4. Divide $59'387 by 8.

OPERATION.

8)59'387

Quotient, 7'4233, that is, 7 dollars, 42 cents, 3 mills, and of another mill. The is the remainder, after the last division, written over the divisor, and expresses such fractional part of another mill. For all purposes of business, it will be sufficiently exact to carry the quotient only to mills, as the parts of a mill are of so little value as to be disregarded. Sometimes the sign of addition (+) is annexed, to show that there is a remainder, thus, $7'423 +.

RULE.

From the foregoing examples, it appears, that division of federal money does not differ from division of simple numbers. The quotient will be the answer in the lowest denomination in the given sum, which may then be reduced to dollars.

Note. If the sum to be divided contain only dollars, or dollars and cents, it may be reduced to mills, by annexing ciphers before dividing; or, we may first divide, annexing ciphers to the remainder, if there shall be any, till it shall be reduced to mills, and the result will be the same.

EXAMPLES FOR PRACTICE.

5. If I pay $46875 for 750 pounds of wool, what is the value of 1 pound? Ans. $0'625; or thus, $0'621. 6. If a piece of cloth, measuring 125 yards, cost $181'25, what is that a yard? Ans. 1'45. 7. If 536 quintals of fish cost $ 1913'52, how much is that a quintal ? Ans. $3'57. 8. Bought a farm, containing 84 acres, for $3213; what did it cost me per acre? Ans. $38'25. 9. At $954 for 3816 yards of flannel, what is that a yard? Ans. $0'25. 10. Bought 72 pounds of raisins for $8; what was that a pound? how much?

Ans. $0'111; or, $0'111+. 11. Divide $12 into 200 equal parts; how much is one of the parts? 200 how much? Ans. $0'006.

how much? 1980 = how much? equal parts; how much will 215 how much?

12. Divide $30 by 750.0 13. Divide $60 by 1200. 14. Divide $215 into 86 one of the parts be?

15. Divide $176 equally among 250 men; how much will each man receive? how much?

SUPPLEMENT TO FEDERAL MONEY.

QUESTIONS.

2.

by different denomina

1. What is understood by simple numbers? by compound numbers? 3. tions? 4. What is federal money? 5. What are the denominations used in federal money? 6. How are dollars distinguished from cents? 7: Why are two places assigned for cents, while only one place is assigned for mills? 8. To what does the relative value of mills, cents, and dollars correspond? 9. How are mills reduced to dollars? 10. -to cents? 11. Why? 12. How are dollars reduced to cents? 13. to mills? 14. Why? 15. How is the addition of federal money performed? subtraction? 17.

multiplication?

18.

16.

divi

sion ? 19. Of what name is the product in multiplication, and the quotient in division? 20. In case dollars only are given to be divided, what is to be done? 21. When is one number or quantity said to be an aliquot part of another? 22. What are some of the aliquot parts of a dollar? 23. When the price is an aliquot part of a dollar, how may the cost be found? 24. What is this manner of operating called? 25. How do you find the cost of articles, sold by

the 100 or 1000?

EXERCISES.

1. Bought 23 firkins of butter, each containing 42 pounds, for 16 cents a pound; what would that be a firkin, and how much for the whole? Ans. $159'39 for the whole.

2. A man killed a beef, which he sold as follows, viz. the hind quarters, weighing 129 pounds each, for 5 cents a pound; the fore quarters, one weighing 123 pounds, and the other 125 pounds, for 4 cents a pound; the hide and tallow, weighing 163 pounds, for 7 cents a pound; to what did the whole amount? Ans. $35'47.

3. A farmer bought 25 pounds of clover seed at 11 cents a pound, 3 pecks of herds grass seed for $2'25, a barrel of flour for $650, 13 pounds of sugar at 124 cents a pound; for which he paid 3 cheeses, each weighing 27 pounds, at 8 cents a pound, and 5 barrels of cider at $1'25 a barrel. The balance between the articles bought and sold is 1 cent is it for, or against the farmer?

4. A man dies, leaving an estate of $71600; there are demands against the estate, amounting to $39876'74; the residue is to be divided between 7 sons; what will each one receive?

5. How much coffee, at 25 cents a pound, may be had for 100 bushels of rye, at 87 cents a bushel? Ans. 348 pounds. 6. At 12 cents a pound, what must be paid for 3 boxes of sugar, each containing 126 pounds?

7. If 650 men receive $8675 each, what will they all receive?

8. A merchant sold 275 pounds of iron, at 64 cents a pound, and took his pay in oats, at $0'50 a bushel; how many bushels did he receive?

9. How many yards of cloth, at $4'66 a yard, must be given for 18 barrels of flour, at $9'32 a barrel ?

10. What is the price of three pieces of cloth, the first containing 16 yards, at $375 a yard; the second, 21 yards, at $450 a yard; and the third, 35 yards, at $ 5'12 a yard?

32. It is usual, when goods are sold, for the seller to deliver to the buyer, with the goods, a bill of the articles and their prices, with the amount cast up. Such bills are sometimes called bills of parcels.

Mr. Abel Atlas

Boston, January 6, 1827.

Bought of Benj. Burdett

12 yards figured Satin, at $2'50 a yard, ... sprigged Tabby, ...

8

$31'25

1'25

10'00

Note. M. stands for the Latin mille, which signifies 1000, and C. for the Latin word centum, which signifies 100.

REDUCTION.

¶ 33. We have seen, that, in the United States, money is reckoned in dollars, cents, and mills. In England, it is reckoned in pounds, shillings, pence, and farthings, called denominations of money. Time is reckoned in years, months, weeks, days, hours, minutes, and seconds, called denominations of time. Distance is reckoned in miles, rods, feet, and inches, called denominations of measure, &c.

The relative value of these denominations is exhibited in tables, which the pupil must commit to memory.

ENGLISH MONEY.

The denominations are pounds, shillings, pence, and farthings.

TABLE.

4 farthings (qrs.) make 1 penny, marked d.

12 pence

20 shillings

1 shilling,

S.

£.

Note. Farthings are often written as the fraction of a penny; thus, 1 farthing is written d., 2 farthings,+ d., 3 farthings, d.

How many pence in 4 farin 8 farthings?

How many farthings in 1
in 2 pence? things?

in 6- -in 12 farthings? — in 24 farthings?

penny?

in 3 pence?

pence?
in 9 pence?

in 8 pence?

in 12 pence? things?

in 32 farin 36 farthings?

in 1 shilling? — in 2 in 48 qrs.? How many

shillings?

shillings in 48 qrs.?

96 qrs.?

in

How many shillings in 24

in pence?

in in 48 d. ?

in 36 d. ?

in 72 d. ?

It has already been remarked, that the changing of one kind, or denomination, into another kind, or denomination, without altering their value, is called Reduction. (T 27.) Thus, when we change shillings into pounds, or pounds into shillings, we are said to reduce them. From the foregoing examples, it is evident, that, when we reduce a denomination of greater value into a denomination of less value, the reduction is performed by multiplication; and it is then call ed Reduction Descending. But when we reduce a denomination of less value into one of greater value, the reduction is performed by division; it is then called Reduction Ascending. Thus, to reduce pounds to shillings, it is plain, we must multiply by 20. And again, to reduce shillings to pounds, we must divide by 20. It follows, therefore, that reduction descending and ascending reciprocally prove each other.

t