shilling we multiply by 12, and, pointing off as before, obtain 9d., which, added to the 19s., gives 19s. 9d. for the answer.

RULE. Multiply the given decimal by the number required of the next lower denomination to make ONE of the given denomination, and point off on the RIGHT, for a REMAINDER, as many places as there are places in the given decimal. Multiply this remainder by the number that will reduce it to the next lower denomination, pointing off for a remainder as before, and thus proceed, until the reduction is carried to the denomination required. The several numbers standing at the left hand of the point will be the answer, in whole numbers, of the different lower denominations.

EXAMPLES FOR PRACTICE.

1. What is the value of .628125 of a pound?

2. What is the value of .778125 of a ton?

Ans. 12s. 6d.

Ans. 15cwt. 2qr. 7lb.

3. What is the value of .75 of an ell English?

4. What is the value of .965625 of a mile?

Ans. 3qr. 3na.

Ans. 7fur. 29rd.

5. What is the value of .94375 of an acre ?

Ans. 3R. 31p.

6. What is the value of .815625 of a pound Troy?

Ans. 9oz. 15dwt. 18gr.

7. What is the value of .5555 of a pound apothecaries' weight? Ans. 63 53 09 191gr.

MISCELLANEOUS EXERCISES IN DECIMALS.

1. What is the value of 15cwt. 3qr. 14lb. of coffee at $9.50 per cwt.?

2. What cost 17T. 18cwt. 1qr. 7lb.

per ton ?

3. What cost 37A. 3R. 16p. of land at

4. What cost 15yd. 3qr. 2na. of cloth

Ans. 150.81+. of potash at $53.80 Ans. $963.86+. $75.16 per acre? Ans. $2844.80+. $3.75 per yard? Ans. $59.53+. per cord? Ans. $71.10+.

at

5. What cost 15g cords of wood at $4.62

6. What cost the construction of 17m. 6fur. 36rd. of rail

road at $3765.60 per mile?

Ans. $67263.03+.

QUESTION.

What is the rule.

7: What cost 27hhd. 21gal. of temperance wine at $ 15.37 per hogshead? Ans. $ 420.24+. 8. What are the contents of a pile of wood, 18ft. 9in. long, 4ft. 6in. wide, and 7ft. 3in. high? Ans. 611ft. 1242in. 9. What are the contents of a board 12ft. 6in. long, and 2ft. 9in. wide? Ans. 34ft. 54in.

10. Bought a cask of vinegar containing 25gal. 3qt. 1pt. at $0.37 per gallon; what was the amount? Ans. $9.70+. 11 Bought a farm containing 144A. 3R. 30p. at $97.621 per acre; what was the cost of the farm?

Ans. $14149.52+. 12. Sold Joseph Pearson 3T. 18cwt. 21lb. of salt hay, at $9.37 per ton. He having paid me $20.25, what remains Ans. $16.40+.

due

Ans. $48.71+.

13. If of a cord of wood cost $5.50, what cost one cord? What cost 72 cords? 14. If 42 yards of cloth cost $ 12, what cost 173 yards? Ans. $46.18+.

§ XXI.

REDUCTION OF CURRENCIES.

ART. 190. REDUCTION OF CURRENCIES is finding the value of the denominations of one currency in the denominations of another.

The nominal value of the dollar, expressed in shillings and pence, differs in the different States of the Union and in different countries, as may be seen by the following

TABLE.

In New England, Indiana, Illinois, Missouri, Virginia, Kentucky, Tennessee, Mississippi, Texas, Alabama, and Florida, the dollar is valued at 6 shillings; $1=£.

In New York, Ohio, and Michigan, the dollar is valued at 8 shillings; $1 = &£. = Z£.

In New Jersey, Pennsylvania, Delaware, and Maryland, the dollar is considered 7 shillings and 6 pence; $1

What is the

QUESTIONS. Art. 190. What is reduction of currencies? value of a dollar, in the different States, expressed in shillings and pence?

In North Carolina the dollar is reckoned at 10 shillings;

$1= }}£. = {£.

In South Carolina and Georgia 4 shillings 8 pence is the value of a dollar; $1

=

£.

In Canada and Nova Scotia the dollar is valued at 5 shillings $1=5£.=1£.

In English or sterling money, the dollar is valued at 4s. 1.6d. nearly; $1 =

NOTE. The value of a pound English or sterling money is very nearly $4.84.

ART. 191. To reduce pounds, shillings, pence, and farthings, of the different currencies, to United States money. Ex. 1. Reduce 18£. 15s. 6d., New England currency, to United States money. Ans. $62.584.

OPERATION.

18£. 15s. 6d.

=

18.775€.

We first reduce the shillings 18.775£.£. = $62.58 pound (Art. 188), and then and pence to the decimal of a annexing it to the pounds, we divide the sum by, because 6s. or a dollar in this currency is of a pound, and thus obtain the answer in dollars and the decimal of a dollar. Hence the

RULE. ·Reduce the shillings, pence, and farthings, if any, to the decimal of a pound, and annex it to the pounds; then divide this number by the value of the dollar in the given currency, expressed as a fraction of a pound. The quotient is the answer in dollars, and the decimal of a dollar.

EXAMPLES FOR PRACTICE.

2. Change 144£. 7s. 6d. of the old New England currency to United States money. Ans. $481.25. 3. Change 74£. 1s. 6d. of the old currency of New York to United States money. Ans. $185.182. 4. Change 129£. of the old currency of Pennsylvania to

Ans. $344.

United States money. 5. Change 144£. 6s. 3d. 2qr. of the old North Carolina currency to United States money. Ans. $288.62,9.

QUESTIONS. What is the value of a dollar in Canada? In English or sterling money? What is the value of a pound, English or sterling money, expressed in United States money?-Art. 191. How do you reduce pounds, shillings, pence, and farthings, New England currency, to United States money? Why divide by £.? How reduce them if in New York currency? How, if in Georgia currency? What is the general rule?

6. Change 84£. of the old currency of South Carolina to United States money. Ans. $360. 7. Change 144£. 4s. of Canada and Nova Scotia currency to United States money. 8. Change 257£. 8s. 6d. English or sterling money to United States money. Ans. $1245.93,7.

Ans. $576.80. ́

ART. 192. To reduce United States money to pounds, shillings, pence, and farthings of the different currencies.

Ex. 1. Reduce $152.625 to old New England currency.

Ans. 45£. 15s. 9d.

Since 6s. or a dollar in this cur rency is of a pound, we multiply the given sum by the fraction, and reduce the decimal to shillings and pence. (Art. 189.) Hence the following

RULE. Multiply the dollars, cents, &c., of the given sum by the value of the dollar in the required currency EXPRESSED AS A FRACTION OF A POUND. The product is the answer in pounds and the decimal of a pound, which must be reduced to shillings, pence, &c. (Art. 189.)

EXAMPLES FOR PRACTICE.

2. Change $481.25 to the old currency of New England. Ans. 144. 7s. 6d.

3. Change $ 185.18 to the old currency of New York.

Ans. 74£. 1s. 6d.

4. Change $344 to the old currency of Pennsylvania.

Ans. 129£.

5. Change $288 to the old currency of North Carolina.

Ans. 144 £.

6. Change $360 to the old currency of South Carolina.

Ans. 84£.

7. Change $576.50 to Canada and Nova Scotia currency.

Ans. 144£. 2s. 6d.

8. Change $1245.93,7 to English or sterling money.

Ans. 257£. 8s. 6d.

QUESTIONS.-Art. 192. How do you reduce United States money to pounds, shillings, pence, and farthings, New England currency? Why multiply by

£.? How would you reduce United States money to pounds, &c., Ohio currency? How, to Pennsylvania currency? What is the general rule?

§ XXII. PERCENTAGE.

ART. 193. PERCENTAGE and per cent. are terms derived from the same Latin words, per and centum, which signify by the hundred. Percentage, therefore, is any rate or sum on a hundred, or it is any number of hundredths. Thus, if an article is bought for $100 and sold for $105, the gain is 5 per cent., because $5 are 5 of $100, or of the original cost. Again, if an article is bought for $25 and sold for $30, the gain is 20 per cent., because $5 are 2 of $25, or of the original

cost.

=

Since per cent. is any number of hundredths, it is a decimal written in the same manner as hundredths in decimal fractions. Thus, 5 per cent., 25 per cent., &c., are written .05, .25, respectively. (Art. 175.)

When the per cent. is more than 100, it is an improper fraction, and if expressed decimally, it becomes a mixed number, thus, 103 per cent., equal to 188, is written 1.03.

If the per cent. is a vulgar fraction, or contains a vulgar fraction, the fraction is a part of one hundredth, and if expressed decimally, must be written at the right of hundredths in the place of thousandths, &c. Thus, per cent., & per cent., 12 per cent., are written .005, .0075, .122, respectively.

EXAMPLES IN WRITING PERCENTAGE.

Write decimally 2 per cent.; 3 per cent.; 5 per cent.; 6 per cent.; 7 per cent., 8 per cent.; 10 per cent.; 15 per cent.; 25 per cent.; 50 per cent.; 100 per cent.; 105 per cent.; 115 per cent.; 6 per cent.; 8 per cent.; 20 per cent.;per cent.; per cent.; per cent.; o per cent.

ART. 194. To find the percentage on any sum or quantity.

Ex. 1. Bought a house for $625, and sold it at 6 per cent. advance; what did I gain by the sale ? Ans. $37.50.

QUESTIONS. Art. 193. From what are the terms percentage and per cent. derived, and what do they signify? How then will you define percentage? How will you illustrate it? How is per cent. written, when less than 100 ? How, when more than 100? If the per cent. is a fraction, or contains a fraction, what is the fraction, and if expressed decimally, what place must it occupy?