3. A man sold 343 barrels of flour, at 5 dollars a barrel, and was paid in cloth, at 4 dollars a yard; how many yards did he receive? 4. A merchant exchanged 24ğ yards of fine linen, at 8 shillings a yard, for broadcloth, at 18 shillings a yard; how many yards did he receive? 5. A farmer exchanged 62 cords of wood, at 4 dollars a cord, for flour, at five dollars a barrel; how much flour did he receive ? 6. A man bought 16 head of young cattle, at 8,3 dollars per head, and paid for them in flour, at 6 dollars a barrel; how much flour had he to pay? 7. If shad cost 8 dollars a barrel, what will 63 barrels cost? and how much plaster of Paris must be paid for the shad, at 3 dollars a ton ? 8. When rice is 33 cents a pound, and flour 4 cents a pound, how much flour must be paid for 8 pounds of rice ? 16 9. If salmon cost 85 dollars a barrel, how much flour, at 6 dollars a barrel, will pay for 16 barrels of salmon ? 10. A man bought 8 hundred weight of rice, at 33 dollars per hundred weight, and 3 hundred weight of coffee, at 61 dollars per hundred weight, and paid for it in cranberries, at 11 dollars per barrel; how many barrels were required? Fractions of Numbers exceeding Unity, continued. SECTION VII. 1. Two is of what number? of what number? 4 is 2 times what number? of what number? 1 49 of what number? 1 4. Five is of what number?? 1 56? 35? 24? 17 5. Nine is of what number? 1 ? t? 6. Nine is 3 times what number? 19 38 1 ? เ Twelve is 3 times what number? 4 times? 6 times? 8. Sixteen is 4 times what number? 8 times? 2 times ? 9. Twenty-four is 12 times what number? 3 times? 4 times? 2 times? 8 times ? 10. Fifteen is 3 times what number? 5 times? 11. If 4 be of some number, what is of that number? If of a number be 2, what is that number? what? 12. If 6 be ber? 2 is of 13. If 8 be of some number, what is what number? Then 6 is of some number, what is Then 4 is of of the same num of what? of that number? 2 is of what number? Then 8 is of what? 14. 6 is g of what number? 17. 25 is § of what number? 18. 32 is of what number? Of how many times ten? Ans. Of 5 times 10 and of 10. 6 Τσ 19. 56 is of what number? Of how many times 4? 20. 42 is g of what number? Of how many times 9? Ans. Of 6 times 9 and 3 of 9. 6 ? 9 ? 5 ? 21. 28 is of what number? Of how many times 10? 9? 22. 21 is g of how many times 10? 15? 14? 26? 7? 23. 50 is 42 of how many times 12? 19? 6? 8? 4? 12? 7? 4? 5? 12? 8? 7? 9? 6? 24. 42 is 7 of how many times 5? 25. 36 is of how many times 10? 26. 72 is g of how many times 12? 27. 18 is of how many times 11? 12? 16? 8? g 28. 15 is § of how many times 8? 15? 6? 8? 4? 29. 21 is of how many times 10? 12? 6? 8? 5? 30. 45 is of how many times 6? 21? 14? 5? 12? SECTION VIII. — Practical Questions. 1. Ir of a pound of coffee cost 6 cents, what would of a pound cost? What would 1 pound cost? 2 pounds? How did you find that 2 pounds cost 18 cents? 2. If of a pound of sugar cost 6 cents, what would cost? What would 1 pound cost? 6 pounds? How did you find that 6 pounds cost 60 cents ? 3. If of a bushel of wheat cost 36 cents, what cost 1 bushel? 5 bushels? Why? 4. If g of a pound of tea cost 24 cents, what cost 6 pounds? Why? 5. If of a box of raisins cost 28 cents, what was the price of the whole box? Why? 6. A man being asked the age of his eldest son, answered, that his youngest son, who was 9 years old, was just of the age of his eldest son. How old was his eldest son? Why? 7. A man sold a cow when dry for 15 dollars, which was just of what he paid for her when fresh. How much did he pay for her? 8. A man bought 12 yards of cloth, and sold it for 54 dollars, which was g of what it cost him. What did it cost per yard? and how much did he gain by the whole transaction? 9. There is a pole standing in the water, so that 12 feet of it are below the surface, being of its entire length. How long is the pole? and how long the part above the surface? 10. There is a pole under water and 4 feet out. How long is the pole ? 11. A pole is under water and 6 feet out. What is its length ? 12. There is a school in which of the pupils learn grammar, learn arithmetic, geography, geometry, and 12 learn to write. How many attend the school? and how many attend to each study? 12 13. In a certain congregation one Sunday, were in the singers' gallery, in the strangers' gallery, in the wall slips, and 100 in the middle slips. Of how many did the congregation consist? and what was the number of singers? 14. A man being asked the age of his youngest son, answered, that the age of his eldest son was 18 years, which was of his own age, and that his own age was 9 times that of his youngest son. What was the age of his youngest son ? of 15. A man sold a cow for 21 dollars, which was only what she cost him. He paid for her with cloth, at 8 dollars a yard. How much cloth did he give for her? 16. A man gave 25 cents for his breakfast, which was only § of what he paid for his dinner. What did his dinner cost him? He paid for both meals in buttons, at 6 cents per dozen. How many buttons did it require? SECTION IX. — Fractions of Numbers greater than Unity, continued. [THERE are three questions in each of the following problems; but the first two are merely leading questions to assist the learner in the solution of the third. To bright pupils they may be unnecessary, and of course should be omitted. With the more dull the section should be repeatedly reviewed, till the third question in each problem can be solved and explained without hesitation, and without the aid of the first and second questions.] 1. % of 24 how many? of 24 are 10 of what number? of 24 are of how many times 5? How do you know? Explain the process. Form of the solution. of 24 is 4; 14; which is 5 therefore, are 20; if 20 are 40, 4 is 2, and 2 times 5 and of 5. 2. 3 of 28 how many? of 28 are of how many times 7? 6 of 30 of 28 are of what number? of 30 are of how many times 8? 4. 8 of 32 how many?g of 32 g of 32 are & of how many times 5? 5. of 36 how many? of 36 are of how many times 6? 6. 2 of 40 how many? 8 of 36 are of what number? Explain. of 40 are of what number? Explain. 2 of 40 are § of how many times 8? of 48 are 40 of how many 3 5 of 45 are of what number? times 7? 9. 4 of 63 how many? of 63 are g of what number? of 63 are g of how many times 8? Explain. 10. of 72 how many? of 72 are of what number? § of 72 are 4 of how many times 9? Explain. 11. 6 ΤΟ 6 ΤΟ of 15 how many? of 15 are of what number? of 15 are of how many thirds of 21? Explain. Form of the solution.— of 15 is 3, and of course 12; if 12 be fo, To will be 2, and 18 20; of 21 is 7, and 20 is two times 7 and § of 7. of 18 how many? 12. of 18 are of what number? of 21 are of 21 are of how many sixths of 24? 14. § of 24 how many? 6 Explain. of 24 are 10 of what number? of 24 are 10 of how many fifths of 40? 15. § of 32 how many? § of 32 are 2 of how many fifths of 35? 16. of 63 how many? 4 of 63 are of 63 are g of how many ninths of 45? 17. of 56 how many? & of 56 are of how many 18. of 64 how many? 8 of 64 are of how many 19. of 72 how many? of 72 are of how many & 10 of 32 are of 56 are fourths of 28? of what number? Explain. SECTION X.-Practical Questions. 1. As 2 boys were counting their money, one said he had 20 cents. The other said, of your money is exactly of mine. How many cents had he? 4 of 20 & of what? 2. A merchant kept his silver money in one part of his till, and his cents in the other. Having found 18 dollars in the former, his clerk, who counted the cents, told him that of the dollars were equal in number to of the cents. How many cents were in the drawer? Prove. 17 3. A man being asked the age of his eldest that his youngest son was 6 years old, and that of the youngest was just of that of the eldest. the age of the eldest? Prove. son, replied, of the age What was 4. A man, being asked how many sheep he had, said, that he kept them in two pastures. In one pasture he had 24; and |