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SECTION 12.

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

We divide the pounds, and £ d.

there remains £1. This £ 1 6,2047 13 9

we reduce to shillings, and

unite it with the 13s. making 341 57 2qr.

33s. We divide the 33s., duce the remainder to pence,

and proceed as before. 2. If 19s. 11d. 3qr. be divided equally among

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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.

This operation is in long £ d. £ d.

division. We first divide 25)59 18 4 (2 7 11

the pounds: the quotient is 50

£2, and the remainder, £9 9

We then reduce the £9 to 20

shillings, adding in the 185., 25)198(75.

and divide this sum (1985.) 175

as before: the quotient is

7s. and the remainder, 23s. 23

We then reduce the 23s. to 12

pence, adding in the 4d., and 25)280(11d.

divide this sum

as before. 25

5d. remain undivided. Ob30

serve, that, in every instance, 25

the quotient and remainder 5d. remaining

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 ower denomination, and divide it therewith.

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6. Divide £460 5s. 10d. equally among 37 men.

7. If 15cwt. 3qr. 181b. 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 in 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 equa! 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. ir. 6 days; what distance must he travel each day?

14. If a field containing 22A. 2R. 12rd. he 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 nun. bers. (6) Recite the rule for multiplication of compound numbers. (7) Recite the rule for divisjon of compound m bers.

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Fractions have been exemplified in page 44, and the aiode 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, i ofą.

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NOTE. The written operations required in the several sections of this chapter, correspond with the mental operations involved in sections of the same nunber, 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 1 and is 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 į and and į? 3. How much is 1 and 1 and in and is and ?

4. A man paid 15 of a dollar for breakfast, of a dollar for dinner, and † of a dollar for supper. What part of a dollar did he spend?

5. How much is 25 and 5 and and is and ?

6. A merchant sold Le of a ship to one man, ana to another. What part of the ship did he sell ?

7. Add together and 4 and 1 and 1 and 4* ?
8. How much is and and į and ģ?
9. How much is iia and 11 and 1 and ?

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SECTION 2. Write npon 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 ?

SECTION 3. 1. If be subtracted fron: 1 , what will remain ?

Both of these numerators express fifteenths; therefore we merely subtract one

numerator from the other, and under the 15 remainder, place the denominator. 2. If 4 be subtracted from , what will remain? 3.. What is the difference between and ? 4. If I be subtracted from what will remain ? 5. What is the difference between and ?

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 we number of eighths that there are in a whole one.

8. Subtract Ig from a whole 1.
9. What is the difference between 124, and 1?
10. Subtract 346 from a whole 1.

11. A merchant owning a ship, sold of her to one man, 4 to another, and to another. What part of the ship did he still own?

12. A hoy having 1 dollar, paid away o% of it, and lost 100. What fraction of a dollar had he left ?

13. Subtract * from a whole 1.

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15

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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 nuniber 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 ? 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 i shilling is I penny? is 7 pence? 8. What part of i peck is 1 quart? is 7 quarts ? 9. What part of 1 hogshead is 1 gallon? is 18 gals. ?

10. If as of a hogshead of wine he worth $1, what is d'y of a hhd. worth? What is 1bhd. worth?

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

12. If a man spend $1, in 3.5 of a year, how much will he spend in of a year? in 28 of a year? How much will he spend in i year? 13. What part of 2016 is 1? is 84 ? is 759 ?

SECTION 5. 1. Suppose of a ship to be worth $4703; what is the whole ship worth?

2. 4703 is į of what number?

3. If } of an acre of land produce 71 bushels of pu atoes, how many bushels will 1 acre produce ?

4. 71 is } of what number?
5 875 is of what number?
6. 1900 is of what number?

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