11. If a man have coffee worth 25 cents a pound, what part of a dollar must he receive for 11 ounces?

Note 2.--When a part of a whole number is required, and the numerator of the fraction expressing that part, is one, we shall obtain the part demanded by dividing the whole number by the denominator.

13. If a man own of a lot of steel worth 1000 dollars, what is his part worth? Ans. $90

14. If a man's income be 725 dollars a year, what per month?

is it

Explanation.-One calendar month is part of a year, and the answer is of 725-$60,

15. If 645 dollars be divided into 15 equal parts, what will one of the parts be; that is, what is the 15th part of 645? Ans. 43.

16. What is of 645?

Explanation. In the last question we found of 645 to be 43, and must be twice as much, therefore if we divide the whole number by the denominator, and multiply the quotient by the numerator, we shall have a correct answer. But if we multiply the whole number by the numerator first, and then divide by the denominator, we shall obtain the same answer, since the dividend will be twice as large. The latter method is generally the most convenient, since we shall not so often have a fraction in the number to be multiplied. In dividing by the denominator, we take such a part of the whole number as would be expressed if the numerator were 1, and

multiplying by the numerator will give that part as many times as there are parts expressed by the nu

merator.

17. What number is equal to of 24?

Explanation. of 24 is 3, and are 9, the an

swer.

of a farm worth $1637; Ans. 446 TT

as much, and Cas

18. A gentleman owns what is the value of his part? 19. A owns of a ship, B much as B. What part of the ship does B own ;also, what is C's part?

SB's 15
Ans. C's 35

20. If the ship mentioned in the last question, is worth 10000 dollars, what is the value of A, B, and C's parts respectively?

A's part is worth $33331.

Ans. B's

C's

21. A gentleman divided 3 shares in a turnpike equally between 5 sons. If a share be worth 75 dollars, what is the value of each son's part?

Ans. $45.

Note 3.-If a mixed number be given, it may be reduced to an improper fraction, and worked in every respect as a proper fraction, and for the same reason.

22. What is 3 of 914?

3

911 and 3 of 133549, or 27%. 23. A man sold 11 bushels of grain for 82 dollars; what did he receive per bushel?

Explanation. of the money he received for the whole will be the price of one bushel.

Ans. of a dollar.

24. If 14 bushels of salt cost 9

per bushel?

dollars, what is it

Ans. 1 of a dollar.

25. If a man buy 13 gallons of gin for 94 dollars, what does he give per gallon?

Ans. of a dollar. 26. If a yard of broadcloth cost five and threeeighths dollars, what will one-third of a yard cost? Ans. $1.

27. A man gave 133 dollars for 8 sheep; what did he give a piece? Ans. $11. 28. If two acres of land are sold for 561 dollars, what will of one acre cost at the same rate?

29. A man bought 3 horses for 376 5 sheep for the value of 1 horse.

Ans. $53. dollars, and What did the 5

20

sheep cost him; what is the cost of one sheep;also, what was the average price of the horses? Average price of the horses, $12533.

Ans. Cost of 5 sheep,

30. What is of

Cost of 1 sheep,

$6,323.

31. A merchant bought

of a stock of goods, of his share at an

valued at 10809 dollars, and sold

advance of of the cost.

the part he sold ?

What did he receive for
Ans. $219.

32. What part of a penny is of a shilling?

- Explanation.- of a shilling is of 12 pence, and the answer, or of a penny. By multiplying the numerator by 12, the fraction expresses 12 fifteenths instead of fifteenth. Now if we still call it a fraction of a shilling, the real value of the fraction is increased 12 fold. But the object of the question is, not to alter the real value of the fraction, and as we have made it a greater part of an unit, we must make it a fraction of an unit as much smaller than a shilling, as the fraction is greater now than it was before. A penny is the 12th part of a shilling;

is 12 times as large as, therefore, of a penny is equal to of a shilling. Any fraction may be made a fraction of a less denomination without alter

ing its real value, by making it a fraction of as many units as it takes of the less denomination to equal 1 in that denomination in which the fraction is given, which is only multiplying the numerator by so many of the next less denomination.

33. What fraction of a shilling is equal to of a pound?

20 shillings equal 1 pound, then of 20 is the number required.

Ans., or 1, or 11 shillings. 34. What part of a farthing is rooo of a pound?

35. What part of a minute, is

36. How many minutes in

37. How many pounds in

Ans.
of an hour.
Ans.

of a day?

Ans. 360.

of a ton, neat weight? Ans. 3331.

38. If a merchant sell of a hundred of sugar, neat, for 1 cent an ounce, what does he receive for the quantity sold?

Explanation. The fraction reduced to the fraction of an ounce, will express the answer.

Ans. $2,28. 39. In of an acre, how many square inches?

40. What part of 8 is of 9?

Ans. 3763584.

of 8,

of 8

Explanation. of 9, and 3. 1 is and 3 must be of 8. We shall find whether be equal to of 9 by reducing both to a simple form: thus, of 9, and of 8=4, both equal to 3. The form of the compound fraction will be thus, of of. Ans. .

41. What part of 2 equals & of 3?

Ans. The whole.

42. What part of 3 equals of 10?

Ans. 1.

Explanation. The scholar must not infer from the answer that 11 equal of 10, for of 10 are 4, and the answer implies that 3 must be taken once and of it again, to make of 10.

48. A man sold 4 yards from a piece of cloth containing 38 yards. What part of the piece did he sell?

Ans.

49. A merchant bought a hogshead of molasses for 36 dollars, and sold enough of it to come to 20 dollars at the same rate. What part of the hhd. did he

sell?

Ans. . 50. of a ship's cargo valued at 7000 dollars, was thrown overboard in a storm. What was A's loss who owned of the cargo?

Ans. $598174.

51. In a certain bridge there are 50 shares, and are owned equally between 7 men. Now if A and B sell of their shares to an eighth person, H, how many shares, and also what proportion of the whole bridge will H own?

?

Ans. 41 shares, or 2 of the whole bridge. 52. What part of a shilling is of a penny This question is the reverse of question 32d.

Explanation. of a penny is of of a shilling, which is equal to of a shilling. Multiplying the denominator by as many of the less denomination as are required to equal 1 in the greater, changes the fraction to a fraction of the greater, without altering its value, because we lessen the fraction as much as the unit is increased.

53. What part of a foot is of an inch?

Ans.