it be sold per pint that there may be a gain of 10 cts. per gallon?

500. A farm cost $4750.37; for what must it be sold that the owner may realize a profit of $673, after paying his agent $39?

QUESTIONS.-What is the use of the numerator of a fraction? (128.) What is the difference between a proper and an improper fraction? (129.) (130.) What is a mixed number? (131.) What is a simple fraction? (132.) What are complex fractions? (133.) What is a compound fraction? (134.) Of what may fractions be considered as indications? (135.)

LESSON LVII.

501. What amount of Government stocks at 3 per cent. premium, can I purchase for $8741 ?

502. I send my agent $4374 with which to purchase R. R. stock at 5 per cent. discount; how much can be purchased after deducting his commission of 2 per cent. ?

503. From a cask of wine containing 270 gallons, 30 gal. 2 qts. are drawn; what per cent. is this?

504. A man purchased a farm of 37 A. for $3000; he sold 29 A. 36 sq. rds. for $2300; what per cent. of his farm did he have remaining?

505. A man owes $4738.03, and his property is worth only $2783.14; what per cent. can he pay of his debts?

506. I used a carriage six months, and then sold it for $100, which was 18 per cent. below cost; what would I have received had I sold it for 12 per cent. above cost?

507. A sells a yoke of oxen to B, and gains 10 per cent.; B sells them to C for $85, thereby gaining 12 per cent.; how much did the oxen cost A?

508, A grocer purchased eight hogsheads of molasses

for $50 per hogshead. On four he gained 25 per cent., and on the others he lost 25 per cent.; how much did he lose or gain on the whole?

$20 per bar

509. A grocer sold six barrels of sugar at rel. On two of them he gained 30 per cent.; on the other four he lost 30 per cent.; what per cent. did he lose on the whole?

To

QUESTIONS.-To what is the numerator equivalent? (136.) what the denominator? (136.) How is the value of a fraction af fected by multiplying both numerator and denominator by the same number? (137., a.) How, by dividing both numerator and denominator by the same number? (137., b.)

LESSON LVIII.

INSURANCE.*

211. Insurance is a contract by which individuals or companies bind themselves for stipulated sums to indemnify owners of property for loss by fire, shipwreck, or any other casualty.

212. The Insurer, or Underwriter, is the party who takes the risk of insurance.

213. The Insured is the party to be indemnified by the insurance against loss.

214. The Policy is the instrument or writing embodying the insurance.

215. The Premium is the amount paid by the insured to the insurer for the insurance, and is estimated at a certain rate per cent. on the amount insured.

216. To find the premium, the rate of insurance and the amount insured being given.

What is the premium on a policy of $3784 at 4 per cent.?

*NOTE.-When property is only partially injured insurance companies usually pay the actual loss not exceeding the amount insured. When insured in different companies, the actual loss is apportioned between them in proportion to the amount insured by each.

MODEL OPERATION.

$3784.X$0.04=$151.36.

ANALYSIS.-If the premium on $1 is ($0.04) 4 hundredths of a dollar, on $3784 it is 3784 times 4 hundredths of a dollar, which is 15136 hundredths of a dollar, equal to $151.36.

Therefore, at 4 per cent., the premium on $3784 is $151.36.

NOTE.-Require the pupil to write a rule from the analysis.

510. What must I pay annually for insuring my house to the amount of $3874.46 at 24 per cent. premium?

511. A vessel and cargo valued at $29347.46 are insured at 33 per cent.; what is the premium?

512. What must I pay for insuring a cargo of wheat valued at $15378, at a premium of 2 per cent.? 513. My house and furniture are valued at $4378.50. I have them insured at $34 per cent. If they are destroyed

by fire, what will be the actual loss to the company?

514. A cotton factory and its contents valued at $38746 is insured at 3 per cent. on its value; what is the premium?

515. A merchant wishes to insure a vessel and a cargo of corn from New York to Liverpool, both valued at $20374; what will be the premium on its value at per cent.?

1

516. I purchased 4964 bales of cotton, each bale containing 641 pounds, at 13 cts. per pound. I effected an insurance at 3 per cent. on the selling price, 18 cts. per pound. The vessel containing it foundered at sea; did I make, or lose?

A

1517. My house and furniture, valued at $4374, are dam、

aged to the amount of 25 per cent.; and there is an insur

ance of 75 per cent. on the loss; how much shall I receive?

518. A merchant owns and insures his interest at 3 cost him?

of a ship valued at $39748, per cent.; what does his policy

QUESTIONS.-How is the value of the fraction affected by multiplying the denominator alone? (137., c.) How by dividing the denominator only? (137., d.) How by multiplying the numerator only ? (137., e.) How by dividing the numerator only? (137., ƒ.)

LESSON LIX.

TAXES.

217. A Tax is a sum of money assessed for public purposes by government, on the person or property of an individual.

218. Taxes are commonly assessed at a certain per cent. on the estimated value of property.

219. A Poll Tax is apportioned equally among the male citizens liable to assessment, and is estimated at a certain amount per poll or head.

220. Real Estate consists of property that is not movable, as lands, houses, &c.

221. Personal Property consists of property that is movable, as money, furniture, tools, &c.

222. An Inventory is a list of articles with their value.

223. Before assessing taxes, make a complete inventory of all the taxable property in the township, together with a full list of taxable polls, if there is to be a poll-tax assessed.

In a certain town $16377.70 are to be raised by tax; the valuation of the taxable property as shown by the as

sessment roll is $800000, and there are 225 polls to be assessed 90 cts. each; what will be Mr. Jones's tax whose property is valued at $3426, and who pays for 3 polls?

MODEL OPERATION.

1. $0.90×225=$202.50, am't raised by poll-tax.

2. $16377.70-$202.50=$16175.20, am't to be assessed on the property.

3. $16175.20÷÷800000 $0.020219 on $1, or 28180 per

cent.

4. $0.020219×3426=$69.37, am't of Mr. Jones's tax on

property.

5. $0.90×3=$2.70, am❜t of Mr. Jones's poll-tax.

6. $69.27+$2.70=$71.97, am't of Mr. Jones's entire tax.

ANALYSIS.-1. Find the amount raised by poll-tax.

If 1 poll is taxed 90 cts., 225 polls will be taxed 225 times 90 cts., which are 20250 cts., equal to $202.50.

2. Find the amount to be raised on the property.

If $16377.70 are to raised by tax, and $202.50 are raised by poll-tax, the amount to be assessed on the property must be the difference of these quantities, which is $16175.20.

3. Find the amount to be assessed on $1.

If $16175.20 are to be assessed on $800000, on one dollar there is to be assessed one eight hundred thousandth of $16175.20, which is $0.020219, or 2,318 per cent.

4. Find the amount of the tax on Mr. Jones's property. If one dollar is taxed $0.020219, $3426 will be taxed 3426 times $0.020219, which are $69.27.

5. Find the amount of Mr. Jones's poll-tax.

If one poll is taxed 90 cts., 3 polls are taxed 3 times 90 cts., which are 270 cts., equal to $2.70.

6. Find the entire amount of Mr. Jones's tax.

If the property of Mr. Jones is taxed $69.27, and his poll-tax