48. Harriet had 40 pins, and gave Maria 2 fifths of them; how many did she give her?

Therefore 2

ANALYSIS. 1 fifth of 40 pins is 8 pins, and 2 fifths of 40 pins are 2 times 8 pins, or 16 pins. fifths of 40 pins are 16 pins.

49. What is 5 sixths of 30? 50. What is 7 eighths of 56? What is 5 twelfths of 60?

51.

Of 72?

Of 80?

Of 84?

52. If 1 half of an orange is worth 2 cents, what is the whole orange worth?

ANALYSIS.

If I half of an orange is worth 2 cents, 2 halves, or the whole orange, is worth 2 times 2 cents, or 4

cents.

53.

If 1 third of an orange is worth 2 cents, what is the whole of it worth?

54. If 1 fourth of a pound of beef is worth 3 cents, what is a pound worth?

55. If 1 sixth of a bushel of apples is worth 10 cents, what is a bushel worth?

56. If 1 twelfth of a vessel is worth $500, what is the whole vessel worth?

57. If 2 thirds of a melon are worth 8 cents, what is 1 third of it worth? What is the whole worth?

ANALYSIS.

If 2 thirds of a melon are worth 8 cents, 1 third of it is worth 1 half of 8 cents, which is 4 cents; and if 1 third of a melon is worth 4 cents, 3 thirds, or the whole melon, is worth 3 times 4 cents, or 12 cents.

58. If 5 sixths of a barrel of sugar are worth $15, what is 1 sixth of a barrel worth? What is 1 barrel worth?

59. If 7 twelfths of an ounce of silver are worth 70 cents, what is an ounce worth?

60.

When 3 tenths of a bushel of corn are worth 18 cents, what is a bushel worth?

61. 3 is 1 half of what number?

ANALYSIS.

Since 1 half of some number is 3, 2 halves, or the number itself, is 2 times 3, or 6. Therefore 3 is 1 half of 6.

62. 7 is 1 seventh of what number? 63. 12 is 1 ninth of what number? 64. 4 is 2 thirds of what number?

ANALYSIS. Since 2 thirds of some number is 4, 1 third of that number is 1 half of 4, or 2; and 3 thirds, or the number itself, is 3 times 2, or 6. Therefore 4 is 2 thirds of 6. 65. 8 is 4 sevenths of what number? 66. 10 is 5 twelfths of what number?

LESSON XXVI.

1. If a pear is worth 2 cents, what part of the pear is worth 1 cent?

2. 1 is what part of 2?

ANS. 1 is 1 half of 2; because 1 taken 2 times equals 2. 3. 1 is what part of 4? Of 3? Of 8? Of 7? Of 10? Of 9? Of 13? Of 21?

4. 1 cent is what part of 6 cents? Of 5 cents? Of 12 cents? Of 20 cents? Of 25 cents?

5. 3 is what part of 6?

ANS. 3 is 1 half of 6; because 3 is contained in 6 2 times.

6. 5 apples are what part of 10 apples? Of 15 apples? Of 25 apples? Of 20 apples?

7. 8 is what part of 24? Of 64? Of 56?

8. What part of 30 is 3? 5? 6? 10? 2? 15? What part of 60 is 30?

9. 2 is what part of 6? 4 is what part of 12?

10.

If a barrel of flour costs $10, what part of a barrel will cost $2?

ANALYSIS. If $10 buy 1 barrel of flour, $2 will buy the same part of a barrel that $2 are of $ 10, or 1 fifth.

11.

If 12 cherries cost 1 cent, what will 4 cherries be worth?

12. When a pound of spice can be bought for 24 cents, what part of a pound can be bought for 4 cents?

13. If $14 will buy a barrel of beef, what part of a barrel will $2 buy? $7 ?

14. If 3 bushels of cranberries cost $12, what part of $16 will 1 bushel cost?

15. When 5 quarts of cherries can be bought for 35 cents, what part of 21 cents will 1 quart cost? 16. If an orange be worth 3 cents, how much of it is worth 1 cent? 2 cents?

ANALYSIS.

If 3 cents buy 1 orange, 1 cent will buy 1 third of an orange; and if 1 cent buy 1 third of an orange, 2 cents will buy 2 times 1 third, or 2 thirds, of an orange.

17. If 4 dimes will purchase a yard of flannel, what part of a yard will I dime purchase? 3 dimes? 18. At the rate of $6 a cord, how much wood can be bought for $5?

19. If 11 pea-nuts are worth 1 cent, how much are 3 pea-nuts worth?

20. 3 is what part of 4?

ANALYSIS. 1 is 1 fourth of 4, and 3 is 3 times 1 fourth, or 3 fourths, of 4.

21. 5 is what part of 6? Of 8? Of 12? Of 9? 22. What part of 5 is 3? 2? 4?

23. What part of 17 is 5? 7? 4? 11? 24. 7 is what part of 8? Of 10? Of 16? 25. 3 apples are what part of 7 apples? apples? Of 11 apples? Of 22 apples?

Of 20?

Of 10

26. 8 are how many times 3?

ANALYSIS. 8 are 2 times 3, with a remainder of 2, which is 2 thirds of 3. Therefore 8 are 2 times 3, and 2 thirds of 3.

27.

28.

7 are how many times 2? 3? 4?

How many times is 2 contained in 13? In

25? In 17? In 19? In 21?

29.

How many times is 3 contained in 4? In 8?

In 16? In 20? In 25 ? In 38?

30.

31.

In 29?

32.

How many times 4 in 5? In 10?
How many times 5 in 8?

In 15?

In 9?

In 11?

In 35?

In 31? In 47? In 49? How many times 6 in 7? In 15? How many times 7 in 17? In 46? In 78? 34. At $9 a barrel, how many barrels of flour can be bought for $64?

33.

35. At 8 cents a pound, how many pounds of rice can be bought for 78 cents?

36. In how long a time will a ship sail 93 miles, at the rate of 10 miles an hour?

37. If 11 pea-nuts cost 1 cent, how much will 100 pea-nuts cost?

38. If strawberries are 6 cents a pint, how many quarts can be bought for 62 cents?

39. How many dozen in 105? In 111?

40. 2 times 2, and 1 half of 2, are how many?

SOLUTION. 2 times 2 are 4, and 1 half of 2 is 1, which added to 4 makes 5.

41. 2 times 3, and 1 third of 3, are how many? 42. 10 times 5, and 1 fifth of 5, are how many? 43. 6 times 7, and 1 seventh of 7, are how many ? 44. 4 times 12, and 7 twelfths of 12, are how many?

SOLUTION. 4 times 12 are 48; 1 twelfth of 12 is 1, and 7 twelfths are 7 times 1, which are 7; 48 and 7 are 55.

45. 5 times 3, and 2 thirds of 3, are how many? 46. 5 times 9, and 5 ninths of 9, are how many? 47. 10 times 10, and 9 tenths of 10, are how many?

48. What is 1 third of 2?

ANALYSIS. 1 third of 1 is 1 third, and 1 third of 2 is 2 times 1 third, which are 2 thirds.

NOTE. When no other denomination is expressed or implied, 2 thirds is understood to mean 2 thirds of 1.

49. 50.

What is 1 fifth of 3? Of 4? Of 2?

What is 1 tenth of 3? Of 2? Of 4? Of 7? Of 9? Of 5? Of 6? Of 8?

51. What is 1 seventh of 5 apples? ANS. 5 sevenths of an apple.

52. What is 1 ninth of 4 oranges? Of 7 oranges? Of 8 oranges? Of 5 oranges?

53. If 5 copies of a book are worth 4 dollars, what is 1 copy worth?

54. If 6 yards of cloth are worth $5, what part of a dollar is 1 yard worth?

55. When 15 cents will buy 4 yards of ribbon, what part of a yard will 1 cent buy?

56. When 4 barrels of flour cost $29, what part of a barrel can be bought for $1?

57. What is 1 third of 5?

ANALYSIS. 1 third of 5 is 1, with a remainder of 2, and 1 third of 2 is 2 thirds. Therefore 1 third of 5 is 1 and 2 thirds.

58. What is 1 half of 3? Of 5? Of 7? Of 11? Of 19? Of 23? Of 31?

59.

What is 1 third of 4? Of 7? Of 10? Of 11? Of 17? Of 22? Of 26?

60.

What is 1 fourth of 21? Of 25? Of 30? Of 35? Of 42? Of 47 ?