5. Add the following sums of Dollars together, viz. $12,34565+7,891+2,34+14,+,0011

Ans. $36,57775, or $36, 5di. 7cts. 775-mills, 6. Add the following parts of an acre together, viz. ,7569+,25,654,199.

Ans. 1,8599 acres.

7. Add 72,5+ 32,071+2,1574+-371,4+2,75.

8. Add 30,07+200,7159,43207,1.

Ans. 480,8784
Ans. 3497,28

9.Add 71,467-27,94 16,084 98,009- 86,5. Ans. 300 10. Add ,7509,0074,69,8408,6109. Ans. 2,9 11. Add ,6,099,37,905+,026.

Ans. 2 12. To 9,999999 add one millionth part of a unit, and the sum will be 10.

13. Find the sum of

Twenty-five hundredths,

Three hundred and sixty-five thousandths,

Six tenths, and nine millionths,

Ans. 1,215009

SUBTRACTION OF DECIMALS.

RULE. Place the numbers according to their value; then subtract as in whole numbers, and point off the decimals as in Addition.

EXAMPLES.

13. From a unit, or 1, subtract the millionth part of itAns. ,999999

self.

MULTIPLICATION OF DECIMALS.

RULE.-1. Whether they be mixed numbers, or pure decimals, place the factors and multiply them as in whole numbers.

2. Point off so many figures from the product as there are decimal places in both the factors; and if there be not so many places in the product, supply the defect by prefixing ciphers to the left hand.

,000274855 ,000016

4. Multiply 2461 by ,0529.

5. Multiply 7853 by 3,5.

6. Multiply ,007853 by ,035.

7. Multiply 004 by,004.

8. What cost 6,21 yards of cloth, at 2 dols. 32 cents, 5

mills, per yard?

Ans. $14, 4d. 3c. 85m.

9. Multiply 7,02 dollars by 5,27 dollars.

Ans. 36,9954 dols. or $36 99 cts. 54m.

10. Multiply 41 dols. 25 cts. by 120 dollars. Ans. $4950

11. Multiply 3 dols. 45 cts. by 16 cts.

Ans. $0,5520=55 cts. 2 mills.

12. Multiply 65 cents, by ,09 or 9 cents.

Ans. $0,0585=5 cts. 8 mills.

13. Multiply 10 dols. by 10 cts. Ans. $1 14. Multiply 341,45 dols. by ,007 or 7 mills. Ans. $2,39 To multiply by 10, 100, 1000, &c. remove the separating point so many places to the right hand, as the multiplier has ciphers.

makes 4,25

Multiplied by 10,

So,425

by 100, makes 42,5

by 1000, is

,425

For ,425 x 10 is 4,250, &c.

DIVISION OF DECIMALS.

RULE.-1. The places of the decimal parts of the divisor and quotient counted together, must always be equal to those in the dividend.

therefore divide as in whole numbers, and from the right hand of the quotient, point off so many places for decimals, as the decimal places in the dividend exceed those in the divisor.

2. If the places in the quotient be not so many as the rule requires, supply the defect by prefixing ciphers to the left hand of said quotient. NOTE. If the decimal places in the divisor be more than those in the dividend, annex as many ciphers to the dividend as you please, so as to make it equal, (at least,) to the divisor. Or, if there be a remainder, you may annex ciphers to it, and carry on the quotient to any degree of exactness.

13. If 21 or 21,75 yards of cloth cost 34,317 doilars, what will one yard cost?

$1,577+

NOTE. When decimals, or whole numbers, are to be di vided by 10, 100, 1000, &c. (viz. unity with ciphers,) it is performed by removing the separatrix in the dividend, so inany places towards the left hand as there are ciphers in the divisor.

To reduce a Vulgar Fraction to its equivalent Decimal. RULE.-Annex ciphers to the numerator, and divide by the denominator; and the quotient will be the decimal required.

NOTE. So many ciphers as you annex to the given numerator, so many places must be pointed in the quotient; and if there be not so many places of figures in the quotient, make up the deficiency by placing ciphers to the left hand of the said quotient.

To reduce quantities of several denominations to a Decimal. RULE.-1. Bring the given denominations first to a vulgar fraction by Problem III. page 71; and reduce said vulgar fraction to its equivalent decimal; or,

2. Place the several denominations above each other, letting the highest denomination stand at the bottom; then divide each denomination (beginning at the top) by its value in the next denomination the last quotient will give the decimal required.

EXAMPLES.

1. Reduce 12 s. 6d. 3 qrs. to the decimal of a pound.

2. Reduce 15s. 9d. 3 qrs. to the decimal of a pound.

Ans. ,790625

3. Reduce 9d. 3 qrs. to the decimal of a shilling.

Ans.,8125

4. Reduce 3 farthings to the decimal of a shilling.

Ans. ,0625 5. Reduce 3s. 4d. New-England currency, to the decimai of a dollar. Ans. ,555555-+ 6. Reduce 12s. to the decimal of a pound. Ans. ,6

NOTE. When the shillings are even, half the number. with a point prefixed, is their decimal expression; but if the number be odd, annex a cipher to the shillings, and then by halving them, you will have their decimal expression. 7. Reduce 1, 2, 4, 9, 16 and 19 shillings to decimals.