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50. What is of 144 ? Synthetic method.

Analytical method. 144

4) 144 Divide by 4 to 3

36 get one fourth, 4) 432

3

and multiply by 3 108 Ans.

108 Ans.

to get 3 fourths. 51. What is of 365 ? Ans. 2283. 52. What is of 128 ? Ans. 544. 53. What is å of 386 ? Ans. 2100: 54. Sold a farm for 1728 dollars ; and, if I give of this sum to indigent persons, what do they receive ?

Ans. 720 dollars. 55. If from 1000 dollars f be taken, what sum will remain ?

Ans. 625 dollars.

IV. To divide by a fraction.

RULE.

Multiply the given number by the denominator, and divide the product by the numerator. 56. Divide 125 by s. 125

In this example, we mul8

tiply by 8 to reduce the 125 5)1000 to eighths ; and then we 200

see how often 5 (eighths)

are contained in them. 57. Sold ß of a house for 3227 dollars ; what was the value of the whole house ?

Ans. 3688 dollars.

V. To divide by a composite number, that is, a number, which is produced by the multiplying of two or more numbers.

RULE.

Divide the dividend by one of these numbers, and the quotient thence arising by another, and so continue ; and the last quotient will be the answer.

Note. To find the true remainder, we multiply the last remainder by the last divisor but one, and to the product add the next preced

OPERATION

ing remainder; we multiply this product by the next preceding divisor, and to the product add the next preceding remainder; and so on until we have gone through all the divisors and reinainders to the first. 58. Divide 67872 by 24.

In this question, we divide 4)67872 by 4 and 6, because they are 6) 16968 the factors, or composite num

bers of 24. 2828

Quotients. 59. Divide 765325 by 25=5 X 5.

30613. 60. Divide 123396 by 84=7 x 12.

1469. 61. Divide 611226 by 81=9 X 9.

7546. 62. Divide 987625 by 125=5 X 5 X 5.

7901.

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Section 6.

APPLICATION OF THE PRECEDING RULES.

1. A farmer bought 5 yoke of oxen at 87 dollars a yoke ; 37 cows at 37 dollars each ; 89 sheep at 3 dollars a piece. He sold the oxen at 98 dollars a yoke ; for the cows he received 40 dollars each ; and, for the sheep, he had 4 dollars a piece ; what did he gain by his trade ?

Ans. 255 dollars. 2. In 4003 hours, how many days? Ans. 167 days. 3. In 169 weeks, how many days ?

Ans. 1183 days. 4. If 12 inches make a foot, how many feet in 48096 inches ?

Ans. 4008 feet. 5. In 15300 minutes, how many hours ?

Ans. 255 hours. 6. If 144 inches make 1 square foot, how many square feet in 20736 inches ?

Ans. 144 feet.
7. An acre contains 160 square rods ; how many in a

farm containing 769 acres ? Ans. 123040 rods.
8. A gentleman bought a house for three thousand forty-
seven dollars, and a carriage and span of horses for five
hundred seven dollars. He paid at one time, two thou-
sand seventeen dollars, and at another time, nine hun-
dred seven dollars. How much remains due ?

Ans. 630 dollars.

9. The erection of a factory cost 68,255 dollars ; suppos

ing this sum to be divided into 365 shares, what is the expense of each ?

Ans. 187 dollars. 10. A gentleman, possessing an estate of 375,846 dollars, bequeathed 7,494 dollars to the Bible Society ; 4,230 dollars for the support of schools ; and one third to his wife ; the remainder was to be equally divided among his 12 sons and 8 daughters; what sum will each receive ?

Ans. 11,942 dollars. 11. There were distilled in the United States in 1840, thirty-six millions three hundred forty-three thousand two hundred thirty-six gallons of ardent spirits ; and the number of free white males, over 15 years, is four millions seventy-four thousand nine hundred fifteen ; now supposing the liquor to be drank by one third of those persons in one year, what quantity would each consume?

Ans. More than 26 gallons. 12. A man gave half of his estate to his wife, one third of what remained to his son, and the residue was equally divided among his 7 daughters, who received each 124 dollars ; what was the whole estate ?

Ans. 2,604 dollars.

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Mills.

10 100 1000 10000

Cents.

1 10 100 1000

Dimes.

1 10 100

Dollars:

1 10

Eagles,

1

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OZ.

24 Grains make 1 Pennyweight, marked dwt. 20 Pennyweights 1 Ounce, 12. Ounces 1 Pound,

lb. grs.

dwt. 24

1 480 20

1

Ib.
5760

1
240
12

1 By this weight are weighed gold, silver, and jewels. Note. “ The original of all weights, used in England, was a grain or corn of wheat, gathered out of the middle of the ear; and being well dried, 32 of them were to make one pennyweight, 20. penny. weights one ounce, and 12 ounces one pound. But, in later times, it was thought sufficient to divide the same pennyweight into 24 equal parts, still called grains, being the least weight now in common use; and from hence the rest are computed.”

APOTHECARIES WEIGHT, 20 Grains make 1 Scruple, marked sc. or . 3 Scruples 1 Dram,

dr. or 3. 8 Drams 1 Ounce,

oz. or 3. 12 Ounces 1 Pound,

lb. or lb.

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Apothecaries mix their medicines by this weight ; but buy and sell by Avoirdupois. The pound and ounce of this weight are the same as in Troy Weight.

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AVOIRDUPOIS WEIGHT. 16 Drams make 1 Ounce,

marked oz. 16 Ounces 1 Pound,

lb. 28 Pounds

1 Quarter,

qr. 4 Quarters

1 Hundred weight, cwt. 20 Hundred weight " 1 Ton,

ton. dr. 16

1

lb.
256
16

1

qr.
7168
448

28 ኖ ai

1

cwt.
28672
1792
112

4

1 573440 = 35840 2240 80 20 1

By this weight are weighed almost every kind of goods, and all metals except gold and silver. By a late law of Massachusetts, the cwt. contains 100 lbs. instead of 112 lbs.

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ton.

LONG MEASURE.

m.

12 Inches

make 1 Foot, marked ft. 3 Feet

1 Yard,

yd. 5} Yards, or 163 feet 1 Rod, or pole,

rd. 40 Rods

1 Furlong,

fur. 8 Furlongs

1 Mile, 3 Miles

1 League,

lea.' 694 Miles (nearly)

1 Degree,

" Deg. or. 360 Degrees

1 Circle of the Earth. -in.

ft. 12

1 36

3 198

51

1

fur. 17920 660 220

40

1 63360 5280

1760

320

8

1

yd.

16)

m.

CLOTH MEASURE.

24 Inches
make 1 Nail,

marked na. 4 Nails

1 Quarter of a yard" qr. 4 Quarters

1 Yard,

yd. 3 Quarters

1 Ell Flemish, E.F. 5 Quarters

1 Ell English,

E. E. Note. The Ell French is not in use.

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