41. What cost 83 bushels of apples, at $14 per bushel ? Ans. $11.

12. Bought 117 bushels of corn, at $13 per bushel, and sold of it for $1 per bushel, and the remainder at $17 per bushel; what is gained on the sale of the corn? Ans. $333. 43. What is the continued product of the following numbers: 27 873 Ans. 3712981' 21'

and

81?

-?

128

SECTION XX.

DIVISION OF VULGAR FRACTIONS.

CASE I.

To divide a fraction by an integer or whole number. 1. How many times will contain 8?

OPERATION.

To illustrate this question we will sup× Ans. pose of an orange to be divided equally among 8 persons. Now, if we divide of an orange into 8 equal parts, one of these parts will be equal to of a whole orange, but as there are to be divided among persons, each person will receive 5 times

8

Ans.

RULE. Multiply the whole number by the denominator of the fraction, and write the product under the numerator. Or, divide the numerator of the fraction by the whole number, if it can be done without a remainder, and write the quotient over the denominator.

To divide a whole number by a fraction.

1. How many times will 17 contain

?

89

3×4 == 1 Ans.

5. Divide of 72 by of 11.

Ans. 송금.

105×77-5452=6148 Ans.

7. Divide of 91 by of 87.

Ans. 7819.

23. Divide

of 15 by 7 of 22.

Ans.

675

24. Bought

of a coal-mine for $3675, and having sold

of my share, I gave of the remainder to a charitable society, and divided the residue among 7 poor persons; what was the share of each ? Ans. $50 for each poor person.

25. Of an estate valued at $ 5000, the widow receives, the oldest son of the remainder; the residue is equally divided among 7 daughters; what is the share of each daughter? Ans. $15819

SECTION XXI.

QUESTIONS TO BE PERFORMED BY ANALYSIS.

1. If of a bushel of corn cost 63 cents, what cost a bushel? what cost 15 bushels? Ans. $10.80.

Illustration. If 7 eighths of a bushel cost 63 cents, 1 eighth will cost 1 seventh of 63 cents = 9 cents; and 8 eighths will cost 8 times 9 cents 72 cents, and 15 bushels will cost 15 times 72 cents = $10.80.

2. If 47lb. of pepper cost $2.15, what cost one pound? what cost 30lb. ? Ans. $13.50. Illustration. In 47lb. there are 43lb. Then, if 43 ninths lb. cost $2,15, 1 ninth will cost 1 forty-third of $2.15 $0.05, and 9 ninths or 1lb. will cost 9 times $0.05 $0.45, and 30lb. will cost 30 times $0.45 = $13.50.

3. When $1728 are paid for 30

ton? what cost 717 tons?

=

tons of iron, what cost 1 Ans. $432.

4. When $432 are paid for 717 tons of iron, what quantity should be received for $1728 ?

Ans.

5. For 713 tons of iron there were paid $432; what sum will

it require to pay for 30

tons?

Ans.

6. For 30 tons of iron $1728 were paid; what quantity should be received for $432?

rye

Ans.

7. Gave 7 bushels of rye for a barrel of flour; how much will it then require to purchase 6 barrels of flour? Ans. 492 bushels. 8. Divide $1728 among 17 boys and 15 girls, and give each boy as much as a girl; what sum does each receive? Ans. each girl $ 6696; each boy $424. 9. If of a ton of hay cost $14.49, what cost 4 tons?

Ans.

10. If 4 tons of hay cost $82.50%, what part of a ton will $14.49 buy? Ans. 11. If $14.49 will buy of a ton of hay, how much hay can be obtained for $82.50%?

Ans.

12. When $82.503 are paid for 43 tons of hay, what will be the cost of of a ton?

Ans.

13. When 147 tons of copperas are sold for $ 500, what is the value of 1 ton? what is the value of 911 tons?

Ans.

14. When 91 tons of copperas are sold for $333.331, what is the value of 147 tons?

Ans.

15. Gave $333.334 for 911 tons of copperas; what quantity of copperas should be received for $500?

Ans.

16. For 147 tons of copperas $500 were paid; how much might be purchased for $333.33}?

Ans.

17. Purchased 973 gallons of molasses for $31.32; what cost 1 gallon? what cost 7633 gallons?

Ans.

18. Sold 763 gallons of molasses for $244.36; what should

I receive for 977 gallons?

Ans.

19. If $244.36 will buy 7633 gallons of molasses, what quantity can be obtained for $31.32?

Ans.

20. Gave 1975lb. of flax for 40 barrels of flour; how many pounds were given for 1 barrel? how many pounds would it require to buy 144 barrels ? Ans. 7110lb.

21. If 17 bushels of rye cost $15.75, what cost 1 bushel? what cost 9 bushels ? Ans. $8.56. 22. If 9 barrels of flour cost $ 504, what cost 1 barrel? what cost 873 barrels ? Ans. $49238. 23. If 13 boarders consume a barrel of pork in 78 days, how long would it last, if 7 more boarders were added to their number?

Ans. 50

days.

24. If a man by laboring 10 hours a day can, in 9 days, perform a certain piece of work, how many days would it require to do the same work, were he to labor 15 hours a day?

25. If a man, by laboring 15 hours a day, in 6 days can perform a certain piece of work, how many days would it require to do the same work by laboring 10 hours a day? Ans.

26. If a man, by laboring 10 hours a day, can in 9 days perform a certain piece of work, how many hours must he labor each day to perform the same work in 6 days? Ans.

27. Sold 17 bushels of corn for $54; what was received for 1 bushel? what should I have charged for 973 bushels ? Ans. $30398.

28. Bought 93 tons of hay at $197 per ton; for what must it be sold per cwt. to gain $7 on my bargain? Ans. $170.

29. If I sell hay at $12 per cwt., what should I give for 93 tons, that I may make $7 on my bargain? Ans. $329. 30. How many bushels of corn at $0.75 per bushel will it require to purchase 47 bushels of wheat at $23 per bushel ? Ans. 168bu.

31. If 15 cords of wood cost $ 57, what cost 1 cord? what

cost 197 cords?

32. If 193 cords of wood cost $76,6%, how

Ans. many cords may

Ans.

17£. 5s. 62d.

be obtained for $ 57,9? 33. At 7

34. When 172£. 15s. 02d. are paid for 47 yards of broadcloth, what is the value of 1 yard? Ans. 3£. 12s. 11328d. 35. If 1lb. of sugar cost of a dollar, what is the value of 43 lb. ? Ans. $23.613. 36. If 173lb. of sugar cost $211, what cost 50lb. ? Ans. $7.581019.

yards?

37. Bought 873 yards of broadcloth for $612; what was the value of 14 Ans. $102.90. 38. If of an acre of land cost $ 43.75, what cost 10 acres ? 39. When $500 are paid for 10 acres of land, how much might be obtained for $43.75?

Ans.

Ans.

40. If 9 hogsheads of sugar cost $71.87, what cost of hogshead ?

41. Paid $4.5633 for of a hogshead of sugar; what ought to be given for 9 hogsheads?

Ans.

42. If 19 men can grade a certain road in 111 days, how long would it require 47 men to perform the same labor?

43. When 47 men can grade a certain road in 444 days, how long would it require 19 men to perform the same labor? 44. If of a ton of hay cost $9.20, what cost 17 tons? 45. When $430.10 are paid for 17 tons of hay, what cost of a ton? Ans.

Ans.

46. If of a tub of butter cost $7.15, what cost 7 tubs ? 47. When $114.40 are paid for 7 tubs of butter, what cost of a tub? 48. If a man can mow a field of 71 acres in 8 days, when they are 11 hours long, how many days will it require to perform the same labor, when the days are 10 hours long?

Ans. 9

49. If 4 yards of cloth cost $19, what cost 25 yards?

days.

Ans. $118.75.

50. When $87.25 is paid for 15 barrels of flour, what cost 100.barrels ? Ans. $581.663.