"II. OPPOSITE to each dividend, on the left hand, place such a number for "a divisor as will bring it to the next superior denomination, and draw a line "perpendicularly between them..

"III. BEGIN With the highest, and write the quotient of each division, as de"cimal parts, on the right hand of the dividend next below it, and so on, till "they are all used, and the last quotient will be the decimal sought."

To find the value of any given decimal in the terms of an integer. RULE.

MULTIPLY the decimal by that number, which it takes of the next less denomination to make one of that denomination in which the decimal is given, and cut off so many figures for a remainder to the right hand of the quotient, as there are places in the given decimal. Proceed in the same manner with the remainder, and continue to do so thro' all the parts of the integer, and the several denominations standing on the left hand make the answer.

EXAMPLES.

1. WHAT is the value of ,528125 of a pound?

OPERATION.
,5 28 12 5

20

Shillings, 10,5 6 2 5 0 0 12/

Pence, 6,7 50000

4

Farthings 3,0 0 0 0 0 0
Ans. 10s. 63d,

THIS question is the first example in the preceding case inverted, by which it will be seen, that questions in these two cases may reciprocally `prove each other.

THE given decimal being the decimal of a pound, and shillings being the next less inferior denomination, because 20 shillings make one pound, I multiply the decimal by 20, and cutting off from the right hand of the product a number of figures, for a remainder, equal to the number of figures in the given decimal, leaves 10 on the left hand which are shillings. I then multiply the remainder which is the decimal of a shilling by 12, and cutting off as before, gives 6 on the left hand for pence, lastly, I multiply this last remainder, or decimal of a penny by 4 and find it to be 3 farthings, without any remainder. It then appears that ,528125 of a pound is in value 108, 63d.

17 is the last remainder, 680 reduced to its lowest terms. A fraction is said to be reduced to its lowest terms when there is no number which will divide both the numerator and the denominator without a remainder. Thus, set to the fraction its proper denominator, 680, then divide the numerator and the denominator by any number which will divide them both without a remainder, continue to do so as long as any number can be found that will divide them in that manner.

5

SUPPLEMENT TO Fractions.

1. WHAT are Fractions?

QUESTIONS,

2. WHAT are integers, or whole numbers? 3. WHAT are mixed numbers?

4. Or how many kinds are fractions?

5. How are Vulgar Fractions written?

6. WHAT is signified by the denominator of a fraction?

7. WHAT is signified 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 Fraction is, if it be not expressed?

11. How do cyphers placed at the left hand of a decimal fraction affect its value? 12. How are decimals distinguished 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 Division ?

15. In what manner is the reduction of a vulgar fraction to a decimal performed? 16. How are numbers of different denominations as pounds, shillings, pence, c. reduced to their decimal values ?

17. Ir 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 similar nature to the examples above. Hence it is seen in some measure the usefulness of Fractions, particularly decimal fractions. The only thing necessary to render any person 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 burthensome; every scholar should have them perfectly committed.

5. If a pile of wood be 18 feet long, 11 wide, and 72 high, how many cords does it contain? Ans. 12 cords 68 feet* 432 inches.

A CORD of wood is 128 solid feet; the proportions commonly assigned are, 8 feet in length, 4 in breadth, and 4 in height.

THE contents of a load or pile of wood of any dimensions may be found by multiplying 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 shew the number of cords, the remainder, if any, will be so many solid feet.

aj

* THE 432 inches in the fraction ,25 of a feot valued according to CASE 3, Re

duc. Dec. Fractions.