TROY WEIGHT.

11. Multiply 14 lb. Ooz. Sdwt. 11gr. by 7. 12. What is the weight of 11 Federal dollars; the weight of 1 dollar being 17dwt. 8gr.?

AVOIRDUPOIS WEIGHT.

13. Multiply 7T. 12cwt. 1qr. 14lb. by 8.

14. What is the weight of 25 hogsheads of fish; each hogshead containing 5cwt. 3qr. 15lb. ?

CLOTH MEASURE.

15. Multiply 29yd. 2qt. 3na. by 9.

16. How many yards of broad-cloth are there in 35 pieces; each piece containing 47yd. 1qr. 2na?

DRY MEASURE.

17. Multiply 33bu. 3pk. 6qt. 1pt. by 5.

18. How many bushels of corn are there in 18 bags, each bag containing 2bu. 2pk. 5qt. 1pt. ?

WINE MEASURE.

19. Multiply 1p. 1hhd. 52gal. 2qt. 1pt. by 4.

20. How many hogsheads of wine are there in 13 casks; each cask containing 49gal. 3qt.?

BEER MEASURE.

21. Multiply 6 bl. 1kil. Ofir. 6gal. 2qt. 1pt. by 7. 22. If 1 man drink 2gal. 3qt. Ipt. of beer in a week, how much will 38 men drink in a week?

LONG MEASURE.

23. Multiply 5lea. 2m. 6fur. 36rd. by 8.

24. If a man travel 55m. 5fur. 17rd. a day, for 18 days, how many miles will he have travelled.

SQUARE MEASURE.

25. Multiply 36A. 3R. 27rd. by 6.

26. How many square yards are there in 14 rolls of carpeting; each roll containing 52sq. yd. 3sq. ft?

CUBIC MEASURE.

27. Multiply 1T. 34ft. 1200 in. of round timber by 3. 28. There are 4 piles of wood; each containing 3C. 6ft.w. 12c.ft. How much wood is there in all.

TIME.

29. Multiply 4Y. 255d. 16h. by 9.

30. If a ship alter her latitude 1 degree in sailing 16h 40m., in what time will she alter it 15 degrees?

SECTION 12.

COMPOUND DIVISION.

1. If £2047 13s. 9d. be divided equally among 6 men, how much will each man receive?

£ $. d. 6)2047 13 9

341 5 7 2qr.

We divide the pounds, and there remains £1. This £1 we reduce to shillings, and unite it with the 13s. making 33s. We divide the 33s., reduce the remainder to pence, and proceed as before.

2. If 19s. 11d. 3qr. be divided equally among 3 men, how much will each man receive?

3. Divide £16 14s. 10d. 3qr. equally among 5 men 4. Divide £3 Os. 8d. equally among 7 men.

5. Divide £59 18s. 4d. equally among 25 men.

£

d. £ s. S.

d.

This operation is in long division. We first divide

25)59 18 4 (2 7 11 the pounds: the quotient is

50

9

20

25)198(7s. 175

23

12

25)280(11d. 25

30

25

5d. remaining.

£2, and the remainder, £9. We then reduce the £9 to shillings, adding in the 18s., and divide this sum [198s.] as before: the quotient is 7s. and the remainder, 23s. We then reduce the 23s. to pence, adding in the 4d., and divide this sum as before. 5d. remain undivided. Observe, that, in every instance, the quotient and remainder are of the same denomination with the dividend.

RULE FOR COMPOUND DIVISION. Divide each denomination separately, beginning with the highest. Whenever a remainder occurs, reduce it to the next lower denomination, add it to the number expressed in the lower denomination, and divide it therewith.

N

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.

1

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, 3 of 1.

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 12 and 12 and 11⁄2?

12

12

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 1 and 3 and 1? 3. How much is and and and and 4. A man paid of a dollar for breakfast, dollar for dinner, and of a dollar for supper.

3

25

?

5

of a

What

and 2

?

part of a dollar did he spend?
5. How much is and and and
6. A merchant sold 12 of a ship to one man, and 18 to
another. What part of the ship did he sell?

7. Add together 44 and 4 and 4 and 12 and 12 ?
8. How much is and and and ?

16

40

9. How much is 14 and 11 and 1and?

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 equa. 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?

1. If

2. If

}}

1/5

SECTION 3.

be subtracted from 1, 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.

be subtracted from, what will remain? 3. What is the difference between 5 and 8? 4. If be subtracted from 16 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.

75

9. What is the difference between 724, and 1? 10. Subtract 246 from a whole 1.

11. A merchant owning a ship, sold of her to one man, 34 to another, and to another. What part of the ship did he still own?

12. A boy having 1 dollar, paid away 5% of it, and ost 10 What fraction. of a dollar had he left? 13. Subtract 244 from a whole 1.