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498. If of the area of the District of Columbia is 14000 acres, what is the total area?

To find a given fractional part of a quantity.

EXAMPLES.

499. How many acres of land in of 750 acres?

5622

500. A man had $8000, and spent of the sum in building a house. What was the cost of the house?

501. I paid $4500 for a lot, and afterwards sold it for 17 of its cost. What did I obtain for the lot? 38.25

502. I sold of a piece of goods containing 39 yards. How many yards remained in the piece?

503. A lady had $75, and paid of her money for a bonnet, for dresses, and for books. How much money had she remaining? /4 504. A speculator bought $18500 worth of real estate, paid 18 of the purchase-money in cash, and gave his note for the remainder. What was the face of the note ?

505. A man owned

of an interest in a factory worth $12432, and sold of his share at its full value. What sum of money did he receive?385

506. A merchant invested $5600 in merchandise, and in selling it realized a profit of of his investment. What did he receive for the goods?

77

50%. A gentleman retired from business with a fortune of $75000 and invested of it in government bonds, of it in a country residence, and deposited the remainder in a bank. What was the amount of his deposit?

508. If bread weighs more than the flour from which it is made, how much bread can be obtained from 45 pounds of flour?

Of

REVIEW OF COMMON FRACTIONS.

INDUCTIVE EXERCISE.

1. At 60c. per lb., what is the cost of lb. of tea? Of lb.? Of lb.? Of lb.? lb.? Of 2 lb.? In obtaining each of the foregoing results, which of the two

given quantities has been taken as the multiplicand? The multiplier? What does each product denote? Hence, if the price of one lb. of tea [multiplicand] and any fractional part of a lb. [multiplier] be given, how may the cost of said fractional part of a lb. [product] be found? If the cost of any fractional part of a lb. [product] and the price of one pound [multiplicand] be given, how may said fractional part of a lb. [multiplier] be found? If the cost of any fractional part of a lb. [product] and said fractional part of a lb. [multiplier] be given, how may the price of one pound [multiplicand] be found?

In answering the following questions, state which terms of multiplication are given and required, and how the required term may be found:

2. At $ per yard, what is the cost of yd. of cashmere? Of yd.? Of § yd.? At $3 per lb., how much tea can be bought for $? For $? For $? At what price per gallon was wine bought if of a gallon cost $? If of a gallon cost $? If of a gallon cost $3? If a man earns $3 in of a day, what are his wages per day? How many yards in a mile if § of a mile contains 1100 yards?

[a] The multiplicand expresses the price, weight, measure, time, quanlity, distance, etc., of a WHOLE unit or quantity.

[b] The multiplier expresses any considered FRACTIONAL PART of the whole unit or quantity.

[c] The product expresses the price, weight, measure, time, quantity, distance, etc., of the considered fractional part of a whole unit or quantity.

EXAMPLES.

8

1. Without previous reduction, state whether $5 or $5 is the larger fractional expression, and why? $5 or $? $% or $? $7 or $3? 2. If 4 be added to both terms of of a gallon of oil, how much greater or less than 3 of a gallon will be the result; and why? If 4 had been similarly subtracted?

3. If both terms of of a pound of cheese be multiplied by 2, will its value be changed? Why not? If both terms had been divided by 2, would its value have been changed? Why not?

4. How many fifteenths of an ounce of sugar are equal to ounce, and why? To of an ounce? To of an ounce? To

ounce
? To of an ounce? To of an ounce? To 1 ounce?
ounces? To 4 ounces? To 53 ounces? To 63 ounces?

of an %

of an To 2

5. How many thirds of an hour in of an hour, and why? In of an hour? In 1 of an hour? In 3 hours? In 31 hours? In 431 hours? In 23 hours?

6. How many years in of a year, and why? In 2 of a year? In

of a year? In 32 of a year? In 15 of a year? In of a year? In 25 of a year? In of a year? In 35 of a year? In 50 of a year?

7. Why is any common multiple of the denominators of two or more fractions a common denominator of those fractions? Why is the least common multiple of the denominators of two or more fractions the . least common denominator to which those fractions can be reduced? Why must fractions have a common denominator before they can be compared, added, or subtracted?

NOTE TO THE TEACHER.-The pupil should be closely questioned upon the principles embraced in the following examples, to prevent purely mechanical methods of solution, which are soon forgotten. "Why?" from the teacher should follow every statement of the pupil.

8. I bought of a grocer 2 pounds of brown sugar, 3 pounds of granulated sugar, and 5 pounds of cut-loaf sugar. What was the total weight of the sugar purchased?

9. What is the sum of 4 of a day, 7 of a day, } of a day, and 1⁄2 of a day? 2

10. If the sum of three addends is of a year, and two of the addends are respectively of a year and of a year, what is the third addend? 11. From a quantity of sugar weighing 153 pounds, 91 pounds were sold. What was the weight of the remainder? >

12. What is the cost of 5 pounds of tea at $3 per pound?

13. What quantity of apples at $3 per bushel can be bought for $15? 14. If of a bushel of wheat cost $, what will be the cost of of a bushel? 447

15. If I sell of my farm to one man and of it to another, what part of my farm shall I have left?

16. What is the cost of 6 acres of land at $20 per acre?

17. A farmer sold 75 bushels of oats, which were of what he had before the sale. How many bushels had he remaining?

18. Jane bought § of a pound of candy and gave her sister of what she bought. How much had she remaining?

19. I bought 54 yards of cloth and sold of it to one customer and of the remainder to another. How many yards had I left?

20. A, B, and C counted their money and found that A had of the total amount, or $30, that B had of the total amount, and C the remainder. How much had B and C?

21. of a month is of what part of a month?

22.

23.

of a gallon is what part of of a gallon?

of a year is of what part of a year? / 24. of a mile is what part of 1 miles?

25. A merchant sold 50 gallons of coal oil and found that he had & of the original quantity left. How many gallons of oil had he remaining? 26. I bought 24 acres of land and divided it into building lots of of an acre each. How many building lots did I obtain? Ca

27. If a bag of coffee cost $183, what will be the cost of of a bag of the same coffee?

28. A tide-gauge 24 feet long has of its length in the mud, § of its length in the water, and the remainder in the air. How many feet of

the gauge are in the air?

29. If 5 yards of gingham cost $35, what will be the cost of 9 yards? 30. At $5 per yard, what is the cost of 24 yards of silk?

31. A farmer exchanged with a grocer 15 of a bushel of corn, worth 64 cents per bushel, for 6 pounds of sugar. What did the grocer charge per pound for the sugar?

in wheat, and the

32. If of a farm is in grass, in corn, remainder, or 16 acres, in oats, how many acres does the farm contain? 33. A boy had of a watermelon and gave of what he had to his sister. What part of the watermelon had he remaining?

34. I bought two books for $7.50, one costing as much as the other. What was the cost of each?

35. I bought a horse and buggy for $550, and the cost of the buggy was more than the cost of the horse. What was the cost of each? 36. I bought a watch and chain for $225, and the cost of the chain What did I pay for each?

was the cost of the watch.

37. At $3 per yard, how many yards of cloth can be bought for $5$? 38. How many cubic inches are in a cubic yard, if of a cubic yard contain 21207 cubic inches?

39. What is the cost of of a ton of iron at $1284 per ton?

40. If a furnace consume 1 of a ton of coal per month, in what time will it consume 3 tons?

41. If a cow eat 4 bushel of bran in one day, in what time will she eat 45 bushels ?

42. How many pounds of cheese at $3 per pound can be bought for

2

43. What amount of honey worth 30 cents per pound can be bought for 25 cents?

44. If I pay 81 cents for of a pound of sugar, how much of the same kind of sugar can I buy for 60 cents?

45. If a ship can sail 2681 miles in one day, how far can she sail in 3ğ days?

46. At the rate of 31 miles per hour, how long will a man require to walk 15 miles?

47. If 3 men can do a piece of work in of a day, how long will it take one man to do it?

48. I owed a man $53, and paid him with oats at $3 per bushel. How many bushels should he receive?

49. If a man spends of his weekly wages for board and for other } expenses, and his total expenditure is $8.40, what are his weekly wages?

50. How many vegetable beds of of an acre each can be obtained from 1 acres of land?

51. In a piece of calico were 40 yards, and its cost was $2.03. At what price per yard was it bought?

52. If there are 9 hours in of a day, how many hours are in 4 days?

53. If 3 tons of hay are worth $62, how much hay will be worth $45g?

54. I mixed three kinds of coffee, weighing respectively 25 pounds, 32 pounds, and 563 pounds, and sold the entire mixture for $217. What price per pound was received?

55. I bought a cow and paid in cash $48, which was of the purchase price. What was the cost of the cow?

56. If a legatee, entitled to of an estate, receives in full $4525, how much should the remaining legatee receive?

57. A partner who is entitled to of the profits of a firm receives $6250. How much should the remaining partners receive who are entitled to receive respectively and of the profits? 58. A grocer bought 5 bags of respectively 129 pounds, 134

coffee, the gross weight of each being pounds, 1313 pounds, 128 pounds,

and 1321 pounds. Allowing 1 pounds for the weight of each bag, what was the total net weight of the coffee?

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