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16. When .0008 is divided by 40000, what is the quotient? 17. How many days must a laborer work at $1.37 per day, to pay for 8 cords of wood at $4.43 per cord?

18. A lady bought the following articles: 27 yards of silk at $2.75 per yard, 11 yards of lace at $6.371⁄2 per yard, 9 pairs of gloves at $2.15 per pair, 10 pairs of hose at $1.10 per pair. What was the amount of the purchase?

19. If a man earns $12 per week, and spends $7ğ per week, in how many weeks can he save $500?

20. What is the value of 95150 bricks at $7.25 per M? 21. What is the value of a farm of 195 acres if 91 acres are worth $6688.50, and the remainder $1.124 per acre more? 22. A drover bought 375 sheep at $4.50 per head. sold 200 of them at a loss of $.20 per head, and gained enough on the rest to balance the loss. What did he get per head for the rest?

23. The expenses of conducting a business enterprise were .40 of the entire profits. If the profits were .15 of the value of the goods sold, how much was received from the sale of goods if the profits were $9000 more than the expenses? (−) × (3 + 3 ) (1+4)+(3-1)x5

24. Express as a decimal

25. A speculator bought 5000 bushels of corn at $.65 per bushel. He sold .25 of it for $.70 per bushel, and the remainder for such price that he realized a profit on the whole, of $447.50. How much did he get per bushel for the remainder?

26. The estimated value of Mr. A.'s farm was $6500. If he sold a portion of it, at its estimated value per acre, for $2275, what decimal part of the farm did he sell?

27. A, B and C divide 645 selves. A takes .37, B, many bushels had each?

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DENOMINATE NUMBERS

DEFINITIONS.

232. A Concrete Number is a number used in connection with some specified thing.

Thus, 5 books, 7 trees, 8 horses, are concrete numbers.

233. An Abstract Number is a number that is not used in connection with any specified thing.

Thus, 5, 7, 8, are abstract numbers.

234. A Denominate Number is a concrete number in which the unit of measure is established by law or custom. Thus, 5 yards, 3 feet, 7 pounds, 3 ounces, are denominate numbers. 235. A Simple Denominate Number is a denominate number composed of units of the same denominations. Thus, 5 feet, 9 pounds, 3 miles, are simple denominate numbers.

236. A Compound Denominate Number is a denominate number composed of units of two or more denominations which are related to each other.

Thus, 6 feet and 4 inches, 8 hours and 32 minutes, are compound denominate numbers.

237. A Standard Unit is a unit of measure from which the other units of the same kind may be derived.

Thus, the yard is the standard unit from which all measures of length are formed; the Troy pound the standard unit of weight.

238. A Scale is the ratio by which numbers increase or decrease. Scales are either uniform or varying.

MEASURES OF VALUE.

239. Money is the measure of value.

It is also called Currency, and is of two kinds, viz: coin and paper money.

240. Coin or Specie is stamped pieces of metal having a value fixed by law.

241. Paper Money is notes and bills issued by the Government and banks, and authorized to be used as money.

UNITED STATES MONEY.

242. The unit of United States or Federal money is the

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The coins of the United States are

Gold: The double-eagle, eagle, half-eagle, quarter-eagle, threedollar piece, one-dollar piece.

Silver: The dollar, half-dollar, quarter-dollar, the twenty-cent

piece, the ten-cent piece.

Nickel: The five-cent piece and three-cent piece.

Bronze: The one-cent piece.

There are various other coins of the United States in circulation, but they are not coined now.

The denominations dimes and eagles are rarely used, the dimes being regarded as cents, and the eagles as dollars.

No examples in Reduction of U. S. Money are given, because the pupil has been familiarized with the process from the beginning.

CANADA MONEY.

243. The currency of Canada is decimal, and the table and denominations are the same as those of United States money. English money is still used to some extent.

The coins of Canada, are, for the most part, of the same denominations as those of the United States, except the gold coins, which are the sovereign and half-sovereign.

ENGLISH OR STERLING MONEY.

244. English money is the currency of Great Britain. The unit is the Pound or Sovereign.

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1. Farthings are commonly written as fractions of a penny. Thus, 7 pence 3 farthings is written 73d.; 5 pence 1 farthing, 5d. 2. The value of £1 or sovereign is $4.8665 in American gold.

The coins of Great Britain in general use are

Gold: Sovereign, half-sovereign, and guinea, which is equal to 21 shillings.

Silver: The crown (equal to 5 shillings), half-crown, florin (equal to 2 shillings), shilling, six-penny and three-penny pieces.

Copper: Penny, half-penny, and farthing.

REDUCTION DESCENDING.

245. 1. How many farthings are there in 2 pence? In 5 pence? In 7 pence? In 8 pence? In 6 pence?

2. How many pence are there in 2 shillings? In 5 shillings? In 7 shillings? In 8 shillings? In 6 shillings?

3. How many pence are there in 5s.? In 5s. and 3d.? In 7s. 4d.? In 4s. 5d.? In 6s. 8d.?

4. How many farthings are there in 5d.? In 6d. 3 far.? In 51d.? In 61d.? In 83d.? In 91d.? In 103d.?

5. How many shillings are there in £2 5s.? In £3 5s.?

246. Reduction of a denominate number is the process of changing it from one denomination to another without altering its value.

247. Reduction Descending is the process of changing a denominate number to an equivalent number of a lower denomination.

WRITTEN EXERCISES.

1. How many farthings are there in £3 5s. 6d. ?

PROCESS.

£3 5s. 6d.

20

65s.

£3 5s.

12

786d.

= £3 5s. 6d.

4

3147 far. £3 5s. 6d.

ANALYSIS. Since in 1 pound there are 20 shillings, in 3 pounds there are 3 times 20 shillings, or 60 shillings; and 60 shillings + 5 shillings 65 shillings.

Since in 1 shilling there are 12 pence, in 65 shillings there are 65 times 12 pence, or 780 pence; and 780 pence + 6 pence 786 pence.

Since in 1 penny there are 4 farthings, in 786 pence there are 3144

farthings; and 3144 farthings + 3 farthings = 3147 farthings.

Hence in £3 5s. 63d. there are 3147 farthings.

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