6. Divide £460 5s. 10d. equally among 37 men. 7. If 15cwt. 3qr. 18lb. of flour be packed equally in 9 barrels, how much will each barrel contain ?

8. If it take 15 yards of cloth to make 6 coats, how much does it take to make 1 coat?

9. If an army consume 492bu. Opk. 6qt. of wheat 'n 42 days, how much does it consume in 1 day?

10. Divide 3qt. 1pt. of wine equally among 7 men. 11. If 30hhd. 13gal. 2qt. of cider will fill 18 casks of equal size, how much does each cask hold?

12. Divide 58m. 2fur. 32rd. into 8 equal distances. 13. Suppose a man is to travel 339m. 4fur. 20rd. in 6 days; what distance must he travel each day?

14. If a field containing 22A. 2R. 12rd. be divided into 4 equal lots, what will each lot contain?

15. Suppose a township, containing 17715 acres of land, should be divided into 80 equal farms, how many acres would each farm contain ?

16. Suppose a rail-way car to perform 4 trips in 5d. 16h. 9m., in what time does it perform 1 trip?

Questions to be answered Orally.

(1) Which of these numbers is a compound number,- £356, or £2 18s.? (2) Why is it called a compound number? (3) Recite the rule for addition of compound numbers. (4) Suppose the sum of a column of numbers expressing furlongs to be 37; what must be written under the column, and what must be carried to the next column ?- Why? (5) Recite the rule for subtraction of compound numbers. (6) Recite the rule for multiplication of compound numbers. (7) Recite the rule for division of compound numbers.

CHAP. VI.

FRACTIONS.

Fractions have been exemplified in page 44, and the mode of expressing them has been. defined in page 74. A proper fraction expresses a quantity, less than a unit. Therefore, the numerator of a proper fraction, must be less than the denominator: for example, .

An improper fraction expresses a quantity, equal to a unit, or greater than a unit: therefore its numerator must equal, or exceed its denominator: thus, ..

A compound fraction is a fraction of a fraction-a part of a part of a unit: for example, of .

NOTE. The written operations required in the several sections of this chapter, correspond with the mental operations involved in sections of the same number, in chapter VI, Oral Arithmetic. Learners will be enabled to perceive the written process to be adopted, by recurring to the oral examples.

SECTION 1.

1. What is the sum of and

and?

These fractions have a common denominator; that is, they all have the same denominator. We add the numerators only, and under the sum of the numerators, place the common denominator.

2. What is the sum of and and and ?

3. How much is, and, and and and? 4. A man paid of a dollar for breakfast, of a dollar for supper. What

dollar for dinner, and

part of a dollar did he spend?

of a

5. How much is and and and and 2? 6. A merchant sold 13 of a ship to one man, and to another. What part of the ship did he sell?

7. Add together and and and 14 and 12 ?

8. How much is

and and and ?

9. How much is 11 and and and ?

SECTION 2.

Write upon the slate, the several fractions required in the following examples.

1. If you divide a bushel of corn into 8 equal parts, and then put 6 of the parts into a sack, what fraction of a bushel will there be in the sack?

2. If an acre of land be divided into 20 equal lots, and 14 of the lots be enclosed by a fence, what fraction of an acre will there be in the enclosure?

3. Suppose any thing to be divided into 45 equal parts; what fraction will express 26 of the parts ¿

4. Suppose 1 dollar to be divided into 100 equal parts; what fraction will express one of the parts? 2 of the parts? 6 parts? 25 parts? 99 parts?

#

SECTION 3.

1. If be subtracted from, what will remain ? Both of these numerators express fifteenths; therefore we merely subtract one numerator from the other, and under the remainder, place the denominator.

2. If

5

be subtracted from, what will remain? 3. What is the difference between and &? 4. If be subtracted from what will remain? 5. What is the difference between and 29?

6. A farmer divided a ton of hay into 20 equal parts, and gave 14 parts to his cows, and the rest to his sheep. What fraction of a ton did the sheep get?

7. Subtract from 1,- that is, subtract from the number of eighths that there are in a whole one. 8. Subtract from a whole 1.

9. What is the difference between 12, and 1? 10. Subtract 46 from a whole 1.

11. A merchant owning a ship, sold man,

to another, and to another.

the ship did he still own?

of her to one What part of

59

of it, and

12. A boy having 1 dollar, paid away 'ost What fraction. of a dollar had he left? 13. Subtract 24 from a whole 1.

RELATIONS OF NUMBERS.

SECTION 4.

We frequently have occasion to view one number as a certain part of another number; and thus we notice the relation that exists between the two numbers. In order to state what part one number is, of another, we make the number which is the part a numerator, and the other number a denominator.

State the fractions, which answer to the following examples, upon the slate.

1. What part of 5 cents is 1 cent? is 3 cents? 2. What part of 10 is 1? is 2? is 5?

is 9?

3. What part of £1 or 20 shillings, is 1 shilling? is 6 shillings? is 14 shillings?

4. What part of 35 is I? is 8? is 11? is 34? 5. What part of $1 or 100 cents, is 1 cent? is 2 cents? is 9 cents? is 46 cents? is 94 cents?

6. What part of 6 pence is 1 penny? is 5 pence? 7. What part of 1 shilling is 1 penny? is 7 pence? 8. What part of 1 peck is 1 quart? is 7 quarts? 9. What part of 1 hogshead is 1 gallon? is 18 gals.? 10. If of a hogshead of wine be worth $1, what is of a hhd. worth? What is 1hhd. worth?

11. What part of 1 year is 1 day? is 10 days? is 40 days? is 100 days? is 275 days?

of a year?

12. If a man spend $1, in 35 of a year, how much will he spend in of a year? in How much will he spend in 1 year? 13. What part of 2016 is 1? is 84?

SECTION 5.

is 759?

1. Suppose of a ship to be worth $4703; what is the whole ship worth?

2. 4703 is of what number?

3. If of an acre of land produce 71 bushels of po tatoes, how many bushels will 1 acre produce?

4. 71 is of what number?

7. If 230 men will lay of a mile of rail-way a week, how many men will it take to lay 1 mile in a week? 8. 230 is of what number?

9. 44 is

of what number?

10. 6902 is of what number?

11. If of a pound of silver be worth $1.09, what is 1 pound of silver worth?

12. If a ship sail 17 miles in of a day, what dis tance would she sail in the whole day?

13. 204 is of what number?

14. If of a pipe of wine be worth $1.15, what is the whole pipe of wine worth?

15. Suppose of the sugar in a hogshead to weigh Icwt. 2qr. 12lb.; what does the whole weigh?

SECTION 6.

1. If 1 acre of land will produce 126 bushels of potatoes, how many bushels will of an acre produce? 2. What is of 126 ?

3. Suppose 38406 needles can be made from a bar of steel; how many can be made from of the bar? 4. What is of 38406?

5. If 1 dollar will pay for 316 quills, what number of quills will of a dollar pay for?

6. If you eat 1095 meals in 1 year, what number of meals do you eat in of a year?

7. What number of cubic inches are there in of a cubic foot? (See Cubic Measure, page 132.)

8. If 1 week's board cost $3.64, what does of a week's board cost?

9. Suppose a packet ship to be worth $17841.50; what is of her worth?

10. A man, having $205.12, paid of his money for a piece of land. What was the price of the land?

11. A man gave $2568 for a house, and then paid part as much for having it repaired. For how much must he sell the house, in order to lose nothing? 12. What is of 1800?

13. Suppose a piece of cloth to contain 60yd. 2qr.; how much cloth is there in of the piece?