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MENTAL EXERCISES.

EXAMPLE.-If pears are worth three cents each, how many can be bought for six cents?

SOLUTION.--If one pear costs 3 cents, as many pears can be bought for 6 cents as 3 cents are contained times in 6 cents, which are 2.

CONCLUSION.-Therefore, if pears are worth 3 cents each, two can be bought for 6 cents.

When an object is divided into two equal parts, one of these parts is called one half (1).

When an object is divided into three equal parts, one of these parts is called one third (}); two parts, two thirds ().

When an object is divided into four equal parts, one of these parts is called one fourth (1); two parts, two fourths (); three parts, three fourths (3).

In the same way, by dividing, we may obtain fifths, sixths, sevenths, tenths, etc.

EXAMPLE.—If two pears cost six cents, what will one pear cost?

SOLUTION.-If 2 pears cost 6 cents, one pear will cost one half of 6 cents, which is 3 cents.

CONCLUSION.-Therefore, if 2 pears cost 6 cents, one pear will

cost 3 cents.

1. How many apples, at three dollars a barrel, can be bought for nine dollars?

2. How many yards of tape, at two cents a yard, can be bought for four cents?

3. If three sheep cost twelve dollars, what is the cost of one sheep?

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4. If I walk eight miles in two hours, how far can I walk in one hour?

5. If there are three feet in one yard, how many yards in eighteen feet?

6. There are twelve trees arranged in four rows; how many trees in a row?

7. How many times is four contained in sixteen?

8. If flour is worth five cents a pound, how many pounds can be bought for fifteen cents?

9. A dime is worth ten cents; what is half a dime worth?

10. A man paid twelve dollars for wood, at six dollars a cord; how many cords did he buy?

11. If one brick cover a space four inches wide, how many bricks will it take to cover eight inches in width? 12. A farmer had fourteen cattle, divided equally in two pastures; how many in each pasture?

13. How much cloth, at five dollars a yard, can be bought for twenty dollars?

14. How many posts, six feet high, can be made from a log eighteen feet long?

15. If a stage travel at the rate of eight miles an hour, in how many hours will it travel sixteen miles?

16. John spent twenty-four cents for oranges, at four cents apiece; how many did he buy?

17. There are seven days in a week; how many weeks in fourteen days?

18. What is one third of twenty-one dollars?

19. The blacksmith uses four shoes for one horse; how many horses can he shoe with twenty shoes?

20. Mary bought six papers of pins for thirty cents; what was the cost of one paper?

21. A farmer paid out twenty-eight dollars to seven men, giving each the same amount; how much did each man receive?

22. A day consists of twenty-four hours; how many hours in one third of a day?

23. How many weeks in twenty-one days?

24. At five cents a pound, how many pounds of shot can I buy for twenty-five cents?

25. When flour is nine dollars a barrel, how many barrels can be bought for twenty-seven dollars?

26. What is the price of one barrel of flour, if six barrels cost thirty-six dollars?

27. John has thirty sticks of wood to carry into the house; how many loads will they make, if he carry five. sticks at a load?

28. How many loads will they make, if he carry seven sticks at a load?

29. How many books, at ten cents each, can be bought for fifty cents?

30. How many boxes will it take to contain forty spools of cotton, if each box hold eight spools?

31. How many raisins, at six cents a pound, can be bought for forty-two cents?

32. If one bushel is equal to four pecks, how many bushels in thirty-two pecks?

33. A school of forty pupils is divided into five classes; how many pupils in each class?

34. Mary has a basket that holds seven apples; how many times can she fill her basket with forty-two apples? 35. Charles bought seven cocoa-nuts for fifty-six cents; what did one cost?

36. Henry's father is forty-five years old, and Henry's age is one ninth of his father's: how old is Henry?

37. If eight quarts make one peck: how many pecks in forty-eight quarts?

38. How many weeks in forty-nine days?

39. What is one ninth of fifty-four dollars?

40. If sixty cents are divided equally among six boys: how much will each receive?

41. At six dollars a pair, how many pairs of boots can be bought for fifty-four dollars?

42. Ten cents make one dime: how many dimes in eighty cents?

43. How many eggs, at nine cents a dozen, can be bought for seventy-two cents?

44. In one square yard there are nine square feet: how many square yards in eighty-one square feet?

45. How many times is eight contained in ninety-six? 46. If a stage go ten miles an hour, in how many hours will it go eighty miles?

47. Eight men can dig sixty-four rods of trench in a day: how much can one man dig?

48. A boy had sixty-three plums, which he divided equally among nine companions: how many did each receive?

49. If a man gain twenty-four miles in three hours, how long will it take him to gain fifty-six miles?

50. Twelve things make a dozen: how many dozens in seventy-two?

51. An orchard contains twelve rows of trees, and six trees in a row; if there were but eight rows, how many trees would there be in a row?

52. How many eggs, at nine cents a dozen, must be given for six yards of muslin at twelve cents a yard?

53. Bought six yards of velvet at five dollars a yard, and four yards of broadcloth at six dollars a yard; gave in exchange six barrels of flour: what was the price per barrel?

54. A merchant bought five dozen eggs at ten cents a dozen, and seven dozen at eleven cents; he sold the whole so as to gain seventeen cents: what did he receive per dozen?

55. Six pine-apples were sold for seventy-two cents, and twelve cents were gained: what did each cost?

56. James and his six playmates had seven plums each, and altogether they received twenty-one more: how many did each have then?

SHORT DIVISION.

There are two methods of division, Long Division and Short Division.

48. In Short Division, the work of dividing is performed mentally, and the result only is written,

Elem. 5.

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