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43. Six times thirteen are how many ? 44. Six times fourteen are how many

? 45. Six times fifteen are how many

y ? 46. Six times sixteen are how many ? 47. Six times seventeen are how many ? 48. Six times eighteen are low 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 y? 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 ? 81. Ten times eleven are how

many

? 82. Ten times twelve are how many

? 83. Ten times thirteen are how

many

? 84. Ten times fourteen are how many

? 85. Ten tiines fifteen are how many ? 86. Ten times sixteen are how many

? 87. Ten times seventeen are how many

? 88. Ten times eighteen are how many? 89. Ten times nineteen are how many ? 90. Ten times twenty are how many ?

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 I 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, rcmark 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 aunit 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 ? How many

halves are there in 3? 18. A boy divided 4 oranges among

his companions, giving them 1 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.

17.

20. A man having some labourers gave them 1 half a dollar apiece ; it took 3 dollars and 1 half a dollar to pay them; how many labourers were there?

21. How many halves are there in 3 and 1 half?
22. How many halves are there in 5 ?
23. How many halves are there in 7 and 1 half ?

24. How can you tell how many halves there are in any number?

Answer. Since there are 2 halves in one, there will be twice as many halves as there are whole

ones.

25. If you had 1 orange, and should divide it among your companions giving them 1 third apiece, how many

could

you give it to ? 26. How many thirds are there in 1 ?

27. If you cut 2 oranges each into 3 pieces, how many pieces would they make ?

28. If you cut 3 oranges into 3 pieces each, how many pieces would they make ?

29. If you cut 4 apples each into 3 pieces, how many pieces would they make ?

30. How many thirds are there in 2? in 3 ? in 4 ? iri 5? 31. How can you tell how

many

thirds there are in any number?

Answer. Since there are 3 thirds in one, there will be 3 times as many thirds as there are whole ones.

32. If you had 2 bushels and I third of a bushel of corn to give to some poor persons, how many could you give it to if you should give them 1 third of a bushel apiece ?

33. How many thirds are there in 2 and 1 third ?

34. If a horse can eat I third of a bushel of oats in 1 day, hov many days would it take him to eat 3 bushels and 2 thirds of a bushel ?

35. How many thirds are there in 3 and 2 thirds ?

36. If 1 horse can eat 1 third of a bushel of oats in a day, how many horses will it take to eat 5 bushels and 2 thirds of a bushel in the same time?

37. In 5 and 2 thirds how many thirds ?
38. In seven and I third how many thirds ?

39. If 1 horse will eat 1 fourth of a ton of hay in 1 month, how many horses will eat a ton in the same time? How many will eat 2 tons ? How many

will eat 3 tons ? 4 tons ? 5 tons ? 6 tons ?

40. How many fourths are there in 1 ? in 2 ? in 3 ? in 4 ? in 5 ? in 6 ?

41. How can you tell how many fourths there are in any number?

42. How many fourths are there in 4 and 1 fourth?

43. In 5 tons of hay and 3 fourths of a ton how many fourths of a ton ?

44. In 5 and 3 fourths how many fourths ? 45. In 7 and 1 fourth how many fourths ? 46. In 9 and 3 fourths how

many

fourths ? 47. If a horse eat 1 fifth of a ton of hay in a month, how many horses will eat a ton in the same time ? 2 tons ? 3 tons ? 4 tons ? 5 tons ?

48. How many fifths are there in 1 ? in 2 ? in 3 ? in 4 ? in 5 ? in 7 ? in 9 ?

49. How can you tell how many fifths there are in any number? 50. In 2 and 1 fifth how many fifths ?

51. In 3 dollars and 2 fifths of a dollar how many fifths of a dollar ?

52. In 3 and 2 fifths how many fifths ? 53. In 5 and 3 fifths how many fifths ? 54. In 6 and 4 fifths how many fifths ?

55. How many sixths are there in 1 ? in 2? in 3? in 4 ? in 5 ? in 7 ? in 8 ?

56. In 2 and 2 sixths how many sixths ? 57. In 3 and 4 sixths bow many sixths ? 58. In 6 and 5 sixths how many sixths ?

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