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Supplement to Fractions.

1. What are fractions?

QUESTIONS.

2. What are integers, or whole numbers ?

3. What are mixed numbers?

4. Of how many kinds are fractions ?

5. How are Vulgar Fractions written?

6. What is fignified by the denominator of a fraction ?

7. What is fignified by the numerator?

8. How are Decimal Fractions written?

9. How do Decimals differ from Vulgar Fractions?

10. How can it be ascertained, what the denominator to a Decimal Frac

tion is, if it be not expreffed ?

11. How do cyphers placed at the left hand of a Decimal Fraction affect its

value?

12. How are Decimals diftinguished from whole numbers ?

13. In the addition of Decimals what is the rule for pointing off ?

14. What is the rule for pointing off Decimals in Subtraction? In Multiplication and in Divifion?

15. In what manner is the reduction of a vulgar Fraction to a decimal performed?

16. How are numbers of different denominations, as pounds, fhillings, pence, &c. reduced to their decimal values?

17. If it be required to find the value of any given decimal in the terms of an integer what is the method of procedure ?

Many persons are perplexed by occurrences of a fimilar nature to the examples above. Hence it is feen in fome measure the usefulness of Fractions, particularly decimal fractions. The only thing neceffary to render any per fon adroit in these operations is to have riveted in his mind the rules for pointing as taught and explained in their proper places. They are not burthenfome; every scholar should have them perfectly committed.

5 If a pile of wood be 18 feet long, 11 wide, and 74 high, how many cords does it contain? Ans. 12 cords 68 feet* 432 inches.

A cord of wood is 128 folid feet; the proportions commonly affigned are, 8 feet in length, 4 in breadth, and 4 in height.

The contents of a load or pile of wood of any dimenfions may be found by mul tiplying the length by the breadth and this product by the height; or, by multiplying the length, breadth, and height into each other. The last product divided by 128 will fhew the number of cords, the remainder, if any, will be fo many folid feet.

* The 432 inches in the fraction,25 of a foot valued according to CASE 3, Reduc. Dec. FRACTIONS.

FEDERAL MONEY is the coin of the United States, established by Congrefs, A. D. 1786. Of all coins this is the most fimple, and the operations in it, the most easy.

The denominations are in a decimal proportion, as exhibited in the following

The expreffion of any fum in Federal Money is fimply the expreffion of a mixed number in decimal fractions. A dollar is the Unit money: dollars therefore must occupy the place of units, the less denominations, as dimes, cents, and mills, are decimal parts of a dollar, and may be distinguished from dollars in the fame way as any other decimals by a comma or feparatrix. All the figures to the left hand of dollars, or beyond Units place are eagles. Thus, 17 Eagles, 5 dollars, 3 dimes, 4 cents, and 6 mills are written

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Of these, four are real coins, and one is imagin

ary.

The real coins are the Eagle, a gold coin; the Dollar and the Dime, filver coins; and the Cent, a copper coin. The mill is only imaginary, there being no piece of money of that denomination.

There are half-eagles, half-dollars, double-dimes, half-dimes, and half cents, real coins.

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This

These denominations, or different pieces of money, being in a tenfold proportion, confequently, any fum in Federal Money does of itself exhibit the particular number of each different piece of money contained in it. 175,346 (Seventeen eagles, five dollars, three dimes, four cents, fix mills) contain 175346 mills, 17534 cents, 1753% dimes, 175, dollars, 170703 eagles. Therefore, eagles and dollars reckoned together, exprefs the number of dollars contained in the fum; the fame of dimes and cents; and this indeed is the ufual way of account, to reckon the whole fum in dollars, cents and mills, thus,

$175 34 6

The Addition, Subracion, Multiplication and Division of Federal Money is performed in all refpects as in Decimal Fractions, to which the Scholar is referred for the afe of rules in thefe operations:

ADDITION OF FEDERAL MONEY.

1. Add 16 Eagles; 3 Eagles, 7 Dollars, 5 Cents; 26 Dollars, 6 Dimes, 4 Cents, 3 Mills; 75 Cents, 8 Mills; 40 Dollars, 9 Cents, together.

2. If I am indebted 59 dollars, 112 dollars, 98 cts. 113 dolls. 15 cts. 15 dolls. 21 dolls. 50 cts. 200 dolls. 73 dolls. 35 dolls. 17 cts. 75 dolls. 20 dolls. 40 dolls. 33 cts. and 16 dolls. What is the fum which I owe?

Ans. $781 13

Accountants generally omit the comma and distinguish cents from dollars by fetting them apart from the dollars.