eight times fourteen are how many? 65. Eight times fifteen are how many? 66. Eight times sixteen are how many? 67. Eight times seventeen are how many? 68. Eight times eighteen are how many? 69. Eight times nineteen are how many? 70. Eight times twenty are how many? 71. Nine times eleven are how many? 72. Nine times twelve are how many? 73. Nine times thirteen are how many? 74. Nine times fourteen are how many? 75. Nine times fifteen are how many? 76. Nine times sixteen are how many? 77. Nine times seventeen are how many 78. Nine times eighteen are how many? 79. Nine times nineteen are how many? 80. Nine times twenty are how many? 1 SECTION VIII. A. 1. If you cut an apple into two equal parts, what is one of those parts called ?* 2. How many halves of an apple will make the whole apple ? 3. If you cut an apple into 3 equal parts, what is 1 of those parts called? what are 2 of the parts called ? 4. How many thirds of an apple will make the whole apple ? 5. If you cut an apple into 4 equal parts, what is 1 of those parts called? what are 2 of those parts called? what are 3 of them called ? 6. How many fourths of an apple make the whole apple? 7. If an apple be cut into 5 equal parts, what is one of the parts called? what are 2 of the parts called? what are 3 of the parts called? what are 4 of the parts called? * See Section III, article B, remark before question 1 and 17. 8. How many fifths of an apple make the whole apple ? 9. If an apple be cut into 6 equal parts, what is 1 of the parts called? what are 2 of the parts called? what 3? what 4? what 5? 10. How many sixths of an apple make the whole apple ? 11. If an apple be cut into 7 equal parts, what is 1 of the parts called? what are 2 of the parts called? what 3? what 4? what 5? what 6? Let the instructer ask the pupil the divisions of a unit in this manner as far as the division into 10 parts. It would be well to ask them further. Then let him begin again, and suppose an orange instead of an apple. After applying the division to several different things, Plate II. may be explained and used. It will often be found useful to refer the pupil to the divisions of some sensible object. For the explanation of Plate II. see the Key. 12. A man had a bushel of corn and wished to give 1 half of a bushel apiece to some labourers; how many could he give it to ? 13. How many halves are there in 1 ? 14. A man divided 2 barrels of flour among his labourers giving them 1 half of a barrel apiece, how many men did he give it to ? 15 How many halves are there in 2?* 16. In 3 bushels of corn how many half bushels? 17. How many halves are there in 3? 18. A boy divided 4 oranges among his companions, giving them I half of an orange apiece; how many boys did he give them to? 19. How many halves are there in 4? * Be careful to make the pupil use the plate. He might answer the questions without, but he will not understand their meaning so well. |