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PRACTICE. 260. An Aliquot Part of a number is an exact divisor (Art. 97) of it. Thus,

2, 21, 33, and 5 are aliquot parts of 10. 261. Practice is an abridged method of computation, by means of aliquot parts.

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Exercises. 1. Let it be required to find the cost of 3632 bushels of wheat, at $1.87} a bushel.

OPERATION.

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3632 bu. at $1

per
bu. will cost

$3632
.50

1 of $3632 = 1816 .25

1 of $1816 908 .12)

1 of $908 454

$6810, Ans. 2. Required the cost of 3 T. 5 cwt. 2 qr. of hay, at $24 a ton.

6 $1.872

OPERATION.

Since 1 T. cost

$24.00 3 T.

will cost $24 x 3= $72.00 5 cwt.

of $24 = 6.00 2 qr.

Ib of $6 .60 3 T. 5 cwt. 2 qr.

$78.60, Ans.

What is an Aliquot Part of a number? What is Practice?

3. What is the amount of a salary for 1 y. 7 mo. 221 d., at $1080 per year?

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• 1 y. 7 mo. 221 d. “

$1777.50 4. What is the value of 60 A. 120 P., at $80 per acre ?

Ans. $4860. 5. What is the cost of 13 gal. 3 qt. 1 pt. of molasses, at $.60 per gallon?

6. Required the cost of grading 10 m. 6 fur. 20 rd. of railroad, at $6490 per mile ?

Ans. $70173.121. 7. Required the cost of 2117 yards of cloth, at 37] cents per yard ?

Ans. $793.87. 8. What cost 120 yards of broadcloth, at $3.663 per yard ?

9. How much must be paid for 24 bu. 2 pk. 4 qt. of corn, at $.88 per bushel ?

Ams. $21.67. 10. If a man can walk 18 m. 5 fur. 16 rd. in one day, how far can he walk in 10 d. 8 h.?

Ans. 192 m. 7 fur. 32 rd. 11. At $240 a year, what is the rent of a house for 9 mo. 25 d.?

12. What is the cost of excavating 108 cu. yd. 18 cu. ft. of earth, at 42 cents per cu. yd. ?

Ans. $45.64.

REVIEW QUESTIONS. What is Reduction of Denominate Numbers ? (244) What is the Rule for reducing from a higher to a lower denomination ? (245) For reducing from a lower to a higher denomination ? (247) For reducing a fraction of a given denomination to integers of lower denominations ? (248) For redncing integers of lower denominations to a faraction of a higher de nomination ? (249)

REVIEW EXERCISES. 1. What cost 1 T. 5 cwt. 56 lb. of sugar, at 11 cents a pound ?

Ans. $281.16 2. At 11 cents a pound, how much sugar can be bought for $281.16?

3. A farmer, having 640 acres in his farm, values one half of it at $20 per acre, and the other half at 20 cents a square rod; how much is the one half worth more than the other?

Ans. $3840 4. A druggist retailed f of a pound Troy of a drug, at 2 cents a grain ; how much did it amount to?

5. How much money can be made on 500 tons of coal bought at $5 per ton of 2240 lb., and sold at the same number of dollars

per

ton of 2000 lb. ? SOLUTION. 2240 lb. 2000 lb. = 240 lb.; if 240 lb. can be made on 1 ton, 500 times 240 lb., or 60 tons, can be made on 500 tons; and 60 tons, at $5 per ton, sell for $300, the money that can be made. Therefore, etc.

6. How much can be made by buying 10 lb. of rhubarb, at $6.50 per pound avoirdupois, and selling it at the same price per lb. Troy?

Ans. $13.99+ 7. A laborer being 8 h. 4 m. doing a job, another man agreed to do a like piece of work in šof that time; how long was that?

Ans. 6 h. 43 m. 20 sec. 8. When $1.80 is paid for 2 of 2 tons of hay, now much is it per hundred weight?

Ans. $1.125 9. At $1.50 per yard, in length, what will be the cost of a carpet, s of a yard wide, that will cover the floor of a room 29.5 feet long by 11.25 feet wide ?

$88.50 10. What must be the length of a rectangular lot, that measures 72 feet on the front, to contain 9432

square

feet?
Ans. 131 feet.

REVIEW QUESTIONS. What is the Rule for Addition of Compound Do nominate Numbers ? (251)

Subtraction ? (253) Multiplication? (256! Division ? (257)

Solution. Since the 9432 must be the product of the number denoting the front and another denoting the length, the latter must be 9432 = 72, or 131 feet.

11. How wide must be a rectangular lot, which is 42.4 rods long, to contain exactly an acre ?

12. How much will a man's wages amount to, at $25 per month, from April 16th to the last day of the next March?

Ans. $287.50. 13. How much money inay be made on 2 bushels of chestnuts, bought at $4.80 a bushel, and retailed at 15 cents a quart, liquid measure ?

Ans. $1.56 + 14. When tea is 75 cents a pound, how much is it per

kilogram?

SOLUTION. Since 1 kilogram is equal to 2.2046 lb., when tea is 75 cents a pound, it is 2.2046 times 75 cents, or $1.65 t, per kilogram. Therefore, etc.

15. When a field produces 40 hectoliters per hectare, how many bushels is that per

Ans. 45.9 + bushels. 16. What is the cost of a stone wall 132 feet long, 4 feet high, and 1.5 feet thick, at $2.25 per perch of masonry ?

Ans. $72. 17. A wagon is 8 feet long and 3.75 feet wide; how high must wood be piled upon it to make a cord ?

SOLUTION. Since 128, the number of cubic feet in a cord, must be the product of the numbers denoting the length and width, and the required hight, the latter must be 128 = (8 X 3.75), or 4.26+ feet.

18. If a pile of wood is 4 feet wide and 6 feet high, how long is it, if it contains 4 C. 6 c. ft. ?

19. What time is it in 30° west longitude, when it is 1 o'clock, A. M., July 4th, in 7° 30' east longitude ?

Ans. 101 o'clock, P. M., July 3d.

acre ?

REVIEW QUESTIONS. What is the Rule for finding the difference of time corresponding to the difference of longitude ? (259) The difference of bongitude corresponding to the difference of time ? (259)

PERCENTAGE. 262. Per Cent., from per, by, or on, and centum, hundred, means by or on a hundred. Thus, 2

per cent. of a quantity, means 2 on a hundred, or 2 hun, dredths of the quantity.

263. Percentage is the process of computing in hundredths; and

The PERCENTAGE of a number is so many hundredths of it as is indicated by the

per

cent. The BASE of percentage is the number upon which it is computed.

The RATE per cent. is the number of hundredths denoted by the per cent.

264. Since rate per cent. is a number of hundredths, it may be expressed in the form of a decimal or of a common fraction, Thus,

1 per cent. is written .01, or Ido.
per
cent.

.05, “ 16 .
10

.10, “ 10% 25 per cent.

.25, “ . 100 per cent.

188 125 per cent.

1.25, “ 138. 1 per cent. is .002, or .005; À per cent. is .004, or .0025; per cent. is .00, or .00125, etc. The sign % is used, in business, to stand for the word

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per cent.

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per cent.

Exercises.

Express decimally, 1. 8 %

Ans. .08. 5. 1%. 2. 15 %.

Ans. .15. 6. 1 %. 3. 123 %. Ans. .12. 7. 26 %. 4. 13 %. Ans. .01. I 8. 736 %.

9. 45 %. 10. 90 %. 11. 150 %. 12. 275 %.

What does Per Cent. mean? What is Percentage? The Percentage of a number or quantity? The Base ? How may per cent. be expressed? What sign for per cent. is used ?

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