Εικόνες σελίδας
PDF

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

Explanation.—25 cents=4 of a dollar, and 11 ounces=}} of a pound; then the question is, what part of a dollar is # of 3 Ans. }}.

12. What number is equal to for of * * Ans. 2.

JNote 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 or of a lot of steel worth 1000 dollars, what is his part worth 2 Ans. $90}}.

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

Explanation.—One calendar month is or part of a year, and the answer is T's of 725=#60;3.

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 or of 645 !

Explanation.—In the last question we found or of 645 to be 43, and P. 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 numerator.

17. What number is equal to # of 24?

Explanation.—# of 24 is 3, and ; are 9, the anSWer.

18. A gentleman owns for of a farm worth $1637; what is the value of his part 2 Ans. 446 Fr. 19. A owns # of a ship, B # as much, and C for as much as B. What part of the ship does B own;– also, what is C’s part? 's Ar. Ans. 3. *: e 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 7 A's part is worth $3333}. Ans. & B's 44 $13334. - C’s (4. $363; r. 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 2 Ans. $45.

JNote 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.

[ocr errors]

23. A man sold 11 bushels of grain for 8; dollars; what did he receive per bushel?

Explanation.—or 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, dollars, what is it per bushel? Ans. HH of a dollar

25. If a man buy 13 gallons of gin for 94 dollars. what does he give per gallon 7 Ans. For 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 2 Ans. $1 ##. 28. If two acres of land are sold for 56}# dollars, what will # of one acre cost at the same rate - Ans. $5%;. 29. A man bought 3 horses for 376; dollars, and 5 sheep for or the value of 1 horse. What did the 5 sheep cost him; what is the cost of one sheep;also, what was the average price of the horses 2 Average price of the horses, $125;}#. Ans. {Cost of 5 sheep, $61%. Cost of 1 sheep, $1}; 30. What is , of or of 111691?, ? - Ans. 21914 g. 31. A merchant bought to of a stock of goods, valued at 10809 dollars, and sold 4 of his share at an advance of or of the cost. What did he receive for the part he sold 7 Ans. $219 row. 32. What part of a penny is or of a shilling?

and the answer #, or 4 of a penny. 'By multiplying the numerator by 12, the fraction expresses 12 fifteenths instead of r 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 or, therefore, # of a penny is equal to or of a shilling. Any fraction may be made a fraction of a less denomination without alter

[ocr errors]

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 or of a pound 2 20 shillings equal 1 pound, then for of 20 is the number required. Ans. ##, or 13%, or 14 shillings. 34. What part of a farthing is rors of a pound? Ans. ##. 35. What part of a minute, is 14; of an hour. Ans. For. 36. How many minutes in 4 of a day? Ans. 360. 37. How many pounds in 3 of a ton, neat weight? - Ans. 3334. 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. $2,284. 39. In # of an acre, how many square inches” Ans. 3763584. 40. What part of 8 is ; of 97

[ocr errors]

Explanation.—The scholar must not infer from the answer that 14 equal # of 10, for # of 10 are 4, and

the answer implies that 3 must be taken once and 3.

of it again, to make # of 10.

[ocr errors]

47. What part of 35 is 22 Ans. #. 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 hbd. did he sell ? Ans. #. 50. or of a ship's cargo valued at 7000 dollars, was thrown overboard in a storm. What was A's loss who owned or of the cargo? - Ans. $598}#}. 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 7 Ans. 4}# shares, or #r of the whole bridge. 52. What part of a shilling is is of a penny ? This question is the reverse of question 32d.

Explanation.—tor of a penny is or of T'a of a shilling, which is equal to row 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 7 Ans. Pr.

« ΠροηγούμενηΣυνέχεια »