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32. John runs 32 rods in a minute, and Henry pursues him at the rate of 44 rods in a minute; how long will it take Henry to overtake John, if John have 8 minutes the start? Ans. 214 minutes. 33. If 4 barrels of flour cost $32.3, what will 7 barrels cost? Ans. $51. 34. If .875 of a ton of coal cost $5.635, what will 9 tons. cost? Ans. $59.57. 35. For the first three years of business, a trader gained $1200.25 a year; for the next three, he gained $1800.62 a year, and for the next two he lost $950.87 a year; supposing his capital at the beginning of trade to have been $5000, what was he worth at the end of the eighth year? Ans. $12100.87. 36. What will be the cost of 18640 feet of timber, at $4.50 per 100? Ans. $838.80.

21

37. Reduce

to a decimal fraction.

31/

Ans..78125.

38. What will 1375 pounds of potash cost, at $96.40 per

ton?

39. Reduce .5625 to a common fraction.

Ans. $66.275.
Ans.

40. Reduce, .021, .37, &, to decimals, and find their

sum.

Ans. 1.464375.

41. A man's account at a store stands thus:

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42. A gardener sold, from his garden, 120 bunches of onions at $.12 a bunch, 18 bushels of potatoes at $.623 per bushel, 47 heads of cabbage at $.07 a head, 6 dozen cucumbers at $.18 a dozen; he expended $1.50 in spading, $1.27 for fertilizers, $1.87 for seeds, $2.30 in planting and hoeing; what were the profits of his garden? Ans. $23.68.

REDUCTION.

175. A Compound Number is a number whose value is expressed in two or more different denominations.

176. Reduction is the process of changing a number from one denomination to another without altering its value. Reduction is of two kinds, Descending and Ascending. 177. Reduction Descending is changing a number of one denomination to another denomination of less unit value; thus, $1=10 dimes=100 cents=1000 mills.

178. Reduction Ascending is changing a number of one denomination to another denomination of greater unit value; thus, 1000 mills=100 cents=10 dimes $1.

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179. A Scale is a series of units, increasing or decreasing, according to a certain law.

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The currency of the Dominion of Canada is decimal, and the table and denominations are the same as those of the

United States money.

The currency of the whole Dominion of Canada was made uniform July 1, 1871. Before the adoption of the decimal system, pounds, shillings, and pence were used.

The Silver Coins are the 50-cent piece, 25-cent piece, 10-cent piece, and 5-cent piece. The 20-cent piece is no longer coined. The Bronze Coin is the cent.

The Gold Coin used in Canada is the British Sovereign, worth $4.86}, and the Half-Sovereign.

II. ENGLISH Money.

181. English Currency is the currency of Great Britain.

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SCALE ascending, 4, 12, 20; descending, 20, 12, 4.

1. Farthings are generally expressed as fractions of a penny; thus, 1 far., sometimes called 1 quarter (qr.), d.; 3 far. = d.

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2. The gold coins are the sovereign (= £1), and the half-sovereign.

3. The silver coins are the crown (= 5s.), the half-crown (= 2s. 6d.), the florin, the shilling, and the sixpenny, fourpenny, and threepenny pieces.

4. The copper coins are the penny, halfpenny, and farthing,

5. The guinea (= 21s.) and the half-guinea (= 10s. 6d. sterling), are old gold coins, and are no longer coined.

6. In France accounts are kept in francs and decimes. A franc is equal to $.193 U. S. money.

CASE I.

182. To perform reduction descending.

1. Reduce £21 18s. 10d. 2 far. to farthings.

OPERATION.

£21 18s. 10d. 2 far.

20

438s.

12

5266d..
4

21066 far., Ans.

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ANALYSIS. Since in £1 there are 20s., in £21 there are 20s. x 21 420s., and 18s. in the given number added, makes 438s. in £21 183. Since in 1s. there are 12d., in 438s. there are 12d. × 438 = 5256d., and 10d. in the given number added, makes 5266d. in £21 18s. 10d. Since in 1d. there are 4 far., in 5266d. there are 4 far. x

5266 = 21064 far., and 2 far. in the given number added, makes 21066

far. in £21 18s. 10d. 2 far.

RULE. I. MULTIPLY the highest denomination of the given number by that number of the scale which will reduce it to the next lower denomination, adding to the product the given number, if any, of that lower denomination.

II. Proceed in the same manner with the results obtained in each lower denomination, until the reduction is brought to the denomination required.

CASE II.

183. To perform reduction ascending.

1. Reduce 21066 farthings to pounds.

OPERATION.

4) 21066 far.
12) 5266d.+ 2 far.
20) 43|8s. +10d.

£21 +18s.

Ans. £21 18s. 10d. 2 far.

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as many shillings as pence, and we find that 5266d. = 438s. + 10d. Lastly divide 438s. by 20, since there are as many pounds as shillings, and we find that 438s. = £12 + 18s. The last quotient with the several remainders annexed in the order of the succeeding denominations, gives the answer £21 18s. 10d. 2 far.

RULE. I. DIVIDE the given number by that number of the scale which will reduce it to the next higher denomination.

II. Divide the quotient by the next higher number in the scale; and so proceed to the highest denomination required. The last quotient, with the several remainders annexed in a reversed order, will be the answer.

Reduction descending and reduction ascending mutually prove each other.

EXAMPLES FOR PRACTICE.

1. In 14194 farthings how many pounds?
2. In £14 15s. Sd. 2 far. how many farthings?
3. In 15359 farthings how many pounds?
4. In 46 sov. 12s. 2d. how many pence?
5. In 11186 pence how many sovereigns?

WEIGHTS.

184. Weight is the measure of gravity, and varies according to the quantity of matter a body contains. Three scales of weight are used in the United States and Great Britain, namely, Troy, Apothecaries', and Avoirdupois.

I. TROY WEIGHT.

185. Troy Weight is used in weighing gold, silver, and jewels, and in philosophical experiments.

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SCALE-ascending, 24, 20, 12; descending, 12, 20, 24.

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3. In 5 lb. 7 oz. 12 pwt. 9 gr., how many grains?

4. In 32457 grains how many pounds?

Define weight. Troy weight. Repeat the table. Give the scale.

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