33. Since of a share signify 3 parts of a share, it 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 takeof, which is, and is 5 times as much as 1, therefore of is. 78. 83 is 42, of 2 is 7. 79. 84 is 49, ofis, consequently, of is f, or 86. We may say 1 of 84 is 2, and 24 over, then 2§ is 22, and of 22 is 44, hence of 83 is 244. 90. of 188 is 2, and is 3 times as much, or 78. B. 4. It would take 1 man 4 times 9, or 37 days, and 7 men would do it in of that time, that is, in 5 SECTION XV. days. 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. 68 is 27. If of a bushel would last a week, 64 bushels would last 27 weeks; but, since it takes, it will last only of the time, or 9 weeks. ই 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, and 14 is 11. 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 1, and 98 is 48. Now is contained in 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, be 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 1. 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 18 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, bushels. *12.8 is 4, and & is 8; 7 is contained in § 15 times, 189 but is contained only as many times; that is, 3 times. Miscellaneous Examples. 5. of a penny is 6. of 12 pence. of 4 farthings. Ans. 10 pence. Ans. 2 farthings 2 quarters and of a quarter; of 4 nails, which is 1g nails. Ans. 7. of 4 quarters is of a quarter is quarters, 1 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 minutes. 28. There being 4 farthings in a penny, 1 farthing is part of a penny. 30. 3 farthings is of a penny. 31. 1 penny is pence in a shilling. of a shilling, because there are 12 34. 5 pence is of a shilling. 41. 1 shilling is 2 of a pound. 43. 3 shillings is of a pound. 48. 1 farthing is of one shilling. 49. 2 farthings is, or of a shilling. 51. 1 penny is of a shilling. 5 farthings is 59. 3s. 5d. is 10 of 1 pound. 7 pence is of £1. pence, which is of £1. 91. 1 lb. is milos of 1 quarter. 9 lbs. is of 1 3 quarter. 100. At the end of 1 hour they would be 7 and apart. In 7 hours, 7 times 7, which is 548 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, another, and the third 2. 126. 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, 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 C, of 88 dollars. and 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 19 months (a dollar is of a cent a month) is 66 cents. The whole amounts to 5 dollars and 41 cents. 140. The interest of 200 dollars for 13 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. The whole interest is 21 dollars and 36 cents. 143. The interest of 100 dollars for 24 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 2 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 24 years is 7 times 131 cents, or 944 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. 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 3 weeks. 152 A and B can build of it in 1 day; A, B, and C, can build of it in 1 day; the difference between and is therefore C can build of it in 1 day; and it would take him 134 days to build it alone. 104. 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 and the purse of 16. 170. He gave one 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, and} is, 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 1 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, the first number is doubled; that is, the number is of the first number; therefore 18 is † of the number. |