10. From .99 subtract 433.

Ans. .55656.

11. What is the sum of 4.638, 8.318, .016, .54, and .45 ?

12. From .4 subtract .23.

MULTIPLICATION AND DIVISION.

243. 1. Multiply 2.428571 by .063.

Ans. 133.
Ans. 3.

ANALYSIS. We first reduce the multiplicand and multiplier to their equivalent fractions, and obtain 47 and 70; then 4×11 = r7% = .154.

=

244. From these illustrations we have the following

RULE. Reduce the given numbers to common fractions; then multiply or divide, and reduce the result to a decimal.

UNITED STATES MONEY.

245. By Act of Congress of August 8, 1786, the dollar was declared to be the unit of Federal or United States Money; and the subdivisions and multiples of this unit and their denominations, as then established, are as shown in the

246. By examining this table we find

1st. That the denominations increase and decrease in a tenfold ratio.

2d. That the dollar being the unit, dimes, cents and mills are respectively tenths, hundredths and thousandths of a doilar.

3d. That the denominations of United States money increase and decrease the same as simple numbers and decimals. Hence we conclude that

I. United States money may be expressed according to the decimal system of notation.

II. United States money may be added, subtracted, multiplied and divided in the same manner as decimals.

NOTATION AND NUMERATION.

247. The character $ before any number indicates that it expresses United States money. Thus $75 expresses 75 dollars. 248. Since the dollar is the unit, and dimes, cents and mills are tenths, hundredths and thousandths of a dollar, the decimal point or separatrix must always be placed before dimes. Hence, in any number expressing United States money, the first figure at the right of the decimal point is dimes, the second figure is cents, the third figure is mills, and if there are others, they are tenthousandths, hundred-thousandths, etc., of a dollar. Thus, $8.3125

expresses 8 dollars 3 dimes 1 cent 2 mills and 5 tenths of a mill or 5 ten-thousandths of a dollar.

249. The denominations, eagles and dimes, are not regarded in business operations, eagles being called tens of dollars and dimes tens of cents. Thus $24.19 instead of being read 2 eagles cents, is read 24 dollars 19 cents. Hence,

4 dollars 1 dime 9

practically, the table of United States money is as follows:

10 mills make 1 cent.

100 cents 66 1 dollar.

250. Since the cents in an expression of United States money may be any number from 1 to 99, the first two places at the right of the decimal point are always assigned to cents. Hence, when the number of cents to be expressed is less than must be written in the place of tenths or dimes. expressed $.07.

10, a cipher Thus, 7 cents is

NOTES. 1. The half cent is frequently written as 5 mills and vice versa. Thus, $.37= $.375.

2. Business men frequently write cents as common fractions of a dollar. Thus, $5.19 is also written $51, read 5 and 1 dollars.

3. In business transactions, when the final result of a computation contains 5 mills or more, they are called one cent, and when less than 5 they are rejected. Thus, $2.198 would be called $2.20, and $1.623 would be called $1.62.

EXAMPLES FOR PRACTICE.

1. Write twenty-eight dollars thirty-six cents.

2. Write four dollars seven cents.

3. Write ten dollars four cents.

4. Write sixteen dollars four mills.

Ans. $28.36.

5. Write thirty-one and one-half cents.

Ans. $48.01.

6. Write 48 dollars 14 cents.

7. Write 1000 dollars 1 cent 1 mill.

8. Write 3 eagles 2 dollars 5 dimes 8 cents 4 mills.

REDUCTION.

251. Since $1 = 100 cents = 1000 mills, it is evident, 1st That dollars may be changed or reduced to cents by annexing two ciphers; and to mills by annexing three ciphers.

2d. That cents may be reduced to dollars by pointing off two figures from the right; and mills to dollars by pointing off three figures from the right.

3d. That cents may be reduced to mills by annexing one cipher. 4th. That mills may be reduced to cents by pointing off one figure from the right.

OPERATIONS IN UNITED STATES MONEY.

252. Since United States Money may be added, subtracted, multiplied and divided in the same manner as decimals, (246, II), it is evident that no separate rules for these operations are required.

EXAMPLES FOR PRACTICE.

1. Paid $3475.50 for building a house, $310.20 for painting, $1287.37 for furniture, and $207.12 for carpets; how much was the cost of the house and furniture? Ans. $5280.20.

2. Bought a pair of boots for $4.621, an umbrella for $1.75, a pair of gloves for $.871, a cravat for $1, and some collars for $.62; how much was the cost of all my purchases?

3. Gave $150 for a horse, $175.84 for a carriage, and $62 for a harness, and sold the whole for $390.37; how much did I gain? Ans. $2.035.

4. A man bought a farm for $3800, which was $190.87 less than he sold it for; how much did he sell it for?

5. A lady bought a dress for $10, a bonnet for $51, a veil for $23, a pair of gloves for $.871, and a fan for $§. She gave the shopkeeper a fifty dollar bill; how much money should he return to her? Ans. $29.875.

6. A farmer sold 150 bushels of oats at $.37 a bushel, and 4 cords of wood at $33 a cord. He received in payment 84 pounds of

sugar at 6 cents a pound, 25 pounds of tea at $§ a pound, 2 barrels of flour at $5.87, and the remainder in cash; how much cash did he receive? Ans. $39.125.

7. A speculator bought 264.5 acres of land for $6726. He afterward sold 126.25 acres for $314 an acre, and the remainder for $33.75 an acre; how much did he gain by the transaction?

8. A merchant going to New York to purchase goods, had $11000. He bought 40 pieces of silk, each piece containing 281 yards, at $.80 a yard; 300 pieces of calicoes, with an average length of 29 yards, at 11 cents a yard; 20 pieces of broadcloths, each containing 36.25 yards, at $3.875 a yard; 112 pieces of sheeting, each containing 30.5 yards, at $.06 a yard. How much had he left with which to finish purchasing his stock? Ans. $6064.621.

9. If 139 barrels of beef cost $2189.25, how much will 1 barrel cost? Ans. $15.75. 10. If 396 pounds of hops cost $44.748, how much are they worth per pound? Ans. $.113.

11. Bought 10 cords of wood at $4 a cord, and received for it 7.74 barrels of flour; how much was the flour worth per barrel? 12. If a hogshead of wine cost $287.4, how many hogsheads can be bought for $4885.80?

Ans. 17.

13. A butcher bought an equal number of calves and sheep for $265; for the calves he paid $3 a head, and for the sheep $2 a head; how many did he buy of each kind?

Ans. 40. 14. If 128 tons of iron cost $9632, how many tons can be bought for $1730.75?

Ans. 23.

15. If 125 bushels of potatoes cost $11.25, how many barrels, each containing 24 bushels, can be bought for $112.20?

16. A grocer on balancing his books at the end of a month, found that his purchases amounted to $2475.36, and his sales to $1936.40; and that the money he now had was but g of what he had at the beginning of the month; how much money had he at the beginning of the month? Ans. $1347.40. and his expenses

17. A person has an income of $3200 a year,

are $138 a month; how much can he save in 8 years?