SECTION XIV.

A. THIS section contains the division of fractions by whole numbers, and the multiplication of one fraction by another. Though these operations sometimes appear to be division, and sometimes multiplication, yet there is actually no difference in the operations.

The practical examples will generally show how the operations are to be performed, but it will be well to use the plate for young pupils.

1 and 2. In the second row, the 2d square is divided vertically into halves, and each of the halves is divided into halves by the horizontal line; is therefore of the whole.

of

2

3 and 4. In the third row, the 2d square shows that of is.

16 and 17. In the 5th row, the 3d square shows that of is of the whole.

33. Since of a share signify 3 parts of a share, it is evident that of the three parts is 1 part, that is.

39. signify 9 pieces or parts, and it is evident that of 9 parts is 3 parts, that is .

43. We cannot take of 5 pieces, therefore we must take of, which is, and is 5 times as much as, therefore of is. This may be readily seen on the plate. In the sixth row, third square, find by the vertical division, then these being divided each into three parts by the horizontal division, and of each being taken, you will have

86. We may say of 8 is 2, and 24 over, then

2 is, and of

is, hence of St is 24.

90. of 18 is 24, and is 3 times as much, or 7.

B. 4. It would take 1 man 4 times 94, or 37 days, and 7 men would do it in of that time, that is, in 51 days.

SECTION XV.

A. THIS section contains the divisions of whole numbers by fractions, and fractions by fractions,

1. Since there are in 2, it is evident that he could give them to 6 boys if he gave them apiece, but if he gave them apiece, he could give them to only one half as many, or 3 boys.

5. If of a barrel would last them one month, it is evident that 4 barrels would last 20 months, but since it takes of a barrel, it will last them but one half as long, or 10 months.

7.6 is. If of a bushel would last a week, 63 bushels would last 27 weeks; but since it takes , it will last only of the time, or 9 weeks.

13. If he had given of a bushel apiece, he might have given it to 17 persons, but since he gave 3 halves apiece, he could give it to only of that number, that is to 5 persons, and he would have 1 bushel left, which would be of enough for another. 23. 94 is, and 14 is . If it had been only of a dollar a barrel, he might have bought 66 barrels for 94 dollars, but since it was a barrel, he could buy only of that number, that is, 6 barrels.

25 and 26. Ans. 94.

31. 4 is, and 9 is. Now is contained in 48 times, and is contained only part as many times, consequently only 2 or 27.

B. 1. is; consequently 5 pounds can be Dought for of a dollar.

3. is, and is. If he had given only apiece, he could have given it to 9 persons, but since he gave he could give it to only 1 half as many, or 4 persons.

5. is, and is. If a pound had cost

of a dollar, 14 pounds could be bought for of a dollar, but since it costs, only as many can be bought; that is, 43 pounds.

4

9. is, and I is 육동. If a bushel had cost

of a dollar, 65 bushels might have been bought, but since it cost 18, only to part as much could be bought; that is, 4 bushels.

12. is, and

that is, 34 times.

times, but

is, is contained in 14 15

is contained only + as many times;

Miscellaneous Examples.

of a penny is of 4 farthings. Ans. 23

5.

farthings.

6.

of 12 pence. Ans. 10 pence.

7. of 4 quarters is 2 quarters and of a quar

ter; of a quarter is 3 of 4 nails, which is 14 nails. Ans. 2 quarters, 13 nails.

13. of 24 hours is 15 hours.

14. of 24 hours is 14 hours and of an hour;

of 60 minutes is 24 minutes.

Ans. 14 hours, 24

is part of a penny.

28. There being 4 farthings in a penny, I farthing

30. 3 farthings is of a penny.

31. 1 penny is

of a shilling, because there are

12 pence in a shilling.

34. 5 pence is

of a shilling.

41. 1 shilling is

of a pound.

43. 3 shillings is

of a pound.

48. 1 farthing is

of one shilling.

of a shilling. 5 far

49. 2 farthings is, or

things is of a shilling.

51. 1 penny is 많이 of 1 pound. 7 pence is to

of 1£.

91. 1 lb. is

quarter.

of 1 quarter. 9 lbs. is f of 1

100. At the end of 1 hour they would be 7 and miles apart. In 7 hours, 7 times 74, which is 543 miles.

121. This is the principle of fellowship; 3 shillings were paid; one paid, the other. 122. One paid, the other.

123. 20 dollars were paid in the whole, one paid ফুঠ, another 흙, and the third

121. 3 and 4 and 5, are 12. The first put in; the second; the third

129. 4 dollars for 2 months, is the same as 8 dollars for 1 month; 3 dollars for 3 months, is the same as 9 dollars for 1 month; and 2 dollars for 4 months, is the same as 8 dollars for 1 month. The question is the same as if A had put in 8 dollars, B 9 dollars, and C 8 dollars. A must have 5, B 3, and C, of 100 dollars.

131. A s money was in 4 times as long as C's. It is the same as if A had put in 8 dollars for the

alt 1805.

Mars.

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