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; of is therefore of the whole.

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

T5

of a share signify 3 parts of a share,
of the three parts is 1 part, that

it is evident that

is 1. 39. that

signify 9 pieces or parts, and it is evident 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 •

18

18

52. In the 4th row, the 3d square shows that ¦ of is, and must be twice as much, or f

56. In the fifth row, the 3d square shows that of is, but must be twice as much as, there& fore of, are 13·

is, consequently

of

78. 83 is 47, } of 4 is 7.

79. 84 is,

is %, or 111.

101

of

86. We may say of 84 is 2, and 24 over, then

24 is, and

90.

of is, hence of 84 is 234.
of 183 is 233, and is 3 times as much, or

B. 4. It would take 1 man 4 times 93, or 374 days, and 7 men would do it in 4 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.

14

7. 63 is 47. If of a bushel would last a week, 62 bushels would last 27 weeks; but since it takes , it will last only of the time, or 9 weeks.

10

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. 9 is 4o, 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 bar

6

rel, he could buy only of that number, that is, 6 barrels.

25 and 26. * Ans. 94.

31. 43 is 3, and 93 is 48. Now is contained in 48 48 times, and 21 is contained only part as many times, consequently only 2 or 24. B. 1. is; consequently 5 pounds can be bought 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.

12

5. is, and is it. If a pound had cost ar 4 of a dollar, 14 pounds could be bought for 1 of a dollar, but since it costs, only as many can be bought; that is, 43 pounds.

9. is, and 1 is 5. If a bushel had cost of a dollar, 65 bushels might have been bought, but since it cost 18, only part as much could be bought; that is, 4

40

bushels.

T8

12. is, and is 1, is contained in § 15 times, but is contained only as many times;

that is, 33 times.

Miscellaneous Examples.

5. of a penny is of 4 farthings. Ans. 2} farthings.

6. & of 12 pence. Ans. 10 pence. 7. of 4 quarters is 2 quarters and of a quarter; of a quarter is 3 of 4 nails, which is 13 nails. Ans. 2 quarters, 13 nails.

13. § of 24 hours is 15 hours. 14. 3 of 24 hours is 14 hours 3 of 60 minutes is 24 minutes. minutes.

and of an hour Ans. 14 hours, 24

28. There being 4 farthings in a penny, 1 far

I

thing is part of a penny.

4

30. 3 farthings is of a penny.

T2

31. 1 penny is of a shilling, because there are 12 pence in a shilling.

34. 5 pence is of a shilling.

43. 3 shillings is
48. 1 farthing is

2

41. 1 shilling is

20

20

of a pound.
of a pound.
of one shilling.

of a shilling. 5 far

of 1 pound. 7 pence is to

of 1£.

of a yard.

of 1

of 1£.

of a yard, 5 nails is

of 1 lb. 15 oz. is 11⁄2 of 1 lb.
of 1 quarter. 9 lbs. is

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 3. 122. One paid 3, the other §.

123. 20 dollars were paid in the whole, one paid 2, another, and the third 2%•

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 B 2o, and C 25, of 100 dollars.

251

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

same time, and B 8 dollars for the same time. A must have, B, and C, of 88 dollars

The examples 127, 128, 129, 130, and 131, are double or compound fellowship.

139. The interest of 50 dollars for 1 year and 6 months is 4 dollars and 50 cents, and for 1 month it is 25 cents. The interest of 7 dollars for 18 months (a dollar is of a cent a month) is 63 cents. whole amounts to 5 dollars and 38 cents.

The

140. The interest of 200 dollars for 11 years is 16 dollars. The interest of 67 dollars is 67 cents for every 2 months, for 16 months it will be 8 times 67 cents, which are 5 dollars and 36 cents. whole interest is 21 dollars and 36 cents.

The

143. The interest of 100 dollars for 21 years, is 13 dollars and 50 cents. The interest of 100 dollars for 60 days would be 1 dollar, the interest for 20 days will be of a dollar, or 33 cents. The interest of 1 dollar for 24 years is 131 cents, for 10 dollars the interest would be 1 dollar and 35 cents, and for 30 dollars, 4 dollars and 5 cents. The interest of 7 dollars for 21 years is 7 times 131 cents or 94 cents. The interest of 37 dollars for 60 days would be 37 cents, and for 20 days of 37 cents, or 12 cents. The whole interest is 18 dollars and 95 cents.

146. They would both together do 3 of the work ៖ in 1 day, and it would take them of a day to do the other. Ans. 14 day.

147. § would be done in 1 day, and it would take of a day to do the other. Ans. 1 days. 149. They both together consume of a bushel in a week, but the woman alone consumes only 1 of a bushel in a week. That is, they both together consume in a week, but the woman alone only fo, consequently, the man alone would consume; and a bushel would last him 3 weeks.