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Practical Questions, to exercise the learner in the preceding rules.

1. The population of the United States, in the year 1820, was 9625734; of which number, 7856269 were whites, 238029 free blacks, and the rest slaves: What was the number of slaves? Ans. 1531436.

2. The number of slaves transported from Western Africa in 25 years, ending in 1819, was stated to be such as would average 60000 a year: What was the whole number transported in that time? Ans. 1500000.

3. A bachelor, at his decease, left an estate worth 12426 dollars; and, in his will, ordered, that 1000 dollars should be given to his niece, and the remainder divided equally between his two nephews. What was the share of each nephew? Ans. 5713 dollars. 4. There are 16 bags of coffee, each weighing 120 pounds; and 8 bags more, weighing each 343 pounds: What is the weight of the whole? Ans. 4664 pounds.

5. There is an excellent well built ship just returned from the Indies. The ship only is valued at 27140 dollars; and one quarter of her cargo is worth 75274 dollars: What is the value of the whole ship and cargo?

Ans. 328236 dollars. 6. I received of A B and C a sum of money: A paid me 54 dollars, B paid me just three times as much as A, and C paid me twice as much as A and B both. Can you tell me how much money C paid me? Ans. 432 dollars. 7. What will 5 tons of hay come to, at 14 dollars a ton? Ans. 77 dollars. 8. If 320 rods make a mile, and each rod contains 5 yards; how many yards are there in a mile?

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Ans. 1760.

9. Sold a ship for 7500 dollars, and I owned & of her: What is my part of the money? Ans. 5625 dollars.

10. If the number 42 be multiplied by 12, the product divided by 3, the quotient increased by 32, the amount divided by 4, and 49 subtracted from the last quotient, what will then remain ?

Ans. 1.

Note.-Some Authors on Arithmetic have given particular rules for the Addition, Subtraction, Multiplication, and Division, of Federal Money, immediately after the rules for performing the like operations in whole numbers. I do

not think it would be useful to insert such rules in this part of the present Treatise, because the Federal currency is purely decimal, and most naturally falls in after Decimal Fractions. If any instructor should think it advisable for his pupils to acquire a knowledge of the method of reckoning in Federal money before they learn the rules of Reduction and the succeeding rules which precede Decimal Fractions, he can direct them to omit those rules until they have gone through with the first four rules in Decimals and the succeeding section on Federal Money.

REDUCTION,

Is the changing of numbers from one name or denomination to another, without altering their value. This is chiefly concerned in reducing money, weights, and meas

ures.

When great names or denominations are brought into small, as pounds into ounces, feet into inches, &c., it is called Reduction Descending. When small names are brought into great, as ounces into pounds, inches into feet, &c., it is called Reduction Ascending. Reduction Descending is performed by Multiplication, and Reduction Ascending, by Division.

Before proceeding to the rules and questions of Reduction, it will be proper to set down the Tables of the denominations of money, weights, and measures. These tables the learner ought to commit to memory, as far as Table 16th, excepting the Supplemental Tables, which may be omitted.

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Supplement to Table 1st.

mills. C.

10= 1 dm.

100= 10= 1 D.

1000= 100= 10= 1 E.

10000 1000=100=10=1

Federal Coins, or Coins of the United States.

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Note. The proportional value of gold to silver, in all coins current by law in the United-States, is as 15 to 1; that is, 15 ounces of pure silver are equal in value to 1 ounce of gold.

2. Sterling Money, and old Currencies of the several States.

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Note.-Farthings are usually written as fractional parts of a penny; 1 farthing being 1, 2 farthings, and 3 farthings of a penny.-People of business often write shillings at the left hand of a stroke, and pence at the right; thus, 15/4, is 15 shillings and 4 pence.

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Note 1.-What Refiners call a Carat, is the 24th part of any quantity, or weight.

Note 2.-The fineness of gold and silver is tried by fire. Gold that will abide the fire without loss, is accounted 24 carats fine: If it lose 2 carats in the trial, it is said to be 22 carats fine, &c. A pound of silver which loses nothing in the trial is said to be 12 ounces fine; but if it lose 5 penny-weights, it is 11oz. 15pwt. fine, &c.

Note 3.-Alloy, or Allay, is some base metal with which gold or silver is mixed to abate its fineness.*

Gold and silver, in their purity, are so very soft and flexible, that they are not so useful, either in coin or otherwise, (except to beat into leaf gold or silver,) as witen they are allayed, or mixed and hardened

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20= 1 dr.

60= 3= 1 oz.

480= 24= 8= 1 lb. 5760-288-96=12=1

Note 1.-Apothecaries make use of this weight in compounding their medicines; but they buy and sell their drugs by Avoirdupois weight. Note 2.-The Apothecaries' pound, ounce, and grain, are the same as the pound, ounce, and grain, Troy.

6. Avoirdupois Weight.

The denominations of Avoirdupois weight are usually

reckoned as follows:

16 Drams, (dr.) make

16 Ounces,

28 Pounds,

4 Quarters, or 112lb.,

1 Ounce,

1 Pound,

1 Quarter of a hundred weight,
1 Hundred weight,

20 Hundred wt., or 2240 lb., 1 Ton,

0%.

lb.

qr.

cwt.

T.

In some of the United-States, the denominations of Avoirdupois weight, are, by law, as follows:

16 Drams =1 Ounce.

16 Ounces=1 Pound.

25 Pounds=1 Quarter of a cwt.

20 Hundred wt. or 2000 lb. =1 Ton.

with copper or brass.-In England, 22 carats of pure gold and 2 carats of copper, melted together, is the standard for gold coin; the alloy being one twelfth part of the mixture: and 11 oz 2 pwt. of fine silver melted with 18 pwt. of copper, is the standard for silver coin. In the United States, the standard for gold coin, is 11 parts pure gold and 1 part alloy; the alloy to be silver and copper mixed, not exceeding one half copper. The standard for silver coin, is 1485 parts fine silver, and 179 parts alloy; the alloy to be pure copper. The copper coins of the United States are to be pure copper.

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