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many times 4 ?

SECTION V. - Fractions of Numbers exceeding Unity,

continued. 1. THREE times 4 are how many times 6? How many

times 2 ?

2. Four times 4 are how many times 2? 8 ? 5? Ans. Three times 5 and į of five. How many times 7 ? Ans. Two times 7 and 4 of 7. 3. Three times 5 and of 5 are how many times 7 ? How

6 ? 8 ? 14 ? 9 ? 17 ? 4. Six times 9 and ; of 9 are how many times 12 ? 15 ? 8? 4 ? 26 ?

5. Nineteen times 6 and of 6 are how many times 4? 7? 9 ? 20 ? 35 ? 17 ? 18?

6. Eighteen times 4 and 1 of 4 are how many times 12 ? 14 ? 8 ? 5 ? 8 ? 16 ?

7. Twenty-five times 8 and 3 of 8 are how many times 7? 24 ? 42 ? 36 ? 44 ? 52 ?

8. Twenty-nine times 7 and 2 of 7 are how many times 9 ? 14? 25 ? 30 ? 57 ? 34 ?

9. Forty-nine times 4 and 4 of 4 are how many times 7 ? 15 ? 24 ? 35 ? 42 ?

10. Fourteen times 5 and of 5 are how many times 4 ? 15 ? 7 ? 25 ? 32 ? 6? 8 ? 5 ?

11. Seventeen times 3 and of 3 are how many times 8 ? 6 ? 9 ? 15 ? 25 ? 19 ? 11 ?

12. Thirteen times 9 and of 9 are how many times 8 ? 10 ? 7 ? 12 ? 15 ? 18 ? 32 ?

13. Twelve times 7 and of 7 how many times 9 ? 8? 15 ? 24? 15 ? 10 ? 25 ?

14. Twenty-four times 8 and 3 of 8 how many times 7 ? 9? 12 ? 10 ? 50? 26 ?

SECTION VI. — Practical Questions. 1. Bought 9 bushels and 4 of a bushel of salt, at 7 shillings a bushel ; how many dollars is that, at 6 shillings to the dollar?

2. Bought 83 yards of cloth at 4 dollars a yard, and paid for it with flour at 5 dollars a barrel; how much flour did it take ?

3. A man sold 34; barrels of four, 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 243 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 63 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 826 dollars per head, and paid for them in flour, at 6 dollars. a barrel ; how much flour bad he to pay ?

7. If shad cost 8 dollars a barrel, what will 6z 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 ?

9. If salmon cost 86 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 6j dollars

per hundred weight, and paid for it in cranberries, at 11 dollars

per barrel ; how many barrels were required ?

SECTION VII. - Fractions of Numbers exceeding Unity,

continued. 1. Two is į of what number ? 4 is 2 times what number?

2. Three is ] of what number? of what number ? ? Ib? 25? 3.2

? 3. Four is of what number ? f of what number? ?? 1?? 4. Five is of what number ? ? 36? ? ?? 5. Nine is of what number ? ? ? ? ? 6. Nine is 3 times what number? 7. 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 į of that number? If į of a number be 2, what is that number? Then 4 is of what?

12. If 6 be of some number, what is of the same number? 2 is į of what number? Then 6 is of what ?

13. If 8 be of some number, what is 7 of that number? 2 is 7 of what number? Then 8 is 6 of what?

14. 6 is of what number? 15. 8 is of what number? 16. 18 is of what number? 17. 25 is ģ of what number?

18. 32 is 4 of what number? Of how many times ten ? Ans. Of 5 times 10 and 2 of 10.

19. 56 is į of what number? Of how many times 4 ?

20. 42 is of what number? Of how many times 9 ? Ans. Of 6 times 9 and ß of 9.

21, 28 is of what number? Of how many times 10 ? 9?

6?

22. 21 is of how many times 10 ? 15 ? 14? 26 ? 7?

9?

23. 50 is 10 of how many times 12 ? 19 ? 6? 8? 4? 5 ?

24. 42 is 7 of how many times 5 ? 12 ? 7? 4? 25. 36 is şof how many times 10? 5? 12 ? 8? 26. 72 is of how many times 12 ? 7 ? 9? 6? 27. 18 is of how many times 11? 10 ? 12? 16 ? 8? 28. 15 is ž of how many times 8 ? 15 ? 6? 8? 4? 29. 21 is 1 of how many times 10 ? 12 ? 6? 8 ? 5 ? 30. 45 is & of how many times 6 ? 21 ? 14 ? 5? 12 ? 31. 80 is jg of how many times 10 ? 12 ? 8 ? 7 ? 32. 56 is of how many times 20 ? 10 ? 5? 6? 33. 60 is 1 of how many times 10 ? 15 ? 8 ? 7 ? 34. 55 is 11 of how many times 8 ? 14 ? 15 ? 9 ? 35. 52 is of how many times 12 ? 7? 20 ?, 30 ? 36. 12 is ii of how many times 7 ? 9? 8? 6? 15 ? 37. 14 is of how many times 8 ? 10 ? 20 ? 25 ? 38. 48 is of how many times 11 ? 5 ? 9 ? 4 ? 39. 32 is of how many times 4 ? 6 ? 9? 11 ? 40. 27 is of how many times 11 ? 12? 15 ? 6?

SECTION VIII. - Practical Questions. 1. IF 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 4 of a bushel of wheat cost 36 cents, what cost 1 bushel ? 5 bushels ? Why?

4. If į 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 s 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, s learn arithmetic, j geography, š geometry, and 12 learn to write. How many attend the school ? and how many attend to each study?

13. In a certain congregation one Sunday, I were in the singers' gallery, iż 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 ?

15. A man sold a cow for 21 dollars, which was only yo of 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 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. á of 24 how many? of 24 are 10 of what number?

of 24 are 4 of how many times 5 ? How do you know? Explain the process. Form of the solution. - of 24 is 4; therefore, á are 20; if 20 are 10, 7 is 2, and 7 14; which is 2 times 5 and of 5.

2. 1 of 28 how many ? of 28 are of what number? ļof 28 are of how many times 7? Explain the process.

3. of 30 how many ? of 30 are of what number? of 30 are of how many times 8 ? Explain. 4. 5 of 32 how many ? of 32 are of what number? of 32 are of how many times 5? Explain. 5. of 36 how many ? $ of 36 are of what number? of 36 are 8 of how many times 6? Explain.

6. of 40 how many ? of 40 are of what number? 4 of 40 are of how many times 8? Explain.

7. 5 of 45 how many ? 5 of 45 are of what number? of 45 are of how many times 7 ? Explain. 8. of 48 how many ? ( of 48 are o of what number ? of 48 are 10 of how many times 3 ? Explain.

9. of 63 how many ? 4 of 63 are of what number? 4 of 63 are of how many times 8 ? Explain.

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