SECTION XV. A. This section contains the divisions of whole numbers by fractions, and fractions by fractions. 1. Since there are 6-3ds in 2, it is evident that he could give them to 6 boys if he gave them 1-3d apiece, but if he gave them 2-3ds apiece, he could give them to only one half as many, or 3 boys. 5. If 1-5th of a barrel would last them one month, it is evident that 4 barrels would last 20 months, but since it takes 2-5ths of a barrel, it will last them but one half as long, or 10 months. 7. 6 and 3-4ths is 27-4ths. If 1-4th of a bushel would last a week, 6 and 3-4th bushels would last 27 weeks; but since it takes 3-4ths, it will last only 1-3d of the time, or9 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 1-3d of that number, that is to 5 persons, and he would have 1 bushel left, which would be 2-3ds of enough for another. 23. 9 & 3-7ths is 66-7ths, and 1 and 4-7ths is 11-7ths. If it had been only 1-7th of a dollar a barrel, he might have bought 66 barrels for 9 and 3-7ths dollars, but since it was 11-7ths a barrel he could buy only 1-11th of that number, that is, 6 barrels. 25 & 26. Ans. 9 and 4-7ths. 31. 4 and 1-5th is 21-5ths, and 9 and 3-5ths is 48-5ths. Now 1-5th is contained in 48-5ths 48 times, and 21-5ths is contained only 1-21th part as many times,consequently only 2 & 6-21ths or 2 & 2-7ths. B. 1. is 5-10ths; consequently 5 pounds can be bought for of a dollar. 3,3-4ths is 9-12ths, and 1-6th is 2-12ths. If he had giv en only 1-12th apiece, he could have given it to 9 persons, but since he gave 2-12ths he could give it to only I half as many, or 4 and 1 half persons. 5. 1-7th is 3-21ths, and 2-3ds is 14-21ths. If a pound had cost 1-21th of a dollar, 14 pounds could be bought for 1421ths of a dollar, but since it costs 3-21ths, only 1-3d as many can be bought; that is, 4 & 2-3ds pounds. 9. 2-5ths is 16-40ths,and 1 &5-8ths is 65-40ths. If a bushel had cost 1-40th of a dollar, 65 bushels might have been bought, but since it cost 16-40ths, only 1-16th part as much could be bought; that is 4 and 1-16th bushels. 12. 2-9ths is 4-18ths, and 5-6ths is 15-18ths, 1-18th is contained in 15-18ths 15 times, but 4-18ths is contained only 1-4th as many times; that is 3 and 3-4ths times. Miscellaneous Examples. 5. 3-5th of a penny is 3-5th of 4 farthings. 2-5ths farthings. 6. 5-6ths of 12 pence. Ans. 10 pence. Ans. 2 and 7. 3-5ths of 4 quarters is 2 quarters and 2-5ths of a quarter; 2-5ths of a quarter is 2-5ths of 4 nails, which is 1 and 3-5ths nails. Ans. 2 quarters 1 and 3-5ths nails. 13. 5-8ths of 24 hours is 15 hours. 14. 3-5ths of 24 hours is 14 hours and 2-5ths of an hour; 2-5ths of 60 minutes is 24 minutes. Ans. 14 hours 24 min utes. 28. There being 4 farthings in a penny,1 farthing is 1-4th part of a penny. 30. 3 farthings is of a penny. 31. 1 penny is 1-12th of a shilling, because there are 12 pence in a shilling. 34. 5 pence is 5-12ths of a shilling. 49. 2 farthings is 2-48ths, or 1-24th of a shilling. 5 farthings is 5-48ths of a shilling. 51. 1 penny is 1-240th of 1 pound. 7 pence is 7-240ths of £ 59. 3s. 5d. is 41 pence, which is 41-240ths of 1£. 75. 1 nail is 1-16th of a yard. 5 nails is 5-16ths of a yard. quarter. 100. At the end of 1 hour they would be 7 and 4-5ths miles apart. In 7 hours,7 times 7 & 4-5ths, which is 54 and 3-5ths miles. 121. This is the principle of fellowship; 3 shillings were paid; one paid 1-3d, the other 2-3ds. 122. One paid 3-8ths the other 5-8ths. 123. 20 dollars were paid in the whole, one paid 6-20ths, another 5-20ths, and the third 9-20ths. 121. 3 and 4 and 5, are 12. The first put in 3-12ths; the second 4-12ths; the third 5-12ths. 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 8-25ths, B 9-25ths, and C 8-25ths 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 do lars for the same time. A must have 8-22, B 8-22, and C 6-22 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 month it is 25 cents. The interest of 7 dollars for 18 months (a dollar is of a cent a month) is 63 cents. The whole amounts to 5 dollars and 38 cents. 140. The interest of 200 dollars for 1 and 1-3d 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 :00 dollars for 2 and 1-4th years, 13 dollars and 50 cents. The interest of 00 dollars for 60 days would be 1 dollar,the interest for 20 days will be 1-3d of a dollar, or 33 cents. The interest of i dollar for 2 and 1-4th 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 would be 7 times 13 cents, or 95 cents. The whole interest is 18 dollars and 83 cents. 146. They would both together do 3-4ths of the work in 1 day, and it would take them 1 3d of a day to do the other 1-4th. Ans. 1 and 1-3d days. 147. 5-6ths would be done in 1 day, and it would take 1-5ta of a day to do the other 1-6th. Ans. 1 & 1-5th days. 149. They both together consume of a bushel in a week, but the woman alone consumes only 1-5th of a bushel in a week. That is, they both together consume 5-10ths in a week, but the woman alone only 2-10ths, consequently, the man alone would consume 3-10ths; and a bushel would last him 3 and 1-3d weeks. 152. A & B can build 1-8th of it in 1 day; A, B and C can build 1-5th of it in 1 day, the difference between 1-5th and 1-8th is 3-40ths; therefore C can build 3-40ths of it in 1 day; and it would take him 13 & 1-3d 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; conseqently the money is 7-8ths, and the purse 1-8th of 16. 170. He gave part for the apple, 2 parts for the orange, and 4 parts for parts tor the melon. These make 7 parts. The apple 3 cents, the orange 6 cents, and the melon 12 cents. 175. If to a number of itself be added, the sum is 3-2ths of that number; hence, subtract 2 from 100, and the remainder is 3-2ths of the number of geese that he had. 180. This must be reduced to 6ths. 1 half is 3-6ths, and 1-3d is 2-6ths, and the number itself is 6-6ths. If therefore to the whole number its half and its third be added, the sum will be 11-6ths; hence, 77 is 11-6ths of the number. 184.is 2-4ths; therefore if to a number and 1-4th of itself be added, the whole number will be 7-4ths; but when 18 more is added to 7-4ths, the first number is doubled; that is, the number is 8-4ths of the first number; therefore 18 is 1-4th of the number. |