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86. We may say

24 is 23, and

90.

734

of

of 84 is 2, and 24 over, then of 23 is 34, hence ¦ of 84 is 214.

of 18 is 233, and 4 is 3 tines as much, or

B. 4. It would take 1 man 4 times 93, or 37% days, and 7 men would do it in of that time, that is, in 5 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 19 months.

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7. 63 ie 27. If of a bushel would last a week, 63 bushels would last 27 weeks; but since it takes 3, 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 g of enough for another. 23. 9 is, and 14 is . If it had been only of a dollar a barrel, he might have bought 66, barrels for 9 dollars, but since it was a bar

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

25 and 26. Ans. 94.

31. 4 is 2, and 93 is 48.

Now is contained

part as

in 48 48 times, and 21 is contained only 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.

5. is, and is 4. 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, 4 pounds.

9. is 18, and 1 is 25. 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 bushels.

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

that is, 33 times.

5.

Miscellaneous Examples.

of a penny is 3 of 4 farthings. Ans. 24

farthings.

6. of 12 pence. Ans. 10 pence.

7.3 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.

14.

of 24 hours is 15 hours.

of 24 hours is 14 hours and of an hour; of 60 minutes is 24 minutes.

Ans. 14 hours, 24

minutes.

43. 3 shillings is

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28. There being 4 farthings in a penny, 1 farthing is part of a penny.

30. 3 farthings is of a penny.

2

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

48. I farthing is of one shilling.

49. 2 farthings is, or

of a pound.

of a pound.

of a shilling. 5 far

things is
51. 1 penny is

of a shilling.

of 1 pound. 7 pence is 375

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75. 1 nail is

89. 1 oz. is

91. 1 lb. is

of a yard.

of I

59. 3s. 5d. is 41 pence, which is of 1£.

quarter.

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of a yard, 5 nails is

of 1 lb. 15 oz. is 1 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, the other.

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

121. 3 and 4 and 5, are 12. the second; the third

The first put in ;

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 raonths, 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 haves, B 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

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 certs.

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 13 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 2 years is 7 times 13 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 of the work in 1 day, and it would take them of a day to do the other. Ans. 1 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 } of a bushel in a week. That is, they both together consume in a week, but the woman alone only , consequently, the man alone would consume; and a bushel would last him 34 weeks.

T

152. A and B can build of it in 1 day; A, B, and C, can build of it in I day, the difference between and is; therefore C can build of it in 1 day; and it would take him 13 days to build it alone.

164. Find how much they might eat in a day, in order to make it last 1 month, and then it will be easy to find how much they may eat in a day to make it last 11 months.

167. The money is 7 parts of the whole, and the purse one part; consequently the money is 7, and the purse of 16.

170. He gave 1 part for the apple, 2 parts for the orange, and 4 parts for the melon. These make 7 parts. The apple 3 cents, the orange 6 cents, and the melon 12 cents.

175. If to a number half of itself be added, the sum is of that number; hence, subtract 2 from 100 and the remainder is of the number of geese that he had.

180. This must be reduced to 6ths. 1 half is, andis, and the number itself is §. If therefore to the whole number its half and its third be added, the sum will be ; hence, 77 is of the number.

181.is; therefore if to a number and of itself be added, the whole number will be ; but when 18 more is added to 7, the first number is doubled; that is, the number is of the first number; therefore 18 is of the number

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