SECTION 7.

1. Suppose that 12 men are to pay a debt of $420, in equal shares; what must 1 man pay?

Solution. 1 man is of 12 men; therefore 1 man must pay of $420. of 420 is

2. If a prize of $3936 be divided equally among 8 men, what part of the money will 1 man receive? How many dollars will 1 man receive?

3. 27 men own 864 acres of land together. What part of 864 acres does 1 man own? What number of acres does 1 man own?

4. If $135.45 will pay for 1hhd. of wine, what part of the money would pay for 1 gallon? What would be the price of 1 gallon?

5. If 170 acres of land produce 6630 bushels of corn, what part of 6630 bushels does 1 acre produce? How many bushels does 1 acre produce?

6. If 6 yards of broad-cloth be worth £11 11s. 9d., what part of the money is 1 yard worth? What is the value of 1 yard, in pounds, shillings, &c. ?

7. A black-smith paid $63 for 15 tons of coal. What did the coal cost him per ton?

SECTION 8.

1. A man purchased a farm for $5642, and paid of the price in cash, and gave his note for the remainder. How many dollars did he pay down?

Direction. First find of $5642, by dividing this sum by the denominator of the fraction; then find 4sevenths, by multiplying the quotient by the numerator. 2. What is of 1905?

3. If an acre of land will produce 14870 ears of corn, how many ears will of an acre produce?

4. What is of 19064?

5. Suppose an acre of land to be worth $48.16; what is the value of 2 of an acre of the same land?

6. If 1 dollar will pay for 270 quills, what number o quills will of a dollar pay for?

7. If 72 gallons of wine leak from a pipe in 1 day, how many gallons leak out in of a day?

8. Suppose a hogshead of sugar to be worth £20 4s 3d.; what is the value of of the sugar?

9. What is 4 of 4720 ?

In the several foregoing examples in this section, the learner has probably divided the given number by the denominator of the fraction, and multiplied the quotient by the numerator. It is, however, sometimes more convenient, to multiply the given number by the numerator, and divide the product by the denominator.

10. What is of 32? (Here are the two methods.)

We may see why these two methods of operation produce the same result, in the following illustration. Here is of 32 units arranged in one line, and of 3 times 32 units arranged in three lines. The number of units [] in the two arrangements is the same.

11. Find

2

of 60156, by each of the above methods.

12. Find of 10849, by the second method. 571 13. A laborer worked of a year, at 92 cents per What did his wages amount to?

day.

14. In of a pipe of wine, how many gallons? 15. What is 16 of $1491?

100

After multiplying by 6 and dividing by 100, reduce the remainder to cents, and divide the cents.

16. A borrowed of B, $758, promising to pay it in one year; and, in addition thereto, he agreed to pay a sum, equal to 100 of the sum borrowed, for the use of the money. How much must B receive?

17. What is 10 of $28?

SECTION 9.

1. If $686.56 should be divided equally among 8 men, what part of the money,-and what number of dollars and cents, would 3 men receive?

2. Suppose that $33 will pay for 198 yards of cloth; what part of 198 yards,-and how many yards can be bought for $14?

3. If 15 acres of land produce 283 bu. Opk. 4qt. of wheat, what part of this quantity,—and how many bushels will 9 acres produce?

4. If 540 barrels of flour will supply an army for 30 days, how many bushels will supply it for 19 days?

Solution. 19 days are 2 of 30 days; therefore the army will consume 12 of 540 barrels.

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5. If a man can build 256 rods of fence, in 60 days, how many rods can he build in 45 days?

6. If 72 tons of hemp cost $13680, what will 20 tons cost, at the same rate?

7. If it take a man 31 days to travel 1178 miles, how many miles can he travel in 25 days?

8. If 24 English watches are worth £108 18s., what is the value of 7 watches of the same kind?

SECTION 10.

1. If 16 men can fell 208 trees in a day, how many trees can 35 men fell in the same time?

2. What is 35 times of 208 ?

3. If 10 barrels of flour cost $59.30, how much will 33 barrels cost, at the same price per barrel?

4. What is 33 times of $59.30?

5. If 64 soldiers eat 448 pounds of beef in a week, how many pounds will 250 soldiers eat in a week? 6. What is 250 times of 448?

7. If 12 gallons of linseed oil be sold for $13.44, what should be the price of 52 gallons of linseed oil? 8. What is 52 times of $13.44 ?

9. If a man earn $91.70 in 7 months, how much can he earn in 2 years ?

10. If 48 pounds of feathers can be bought for $16, how many pounds can be bought for $25?

SECTION 11.

1. If of an acre of land will produce 28 bushels of potatoes, how many bushels will of an acre produce? How many bushels will 1 acre produce?

2. If of a hogshead of sugar be worth $22.50, what is of it worth? What is the whole worth?

3. $22.50 is of what sum of money ? 4. Suppose a ship to sail 105 miles in what distance will the ship sail in distance will she sail in the whole day?

5. 105 is of what number?

6. If

of a day; of a day? What

of a chest of tea be worth $23, what is

of it worth? What is the whole of it worth? 7. $23 is of what sum of

money ?

8. If of a bag of coffee be worth $38.46, what is the whole bag of coffee worth?

9. Suppose a rail-way car to run 198 miles, in of a day; what distance will it run in 1 day?

10. If 192 men will perform

of a certain piece of work in a week, what number of men will it take, to perform the whole of the work in a week?

11. 192 is of what number?

12. A man purchased a farm, and after he had paid of the price, he still owed $1288.

been the price of the farm?

What must have

13. A trader purchased a pipe of wine, and after of it had leaked out, he sold the remainder at $1.15 per gallon. How much did it amount to?

Questions to be answered Orally.

(1) What is meant by a common denominator of two or more fractions? (2) How do you add fractions, that have a common denominator? (3) How do you subtract one fraction from another; the two fractions having a common denominator? (4) When a certain fractional part of a number is known, how do you find the whole of the number? (5) When the whole of a number is known, how do you find any certain fractional part of it?

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SECTION 12.

REVIEW.

17

1. (§ 1.) If you should pay 1% of a dollar for a quire of paper, 10 of a dollar for a slate, and 10% for a book, what fraction of a dollar would you spend ?

2. (§2.) If a ton of hay be rolled up in 20 equal heaps, what fraction of a ton will 14 heaps be?

3. (§3.) Suppose a young man to lay out 16 of his money for a farm; what part of his money has he left? 4. (§4.) Suppose a school to be allowed 15 minutes for recess; what fraction of an hour is the recess?

5. (§ 5.) of an ounce, or 1dwt. of pure gold, is sufficient to gild a silver wire, 65 miles in length. What length of wire may be gilded with 1 ounce?

how

6. (§ 6.) If a man's income be $198 a year, much is his income for of a year, or 1 month? 7. (§7.) If $14 will pay for 70 books, what part of 70 books, and how many books, will $1 buy?

8. (§8.) If a man's income be $803 a year, how much is his income for 30 of a year, or 30 days?

9. (§ 9.) Suppose $93.66 to be paid for 14 yards of broad-cloth; what part of the money does 6 yards cost? How many dollars do 6 yards cost?

10. (§ 10.) If 11 barrels of flour are worth $59.07, what is the value of 25 barrels, at the same rate?

11. (§ 11.) If 18 shillings be given for of a hundredweight of fish, what must be given for 1 cwt. ?

FRACTIONS AND RELATIONS.

SECTION 13.

1. Suppose you can read 12 pages in an hour; how many hours will it take you to read 160 pages?

12)160(1312

12

40

36

4

We find, by division, it will take 13 hours, and still 4 pages remain to be read. Now, since it takes of an hour to read 1 page, it will take of an hour to read 4 pages. Ans. 13 hours.