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. square shows 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 that of } is t's of the whole. 33. Since of a share signify 3 parts of a share, it is evident that į of the three parts is 1 part, that is 4 39. signify 9 pieces or parts, and it is evident that 1 of 9 parts is 3 parts, that is . 43. We cannot take } of 5 pieces, therefore we must take of ], which is th, and is 5 times as much as š, therefore į ofis ta. This may be readily seen on the plate. In the sixth row, third square, find i by thë vertical division, then these being divided each into three parts by the horizontal division, and į of each being taken, you will have it 52. In the 4th row, the 3d square shows that of is t's, and must be twice as much, or is. 56. In the fifth row, the 3d square shows that } of f is i's, but must be twice as much as ļ, therefore of ], are is: 78. 87 is y, i of is. 79. 8 is, of is to, consequently 4 of is to, or 115. 86. We may say 1 of 8% is 2, and 2 over, then 24 is , and į of 4 is 34, hence of 84 is 234. 90. 4 of 183 is 233, and of is 3 tiines as much, or 74 B. 4. It would take 1 man 4 times 9, or 375 days, and 7 men would do it in : of that time, that is, in 515 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. 7. 64 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 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 he of enough for another. 23. 94 is , and 14 is If it had been ouly of a dollar a barrel, he might have bought 66 barrels for 99 dollars, but since it was ų a barrel, he could buy only it of that number, that is, 6 barrels. 25 and 26. Ans. 94. 31. 4} is , and 9 is 44. . Now } is contained in 48 48 times, and is contained only z'ı part as many times, consequently only 21 or 24 B. 1. } is ; consequently 5 pounds can be bought for of a dollar. 3. is is, ayd } is . If he had given only ı i' apiece, he could have given it to 9 persons, but since he gave it he could give it to only 1 half as many, or 4) persons. 5. is 1, and is it. If a pound had cost y's of a dollar, 14 pounds could be bought for 24 of a dollar, but since it costs zi, only į as many can be bought ; that is, 4 pounds. 9. is lo, and is If a bushel had cost th of a dollar, 65 bushels might have been bought, but since it cost me, only part as much could be bought ; that is, 41, bushels. 12. g is is, and is il, iis contained in ii 15 times, but is contained only as many times ; that is, 3 times. Miscellaneous Examples. 6. f of a penny is of 4 farthings. Ans. 23 farthings. 6. of 12 pence. Ans. 10 pence. 7. of 4 quarters is 2 quarters and of a quarter; } of a quarter is of 4 nails, which is 13 nails. Ans. 2 quarters, 1 nails. 13. i 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 far. thing is á part of a penny. 30. 3 farthings is of a penny. 31. 1 penny is ta of a shilling, because there are 12 pence in a shilling. 34. 5 pence is a of a shilling. 49. 2 farthings is to, or i of a shilling. 5 farthings is of a shilling. 51. 1 penny is zio of 1 pound. 7 pence is to of 1£. 59. 3s. 5d. is 41 pence, which is ab of 1£. 75. 1 nail is já of a yard, 5 nails is too of a yard. 89. 1 oz. is o of 1 lb. 15 oz. is li of 1 lb. 91. 1 lb. is ze of 1 quarter. 9 lbs. is of quarter. 100. At the end of 1 hour they would be 7 and miles apart. In 7 hours, 7 times 73, which is 54} miles. 121. This is the principle of fellowship; 3 shillings were paid ; one paid }, the other j. 122. One paid , the other 123. 20 dollars were paid in the whole, one paid , another s, and the third : 121. 3 und 4 and 5, are 12. The first put in is; the second ; the third i 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 ne, 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 6 sarne time, and B 8 dollars for the same time. A must have , B, and com, 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. The whole amounts to 5 dollars and 38 cents. 140. 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 ceris. 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 į 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 131 cents or 94į cents. The interest of 37 dollars for 60 days would be 37 cents, and for 20 days į 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 fo in a week, but the woman aloue only fo, consequently, the man alone would consume dai and a bushel would last him 3} weeks. |