SECTION 9.

1. If $686.56 should be divided equally among 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 3 of 30 days; therefore the army will consume 12 of 540 barrels.

19

30

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 wili 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 car ne 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 sof 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 12 of what number?

6. If

of it worth? 7. $23 is

of a day;

of a day? What

of a chest of tea be worth $23, what is
What is the whole of it worth?

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 24 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 $1238. What must have been the price of the farm?

20

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? 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?

(4)

SECTION 12.

REVIEW.

46

1. (§1) If you should pay of a dollar for a quire of paper, of a dollar for a slate, and 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 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?

6. (§ 6.) If a man's income be $199 a year, how 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 of a year, or 30 days?

365

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 hun dredweight of fish, what must be given for 1 cwt.?

FRACTIONS AND RELATIONS.

SECTION 13.

1. Suppose you can read 12 pages in an hour, now 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.

Any REMAINDER, which appears after the operation of division, is the numerator of a fraction, the divisor being the denominator; and this fraction forms a part of the quotient. Therefore, place the remainder and the divisor, as a fraction, to the right of the quotient.

2. At $2 per yard, how many yards of cloth can be bought for $49; that is, how many whole yards, and what part of another yard can be bought?

3. How many times 2 are there in 49?

4. How much flour can be bought for $639, at $5 per barrel; that is, how many barrels, and what part of another barrel can be bought?

5. In 639, how many times 5;- that is, how many fives, and what part of another 5, in 639?

6. How much salt can be bought for 87 shillings, at 4 shillings per bushel?

7. Suppose a rail-way car to run 16 miles an hour in how many hours will it run 350 miles ?

8. How many times 12 are there in 1049?

9. How many times 39 are there in 76800? 10. In 438 shillings, how many pounds are there? Observe that 1s. is of £1; therefore the remainder in this example, may be expressed as a fraction. 11. How many yards of cloth can be bought for 549 shillings, at £1 per yard?

12. Suppose a ton of hay to be equal in value to 34 bushels of oats; how many tons of hay must be given for 450 bushels of oats?

13. How many times 17 are there in 23 times 31? 14. How much rice, at $4 per cwt., must be given for 620 lb. of cheese, at 10 cents per pound?

SECTION 14.

CHANGE OF WHOLE NUMBERS TO FRACTIONS.

1 How many thirds are there in 14?

14

3

42

In 1 there are 3-thirds; therefore, there are 3 times thirds as whole ones.

as many

42-thirds. Ans. 43. in any whole number.

RULE. To change a whole number to an improper fraction, multiply the whole number by the denominator, and the product will be the numerator.

2. If you cut 17 sheets of paper into half-sheets, how many halves will there be?

3. How many fifths of a dollar are there $16? 4. In 31 pounds, how many sixths of a pound? 5. In 73 yards, how many eighths of a yard? 6. Change 641 to ninths. Change 641 to tenths. 7. If a stage run 1 mile in of an hour, how many miles would it run in 126 hours?

8. How many fourths are there in 152?

152 4

63-fourths.

In this example, we add the 3-fourths to the fourths produced by the multiplication of 15 by 4, and thus obtain 3.

Note. A whole number and a fraction expressed together, thus, 15, is called a mixed number."

9. How many eighths of a mile in 57 miles?
10. Change 861 to an improper fraction.

1

11. Change 4 to an improper fraction.

12. If of a dollar will pay for 1 gallon of beer, how much beer can be bought for $63?

13. If of a dollar will pay for 3 yards of ribbon, how many yards can be bought for $65?

SECTION 15.

CHANGE OF FRACTIONS TO WHOLE NUMBERS.

1. How many whole ones are there in 42 ?

3)42-thirds.

RULE.

14 wholes.

Since 3 make a whole 1, there

are as many whole ones in 42 as there are times 3 in 42.

To change an improper fraction to a whole number, divide the numerator by the denominator, and the quotient will be the whole number.

2. How many whole sheets of paper must be cut intc ualves, to make 48 of a sheet?