19. 20. 21. FRACTIONS AND RELATIONS.

161

8. A tenant raised 28 bushels of corn, and gave his landlord of it. What improper fraction of a bushel, [how many thirds of a bushel,] did the landlord receive? How many bushels did the landlord receive?

9. of 28 is equal to what improper fraction? Then of 28 is equal to how many whole ones?

10. of 42 is equal to what improper fraction? Then of 42 is equal to what mixed number?

11. of 29 is equal to what improper fraction? Then of 29 is equal to what mixed number?

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12. If $721 should be divided equally among 6 men, how many sixths of a dollar would each man have? How many dollars would each man have?

SECTION 21.

1. Suppose a hogshead of brown sugar to be worth $115; what is the value of of the sugar?

2. What is of 115?

3. 5 men from Connecticut, bought 793 acres of land in Michigan, and divided it into 5 equal farms. How many acres were there in each farm?

To find of 793 acres, we divide 793 by 5. The quotient is 158 acres, and there is a remainder of 3 acres. To divide these 3 acres, we take of each acre for each farm. of 3 acres is of 1 acre.

4. What is of 1315? of 530? of 8201? 5. Suppose 12 men to share equally in a prize of $551.20; what is each man's share?

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6. What is of 55120? of 967 of 700? 7. The Young Ladies' Class Book, which consists of 408 pages of select reading lessons, has been read through by 25 scholars; each reading an equal portion. How many pages did 1 scholar read?

8. of £1 [ of 20s.] is how many shillings, and what fraction of a shilling?

9. Find of £7 in shillings—that is, reduce £7 to shillings, and find of the number of shillings.

10. of 5 shillings is how many pence?
11. How many grains in of 6 pennyweights?
12. of 3 ounces is how many drams?

13. 11 men divided 9 hogsheads of molasses equally among them. How many gallons had each man? 14. of 7 furlongs is how many rods?

15. of 6 square feet is how many square inches ? 16. How many seconds are there in of 10 hours? 17. A trader sold of a hogshead of wine at 37 cents for every of a gallon. What did it amount to?

SECTION 22.

1. If 34 barrels of flour be made from 147 bushels of wheat, how much wheat will make 9 barrels of flour? 2. What is 9 times 4 of 147?

3. If 8 yards of broad-cloth cost $38, what will 13 yards cost, at the same rate?

4. What is 13 times

of 38? 7 times of 654?5 times of 270? 21 times of 40975?

5. If it cost $1.25 to ride 20 miles in a stage, how much will it cost to ride 32 miles?

6. If $16 will pay for 85 pounds of butter, how many pounds will $25 pay for?

7. If 12 cords of wood cost $75, what will be the cost of 19 cords, at the same rate?

8. Suppose 21cwt. of flour to be worth the same as 65 bushels of salt; how many bushels of salt must be given in exchange for 18 cwt. of flour?

9. If 8 barrels will hold 19 bu. 3pk. 4qt. of corn, how much corn can be put into 15 barrels ?

SECTION 23.

1. When writing paper is sold at $5.42 per ream, what is the price of of a ream?

2. If of a ream of paper is worth $1.352, what is of a ream worth?

3. Suppose a hogshead of sugar to be worth $93; what is of it worth?

4. If of a hogshead of sugar is worth $13.284, what is of it worth?

5. What is of 3765? What is g of 3765?

6. How many gallons are there in of a pipe of wine? How many gallons in of a pipe?

In the following examples, it will be most convenient to multiply by the numerator of the fraction, before dividing by the denominator. See Second Method of

operation, exemplified in page 152.

7. The highest point of the Andes, is 21440 feet Mont Blanc, of the Alps, is as high. What is the height of Mont Blanc ?

8. Virginia contains 66000 square miles: Rhode Island is only as large. How many square miles are there in Rhode Island?

9. If a man's income be $1000 per year, what is his income for 9 months, or of a year ?

10. Suppose a man by constant industry can earn $1.50 per day; what will he earn in 10 days, allowing him to rest of the time?

11. How much must be paid for 13 of a ton of Russia hemp, when the price is $210 per ton?

12. A man having 4 miles to go, rode of the way, and walked the remainder. How many rods did he walk? 13. Suppose 45000 pounds of iron to be sufficient to lay the track on 1 mile of rail-way; how many pounds of iron are required to lay the track on 17 mile?

14. How much is 4500 plus of 4500 ?

15. Suppose a rail-way car to run 350 miles a day; what distance will it run in 52 days?

16. How much is 5 much is 5 times 350 and 17. How much is 6

times 350?— That is, how of another time 350?

times 91? 84 times 146?

31⁄2 times 244? 12 times 379? 167 times 978?

PERCENTAGE.

The term, per cent., is an abbreviation of per centum, and signifies, by the hundred. ber, is of that number; 2 cent. is 13; 4 per cent. is

1 per cent. of any numper cent. is Too 3 per; and so on.

18. What is 5 per cent. of 360 dollars? 360

5
$18.00

Since 5 per cent. is 15 we multiply by 5, and divide by 100. To divide by 100, we merely point off two figures from the right, as taught in page 116.

19. What is 1 per cent. of 100? 2 per cent. of 100? 20. What is 2 per cent. or 13 of 350 dollars?

2

21. A merchant, who has $3875 deposited in the bank, wishes to draw out 4 per cent. of his deposit. How many dollars must he draw?

6

22. What is 6 per cent. or 180 of 4250 dollars?

23. What is 6 per cent. of $92.50, or 9250 cents? 24. What is 4 per cent. of $132.75?

25. A merchant having 2513 gallons of wine on hand, lost 1 per cent. of the whole, by leekage from the casks. How many gallons did he lose?

26. Find 6 per cent. of 128 dollars.

128

6

$7.68

68

After multiplying and dividing, our quotient is $700. Now, since of a dollar is 1 cent, 68 of a dollar is 68 cents: therefore the answer is $7.68.

100

27. Find 7 per cent. of 2517 dollars.

28. Find 18 per cent. of 20 dollars.

29. What is 4 per cent. of $70.14, or 7014 cents? In this example, after multiplying by 4, and dividing

by 100, there is a remainder of 56.

And since the

quotient is cents, this remainder is 5% of a cent.

6

100

30. What is 9 per cent. of $470.46 ?

31. What is 55 per cent. of $964.07 ?

32. A and B have $500 apiece. If A should give B per cent. of his cash, what would each then have?

33. What is of 1 per cent. of 62 dollars?

34. What is 4 35. What is

36. What is 5

per cent. of 62 dollars?

per cent. of 246 dollars?

per cent. of 246 dollars?

37. A merchant paid $491 for a quantity of salt: for how much must he sell it, to gain 9 per cent.?

38. A trader paid $230 for a piece of cloth, containing 46 yards, and sold it so as to lose 4 per cent. At how much did he sell it per yard?

39. If I pay $525 for 90 barrels of flour, at what price per barrel must I sell it, to gain 7 per cent.?

40. Suppose a merchant to pay $85 per ton for 6 tons of iron; at what price must he sell it per hundred weight, in order to gain 12 per cent.?

41. A merchant failed in business, and was able to pay his creditors only 65 per cent. of their demands. What did he pay on a demand of $534 ?

INTEREST.

Interest is money paid for the use of money that has been owed. For instance, suppose that A lends B $100 for one year, and at the end of the year, B pays, not only the $100, but also pays $6 for the use of the $100: in this case, $6 is the interest.

The money for which interest is paid, is called the Principal. The sum per cent. paid for one year's interest, is called the Rate. The principal and interest added together, are called the Amount.

RULE FOR COMPUTING INTEREST Multiply the principal by the rate per cent., and divide the product by 100: the quotient will be the interest for 1 year.

42. What is the interest of $100, for 1 year, at 5 per cent.? What is the amount?

43. What is the interest of $1 or 100 cents, for 1 year, at 5 per cent.? What is the amount?

44. What is the interest of $354, at 6 per cent. for 1 year for 2 years? for 3 years ? for 4 years? What is the amount for 4 years?

45. What is the interest of $40.50, for 4 years, at 6 per cent.? What is the amount ?

46. What is the interest of $18, for 3 years, at 7 per cent.? What is the amount?

47. What will $8410 amount to in 15 years; the rate of interest being 4 per cent.?

48. What is the interest of $6470, for 3 per cent.? What is the amount?

years, at 51

of

When interest is to be computed for any number months, First find the interest for 1 year; then take 12 of a year's interest for 1 month; or for 2 months, 1 or, for 3 months; and so on.

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49. What is the interest of $35, for one month, at 6 per cent. per annum? What is the amount ?