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3. What is the neat weight and value of 3 boxes of figs, weighing 25 pounds each, with allowance of 4 per cent. tare, and per cent. salvage, at 11 cents per pound?

Ans. neat71 lbs.; value, $7.81.

CASE III. When the tare is so much per barrel, box, chest, &c., either with or without the allowance for draft or scalage.

RULE. If any

allowance be made for draft or scalage, cast and deduct it as before directed.

Multiply the number of barrels, boxes, chests, &c., by the tare of one; subtract this product from what remained after the scalage was deducted; but when no scalage is allowed, deduct the tare from the whole gross weight: the remainder will be the neat weight.

Ecamples. 1. What is the neat weight and value of twenty chests of hyson tea, weighing 1500 pounds gross, tare 24 pounds per chest, at 50 cents per pound?

lbs. 20

1500 24

480

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8510.00 Value. 2. What is the neat weight and value of 9 casks of raisins, weighing 720 pounds gross, tare 12 pounds per cask, allowing à per cent. scalage, at 6 cents per pound?

Ans. neat 608 lbs.; value, $36.48. 3. What is the neat weight of 5 chests of tea, each weighing gross 75 lbs., tare 5 lbs. per chest? and how much is the value of the neat weight, at 60 cents per pound?

Ans, neat 350 lbs.; value $200.

UNITED STATES DUTIES. Goods, wares and merchandise, imported into the Uniteit

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hundred, gallon, &c. The ad valorem rates of duty are computed by adding 20 per cent to the actual cost of the goods, if imported from the Cape of Good Hope, or any place beyond it; and 10 per cent. if imported from any other place or country.

CASE I. To find the amount of duty for any amount of goods, wares or merchandize, when the rate per centum ad valorem is given.

RULE. To the sum reduced to federal money, add 20 per cent., if imported from or beyond the Cape of Good Hope; or 10 per cent. if imported from any other place or country; multiply this amount by the given rate per cent. and divide by 100, for the duty required.

Examples. 1. What is the duty on an invoice of cloth imported from London, which cost 873 pounds sterling, at 40 per cent. ad valorem?

£
As 9 873 40

40

:

934920

10)3880. actual cost in federal money.

388 10 per cent. added.

4268

40

$1707:20 duty required. 2. What will be the duty on an invoice of raisins, imported from Spain, which cost 320 piasters, at 30 per cent. ad valorem?

Ans. $84.48 cts. 3. What will be the duty on an invoice of silk goods, imported from India, which cost 2000 rupees of 50 cents each, at 20 per cent. ad valorem?

Ans. $240.

CASE II. To find the duty on any amount of goods, wares or merchandize, at any given rate per gallon, pound, &c.

RULE. Multiply the number of gallons, pounds, &c. by the given rate per gallon, pound, &c. and the product will be the duty required.

Examples. 1. What will be the duty on 300 chests of tea, imported direct from China, in a vessel of the United States, weighing gross 22500 lbs. tare 20 lbs. per chest, at 40 cents per pound?

lb. 300

22500 gross. 20

6000 tare,

6000 lbs, tare. 16500 neat.

40

S6600.00 Anster. 2. What will be the duty on 30 pipes of French brandy, containing 3780 gallons, at 50 cents per gallon?

Ans. $1890. 3. What will be the duty on 675 gallons of wine, imported from France, at 48 cents per gallon?

Ans. 8324.

VULGAR FRACTIONS. A VULGAR FRACTioN is a part or parts of a whole number, and is written thus, ., one-fourth; i, one-sixth; 4, fourseventhis.

The figure above the line is called the numerator, and the under figure the denominator, which shows how many parts the integer is divided into; and the numerator shows how many of those parts are meant by the fraction.

There are four sorts of vulgar fractions; proper, improper, compound and mixed, viz.

1. A proper fraction is when the numerator is less than the denominator, as, , 11, 10's, &c.

2. An improper fraction is when the numerator is equal to or greater than the denominator, as , ,

3. A compound fraction is the fraction of a fraction, and known by the word of; as į of i of sof of , &c.

4. A mixed number or fraction is composed of a whole number and a fraction; as 1), 34, 61, 120, 1514, &c.

12
7)

151

1, &c.

Votc-Any whole number may be made an improper fraction, by drawing a line under it, and putting unity or 1. for a cenominator ; as 7 may be expressed" fraction-wise, thus, 1, an! 15 thus, 1, &c.

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REDUCTION OF VULGAR FRACTIONS Is the bringing of them out of one form into another, in order to prepare them for the operation of addition, subtraction, multiplication, division, &c.

Case I.
To reduce a vulgar fraction to its lowest terms.

RULE. 1st. Divide the greater term by the less, till nothing be left; the last divisor will be the common measure, by which divide both terms for the fraction required: Or,

24, Which is often the shortest way, take the aliquot parts of both terins continually, till in their lowest terms.

Examples. 1. Re:luce o to its lowest terms. 66)84(1

66 11 60

6

34 14 Answer.
18 663

51
19)18(1

12

110

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6,122

12
2. Reduce 94. to its lowest terms. Ans.
3. Reduce 102 to its lowest terms.
4. Reduce 36 to its lowest terms.
5. Reduce 1 to its lowest terms.
6. Reduce 2796 to its lowest terms.
7. Reduce 28 4.8 to its lowest terms.
8. Reduce 3.1.3 to its lowest terms.

Too
Case II.
To relics a mirol run to its bylor

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25

4000

RULE. Multiply the whole number by the denominator of the fractión, and to the product aıld the numerator of the fraction, urder which write the denominator.

Examples 1. Reluce 411 to its equivalent imprope: fraction.

4111 47

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2 110

9 119 6

2. Reduce 1} to its equivalent improper fraction. Ans.
3. Reduce 12, to its equivalent improper fraction.
4. Reduce 19. to its equivalent improper fraction.
5. Reduce 415 to its equivalent improper fraction.
6. Reduce 75 to its equivalent improper fraction.
7. Reduce 10287 to its equivalent improper fraction. “
8. Reduce 5.3 to its equivalent improper fraction.

5

301

3297

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2 93

CASE III. To reduce a whole number to an equivalent fraction, that shall have a given denominator.

RULE. Multiply the whole number by the given denominator ; place the said denominator under the product, and it will forin the fraction required.

Note. All fractions represent a division of the numerator by the denominator. Thus, 1 denotes 12 to be divided by 4, and 3; and denotes 4 to be divided by 5, and

Examples. 1. Reduce 12 to a fraction whose denominator shall be 5.

12 x 5= : 60, and the answer. 2. Reduce 16 to a fraction whose denominator shall be 7.

Ans. . 8. Reduce 19 to a fraction whose denominator shall be 9.

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