78. 8z is y, s of u is 3. 79. 84 is, of 4 is to, consequently of is fó, or 115 86. We may say of 8 is 2, and 2 over, then 24 is *, and of % is jy, hence of 8f is 234. 90. 4 of 18} is 23}, and } is 3 tiines as much, or 72 B. 4. It would take 1 man 4 times 9, or 375 days, and 7 men would do it in t 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 fin 2, it is evident that he: could give them to 6 boys if he gave them į apiece, but if he gave them şapiece, 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. 7. 61 is . If į of a bushel would last a week, 6 bushels would last 27 weeks ; but since it takes *, it will last only { of the time, or 9 weeks. 13. If he had given į of a bushel apiece, he. might have given it to 17 persons, but since he gave 3 balves apiece, he could give it to only of that: number, that is to 5 persons, and he would have i bushel left, which would be of enough for another. 23. O is , and 14 is y. If it had been only 4 of a dollar a barrel, he might have bought 66: barrels for 97 dollars, but since it was y a bar-: rel, he could buy only 1 of that number, that is, 6 barrels. 25 and 26. Ans. 94. 31. 4} is 3, and 93 is . Now } is contained in 48 48 times, and y is contained only a part as many times, consequently only 2 or 2. B. 1. } is consequently 5 pounds can be bought for ļof a dollar. 3. is i'a, and is fa. If he had given only in apiece, he could have given it to 9 persons, but since he gave ia he could give it to only 1 half as many, or 41 persons. 5. is , and } is it. If a pound had cost or of a dollar, 14 pounds could be bought for it of a dollar, but since it costs, only į as many can be bought; that is, 4 pounds. 9. is , and lis If a bushel had cost an of a dollar, 65 bushels might have been bought, but since it cost if, only is part as much could be bought; that is, 4 1 bushels. 12. f is it, and is fibi te is contained in 115 times, but it is contained only { as many times ; that is, 37 times. Miscellaneous Examples. 5. of a penny is of 4 farthings. Ans. 21 farthings. 6. of 12 pence. Ans. 10 pence. 7. of 4 quarters is 2 quarters and of a quarter; } of a quarter is of A nails, which is l_nails, Ans. 2 quarters, 14 nails. 13. 1 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 ja of a shilling, because there are 12 pence in a shilling. 34. 5 pence is of a shilling. 49. 2 farthings is , or of a shilling. 5 farthings is of a shilling. 51. 1 penny is gio of 1 pound. 7 pence is 273 of 1£. 59. 3s. 5d. is 41 pence, which is zo of 1£. 75. 1 nail is io of a yard, 5 nails is of a yard. 89. 1 oz. is its of 1 lb. 15 oz. is iš of 1 lb. 91. 1 lb. is a of 1 quarter. 9 lbs. is za of i quarter. 100. At the end of 1 hour they would be 7 and miles apart. In 7 hours, 7 times 74, which is 547 miles. 121. This is the principle of fellowship; 3 shillings were paid ; one paid , the other . 122. One paid }, the other s. 123. 20 dollars were paid in the whole, one paid 7, another , and the third 27 121. 3 und 4 and 5, are 12. The first put in isi the second in; the third g. 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 mouth. The question is the same as if A had put in 8 dollars, B 9 dollars, and C 8 dollars. A must have it, B is, and Cig, 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 į of a cent a month) is 63 cents. The whole amounts to 5 dollars and 38 cents. 146. The interest of 200 dollars for 1} 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 certs. 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 2+ years is 13į 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 27 years is 7 times 134 cents or 944 cents. The interest of 37 dollars for 60 days would be 37 cents, and for 20 days of 37 cents, or 124 cents. The whole interest is 18 dollars and 95cents. 146. They would both together do i of the work in 1 day, and it would take them of a day to do the other Ans. l { day 147. i would be done in 1 day, and it would take of a day to do the other . Ans. )} 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 fo in a week, but the woman alone only to, consequently, the man alone would consume vi and a bushel would last him 31 weeks. 152. A and B can build į of it in 1 day; A, B, and C, can build } of it in 1 day, the difference between } and } is ab; therefore C can build as of it in 1 day ; and it would take him 131 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 lust 11 months. 167. The money is 7 parts of the whole, and the purse one part; consequently the money is 7, and the purse i 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 , and į 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 y 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 |