SECTION XIV. A. This section contains the division of fractious bý 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. 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 square shows that ofis of the whole. of a share signify 3 parts of a share, 33. Since it is evident that is . of the three parts is 1 part, that 39. signify 9 pieces or parts, and it is evident that of 9 parts is 3 parts, that is 3. 43. We cannot take of 5 pieces, therefore we must take of 1, which is, and is 5 times as much as, therefore of is. This may be readily seen on the plate. In the sixth row, third square, find by the vertical division, then these being divided each into three parts by the horizontal division, and of each being taken, you will have 52. In the 4th row, the 3d square shows that of is, and must be twice as much, or 56. In the fifth row, the 3d square shows that of is, but must be twice as much as, there fore of, are 15 B. 4. It would take 1 man 4 times 9, or 374 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 10 months. 7. 63 is 27. If of a bushel would last a week, 63 bushels would last 27 weeks; but since it takes 2, 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 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 93 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, and 93 is 43. Now is contained in 48 times, and 2 is contained only part as many times, consequently only 2 or 24. B. 1. is; consequently 5 pounds can be Dought 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. 23 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, 43 pounds. 9. is 18, and 1 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, 4 bushels. 12. ↑ is, and is, is contained in § 15 times, but is contained only as many times; that is, 33 times. 5. Miscellaneous Examples. 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 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. 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 of a shilling, because there are of a shilling. 12 pence in a shilling. 48. 1 farthing is of a pound. of a pound. of one shilling. of a shilling. 5 far of 1 pound. 7 pence is to 49. 2 farthings is, or of 1£. 59. 3s. 5d. is 41 pence, which is % of 1£. of a yard, 5 nails is of a yard. 75. I nail is of 1 lb. 15 oz. is 11⁄2 of 1 lb. 99. 1 oz. is 91. 1 lb. is quarter. of i 100. At the end of 1 hour they would be 7 and miles apart. In 7 hours, 7 times 7, which is 54 miles. 121. This is the principle of fellowship; 3 shillings were paid; one paid, the other. 122. One paid 3, 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 first put in i 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 haves, B , and C, of 100 dollars. 131. As money was in 4 times as long as C's. It is the same as if A had put in 8 dollars for the |